Bounding the Probability of Failure for Levee Systems

逐梦人生英语作文Pursuing ones dreams is a journey that can be both exhilarating and challenging. Here is an English composition that explores the theme of chasing dreams in lifeTitle The Pursuit of DreamsEveryone has dreams those aspirations and goals that we hold dear to our hearts. The pursuit of these dreams is what shapes our lives and gives us a sense of purpose. This essay will delve into the importance of chasing dreams the obstacles one may encounter and the ultimate rewards that come from achieving them.IntroductionThe journey of life is filled with countless opportunities and choices. One of the most significant decisions we make is to pursue our dreams. Dreams are the driving force behind our ambitions and the catalyst for personal growth. They inspire us to strive for excellence and to push beyond our limits.The Importance of Chasing Dreams1. Selffulfillment Chasing dreams allows us to explore our passions and interests leading to a sense of fulfillment and satisfaction in life.2. Personal growth The pursuit of dreams challenges us to learn new skills overcome obstacles and grow as individuals.3. Contribution to society Achieving our dreams often leads to positive contributions to society whether through innovation creativity or leadership.Obstacles in the Pursuit of Dreams1. Fear of failure The fear of not achieving our goals can hold us back from taking risks and pursuing our dreams.2. External pressures Societal expectations and the opinions of others can create barriers to pursuing our true desires.3. Limited resources Financial constraints lack of time or other limitations can make it difficult to pursue our dreams.Overcoming Obstacles1. Cultivating resilience Developing the ability to bounce back from setbacks and maintain a positive attitude is crucial in overcoming obstacles.2. Seeking support Surrounding ourselves with supportive friends family and mentors canprovide encouragement and guidance.3. Setting realistic goals Breaking down our dreams into smaller achievable goals can make the pursuit more manageable and less overwhelming.The Rewards of Achieving Dreams1. Sense of accomplishment Achieving our dreams brings a deep sense of satisfaction and pride in our abilities.2. Personal development The journey to achieving our dreams often leads to personal growth and selfdiscovery.3. Inspiring others Our success in achieving our dreams can inspire and motivate others to pursue their own aspirations.ConclusionThe pursuit of dreams is an essential aspect of life that shapes our character and defines our legacy. While the journey may be filled with challenges and obstacles the rewards of achieving our dreams are immeasurable. By cultivating resilience seeking support and setting realistic goals we can overcome these challenges and ultimately realize our dreams. Let us embrace the pursuit of our dreams and make our lives a testament to the power of ambition and determination.。

准备失败就是避免失败（Failure to prepare is to avoid failure）1, project: product, product operation of the rear is not stable enough? The strategic vision and operation of the team, the business leaders. Can the brand itself cooperate effectively?. Is it competitive: brand, price, service - speed?.Does it match the market? - do market research ahead of time. Before July 25th. Get a price list of other products.Double brand management strategy: household appliances, kitchen ware --- strengthening B brand strategy2, self operation: Time - time entry point is too late, at the latest can not exceed August 1st, product promotion in the market is not enough time. Form potential energy.Team: no service and promotion team, No. 25 in place, professional training.Management: the proper management of small companies. Benevolence is the law. Can not retain people: hope, belonging. CommunicationFeedback: market feedback can not be timely feedback, resulting in no timely adjustments. Products, prices, services,Finance: funds can not be in place or in short supply.Sample: all your own samples. The customer must ensure that the base sample is in place.Communication: a powerful amount of communication.Follow up: plan ahead, timely grasp the process, follow up.Use: CooperationEntrepreneurship starts with preparation failureStarting a business is not about looking for success, it's about preparing for failure!Li Xiang, founder and CEO of bubble network, has been selected as "China's ten new cutting-edge entrepreneurs"". As for entrepreneurship, he once said, "you can ruin your life by starting a business yourself."." In my opinion, what he says is "casual", that is, without blind thinking about the problems and frustrations that may arise, or blindly preparing for business, or preparing for failure.Now that you're ready to start your business, let's start thinking about the first step in Entrepreneurship: preparing for failure.Is entrepreneurship not for success? Shouldn't entrepreneurship be passionate? Why do you prepare for failure? Why is it so negative?Yes, entrepreneurship is passionate and full of opportunities, but the road to entrepreneurship is also covered with thorns and traps. According to incomplete statistics, the failure rate of the first venture is as high as 90%. The successful ones crossover the losers, and this is called "the remnant is king"".The ancients said: "without thinking about the first retreat", especially for those to be entrepreneurial. At the very beginning of your business, you can only anticipate the difficulties and setbacks ahead of you by preparing for possible failures.Why should entrepreneurship begin with failure?Because failure is the other side of the coin. We've all played coin flipping, and we all know coins have two sides, one word and one flower. So, who can flip a coin every time it's a word or a flower? Some say it's OK to just throw it once. But entrepreneurship is not a behavior can be, that is, Ma Yun, Ren Zhengfei has been successful entrepreneurs, are also shouting, "companies may die every day."."Robin Li started with a small company of 7 people, and in less than 10 years, Baidu has become the largest trading stock in the US stock market. When Robin Li decided to go back to business, he thought of not becoming China's richest man, not creating China's GOOGLE. His only thought was that he would experience all kinds of setbacks. It is because of the psychological preparation, so after he faces difficulties, not freezing.Prepare for failure and let yourself avoid failure.If you never think of failure, then the system will inevitably have loopholes, the operation process is bound to have a link, but also lack. Perfect, everyone pursues, but the idea is notenough to make perfection a natural thing. In order to perfect, you need it again and again in their own ideas. The so-called Homer sometimes nods, and in the "succeed" of the faith, you will see it as the subconscious is a seamless heavenly robe.Unless first of all deny it!When you start it is a piece of work, as it is a fail, you will seriously consider what is the reason for the failure of (this and you think "what reason could lead to failure" will get a different answer), is the only way you can improve it before failure occurs.At the opening ceremony of the 08 year Olympic Games in Beijing, Zhang Yimou showed us the essence of "preparing for failure or avoiding failure".The most worrying thing about the lighting ceremony is the fear of the torch falling from high altitude. Because Lining's body for a long time should be in a state of tilt, if missed torch down, there is no chance of any remedy. Zhang Yimou, first of all, what if the torch must fall from Lining's hands? Zhang Yimou wore the seat belt for the torch. The torch was held in Lining's hand, and a string of steel was hung above it so that the torch wouldn't fall to the ground even if it fell off.In the absence of a normal balance of the body, anyone hangs around the bird's nest for a week, while the right hand holds up the torch, which is difficult. Although Lining is a sports athlete origin, but has retired so many years, he also can withstand such heavy sports consumption? Zhang Yimou thoughtof defeat ---- Lining would not lift the torch. So Zhang Yimou Lining created a arm support, this support can not only help Lining and labor, also can be in the case of Lining collapses the arm, try to keep high attitude.When Lining ran in the air, in order to keep pace with the scroll, Zhang Yimou designed a track car to maintain speed synchronization. But any machine will malfunction. What if the track car suddenly fails? Assuming Zhang Yimou failed, he took the track car off work as inevitable. In order to make up for the failure, he arranged for the special staff to keep track of the track car, and if it failed, it would be switched on immediately.Unlike ordinary people, a master is never sure of success in the first place, but rather examines what he is about to do with some notion of failure. Find problems, and then design backup programs to ensure that the whole process is foolproof.It is precisely because of "sure failure" rather than "a certain success" as the starting point, you will act in the choice of more attention to efficiency, more attention to the essence, rather than the opposite, blindly pursue the surface of vanity. Many entrepreneurs, in the early days of entrepreneurship, often fall into a trap - - one-sided pursuit of form, and ignore the real value of the connotation. Because in their view, success should be like someone who has been successful.But in fact, the real decision to start a business can not be successful, not in the form, but something inherent. People always love to do things carelessly some successful experience,it is a simple summary of the success equation. But in fact, every successful person has his own password, and their reasons for success are different. Only by denying the successful mode and experience before we can deeply explore the true value root of the model can we do it, so that everything is necessary and beneficial at the beginning of the venture.Of course, there's another key reason for starting a business from failure: if you fail, can you afford it? Yes, success needs to be aggressive, need to struggle, need to go forward courageously. Entrepreneurship is the assault team, but the charging team is not the death squads. It is certainly not the death squads team. Before you succeed, think of yourself if you can accept failure, so as to avoid losing your life.。

对失败者的定义英文作文Defining FailureFailure, a word that carries a weight of negative connotations, is a concept that has been debated and discussed throughout the ages. It is a term often used to describe an individual or a situation that has not met the expected or desired outcome. However, the definition of failure is not as straightforward as it may seem. In fact, the perception of failure can vary greatly depending on one's perspective and personal experiences.One perspective on failure is that it is simply the absence of success. This view holds that if an individual or an endeavor does not achieve the intended goal, then it is considered a failure. This definition is often used in the context of business, where the bottom line is the ultimate measure of success. In this regard, a company that fails to meet its financial targets or loses market share can be deemed a failure.However, this narrow definition of failure fails to account for the complexities of human experience. Oftentimes, the path to success is not a straight line, but rather a winding road filled with obstacles andsetbacks. These setbacks, which may be perceived as failures, can actually be essential stepping stones on the journey to achieving one's goals. Thomas Edison, the renowned inventor, famously said, "I have not failed. I've just found 10,000 ways that won't work." This perspective suggests that failure is not the end, but rather an opportunity to learn and grow.Another perspective on failure is that it is a necessary part of the learning process. This view holds that failure is an inevitable consequence of taking risks and trying new things. In this sense, failure is not something to be feared, but rather embraced as a valuable learning experience. By acknowledging and reflecting on their failures, individuals can gain valuable insights that can help them to improve and ultimately achieve greater success.Furthermore, the definition of failure can be heavily influenced by cultural and societal norms. In some cultures, failure is seen as a shameful and unacceptable outcome, while in others, it is viewed as a natural part of the learning process. This difference in perspective can have a significant impact on how individuals approach and respond to failure.For example, in many Asian cultures, failure is often seen as a reflection of one's character and can have significant social and familial consequences. This can lead to a fear of failure and areluctance to take risks, which can ultimately hinder personal and professional growth. In contrast, in Western cultures, failure is often viewed as a necessary step on the path to success, and individuals are encouraged to take risks and learn from their mistakes.Ultimately, the definition of failure is a complex and multifaceted concept that cannot be easily reduced to a single, universal definition. It is a highly personal and subjective experience that is shaped by a variety of factors, including individual beliefs, cultural norms, and personal experiences.One perspective that may be helpful in navigating the concept of failure is to view it not as a binary outcome, but rather as a continuum. On this continuum, there may be varying degrees of success and failure, and the line between the two may not always be clearly defined. By adopting this perspective, individuals can approach failure with a more nuanced and compassionate understanding, recognizing that it is not the end, but rather an opportunity for growth and learning.In conclusion, the definition of failure is a complex and multifaceted concept that cannot be easily reduced to a single, universal definition. It is a highly personal and subjective experience that is shaped by a variety of factors, including individual beliefs, cultural norms, and personal experiences. By adopting a more nuanced andcompassionate understanding of failure, individuals can learn to embrace it as a necessary part of the learning process and use it as a stepping stone to greater success.。

Fatigue performance of plain and steel fibre reinforced self compacting concrete using S–NrelationshipS.Goel a ,S.P.Singh b ,⇑a Department of Civil Engineering,DAV Institute of Engineering &Technology,Jalandhar 144008,IndiabDepartment of Civil Engineering,Dr.B.R.Ambedkar National Institute of Technology,Jalandhar 144011,Indiaa r t i c l e i n f o Article history:Received 30December 2012Revised 8May 2014Accepted 12May 2014Available online 2June 2014Keywords:Fatigue FibresStress levelProbability of failurea b s t r a c tThe paper presents the results of the study conducted to explore the fatigue performance of plain self compacting concrete (SCC)and steel fibre reinforced self compacting concrete (SFRSCC).Approximately 250flexural fatigue tests and 195complementary static flexural tests were executed on beam specimens of size 100mm Â100mm Â500mm under four point flexural loading.The distribution of fatigue life of SCC and SFRSCC was examined at different stress levels,which is a prerequisite for estimating the mean and design fatigue lives.The flexural fatigue performance of SCC and SFRSCC containing three different fibre volume fractions was evaluated in terms of mean and design fatigue lives,and two-million cycles of fatigue strengths/endurance limits.The flexural fatigue performance of SCC as well as SFRSCC was found to be better than the conventionally vibrated concrete (CVC)and fibre reinforced concrete (CVFRC).Ó2014Published by Elsevier Ltd.1.IntroductionThe need of large scale construction of concrete bridges,airport and highway pavements to accommodate rapidly growing traffic volume have increased the demand of high performance construc-tion materials.Self compacting concrete (SCC)is one of the latest innovations in concrete technology which provides solution to the various challenges in today’s highly demanding concrete con-struction.Self compacting concrete does not require compaction,flows under its own weight which saves time,labour,reduces over-all cost,improves the working environment and paves the way for automation in concrete construction.Since SCC offers a number of benefits over conventionally vibrated concrete (CVC),it has gener-ated tremendous interest amongst the researchers,engineers and concrete technologists to explore its various mechanical properties [1–8].The inclusion of fibres,especially steel fibres to develop SFRSCC with improved fresh and hardened properties has been a subject of interest for many researchers in the recent past [9–14].The majority of applications of SCC are in bridge decks and piers,pavements,road surfaces,rapid transportation systems,industrial yards,precast structural elements,high rise buildings,etc.[15],wherein the fatigue loading is the predominant mode of loading.Concrete structures such as bridges,pavements and off-shore structures are normally subjected to millions of cyclesof repetitive fatigue load during their service life,making fatigue strength a critical parameter in the design of these structures.The fatigue behaviour of concrete may generally be character-ised by the so-called S–N curve,which allows the mean fatigue life of concrete under a given stress level to be predicted [16–18].Because of the practical need to design bridges and pavements,the majority of research in the literature on the fatigue of concrete has been focused to study its behaviour in flexure [19],however some studies investigated other aspects of fatigue such that trans-verse fatigue [20]effect of fatigue degradation in the compression zone of reinforced concrete sections [21]and transverse tension [22],compression fatigue of steel fibre reinforced slender columns [23,24],fatigue resistance of concrete pavements reinforced with recycled steel fibres [25].Researchers have carried out laboratory fatigue experiments to investigate the flexural fatigue performance of CVC [26,27].Researchers also carried out extensive studies on the fatigue behaviour of conventionally vibrated fibre reinforced concrete (CVFRC),that were mainly confined to determination of flexural fatigue strength and endurance limits for different type/volume fraction/aspect ratio of steel fibres [28–30].Since fatigue test data of CVC as well as CVFRC show significant scatter and is random in nature,attempts have been made to apply the probabi-listic concepts to predict its flexural fatigue strength [16,17,31,32].1.1.Research significanceThe increased use of SCC globally and the scope of applications for SFRSCC in structures like long span bridges,airport and highway/10.1016/j.engstruct.2014.05.0100141-0296/Ó2014Published by Elsevier Ltd.⇑Corresponding author.Tel.:+919814088475(M);fax:+911812690932.E-mail address:spsingh@nitj.ac.in (S.P.Singh).pavements,prompts one to explore the fatigue performance of SCC and SFRSCC underflexural fatigue loading,as scanty information is available in the literature regarding the fatigue behaviour of SCC or SFRSCC[33,34].Thus,the present investigation was designed to study theflexural fatigue performance of SCC and SFRSCC contain-ing differentfibre volume fractions.Firstly the mean and design fatigue lives of SCC and SFRSCC has been determined,for which the two-parameter Weibull distribution was verified at different stress levels and the distribution parameters have been obtained from the S–N relationships.Secondly,the two million cycles fatigue strength/endurance limit of SCC and SFRSCC has been estimated from S–N diagrams.2.Experimental proceduresThe experimental work planned in this investigation consists of 250flexural fatigue and195staticflexural tests executed on beam specimens of size100mmÂ100mmÂ500mm under four point flexural loading.One SCC mix without anyfibre content and three SFRSCC mixes withfibre volume fractions of0.5%,1.0%,and1.5% were prepared using Ordinary Portland Cement,Class Fflyash, crushed stone aggregates(maximum size12.5mm)and locally available coarse sand.All the materials conformed to relevant Indian Standard specifications.A polycarboxylate based superp-lasticizer was used to ensure adequate workability of the mix. The circular corrugated steelfibres of30mm length and1mm diameter was used in SFRSCC mix with volume fraction of0.5%,1.0%,and1.5%.Viscosity Modifying Agent was used to stabilize the SFRSCC mixes.The mix proportions for SCC and SFRSCC mixes used for casting the specimens is shown in Table1.2.1.Workability and casting of specimensIn the present investigation four workability tests namely slump flow,V-funnel,J-ring and L-box tests were conducted in accordance with the guidelines of EFNARC[35,36]for SCC.The average values of the results of the workability tests conducted for SCC and SFRSCC mixes are presented in Table2.All the mixes were prepared in a rotary drum mixer and moulds werefilled without any mechanical vibrations or tamping.The specimens were cast in batches,each batch consisting of seven standard beam specimens of size 100Â100Â500mm for staticflexural andflexural fatigue tests and three cube specimens of size150Â150Â150mm for obtain-ing its28days compressive strength.The specimens were cast in the horizontal direction and hence,the influence of casting direc-tion on the results is ignored.The specimens were demoulded after 36h of casting.The quality of each batch of concrete was controlled by obtaining its28days compressive strength.The average28day compressive strength of35.90MPa was obtained for the SCC mix and for SFRSCC mixes it was38.10MPa,40.30MPa and42.40MPa respectively for0.5%,1.0%and1.5%fibre volume fractions.The beam specimens were cured under laboratory conditions for the 75days in order to avoid a possible strength increase during the fatigue tests.NotationsS stress level=f max/f rR stress ratio=f min/f maxf r staticflexural strengthf max maximum fatigue stressf min minimum fatigue stressL N survival probabilityN number of cycles to failure E[N]mean fatigue lifeN D design fatigue life a shape parameteru characteristic life or scale parameterP f probability of failureU()gamma functionSCC self compacting concreteSFRSCC steelfibre reinforced self compacting concrete CVC conventionally vibrated concreteCVFRC conventionally vibratedfibre reinforced concreteTable1Proportions for SCC and SFRSCC mixtures.Mix.Cement kg/m3Flyash kg/m3Fine aggregates kg/m3Coarse aggregates kg/m3Fibre volumefraction,V f SP a(by weightof cement)VMA b(by weightof cement)SCC410205846602Nil 1.7%NilSFRSCC0.54102058466020.5% 1.9%0.25% SFRSCC1.0410205846602 1.0% 2.2%0.35% SFRSCC1.5410205846602 1.5% 2.5%0.50%a SP–Superplastisizer.b VMA–Viscosity Modifying Agent.Table2Workability tests on fresh SCC and SFRSCC mixtures.Tests Parameter SCC a SFRSCC0.5a SFRSCC1.0a SFRSCC1.5a EFNARC/ACI guidelinesSlumpflow T500(s) 3.12 3.29 3.66 4.402–5sFlow spread(mm)750710705700650–800mm J-Ring T500J(s) 3.26 4.53 3.78 5.353–6sFlow spread(mm)725710700690600–750mmBlocking step Bj.(mm) 6.57.58.59.750–10mm V-funnel V-funnel Time(s)7.287.88.949.826–12sL-Box L-box passing ability0.910.900.830.810.8–1.0Visual stability index VSI value0(highly stable)0(highly stable)1(stable)1(stable)0,1,2,&3a Average values of the batched mixes.66S.Goel,S.P.Singh/Engineering Structures74(2014)65–732.2.Flexural tests under static and fatigue loadingThe staticflexural strength tests on a particular batch of SCC or SFRSCC were conducted just prior to fatigue tests to select the maximum and minimum load limits for the fatigue tests.For this purpose,three specimens from a particular batch were tested under four point staticflexural loads and the mean staticflexural strength was obtained.The average staticflexural strength at the time of fatigue testing was4.85MPa for SCC mix and6.05MPa, 7.20MPa and9.00MPa respectively for SFRSCC mixes containing 0.5%,1.0%and1.5%fibre volume fraction.After establishing the staticflexural strength of a particular batch,the remaining beams were tested inflexural fatigue.The staticflexural andflexural fati-gue tests were conducted on a100kN servo controlled actuator. The span/points of loading were the same as for the static tests i.e.450mm and four points loading.Theflexural fatigue tests were conducted at different stress levels S(S=f max/f r),ranging from0.90 to0.65.The fatigue stress ratio R(R=f min/f max)was kept constant at0.10throughout the investigation.Constant amplitude,sinusoi-dal loads were applied at a frequency of10Hz.The number of cycles to failure of each specimen under loading conditions was noted from the cycle counter of the machine.Since a large number of specimens were proposed to be tested in this investigation,thus to save time and expenses an upper bound of two-million cycles ofTable3Laboratory fatigue life data(number of cycles to failure N,in ascending order)for SCC and SFRSCC.Fatigue life data‘N’Stress level,S?Sample no.0.95c0.900.850.800.750.700.65SCC1–18c32a824329,68424,862a682,365 2–49c1292926839,65289,080795,6243–86c138710,72442,56297,842867,4754–102c145311,89246,881129,324964,6885–185c176812,98454,925139,5761,135,7466–212c189213,82159,493150,8361,385,1727––191814,35263,358166,7091,634,1258––211615,25770,312182,8921,771,5899––222016,90678,237204,1701,889,57710––232817,53283,111211,5872,000,000b11––282218,11288,165244,276–12–––22,464178,704a270,671–13–––150,187a–––SFRSCC0.511277a972a15,98675,668282,014–2181114431617,41496,251380,132–3211240568519,650119,562472,329–4–1327610623,237131,198518,928–5–1522683224,363150,947635,492–6–1617722931,927178,217724,120–7–1726798734,256191,326812,596–8–1810892137,236211,319893,415–9–1918954242,035235,2821,022,520–10–210310,14651,089346,6031,698,642–11–268513,24063,549394,3521,882,857–12–294814,53872,6324685,812,000,000b–13––15,831––––SFRSCC1.0127360a214a2712a21,628a––232267316,8553190⁄303,149––341326220,69681,435368,552––488388129,52196,143469,113––5103435634,516118,367531,692––6–485639,482127,302582,677––7–511241,214158,191639,778––8–552644,772185,667694,655––9–576448,380217,553756,619––10–611652,428240,7121,102,778––11–673573,589309,8681,784,655––12–881284,066388,2821,896,547––13–9837105,267506,7751,956,619––14––––2,000,000b––SFRSCC1.513456a518a262a92,727155,409–246852785335,924154,211237,568–389955926842,797226,566292,217–4198108911,45848,831289,967351,867–5306122012,22660,100318,576522,958–6–134215,21875,038345,2911,216,136–7–156817,75785,940370,5381,325,827–8–164019,33596,501410,7831,431,136–9–200121,691106,145478,9591,802,896–10–215824,821120,726614,1721,932,348–11–288136,745173,447918,632––12–328644,830214,5211,181,462––13–––251,038–––a Rejected as Outlier by Chauvenet’s Criterion,not included in analysis.b Specimen did not show any crack,test terminates at2million cycles,treated as run out,not included in analysis.c Used for S–N curves only.S.Goel,S.P.Singh/Engineering Structures74(2014)65–7367fatigue loading was adopted.The test was terminated as and when the failure of the specimen occurred or this upper bound was reached,whichever was earlier.The results of the flexural fatigue test conducted on SCC and SFRSCC mixes are presented in Table 3,which also shows the number of samples tested at each stress level.3.Theoretical approachThe main objective of this paper is to obtain the mean and design fatigue lives for SCC and SFRSCC.For this purpose,it is essential to establish the fatigue life distributions for fatigue test data obtained for SCC and SFRSCC and to estimate the distribution parameters.Weibull distribution is most commonly used for the statistical description of the fatigue data of concrete due to its physical valid assumptions and sound experimental verification [16,37,38].Later on the two-parameter Weibull distribution has been employed by Singh and Kaushik [17,39],Mohammadi and Kaushik [40]and Singh et al.[18]to describe the fatigue life distributions for Steel Fibre Reinforced Concrete (SFRC).Thus,in the present investigation the two-parameter Weibull distribution has been verified for the fati-gue life distribution of SCC and SFRSCC and then distribution parameters were obtained using S–N relationships.3.1.Graphical method for verification of Weibull distribution The present paper shows the results of the graphical method for verification of two-parameter Weibull distribution for fatigue life of SCC and SFRSCC at a given stress level S ,however the detailed presentation of the method and the calculations in this regard is presented elsewhere [34].The survivorship function L N (n )of the two-parameter Weibull distribution may be written as follows [16,37,39,40]:L N ¼exp Ànuað1Þwhere n is the specific value of random variable N ,a is the shape parameter at stress level S and u is the scale parameter at stress level S .A graph is plotted between ln[ln(1/L N )]and ln(N ),and if the test data,at a particular stress level,follows approximately a linear The corresponding values of correlation coefficient C C are 0.9768,0.9919,0.9912,0.9926,and 0.9911for fatigue life data of SCC at stress levels 0.85,0.80,0.75,0.70,and 0.65respectively.The values of correlation coefficient for all stress levels were more than 0.97,which further substantiated the validity of two-parameter Weibull distribution for fatigue life of SCC.Similarly,the fatigue life data of SFRSCC with 0.5%,1.0%and 1.5%volume fractions of fibres at dif-ferent stress levels has been analyzed by graphical method and it has been shown to follow the two-parameter Weibull distribution with statistical correlation coefficient exceeding 0.90[34].3.2.Probability distribution parameters from S–N relationship In the previous section it has been shown that the probability distribution of fatigue test data for SCC and SFRSCC obtained in this investigation follows the two-parameter Weibull Distribution at different stress levels.Different methods have been used by the researchers to estimate the Weibull distribution parameters for CVC [16,17]and CVFRC [39,40]at different stress levels.There is however,a simpler way of obtaining the distribution parameters,namely,from S–N relationship [16,17],even though this method is based on an approximate assumption of constant variance for all values of stress levels.For this the following S–N relationship may be assumed [16,41].N f max f rm ¼Cð2Þwhere m and C are empirical constants.Eq.(2)is more reasonable in the sense that the stress term is treated as a non dimensional form and thus may have wider applicability.Taking logarithm of both sides of the Eq.(2)log 10ðN Þ¼log 10ðC ÞÀm log 10f maxf rm ð3Þthe Eq.(3)can be written in the form,Y ¼a þbX ;ð4Þin which Y =log 10(N);X ¼log 10f maxf r;a ¼log 10ðC Þ;and b ¼Àm :The coefficients ‘a ’and ‘b ’for SCC and SFRSCC can be obtained by fitting Eq.(4)into the respective fatigue life data obtained in this investigation.The values of the empirical constants ‘m ’and ‘C ’were obtained from the regression analysis of the fatigue life data of SCC and SFRSCC using Eqs.2–4.The S–N relationship depicted by Eq.(2)can be represented in terms of following relations:N f max f r22:70¼64:91for SCCð5ÞN f max f r 24:10¼154:45for SFRSCC ;V f ¼0:5%ð6ÞN f max f r 26:93¼398:20for SFRSCC ;V m ¼1:0%ð7ÞN f max f r24:08¼247:57for SFRSCC ;V f ¼1:5%ð8ÞIf the fatigue life N is assumed to follow the Weibull distribution (as has been shown in the previous section),the parameters of the distribution i.e.shape parameter ‘a ’and characteristic life ‘u ’may be determined by the following expressions [16,17,41].Graphical analysis of fatigue life data of SCC at different stress levels 68S.Goel,S.P.Singh /Engineering Structures 74(2014)65–732p2mechanical behaviour of the constituents compared with that of conventional concrete.Self Compacting Concrete possesses good fluidity and deformability making it more suitable for addition of fibres as compared to CVC and allows a much easier construction task and results in a more reliable quality in concrete placement and a more homogeneous material structure.It may be noted that the main objectives of this paper are to determine the mean and design fatigue lives and hence,the variability aspect is discussed in detail elsewhere[34].4.1.Mean and design fatigue lives for SCC and SFRSCCUsing the Weibull distributions parameters obtained in the pre-vious section for the fatigue life data of SCC and SFRSCC,the mean fatigue life E[N]for a given stress level may be obtained from the following relation[16,17].E½N ¼Cf maxf rÀmexp0:5772aC1þ1að11Þwhere U=Gamma function and empirical constants m and C of Eq.7–10for SCC and SFRSCC.The values of E[N]obtained for SCC and SFRSCC with0.5%, 1.0%and 1.5%fibre volume fractions at different stress levels is presented in Table5.For comparison purpose the mean fatigue lives of SCC and SFRSCC has been plottedFig.2along with the mean fatigue lives estimated by Oh[16] CVC and Singh and Kaushik[17]CVFRC.The curves plotted in Fig. shows better fatigue performance of SCC and SFRSCC compared CVC and CVFRC in terms of higher values of mean fatigue lives.It can also be seen from Table5that the best fatigue performance is shown by SFRSCC with 1.0%of steelfibres with highest mean fatigue lives at all the stress levels.The fatigue life data obtained in the present investigation for SCC and SFRSCC witness large scatter,which is usually expected in the fatigue life data of plain as well asfibre reinforced concrete even at a given stress level under carefully controlled test proce-dures.Thus the design fatigue life N D,should be selected such that there is only a small probability that a fatigue failure will occur [16].Oh[16],Singh and Kaushik[17],Singh et al.[18]estimated the design fatigue lives for CVC and CVFRC for different probabili-ties of failure(P f).The design reliability may be expressed as L N [N>N D]=1ÀP f,in which P f is the probability of failure.Thus the design fatigue life N D corresponding to a permissible probability of failure P f can be obtained from Eq.(12)as follows[16–18]:N D¼u ln11ÀP f1að12ÞUsing the values of the Weibull parameters a and u as presented in Table4corresponding to different stress levels for the fatigue life data of SCC and SFRSCC,the design fatigue lives have been calcu-lated corresponding to selected acceptable probabilities of failureTable4Values of Weibull distribution parameters using S–N relationships.Mix.Shape parameter a Characteristic Life,u*S=0.90S=0.85S=0.80S=0.75S=0.70S=0.65SCC 1.3833–394215,60967,551323,4431,739,360 SFRSCC0.5 1.3577299311,86951,163242,3511,278,080–SFRSCC1.0 1.5123995746,410237,4921,350,400––SFRSCC1.5 1.3018487619,31383,418393,3522,071,550–*S=Stress Level.Table5parison of mean fatigue lives of SCC,SFRSCC with CVC and CVFRC.S.Goel,S.P.Singh/Engineering Structures74(2014)65–73694.2.Two-million cycles fatigue strength/endurance limit for SCC and SFRSCCThe flexural fatigue strength and the endurance limit are impor-tant design parameters,particularly in bridge deck overlays and highway or airfield pavements because these structures are designed on the basis of fatigue load cycles.Most of the researchers interpret endurance limit as the maximum stress at which the two-million cycles of non-reversing load can be sustained [27,29,30].It is known from previous investigations that if the specimen could withstand two-million cycles without failure,it0.7564,479189,451304,939406,141592,477Table 9Design fatigue lives ‘N D ’at different probabilities of failure P f ,for SFRSCC,V f =1.5%.P f ?0.010.050.100.150.25Stress Design fatigue lives,N D 0.90142498866120818720.8556419723428478374170.802436851914,80920,65932,0340.7511,48540,16969,82997,415151,0550.7060,483211,547367,747513,024795,518parison of design fatigue lives of SCC,SFSRSCC with CVC and CVFRC 0.01.parison of design fatigue lives of SCC,SFSRSCC with CVC and CVFRC 0.05.parison of design fatigue lives of SCC,SFSRSCC with CVC and CVFRC 0.10.could last for all practical purposes for ever[42].Thus,in the pres-ent investigation,an upper limit of two-million cycle limit was chosen to approximate the life span of a structure that may typi-cally be subjected to fatigue loading.Two million cycles fatigue strength/endurance limits of SCC and SFRSCC containing0.5%, 1.0%and1.5%fibre volume fractions is obtained and compared with that reported in previous investigations for CVC[17,43]and CVFRC[44]containing comparable steelfibres.In the present investigation,S–N relationships have been used to determine the fatigue performance in terms of two-million cycles fatigue strength/endurance limit.In earlier investigations on CVFRC[29,30,43,44],two approaches were used to determine the endurance limit,i.e.in terms of the applied maximum fatigue stress expressed as a percentage of corresponding staticflexural strength and in terms of actually applied fatigue stress.In the pres-ent investigation,both the approaches have been employed to ana-lyze the fatigue performance of SCC and SFRSCC.A linear regression has been carried out on each set of data and plotted on semi-logarithmic format in the form of S–N curves.The S–N relationships were plotted in Fig.6using the fatigue test results obtained,with the maximum fatigue stress expressed as a percent-age of the average staticflexural strength of SCC or a particular SFRSCC under static loading.The two-million cycles fatigue strength/endurance limit obtained for SCC tested in the present investigation is63%of its average staticflexural strength.Similarly the two-million cycles fatigue strength/endurance limit obtained for SFRSCC is71%,76%and71%of the staticflexural strength respectively for0.5%,1.0%and1.5%offibre volume fractions.The two-million cycles fatigue strength/endurance limit can also be represented in terms of actually applied fatigue stress.Fig.7repre-sents S–N curves plotted for SCC and SFRSCC having0.5%,1.0%and 1.5%fibre volume fraction.Here the ordinate represents the actu-ally applied maximum fatigue stress.The two-million cycles fati-gue strength/endurance limit for SCC in terms of actually applied fatigue stress is3.00MPa.While the two-million cycles fatigue strength/endurance limits obtained for SFRSCC are 4.30MPa, 5.50MPa,6.40MPa respectively,forfibre volume fraction of0.5%, 1.0%and1.5%.The S–N curves plotted in Fig.6shows that the best fatigue per-formance in terms of the two-million cycles is given by SFRSCC containing1.0%of steelfibres volume fraction(76%of the staticSFRSCC containing1.5%of steelfibres i.e.6.40MPa.Similar trends are observed for fatigue performance of CVFRC tested in the previ-ous investigations by Mohammadi[43]and Singh and Kaushik [44].To compare the results for two-million cycles fatigue strength/ endurance limits of SCC with that of CVC,the regression curves for the CVC using the fatigue test data for CVC tested in previous investigations are plotted in Fig.8.The two-million cycles fatigue strength/endurance limit obtained for CVC tested in present inves-tigation is57%of the average staticflexural strength compared to 58%for CVC tested by Oh[16]and Mohammadi[43],whereas,it is 63%for SCC as obtained in this investigation.The two-million cycles fatigue strength/endurance limit of SCC when expressed in terms of actually applied fatigue stress is found to be3.00MPa compared to2.67MPa[16]and2.85MPa[43]for CVC.Thus higher two-million cycles fatigue strength for SCC than that of CVC exhib-its better fatigue performance of SCC in terms of two-million cycles fatigue strength/endurance limit.Similarly,it can be seen from the Fig.9.that the fatigue strength at two-million cycles for SFRSCC with0.5%,1.0%and1.5%fibres is 71%,76%and71%respectively compared to67%,73%and62%of staticflexural strength obtained for CVFRC[44]when expressedComparison of fatigue strength/endurance limit based on percentage average staticflexural strength for SCC with CVC.S.Goel,S.P.Singh/Engineering Structures74(2014)65–7371corresponding static flexural strength as well as actually applied fatigue stress.It is observed from the results obtained in this investigation that for SFRSCC,there exists a threshold limit in terms of fibre content for two million cycle fatigue strength if the results are interpreted in terms of stress level,i.e.maximum fatigue stress expressed as a percentage of static flexural strength.This threshold limit has been found to be 1.0%fibre content for SFRSCC.Similarly,literature [44]indicates that for CVFRC,the fatigue strength increases with the increase in fibre content up to 1.0%and further increase in fibre content results in decrease in fatigue strength when the perfor-mance is evaluated in terms of stress level.It may be noted that the results obtained in this investigation for SFRSCC are applicable to the type,size and volume fraction of the fibres employed and additional research work is required to estimate mean and design fatigue lives for other type,size and vol-ume fraction of fibres.However,it is hoped that the results of the present investigations will instill confidence in the designers and engineers for the use of SCC and SFRSCC in concrete structures sub-jected to fatigue loadings.5.Failure modeAs the fatigue testing deals with load levels,the fatigue test equipment was run in force control mode for SCC and SFRSCC spec-imens.The SCC specimens split instantaneously into two parts under fatigue load after initiation of crack.The failure of almost all the SFRSCC specimens under flexural fatigue loading was due to initiation of a single crack in the middle third span of the spec-imens.With an increase in the number of cycles of load,the crack propagated and widened leading to failure of the specimens.At higher stress levels,the failure was almost immediate after the ini-tiation of the first visible crack,whereas,at lower stress levels,the specimens sustained a sufficient number of cycles of load (a few hundred thousand cycles in some cases),even after the initiation of first visible crack,thus indicating the crack arrest characteristics and increased bond properties of fibres due to their deformed sur-face.Few specimens of SFRSCC containing 1.5%steel fibres showed initiation of multiple cracks,out of which one propagated and wid-ened with the increase in number of cycles of load,leading to the failure of specimen.It has been observed during the static as well as the fatigue flexural tests on SFRSCC specimens that the predom-inant mode of failure was by pulling out of the fibres from the con-crete matrix.The fracture failure of fibres was observed only in few specimens.No local crushing at the loading points or support of specimens was observed.Typical failure pattern in SCC and SFRSCC specimens under fatigue loading is shown in Fig.10.It is worthwhile to mention here that relatively small size spec-imens have been used in the investigation.This is demanded by the economy of the investigation,since a large number of specimens are required to be tested for improving the reliability of scattering fatigue test results.The results obtained for SCC and different SFRSCC mixes are valid for the type and proportion of the mineral admixture;and type,size,aspect ratio and volume fractions of fibres used in this investigation and can therefore not be general-ised at this stage.Additional research work is required to generate fatigue data for other type and mineral admixture;and type,size,aspect ratio and volume fractions of the fibres.Moreover,the effect of stress gradient,steady changing bond stress has been ignored.However,the trends of the results obtained in this investigation are well defined and it can reasonably be considered that the results established are representative of the fatigue behaviour of SCC and SFRSCC.6.ConclusionExperimental and theoretical studies have been conducted to investigate the fatigue performance of SCC and SFRSCC.The flex-ural fatigue lives for SCC and SFRSCC with 0.5%,1.0%and 1.5%of steel fibres were experimentally obtained at different stress levels.S–N relationships were established for SCC and SFRSCC and the parameters of the Weibull distribution have been obtained for the fatigue life data of SCC and SFRSCC.Subsequently,the mean fatigue lives for SCC and SFRSCC corresponding to different stress levels have been estimated and compared with the mean fatigue lives for CVC and CVFRC.The design fatigue lives for SCC and SFRSCC have also been determined corresponding to acceptable probabilities of failure and results were compared with that of CVC and CVFRC obtained in previous investigations.The estimated values of mean as well as design fatigue lives of SCC and SFRSCC with all three fibre volume fractions were higher compared to that of CVC and CVFRC.The two million cycles fatigue strength/endur-ance limit were estimated for SCC and SFRSCC with 0.5%,1.0%and 1.5%steel fibres.The fatigue strengths for SCC and SFRSCCobtainedComparison of fatigue strength/endurance limit based on percentage average static flexural strength for SFRSCC with CVFRC.Fig.10.Typical failure pattern in SCC and SCFRC specimens under fatigue loading.Structures 74(2014)65–73。

The path to success is often fraught with obstacles that can deter even the most determined individuals. These barriers can be external or internal, and understanding them is crucial for overcoming them and achieving ones goals.External Obstacles1. Competition: In many fields, the level of competition can be intense. Its important to recognize that competition can be a motivator, but it can also be overwhelming if not managed properly.2. Financial Constraints: The lack of financial resources can hinder ones ability to pursue education, training, or to start a business. It requires creativity and resourcefulness to navigate these challenges.3. Lack of Opportunities: Sometimes, the opportunities one seeks are simply not available. This can be due to economic conditions, location, or timing.4. Social and Cultural Barriers: Prejudices, stereotypes, and societal expectations can create significant barriers, especially for those from marginalized groups.5. Technological Limitations: In the rapidly evolving world, staying updated with the latest technology can be a challenge. Those who fall behind may find it difficult to compete in certain industries.Internal Obstacles1. Fear of Failure: The fear of not succeeding can be paralyzing. Its essential to embrace failure as a learning opportunity rather than a setback.2. Lack of SelfBelief: Selfdoubt can be a significant barrier to success. Building selfconfidence and a strong belief in ones abilities is crucial.3. Procrastination: Putting off tasks until the last minute can lead to stress and subpar results. Developing discipline and time management skills is key to overcoming procrastination.4. Mental Health Issues: Anxiety, depression, and other mental health issues can greatly affect ones ability to focus and perform at their best.5. Lack of Clarity in Goals: Without clear and specific goals, its easy to lose direction andmotivation. Setting SMART Specific, Measurable, Achievable, Relevant, Timebound goals can help provide a clear path to success.Overcoming Obstacles1. Develop a Growth Mindset: Embrace challenges as opportunities for growth and learning.2. Seek Mentorship and Guidance: Find individuals who have navigated similar paths and learn from their experiences.3. Build a Support Network: Surround yourself with positive influences who encourage and support your journey.4. Continuous Learning: Stay curious and committed to learning new skills and knowledge relevant to your field.5. Adapt and Pivot: Be flexible and willing to change your approach when faced with obstacles.6. Maintain a Positive Attitude: A positive outlook can help you stay resilient in the face of adversity.7. Setbacks as Stepping Stones: Use setbacks as opportunities to reassess and refine your strategy.In conclusion, while obstacles are a natural part of the journey to success, they are not insurmountable. With the right mindset, strategies, and support, one can navigate and even thrive amidst these challenges.。

英语 墨菲定律金句以下是5 个英语墨菲定律金句及其出处意思赏析：1. "Anything that can go wrong will go wrong." - Murphy's Law这句话是墨菲定律的核心思想，意思是任何可能出错的事情最终都会出错。

这句话表达了一种悲观的态度，但也提醒人们要对可能发生的事情做好充分的准备。

2. "If you think something will take a long time, it will take even longer." - Murphy's Law这句话的意思是，如果你认为某件事情会花费很长时间，那么它实际上会花费更长的时间。

这句话提醒人们要有耐心，并做好长期等待的准备。

3. "If anything can go wrong, it will, at the worst possible time." - Murphy's Law这句话的意思是，如果任何事情可能出错，那么它一定会在最糟糕的时间出错。

这句话提醒人们要时刻保持警惕，并在关键时刻做出正确的决策。

4. "The more complicated a system is, the more likely it is to fail." - Murphy's Law这句话的意思是，系统越复杂，出现故障的可能性就越大。

这句话提醒人们要尽可能简化系统，并确保系统的可靠性。

5. "If there are two or more ways to do something, and one of those ways can result in a catastrophe, then someone will do it." - Murphy's Law这句话的意思是，如果有两种或更多的方法来做某件事情，其中一种方法可能会导致灾难，那么一定会有人选择这种方法。

听力：Part ⅢListening ComprehensionSection A11. What can we infer from the conversation?【答案】A The man is the manager of the apartment building【解析】从对话中看出女士在找apartment building，不是男士。

因此选A。

12. What is the woman eager to know?【答案】B How the pictures will turn out.【解析】女士想知道的是if the shots I took are as good as I thought. 照片是不是和她想的异样好。

这里shots指照片。

turn out指照片拍出来的效果。

因此选B。

13. What does the man mean?【答案】C The suitcase can be fixed in time.【解析】男士说到find a handle后面提到 but that shouldn’t take too long说明不是没有handle可以匹配。

因此排除A,B。

14. What do we learn about the man from the conversation?【答案】B He needs a vehicle to be used in harsh weather. 【解析】男士说到truck需要operate for long periods of time in very cold temperatures，因此选择选项B。

very cold temperatures对应harsh weather.15. What do we learn about the woman?【答案】A She has made up her mind to resign.【解析】从文中女士强硬的口气I could no longer live with…可以看出她下定决心。

In the realm of English composition,the term resolution can be approached from various angles,depending on the context and the specific theme of the essay.Here are several aspects that could be explored when writing an essay on resolution:1.Personal Growth and SelfImprovement:Discuss how making a resolution can be a pivotal moment in ones life,leading to personal growth and selfimprovement.For example,a resolution to exercise more can lead to better physical health and mental wellbeing.2.Overcoming Challenges:Elaborate on how resolutions can be a tool for overcoming obstacles and challenges.This could include setting a resolution to learn a new skill,face a fear,or tackle a difficult task.3.The Power of Commitment:Explore the idea that the act of making a resolution is a demonstration of commitment.Discuss the importance of following through on a resolution and the benefits of maintaining that commitment.4.Cultural and Social Aspects:Discuss how resolutions are not just personal but can also be cultural or societal.For instance,New Years resolutions are a common practice worldwide,reflecting collective aspirations for a better future.5.The Role of Goals:Analyze the role that setting goals,such as resolutions,plays in achieving success.Discuss the process of goal setting,the importance of SMART goals Specific,Measurable,Achievable,Relevant,Timebound,and how they can guide ones actions.6.The Psychological Impact:Delve into the psychological aspects of making resolutions, including the motivation behind them,the satisfaction of achieving them,and the potential for disappointment if they are not met.7.Strategies for Success:Offer practical advice on how to make and keep resolutions. This could include setting realistic expectations,breaking down larger goals into smaller steps,and finding support systems.8.Reflection and Evaluation:Encourage readers to reflect on their past resolutions and evaluate what worked and what didnt.Discuss the importance of learning from past experiences to improve the chances of success in future resolutions.9.The Impact of Failure:Address the topic of failure in the context of resolutions. Discuss how failure can be a stepping stone to success,providing valuable lessons andinsights for future attempts.10.Inspirational Stories:Share stories of individuals who have successfully achieved their resolutions,inspiring readers to believe in their own ability to make and keep resolutions.When writing an essay on resolution,its important to choose a clear focus and provide concrete examples to support your arguments.Whether youre discussing the personal impact of resolutions or their broader implications,a wellstructured and thoughtful essay can provide valuable insights into the power of setting and achieving goals.。

From Static to Dynamic Routing:Efficient Transformations of Store-and-Forward ProtocolsChristian Scheideler Berthold V¨o ckingAbstractWe investigate how static store-and-forward routing algorithms can be transformed into efficient dynamic algorithms,that is,how algorithms that have been designed for the case that all packets are injected at the same time can be adapted to more realistic scenarios in which packets are con-tinuously injected into the network.Besides describing specific transformations for well-known static routing algorithms,we present a black box transformation scheme applicable to every static, oblivious routing algorithm.We analyze the performance of our protocols under a stochastic and an adversarial model of packet injections.One result of our specific transformations is thefirst dynamic routing algorithm for leveled networks that is stable for arbitrary admissible injection rates and that works with packet buffers of size depending solely on the injection rate and the node degree,but not on the size of the network. Furthermore,we prove strong delay bounds for the packets.Our results imply,for example,that a throughput of99%can be achieved on an-input butterfly network with buffers of constant size while each packet is delivered in time,with high probability.Our black box transformation ensures that if the static algorithm is pure(i.e.,no extra packets apart from the original packets are routed),its dynamic variant is stable up to a maximum possible injection rate.Furthermore,in the stochastic model,the routing time of a packet depends on local parameters such as the length of its routing path,rather than on the maximum possible path length, even if the static algorithm chosen for the transformation does not provide this locality feature and is not pure.In the adversarial model,the delay bound of the packets is closely related to the time bound given for the static algorithm.Key words:communication networks,store-and-forward routing,packet schedulingAMS subject classification:68Q22,68Q25,68M20,68R10,90B351IntroductionMany static routing protocols have been developed in recent years(see,e.g.,[6,8,9,10,12,13]).These protocols aim to route some initially given set of packets along predetermined paths in a network as fast as possible.In practice however,networks are rarely used in this static fashion but packets are injected dynamically into the network.Since much less is known in the area of dynamic routing(see e.g.[5,15,17])than in the area of static routing,it would be highly desirable to transfer the results gathered for static routing to dynamic routing.In this paper we present transformations for oblivious algorithms,i.e.,the path of a packet is alreadyfixed when the packet is injected into the system.We investigate how static,oblivious routing algorithms can be transformed into dynamic routing algorithms that are stable and efficient under a stochastic or adversarial model of packet injections.In particular,we will show that the ghost packet protocol[8,14]and the growing rank protocol[10,11]can be transformed into dynamic routing protocols that are stable up to a maximum possible injection rate.Furthermore,we will present a simple and elegant scheme that transforms almost any static protocol into an efficient dynamic protocol that is also stable up to a maximum possible injection rate.Besides showing the stability of these protocols,we will prove bounds on the routing time of the packets.For the protocols derived by the black box transformation we further prove that they recover quickly from any worst case scenario,that is,packets generated a certain amount of time after a bad event are not influenced by this event anymore.1.1Models and problemsWe consider arbitrary network topologies modeled as undirected graphs of nodes.The nodes represent switches,and the edges represent bidirectional communication links,unless otherwise stated,with buffers for incoming packets on either side.These buffer are called edge buffers,and bounds on the buffer size always refer to the maximum number of packets that these buffers can hold.Additionally,every node contains an injection buffer in which the initial packets,in case of static routing,or the newly injected packets,in case of dynamic routing,are stored.Routing is performed in a synchronous“store and forward”manner,that is,in every step, each edge can be crossed by at most one packet in each direction.(For simplicity,we assume that time proceeds in discrete time steps.)Once a packet reaches its destination it is discarded.We present routing protocols in which the nodes locally decide which packets to move forward in each step,i.e.,a decision only depends on the routing information carried by the packets and on the local history of the execution.These algorithms are called local control or on-line algorithms.In general,a packet routing scheme consists of two(not necessarily independent)parts:thefirst part is responsible for selecting a path for each packet,and the second part is responsible for scheduling the packets along their chosen paths.We assume that some suitable strategy for the path selection is given.Hence,in the following we only concentrate on the question of how to schedule the packets along theirfixed paths.We use the following models.1.1.1Static packet routingHere we assume that afixed collection of paths is given with congestion and dilation,that is,denotes the maximum number of paths crossing an edge,and denotes the maximum length of a path.Along each of these paths a packet has to be sent.Further,let denote the complexity of the routing problem,i.e.,is defined to be the maximum of the number of edges,the number of paths,and the dilation.Let us give some examples of known results on the routing time for static packet routing,i.e.,the time needed to deliver all packets: :trivial upper bound for any greedy protocol in case of unlimited buffers,i.e.,protocols in which a packet is only delayed because other packets move along the next edge on the packet’s routing path;1,w.h.p.1,for any constant:upper bound for arbitrary paths in arbitrary networks with unbounded buffers[9].,w.h.p.:upper bound in leveled networks with bounded buffers of constant size, where is the depth of the network[14,8],and upper bound for routing along shortest paths in arbitrary networks with unbounded buffers[10,11];,w.h.p.,for any constant:upper bound for routing along simple paths,i.e.,paths without cycles,in arbitrary networks with unbounded buffers[13];,w.h.p.,for any constant:upper bound for routing along simple paths in arbitrary networks with unbounded buffers[12].We will come back to some of these results when using our black box transformations.1.1.2Dynamic packet routingThe most commonly used injection models in the dynamic setting are the stochastic and the adversarial injection model.The stochastic model.Here the packets are injected by a set of generators,each of them mapped to one of the nodes in the network.We allow any relationship between the number of generators and the number of nodes in the network.Furthermore,we place no restrictions on the distribution of the generators among the nodes.That is,one node could have several generators,whereas another node may have none.So a generator may represent a user thread or process,whereas a node may represent a processor.In each time step,each generator placed on a node injects a packet with some probability.This probability is called the injection rate of.For each packet,the generator randomly selects a destination and a routing path from to this destination according to an arbitrary,fixed probability distribution.We assume that each generator is operating independently from other generators,and the injection of a packet and its routing path is independent from injections in previous time steps.Note that we do not demand that the destinations are chosen uniformly from the set of all nodes,or that packets with the same source and destination node follow the same routing path.Finally,we define the(overall) injection rate,which is denoted by.Define to be the expected number of messages generated in a time step that contain the edge in their routing paths.Then is defined to be the maximum over all edges.The adversarial model.An adversary is allowed to demand network bandwidth up to a prescribed injection rate.For any,an adversary is called a bounded adversary of rate if for all edges and all time intervals of length,it injects no more than packets during that contain edge in their routing paths.As in the stochastic model,is defined to be the injection rate.(We use the adversarial model as defined by Andrews et al[1]rather than the original model introduced by Borodin et al[3]because this model avoids calculating withfloors and ceilings.Apart from minor changes in constants,however,all our results hold in the original model of Borodin et al,too.)For both injection models,a protocol is called stable for a given injection rate if the number of packets stored in injection or edge buffers does not grow unboundedly with time.We are interested in protocols that are stable for high injection rates.Of course,since an edge can transport at most one packet per step,can be at most1.Our aim is to construct algorithms that are stable under injection rates that are close to1.Additionally, we are interested in short delays for the packets,i.e.,we aim to minimize the time from injection to service for each packet.Apart from the stability and the routing time we will consider another property of dynamic routing protocols, the recovery from worst case scenarios.Although our bounds on the routing time guarantee that bad configu-rations are very unlikely,they eventually occur from time to time when the routing protocol runs for an infinite number of time steps.Let a worst case scenario denote an arbitrarily bad configuration of the network.Then the recovery time with regard to some property of the routing protocol is defined as the time that has to pass by after the occurence of a worst case scenario until holds again.(In our case,we are interested in properties such as the expected routing time of a packet and time bounds that hold w.h.p.)As in the static model we define the complexity of a dynamic routing problem to be a value capturing all relevant parameters.In particular,the complexity is defined to be the maximum of the number of edges,the number of generators,the maximal possible length of a routing path,and.(The number of generators in the adversarial model is defined to be times the number of edges,which corresponds to the maximum number of packets that can be injected in a single step.)In the following sections,we will prove results for both the stochastic and the adversarial injection model.1.2Previous ResultsIn the last two years a new model called adversarial queuing theory emerged.This approach was introduced by Borodin et al in[3].Most research in this model focuses on the stability of routing protocols and networks. For example,Borodin et al[3]show several stability results for greedy protocols on DAGs and directed cycles. Andrews et al[1]extend their results by showing that there exist simple greedy protocols(such as longest-in-system,shortest-in-system and farthest-to-go)that are stable against any adversary for all networks.However, the delay of the packets and the number of packets stored in a queue might get exponential in the length of the longest path.Furthermore,Andrews et al[1]present a transformation of the static protocol presented in[9]into a dynamic protocol that is stable for any injection rate and fulfills the following constraint on the buffer size:For any fixed time step,at most packets are stored in any queue at time,w.h.p.,where denotes the longest routing path,the number of edges,and is a suitable constant.Note that this result implies that the delay of the packets is also bounded by,w.h.p.However,as the bound on the buffer size does not hold deterministically,any buffer offixed size will overflow eventually.Rabani and Tardos[13]present a transformation scheme which yields much better routing times.Assuming there is a static algorithm that delivers all packets in steps for some constant ,their tansformation yields a dynamic algorithm that delivers each packet to its destination,w.h.p.,inagainst an adversary of rate,where and denote the complexity of the static and dynamic routing problems,respectively.The stability of the dynamic algorithms,however,is not shown.In fact,although most packets will be delivered fast,some packets will never reach their destination and queues will grow to infinity assuming either the stochastic model or the adversarial model in combination with a randomized,static algorithm.Broder et al[4]introduce a general approach to dynamic packet routing with bounded buffers in the stochas-tic and adversarial model.They show sufficient conditions for the stability of dynamic packet routing algorithms and investigate how some well-known static routing protocols for the butterfly network can be transformed into dynamic algorithms that fulfill these conditions.In particular,they present a dynamic routing algorithm for the butterfly that is stable for a small constant injection rate,and they show that the expected routing time for each packet is,with denoting the number of nodes on a level.Andrews et al[2]investigate another,more restrictive dynamic routing model.In contrast to the stochastic and the adversarial model,the packets are injected regularly in“sessions”.For each session,packets are injected at a rate to follow afixed path of length.They describe a schedule that delivers each packet in a time depending only on local parameters,that is,each packet reaches its destination in time, which is worst case optimal.We will see that similar local properties,i.e.,the routing time depends on,can3be achieved also in the stochastic model.1.3New ResultsIn this paper,we present specific transformations of well-known routing protocols and introduce a powerful black box transformation scheme applicable to every static,oblivious routing protocol.In the following,denotes the complexity of the routing problem(as defined in Section1.1),denotes the maximum length of a routing path,and,where denotes the injection rate.Further,we define ,for suitable constants.For simplicity,we only state our results for networks of constant degree.For more detailed results the reader is referred to the following sections.In this paper,we give three specific transformations of well-known routing protocols.In Section2,we present a dynamic variant of the ghost packet protocol[8,14]for leveled networks that is stable for any in the stochastic model and in the adversarial model,given a sufficiently large butfixed buffer size of in the stochastic model and in the adversarial model.In the stochastic model,each individual packet is delivered in expected time,and in time, w.h.p.,where denotes the depth of the network.In the adversarial model,each packet reaches its destination in at most time steps.For example,the tuned ghost packet protocol achieves a throughput of,for any,on an-input butterfly network with buffers of size if we place two generators on each node of level0each of which injects packets that are sent to randomly selected nodes of level,using a rate of.Furthermore,the algorithm delivers each individual packet in time,w.h.p.Previous results on routing with bounded buffers in leveled networks obtain stability only for constant injection rates[4,16](stochastic model)or require buffers whose size is exponential in the depth of the network[1](adversarial model).In Section3,we present a dynamic routing protocol for arbitrary networks that is stable for any injection rate,assuming buffers offixed size.We prove an expected routing time of,and,w.h.p.,for every individual packet.These bounds hold both for the adversarial model and for the stochastic model(with).To the best of our knowledge,this is thefirst protocol that is stable for buffers of smallfixed size under any injection rate.Previous results in the stochastic model with bounded buffers requireand besides assume that packets can be dropped and reinjected in later time steps[16].Previous results in the adversarial model require buffers whose size is exponential(or polynomial,w.h.p.)in[1].Note that a bound on the buffer size that does not hold with certainty leaves open the question of what to do in the rare case of a buffer overflow(e.g.,dropping or blocking incoming packets),and hence does not guarantee stability for networks with afixed buffer size.In Section4,we describe a dynamic variant of the growing rank protocol[10]for shortest paths in arbitrary networks.The dynamic protocol is stable for any if unbounded buffers are given.In the stochastic model,each individual packet with a routing path of length is delivered in time,expected,and ,w.h.p.In the adversarial model,the in the time bound has to be replaced by.Previously,similar results have only been shown for in the stochastic model[16].Furthermore,in Section5,we present a powerful black box transformation scheme that is applicable to every static,oblivious routing algorithm in networks with unlimited buffers.Basically,we combine the ideas of Rabani and Tardos[13]for the fast delivery of packets with the universal stability of the shortest-in-system protocol originally shown by Andrews et al[1]for the adversarial model.The major problem that we solve4is merging these two approaches so that we obtain dynamic protocols that are stable up to some injection rate depending on the static protocol without any significant slowdown due to the inefficiency of the shortest-in-system protocol.Let denote any set of paths,e.g.,the set of all simple or all shortest paths in the network.Suppose we are given a static routing algorithm that routes all packets in steps,with high probability(or even with certainty),for any collection of paths or subpaths in with congestion,dilation ,and complexity.Assume that in the dynamic setting only paths in are allowed to be generated.Then our black box transformation yields a dynamic variant of this protocol with the following properties.(In the following overview,we only describe the results for the case that and do not depend on or andis a constant.Similar results will be shown for other choices of,and.)If the given static protocol is pure(i.e.,no control messages or copies of packets are allowed),the dynamic algorithm is stable for any injection rate.Otherwise,it is stable for any injection rate.If then the algorithm guarantees that any packet that has to travel a distance of is delivered in time,w.h.p.,in the stochastic injection model,and in time, w.h.p.,in the adversarial injection model.The algorithm recovers from any worst case scenario in time steps(within the stochastic model).The bound on the routing time implies that it might be important for static routing protocols to know the exact factor in front of the since this can be decisive for the performance of their dynamic counterparts.In-terestingly,in the stochastic injection model,the dynamic variant is able to exploit locality,whereas the static algorithm does not need to provide this feature.For example,the transformation of a well-known static routing algorithm(see,e.g.,[9])that delivers all packets in time,w.h.p.,for any constant ,yields a dynamic algorithm that delivers each packet in time,w.h.p.,for any constant injection rate,where is the length of’s path.1.4ToolsWe will frequently apply the following Chernoff bounds.Lemma1.1(Chernoff)Let be independent random variables with for all .Furthermore,let and.Then it holds for all thatthe higher level.Packet injections and arrivals are assumed to happen at the beginning of a time step,so that apacket may leave a node at the end of the time step in which it is injected or arrives at the node.The packets’routing paths may start on any level and end on any level with.Each node has a buffer for each of its incoming edges and a buffer for newly injected packets.Each of the edge buffers has space forstoring at most packets.Static batches of packets can be routed efficiently on leveled networks by a protocol known as Ranade’s orghost packet protocol[7,8,14].The disadvantage of the static ghost packet protocol is that each node is allowedto forward only one data packet at each time step,rather than forwarding data packets along all outgoing edgesin parallel.All edges that are not passed by a data packet in a step are used to exchange control packets thatare called ghost packets.As a consequence,most of the transmitted packets are ghost packets,which showsthat a simple transformation of the static ghost packet protocol into a dynamic protocol cannot yield stability forinjection rates close to1.In order to achieve stability for any injection rate,we introduce a tuned variantof the ghost packet protocol that only uses a very limited number of ghost packets.The tuned ghost packet protocol.The packets are assigned ranks in order to decide which packet is preferredin case of contention.For each packet,let denote the time step at which was injected.The rank ofis set to plus some small value from the interval,for some,where is chosen such thateach packet has its own,unique rank(e.g.,based on the identification number of the generator that injected thepacket).Packets with smaller ranks,i.e.,older packets,are always preferred against packets with higher rank,i.e.,younger packets.As in the static ghost packet protocol,special ghost packets help the algorithm to maintainthe following invariant:A packet is routed along an edge only after all the other packets with lower ranks thatmust pass through the edge have done so.The nodes on level start working in step,for.In orderto give time for initializing the network,we assume that packet injections on level do not start before time step .Figure1describes the rules for contention resolution in detail.Ghost packets are discarded as soon as they are delayed in a step.Thus,they never block the buffer forfollowing packets.The role of the ghost packets is to slow down too fast packets in order to avoid that a relativelyold packet is blocked because younger packets occupy the slots in the next buffer.Note that each outgoing linkon level k transmits one packet in each time step,either a ghost or a real packet.This mechanism ensuresthat each link transmits packets and ghost packets in the order of increasing rank.(Obviously,this propertyholds for the links on level0.For higher levels the property follows by induction.)We will see that this propertyis crucial for the analysis.Analyzing the performance of a variant of the protocol described above that does notuse ghost packets is an interesting open problem,even in the static case.The following analysis shows that the tuned ghost packet protocol is stable for any injection rate inthe adversarial model,and in the stochastic model,provided that the edge buffer size is sufficiently large. Theorem2.1Let denote the depth of the network,the maximum node degree,and the size of the edge buffers.Suppose the packets are injected according to the adversarial model with injection rate,for any and.Then the tuned ghost packet protocol is stable,and each packet reaches its destination in at most time steps.Suppose the packets are injected according to the stochastic model with injection rate,fora suitably chosen.Then the tuned ghost packet protocol is stable,and the routingtime for each individual packet is,expected,and,w.h.p.,where the probability is with respect to the stochastic packet injections.Proof.We use a“delay sequence argument”to analyze the tuned ghost packet protocol.Our analysis is similarto the one for the static ghost packet protocol given in[8].A delay sequence witnesses that a packet needs many6The following algorithm is executed for each outgoing link of a node on level in each time step .Each edge buffer can hold up to packets.Let denote the minimum rank of a packet that is stored in one of’s buffers and aims to passedge.If there is no such packet then.Let denote the minimum over all ranks of packets or ghost packets that arrived on at thebeginning of step.If there is no such packet(as is a node without incoming edges,e.g.,onlevel0)then is set to.if thenif the buffer of contains less than packets at the beginning of step thenforward the(unique)packet with rank alongelsesend a ghost packet with rank alongelsesend a ghost packet with rank along.Figure1:Contention resolution in the tuned ghost packet protocol.time steps to reach its destination.For the adversarial model,we will show that a delay sequence witnessing a long routing time does not exist,so that every packet reaches its destination within the time bound given in the theorem.For the stochastic model,we will show that“large”delay sequences are very unlikely so that each packet needs only limited time,with high probability,to reach its destination.The ghost packet protocol uses fractional ranks.The only reason for the fractional additive is to define a total order among all packets such that a packet or a ghost packet corresponding to(i.e.,a ghost packet that has the same rank as)that delays a packet in a step cannot be delayed by packet or a ghost packet corresponding to in another time step.In the following,however,we mainly use integral ranks,i.e.,the integral values of the fractional ranks,which,in the case of the ghost packet protocol,are equal to the birth date of the corresponding packet.Definition2.2(-delay sequence)Let denote a packet,and let denote integers.Then a -delay sequence consists ofa path of length starting at the destination node of packet.This path is called the delay path.Letdenote the nodes on the delay path.The delay path may include edges in both directions and, hence,follows a course going up and down the levels of the network.delay edges such that is incident to,for.These edges are not necessarily included in the delay path.7non-empty intervals of integral ranks such that,where denotes the length of interval.The maximum integral rank in is equal to the birth date of packet,and,for, the maximum integral rank in is equal to the minimum in.A-delay sequence is called active if the adversary or the stochastic generators inject packets (different from)such that,for every,packet has an integral rank in and its routing path includes edge,for some.These packets are called delay packets.The following lemma shows that a long routing time of a packet is always accompanied by an active -delay sequence with relatively large and small and.Lemma2.3Suppose a packet takes or more steps to reach its destination,for any.Then there is an active-delay sequence with,where denotes the difference between the level of thefirst node,,and the level of the last node,,of the delay path.Proof.We will construct a sequence of packets or ghost packets and nodes such that denotes the destination of,and packet or a ghost packet corresponding to this packet delays packetat node,for.(Ultimately,will be set either to or to.)There are two reasons why a packet may be delayed:It is delayed either by a packet or ghost packet with lower rank that wants to traverse the same link,or it is delayed by other packets with lower ranks occupying the next edge buffer on its path.Thefirst kind of delay is called-delay,the second kind of delay is called-delay.The active delay sequence is constructed incrementally.Suppose we have alreadyfixed the packets and nodes.Starting from the time step in which delayed on node or,if,the time step in which reached its destination node,we follow the course of the packet backwards in time.If is a ghost packet whose generation was caused by the arrival of another packet, then we identify with that packet and continue the trace.We stop following either when we reach a node on which was delayed,on which was injected as a non-ghost packet,or on which was injected as a ghost packet on a node without incoming edges.The node on which this event happened is called.If we stop because of an-delay,then the packet that caused the delay is called.If we stop because of an-delay, then the packets that occupy the corresponding buffer are called,in decreasing order of ranks. Moreover we set.In both of these cases we can continue our construction.In the other cases,however,our construction ends with a packet that was injected at node,and we define.The path from the destination of to the source of recorded by this process is called the delay path.The nodes on this path are defined to be.Note that these nodes are not necessarily identical to, but.The edges on which the recorded delays of the packets take place are defined to be the delay edges.We have to show that the number of these edges is at most.(Note that the delay edges are not necessarily included in the delay path.Consider,for example,the following scenario. Suppose packet is delayed in step on level by an-delay caused by the packets stored in a buffer on level.Suppose the next event recorded by the delay sequence is an-delay of packet caused by packet moving along an edge to level in step,and suppose this packet arrived on level coming from level in step.Then the delay path goes from level to level and then back to level,and hence,skips the delay edge.)Although not every delay edge is included in the delay path,each of these edges is incident to a node of the delay path,and the number of different delay edges is at most,which can be shown as follows.All delay events in a sequence of consecutive-delays recorded by the construction above in consecutive time steps,i.e., not separated by packet movements or-delays,take place at the same edge.Further,an-delay following immediately after a sequence of-delays takes place at the same edge,too.(Note that these properties are not given for the original ghost packet protocol.)Hence,considering the incremental construction of the delay sequence,the delay edge changes only in those incremental steps in which the delay path is increased by at least8。

Chapter12Event Tree Analysis12.1INTRODUCTIONEvent tree analysis (ETA)is an analysis technique for identifying and evaluating the sequence of events in a potential accident scenario following the occurrence of an initiating event.ETA utilizes a visual logic tree structure known as an event tree (ET).The objective of ETA is to determine whether the initiating event will develop into a serious mishap or if the event is sufficiently controlled by the safety systems and procedures implemented in the system design.An ETA can result in many different possible outcomes from a single initiating event,and it provides the capa-bility to obtain a probability for each outcome.12.2BACKGROUNDThe ETA technique falls under the system design hazard analysis type (SD-HAT)and should be used as a supplement to the SD-HAT analysis.Refer to Chapter 3for a description of the analysis types.The ETA is a very powerful tool for identify-ing and evaluating all of the system consequence paths that are possible after an initiating event occurs.The ETA model will show the probability of the system design resulting in a safe operation path,a degraded operation path,and an unsafe operation path.223Hazard Analysis Techniques for System Safety ,by Clifton A.Ericson,II Copyright #2005John Wiley &Sons,Inc.224EVENT TREE ANALYSISThe purpose of ETA is to evaluate all of the possible outcomes that can result from an initiating event.Generally,there are many different outcomes possible from an initiating event,depending upon whether design safety systems work prop-erly or malfunction when needed.ETA provides a probabilistic risk assessment (PRA)of the risk associated with each potential outcome.The ETA technique can be used to model an entire system,with analysis cover-age given to subsystems,assemblies,components,software,procedures,environ-ment,and human error.ETA can be conducted at different abstraction levels, such as conceptual design,top-level design,and detailed component design.ETA has been successfully applied to a wide range of systems,such as nuclear power plants,spacecraft,and chemical plants.The technique can be applied to a system very early in design development and thereby identify safety issues early in the design process.Early application helps system developers to design in safety of a system during early development rather than having to take corrective action after a test failure or a mishap.The ETA technique,when applied to a given system by an experienced analyst,is thorough at identifying and evaluating all of the possible outcomes resulting from an initiating event(IE).A basic understanding of ETA and FTA theory is essential to developing an ETA model.In addition it is crucial for the analyst to have a detailed understanding of the system.Overall,ETA is very easy to learn and understand. Proper application depends on the complexity of the system and the skill of the analyst.Applying the ETA technique to the evaluation of a system design is not a difficult process;however,it does require an understanding of FTA and probability theory.A cause–consequence analysis(CCA)is very similar to ETA and is a possible alternative technique.Additionally,multiple FTAs could be performed to obtain the same results as an ETA.The ETA produces many different potential outcomes from a single event,whereas the FTA only evaluates the many causes of a single outcome.The use of an ETA is recommended for a PRA of the possible outcomes resulting from an initiating event.The resulting risk profiles provide management and design guidance on areas requiring additional safety countermeasure design methods.12.3HISTORYEvent tree analysis is a binary form of a decision tree for evaluating the various mul-tiple decision paths in a given problem.ETA appears to have been developed during the WASH-1400[1]nuclear power plant safety study(circa1974).The WASH-1400team realized that a nuclear power plant PRA could be achieved by FTA;however,the resulting fault trees(FTs)would be very large and cumbersome, and they therefore established ETA to condense the analysis into a more manageable picture,while still utilizing FTA.12.5THEORY225 12.4DEFINITIONSThe ETA technique is based on the following definitions:Accident scenario Series of events that ultimately result in an accident.The sequence of events begins with an initiating event and is(usually)followed by one or more pivotal events that lead to the undesired end state.Initiating event(IE)Failure or undesired event that initiates the start of an acci-dent sequence.The IE may result in a mishap,depending upon successful oper-ation of the hazard countermeasure methods designed into the system.Refer to Chapter2on hazard theory for information on the components of a hazard. Pivotal events Intermediary events between the IE and thefinal mishap.These are the failure/success events of the design safety methods established to prevent the IE from resulting in a mishap.If a pivotal event works successfully,it stops the accident scenario and is referred to as a mitigating event.If a pivotal event fails to work,then the accident scenario is allowed to progress and is referred to as an aggravating event.Probabilistic risk assessment(PRA)Comprehensive,structured,and logical analysis method for identifying and evaluating risk in a complex technological system.The detailed identification and assessment of accident scenarios,witha quantitative analysis,is the PRA goal.Event tree(ET)Graphical model of an accident scenario that yields multiple out-comes and outcome probabilities.ETs are one of the most used tools in a PRA.A common definition of risk in the PRA discipline is that risk is based upon a set of triplets:1.Accident scenarios—what can go wrong?2.Scenarios frequencies—how likely is it?3.Scenarios consequences—What are the consequences?12.5THEORYWhen performing a PRA,identifying and developing accident scenarios is funda-mental to the concept of risk evaluation.The process begins with a set of IEs that perturb the system(i.e.,cause it to change its operating state or configuration). For each IE,the analysis proceeds by determining the additional failure modes necessary to lead to the undesirable consequences.The consequences and fre-quencies of each scenario are computed for the individual IEs and the collection of probabilities form a risk profile for the system.Event trees are used to model accident scenarios.An ET starts with the IE and progresses through the scenario via a series of pivotal events(PEs)until an end state is reached.The PEs are failures or events that are mitigating or aggravating226EVENT TREE ANALYSISto the scenario.The frequency(i.e.,probability)of the PE can be obtained from an FTA of the event.The PRA theory relates very closely with standard system safety terminology. An accident scenario is equivalent to a hazard;scenario frequency is equivalent to hazard probability;scenario outcome is equivalent to hazard severity.Risk management involves the identification and prevention or reduction of adverse accident scenarios and the promotion of favorable scenarios.Risk manage-ment requires understanding the elements of adverse scenarios so that their com-ponents can be prevented or reduced,and an understanding of favorable scenarios in order that their components can be enhanced or promoted.An accident scenario contains an IE and(usually)one or more pivotal events leading to an end state as shown in Figure12.1.As modeled in most PRAs,an IE is a perturbation that requires some kind of response from operators and/or one or more systems to prevent an undesired conse-quence.The pivotal events include successes or failures of these responses or possibly the occurrence or nonoccurrence of external conditions or key phenomena.The end states are formulated according to the decisions being supported by the analysis.Scen-arios are classified into end states according to the kind and severity of consequences, ranging from completely successful outcomes to losses of various kinds,such as: .Loss of life or injury/illness to personnel.Damage to or loss of equipment or property(including software).Unexpected or collateral damage as a result of tests.Failure of mission.Loss of system availability.Damage to the environmentAn ET distills the pivotal event scenario definitions and presents this information in a tree structure that is used to help classify scenarios according to their consequences. The headings of the ET are the IE,the pivotal events,and the end states.The tree struc-ture below these headings shows the possible scenarios ensuing from the IE,in terms of the occurrence or nonoccurrence of the pivotal events.Each distinct path through the tree is a distinct scenario.According to a widespread but informal convention, where pivotal events are used to specify system success or failure,the“down”branch is considered to be“failure.”The ET concept is shown in Figure12.2.MishapFigure12.1Accident scenario concept.In most ETs,the pivotal event splits are binary:A phenomenon either does or does not occur;a system either does or does not fail.This binary character is not strictly necessary;some ETs show splits into more than two branches.What is necessary is that distinct paths be mutually exclusive and quantified as such (at least to the desired level of accuracy).An example of ET structure with quantitative calculations is displayed in Figure 12.3.The ET model logically combines all of the system design safety countermeasure methods intended to prevent the IE from resulting in a mishap.A side effect of the analysis is that many different outcomes can be discovered and evaluated.Note how the ET closely models the scenario concept shown in Figure 12.1.Pivotal Events Initiating EventEvent 1Event 2Event 3 OutcomesAccident ScenariosFigure 12.2Event tree concept.Pivotal Events Initiating EventEvent 1Event 2 Event 3 Outcomes Success (P 2S )Success (P 3S )Outcome AP A =(P IE )(P 1S )(P 2S )(P 3S )Success (P 1S )Fail (P 3F )Outcome BP B =(P IE )(P 1S )(P 2S )(P 3F )Event Fail (P 2F )Success (P 3S )Outcome CP C =(P IE )(P 1S )(P 2F )(P 3S )(P IE )Fail (P 3F )Outcome DP D =(P IE )(P 1S )(P 2F )(P 3F )Fail (P 1F )Outcome E P E =(P IE )(P 1F )Figure 12.3ETA concept.12.5THEORY227228EVENT TREE ANALYSIS12.6METHODOLOGYFigure12.4shows an overview of the basic ETA process and summarizes the important relationships involved in the ETA process.The ETA process involves uti-lizing detailed design information to develop event tree diagrams(ETDs)for specific IEs.In order to develop the ETD,the analyst must havefirst established the accident scenarios,IEs,and pivotal events of interest.Once the ETD is con-structed,failure frequency data can be applied to the failure events in the diagram. Usually this information is derived from FTA of the failure event.Since 1¼P SþP F,the probability of success can be derived from the probability of fail-ure calculation.The probability for a particular outcome is computed by multiplying the event probabilities in the path.Table12.1lists and describes the basic steps of the ETA process,which involves performing a detailed analysis of all the design safety features involved in a chain of events that can result from the initiating event to thefinal outcome.Complex systems tend to have a large number of interdependent components, redundancy,standby systems,and safety systems.Sometimes it is too difficult or cumbersome to model a system with just an FT;so,PRA studies have combined the use of FTs and ETDs.The ETD models accident/mishap cause–consequence scenarios,and FTs model complex subsystems to obtain the probability of these sub-systems failing.An accident scenario can have many different outcomes,depending on which PEs fail and which function correctly.The ET/FT combination models this complexity very well.The goal of ETA is to determine the probability of all the possible outcomes resulting from the occurrence of an IE.By analyzing all possible outcomes,it is possible to determine the percentage of outcomes that lead to the desired result and the percentage of outcomes that lead to the undesired result.Event trees can be used to analyze systems in which all components are continu-ously operating or for systems in which some or all of the components are in standby mode—those that involve sequential operational logic and switching.The starting point(referred to as the initiating event)disrupts normal system operation.The event tree displays the sequences of events involving success and/or failure of components.the systemIn the case of standby systems and,in particular,safety and,mission-oriented systems,the ET is used to identify the various possible outcomes of the system following a given IE,which is generally an unsatisfactory operating event or situ-ation.In the case of continuously operated systems,these events can occur (i.e.,components can fail)in any arbitrary order.In the event tree analysis,the com-ponents can be considered in any order since they do not operate chronologically with respect to each other.The ETA is based on binary logic in which an event either has or has not hap-pened or a component has or has not failed.It is valuable in analyzing the conse-quences arising from a failure or undesired event.An ET begins with an IE,such as a component failure,increase in temperature /pressure,or a release of a hazardous substance that can lead to an accident.The consequences of the event are followed through a series of possible paths.Each path is assigned a probability of occurrence and the probability of the various possible outcomes can be calculated.The ETD is a diagram modeling all of the possible events that follow an originat-ing failure or undesired event.The originating event can be a technical failure or an operational human error.The objective is to identify the chain of events following one or more specified basic events,in order to evaluate the consequences and determine whether the event will develop into a serious accident or are sufficiently controlled byTABLE 12.1ETA Process Step TaskDescription1Define the system.Examine the system and define the system boundaries,subsystems,and interfaces.2Identify the accident scenarios.Perform a system assessment or hazard analysis to identify the system hazards and accident scenarios existing within the system design.3Identify the initiating events.Refine the hazard analysis to identify the significant IEs in the accident scenarios.IEs include events such as fire,collision,explosion,pipe break,toxic release,etc.4Identify thepivotal events.Identify the safety barriers or countermeasures involved with the particular scenario that are intended to preclude a mishap.5Build the event tree diagram.Construct the logical ETD,starting with the IE,then the PEs,and completing with the outcomes of each path.6Obtain the failure event probabilities.Obtain or compute the failure probabilities for the PEs on the ETD.It may be necessary to use FTs to determine how a PE can fail and to obtain the probability.7Identify theoutcome pute the outcome risk for each path in the ETD.8Evaluate the outcome risk.Evaluate the outcome risk of each path and determine if the risk is acceptable.9Recommendcorrective action.If the outcome risk of a path is not acceptable,develop design strategies to change the risk.10Document ETA.Document the entire ETA process on the ETDs.Update for new information as necessary.12.6METHODOLOGY229the safety systems and procedures implemented.The results can therefore be rec-ommendations to increase the redundancy or to modifications to the safety systems.The ETA begins with the identified IE listed at the left side of the diagram in Figure 12.5.All safety design methods or countermeasures are then listed at the top of the diagram as contributing events.Each safety design method is evaluated for the contributing event:(a)operates successfully and (b)fails to operate.The resulting diagram combines all of the various success /failure event combinations and fans out to the right in a sideways tree structure.Each success /failure event can be assigned a probability of occurrence,and the final outcome probability is the product of the event probabilities along a particular path.Note that the final outcomes can range from safe to catastrophic,depending upon the chain of events.12.7WORKSHEETThe primary worksheet for an ETA is the event tree diagram (ETD),which provides the following information:1.Initiating event2.System pivotal events3.Outcomes4.Event and outcome probabilitiesFigure 12.5demonstrates the typical ETD.Each event is divided into two paths,success and failure.The success path always is the top path and the failure path is the lower path.The ETD has only one IE,which is identified at the far left of the dia-gram.As many contributing events as necessary to fully describe the system are listed at the top of the diagram.The more contributing events involved the larger the resulting ETD and the more tree branches required.Pivotal Events Initiating EventEvent 1Event 2 Event 3OutcomesOutcome AP A = (P IE )(P 1S )(P 2S )(P 3S )Outcome BP B = (P IE )(P 1S )(P 2S )(P 3F )Outcome CP C = (P IE )(P 1S )(P 2F )(P 3S )Outcome DP D = (P IE )(P 1S )(P 2F )(P 3F )Outcome E P E = (P IE )(P 1F )Figure 12.5ETD development.230EVENT TREE ANALYSIS12.8EXAMPLE 1Figure 12.6contains an example ETA for a fire detection and suppression system in an office building.This ETA analyzes all the possible outcomes of a system fire.The IE for the ET is “fire starts.”Note the range of outcomes resulting from the success or failure of the safety subsystems (pivotal events).Note from this example that when computing the success /fail probability for each contributing PE that the PE states must always sum to 1.0,based on the reliability formula that P SUCCESS þP FAILURE ¼1.Also note that in this case there are three contributing PEs that generate five possible different outcomes,each with a different probability.12.9EXAMPLE 2Figure 12.7contains an example ETA for an automobile system,where the car battery has failed.The dead battery is the IE that begins the scenario analysis.12.10EXAMPLE 3Figure 12.8contains an example ETA for a missile system.The IE is the missile being dropped during handling or transportation.12.11EXAMPLE 4Figure 12.9contains an example ETA for a nuclear power plant system.The IE is a pipe break in the cooling subsystem.Pivotal EventsInitiating EventFireDetection WorksFireAlarm Works Fire Sprinkler System Works Outcomes ProbYES (P = 0.7)YES (P = 0.8)Limited damage 0.00504YES (P = 0.9)NO (P = 0.2)Extensive damage, people escape 0.00126Fire Starts NO (P = 0.3)YES (P = 0.8)Limited damage, wet people0.00216(P = 0.01)NO (P = 0.2)Death/Injury, extensive damage0.00006NO (P = 0.1)Death/Injury, extensive damage0.001Figure 12.6ETA example 1.12.11EXAMPLE 4231Pivotal EventsOutcomeInitiating Event ElectricityFission ProductRemoval AvailableVery smallAvailableSmallFailsSmallAvailableAvailableAvailableAvailableContainment Medium Pipe BreaksFailsFailsFailsFailsLargeVery largeFailsVery largeEmergency Core CoolingFission Release Figure 12.9ETA example 4.Pivotal Events Initiating EventArm-1 RemainsSafeArm-2 RemainsSafeArm Power Remains SafeOutcomes ProbMissile is safe0.009Missile Dropped YES (P = 0.7)Missile is safe0.0007(P = 0.01)NO (P = 0.1)NO (P = 0.3)YES (P = 0.8)Missile is safe 0.00024NO (P = 0.2)Missile is armed and powered 0.00006Figure 12.8ETA example 3.Pivotal EventsInitiating EventJumper Cables Available Donor BatteryAvailableCablesConnectedProperlyDonor Battery Starts Car Outcomes ProbYES (P = 0.9)Car is jump started, mission success0.03024YES (P = 0.8)YES (P = 0.7)NO (P = 0.1)Car not started, mission failure0.0048YES (P = 0.6)NO (P = 0.2)Car not started, possible damage, mission failure0.0084Dead Battery (P = 0.1)NO (P = 0.3)Car not started, mission failure0.018NO (P = 0.4)Car not started, mission failure0.04Figure 12.7ETA example 2.232EVENT TREE ANALYSIS12.14SUMMARY233 12.12ADVANTAGES AND DISADVANTAGESThe following are advantages of the ETA technique:1.Structured,rigorous,and methodical approach.2.A large portion of the work can be computerized.3.Can be effectively performed on varying levels of design detail.4.Visual model displaying cause/effect relationships.5.Relatively easy to learn,do,and follow.6.Models complex system relationships in an understandable manner.7.Follows fault paths across system boundaries.bines hardware,software,environment,and human interaction.9.Permits probability assessment.mercial software is available.The following are disadvantages of the ETA technique:1.An ETA can only have one initiating event,therefore multiple ETAs will berequired to evaluate the consequence of multiple initiating events.2.ETA can overlook subtle system dependencies when modeling the events.3.Partial successes/failures are not distinguishable.4.Requires an analyst with some training and practical experience.12.13COMMON MISTAKES TO AVOIDWhenfirst learning how to perform an ETA,it is commonplace to commit some typical errors.The following is a list of typical errors made during the conduct of an ETA:1.Not identifying the proper IE2.Not identifying all of the contributing pivotal events12.14SUMMARYThis chapter discussed the ETA technique.The following are basic principles that help summarize the discussion in this chapter:1.ETA is used to model accident scenarios and to evaluate the various outcomerisk profiles resulting from an initiating event.2.ETA is used to perform a PRA of a system.234EVENT TREE ANALYSIS3.The ETA diagram provides structure and rigor to the ETA process.4.ETA can be a supplement to the SD-HAT.5.Fault trees are often used to determine the causal factors and probability forfailure events in the ETA.REFERENCE1.N.C.Rasmussen,Reactor Safety Study:An Assessment of Accident Risks in US Commer-cial Nuclear Power Plants,WASH-1400,Nuclear Regulatory Commission,Washington, DC,1975.BIBLIOGRAPHYAndrews,J.D.and S.J.Dunnett,Event Tree Analysis Using Binary Decision Diagrams,IEEE Trans.Reliability,49(2):230–238(2000).Henley, E.J.and H.Kumamoto,Probabilistic Risk Assessment and Management for Engineers and Scientists,2nd ed.,IEEE Press,1996.Kapan,S.and B.J.Garrick,On the Quantitative Definition of Risk,Risk Analysis,1:11–37 (1981).NASA,Fault Tree Handbook with Aerospace Applications,version1.1.NASA,August2002. Papazoglou,I.A.,Functional Block Diagrams and Automated Construction of Event Trees, Reliability Eng.System Safety,61(3):185–214(1998).。

关于失败的辩证观点的英文作文Failure is often seen as the antithesis of success, a stumbling block on the path to achievement. However, it is through failure that we learn the most valuable lessons.It is in the crucible of failure that resilience is forged. Each setback offers an opportunity to reassess, to refine strategies, and to grow stronger in character.Moreover, failure is a necessary component of innovation. Without the courage to fail, we would never venture into uncharted territory, and progress would stagnate.Yet, it is crucial to approach failure with the right mindset. Embracing it as a teacher rather than a defeat can transform it into a stepping stone towards success.In the end, it is not the absence of failure that defines greatness, but the ability to rise above it. Greatness is not found in never failing, but in never giving up after failing.Thus, we must teach our youth to view failure not as a barrier, but as a bridge to their goals. It is through understanding and accepting failure that true learning and growth occur.Let us not fear failure, but rather, let it be the catalyst for our ambition. It is in the face of adversitythat our true potential is revealed.In conclusion, failure is an integral part of the journey to success. It is not a sign of weakness, but a testament to our courage to try, to strive, and to persist in the face of challenges.。

Embracing Failure as a Stepping Stone Embracing failure as a stepping stone is a concept that can be quite challenging for many individuals. Failure is often associated with negative emotions such as disappointment, shame, and fear. However, it is important to recognize that failure is a natural part of life and can actually be a valuable learning experience. In this response, I will explore the idea of embracingfailure as a stepping stone from multiple perspectives, including the emotionaland psychological impact of failure, the importance of resilience, and thepotential for growth and success that can come from failure. From an emotional perspective, failure can be incredibly difficult to cope with. It can lead to feelings of inadequacy, self-doubt, and even depression. Many people fear failure because they worry about how it will make them look in the eyes of others, and how it will affect their self-esteem. However, it is important to remember thatfailure is not a reflection of one's worth as a person. It is simply a part of the human experience, and everyone goes through it at some point in their lives. By embracing failure as a stepping stone, individuals can shift their mindset andview failure as an opportunity for growth and self-improvement rather than a personal flaw. Psychologically, failure can also have a significant impact on an individual's mindset and behavior. Some people may become discouraged and give up after experiencing failure, while others may become more determined and resilient. This is where the concept of embracing failure as a stepping stone becomes crucial. By reframing failure as a learning opportunity, individuals can develop a growth mindset and become more resilient in the face of adversity. This can lead to increased motivation, perseverance, and a greater willingness to take risks in the future. Furthermore, embracing failure as a stepping stone can also lead to personal and professional growth. When individuals are able to learn from their failures and use them as a springboard for improvement, they can develop new skills, insights, and perspectives that they may not have gained otherwise.Failure can also provide valuable feedback that can help individuals identifytheir strengths and weaknesses, and make more informed decisions in the future. In this way, failure can actually be a catalyst for success, as it can lead to new opportunities and achievements that may not have been possible without the lessonslearned from failure. In addition, embracing failure as a stepping stone can also have a positive impact on relationships and teamwork. When individuals are open about their failures and the lessons they have learned, it can create a culture of trust, vulnerability, and support. This can foster stronger connections and collaboration among team members, as they are more willing to take risks, share their ideas, and learn from each other's experiences. It can also create a more inclusive and empathetic environment, where individuals feel comfortable being themselves and embracing their imperfections. In conclusion, embracing failure as a stepping stone is a powerful concept that can have a profound impact on individuals, both personally and professionally. By shifting their mindset and viewing failure as a natural part of the learning process, individuals can develop resilience, motivation, and a growth mindset. They can also use failure as a catalyst for personal and professional growth, as well as a means to strengthen relationships and teamwork. Ultimately, embracing failure as a stepping stone can lead to greater self-awareness, success, and fulfillment in life.。

Facing Failure with Fortitude Facing failure with fortitude is a challenge that many people encounter at some point in their lives. Whether it's a personal failure, such as a relationship ending, or a professional failure, such as a project not meeting expectations, it can be difficult to navigate the emotions that come with falling short of our goals. However, it's important to remember that failure is a natural part of life and can provide valuable lessons and opportunities for growth. One perspective on facing failure with fortitude is to embrace the emotions that come with it. It's okay to feel disappointed, frustrated, or even angry when things don't go as planned. These emotions are a natural response to failure and shouldn't be ignored or suppressed. Instead, it's important to acknowledge them and allow yourself to experience them fully. By doing so, you can process the emotions and begin to move forward in a healthy way. Another perspective is to reframe failure as a learning opportunity. Instead of viewing failure as a definitive end, try to see it as a chance to learn and grow. Reflect on what went wrong and consider what you can do differently in the future. By approaching failure with a growth mindset, you can turn a negative experience into a positive one by gaining new insights and skills that can help you succeed in the long run. It's also important to seek support from others when facing failure. Whether it's friends, family, or colleagues, having a strong support system can make a big difference in how you cope with failure. Talking about your experience with others can provide new perspectivesand insights, as well as emotional support. Additionally, seeking out mentors or role models who have overcome similar challenges can offer valuable guidance and inspiration. In addition to seeking support from others, it's important topractice self-compassion when facing failure. It's easy to be hard on ourselves when things don't go as planned, but being kind and understanding towardsourselves is crucial for resilience. Treat yourself with the same compassion and empathy that you would offer to a friend in a similar situation. Remind yourself that failure is a part of life and doesn't define your worth or potential. Furthermore, it's important to maintain a sense of perspective when facing failure. While it may feel like the end of the world in the moment, it's important to remember that failure is often temporary and can lead to new opportunities.Keeping things in perspective can help you see the bigger picture and avoidgetting stuck in a negative mindset. Remember that setbacks are a normal part of the journey towards success and that they can ultimately make the achievement even more meaningful. Finally, it's important to take proactive steps towards moving forward after facing failure. This could involve setting new goals, seeking out new opportunities, or revising your approach based on what you've learned. By taking action, you can regain a sense of control and agency in your life, which can help you overcome the feelings of helplessness that often accompany failure. In conclusion, facing failure with fortitude is a challenging but important skill to develop. By embracing your emotions, reframing failure as a learning opportunity, seeking support, practicing self-compassion, maintaining perspective, and taking proactive steps, you can navigate failure in a healthy and resilient way. Remember that failure is a natural part of life and can ultimately lead to growth and success.。