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International Journal of Emerging Electric Power Systems Volume9,Issue42008Article1Application of Fuzzy Fault-Tree Analysis to Assess the Reliability of a Protection Systemfor a SwitchyardYing-Yi Hong∗Lun-Hui Lee†Heng-Hsing Cheng‡∗Chung Yuan Christian University,yyhong@.tw†Chung Yuan Christian University,lhlee@.tw‡Chung Yuan Christian University,xingxing@Copyright c 2008The Berkeley Electronic Press.All rights reserved.Application of Fuzzy Fault-Tree Analysis to Assess the Reliability of a Protection Systemfor a Switchyard∗Ying-Yi Hong,Lun-Hui Lee,and Heng-Hsing ChengAbstractThis paper proposed a method for reliability assessment of the protection system for a switch-yard by fault-tree analysis considering uncertainty of unavailability for an element.Unavailability of an element with uncertainty is expressed with the fuzzy set.The fault-tree analysis incorpo-rated with the fuzzy set is employed to conduct the reliability assessment.The importance of elements influencing reliability can be achieved by the Fuzzy Importance pared with traditional methods,the fault-tree analysis requires less computation.In this paper,a345 kV switchyard in the3rd nuclear power plant in Taiwan serves as an example for illustrating the results of the proposed method.KEYWORDS:reliability,protection system,switchyard,fault-tree analysis,fuzzy set theory∗This work is sponsored by the National Science Council(Taiwan)under the grant96-2221-E-033-069-MY2.I. I NTRODUCTIONReliability assessment is important for both operation and planning in the power system [1]. A protection system for the switchyard will be activated if a bus or transmission line is faulted. The protection system will enable breakers to trip in order to retain the remaining power system in a normal condition. Therefore, reliability of the protection system for the switchyard is very important.There are many methods for reliability assessment such as fault-tree (FT) analysis, reliability block diagrams (RBD), Markov modeling (MM) and Monte Carlo (MC) method, and so on [2, 3]. An FT is a logic diagram that shows potential events affecting system performance and the relationship between potential events. For a complicated system, the ultimate (top) event can be decomposed into different fault events. The structure of a FT is just like a tree that is built from top to bottom [4]. The RBD is similar to the FT analysis. Blocks can be connected through sets of series and parallel connections in order to accurately present a system. The reliability, obtained by the RBD, is required to be assessed again when the structure of a system is changed. The state-space based MM is different from others described previously in that it is a dynamic approach [5]. For the MM, more calculation time is required for a large system because a more complicated state transition matrix needs to be solved. Calculation for the MM method becomes complicated and dimension of the matrix becomes very large when the number of the system components increases. The MC method doesn’t need any mathematical models, just using random variables to simulate the random process [6]. The MC simulation can be divided into two types: One is sequential simulation and the other is non-sequential simulation. Each method described above has its advantages and defects. Compared with the others, the MC method and MM require more computation time.Compared with the others, the FT analysis is an analytical technique and requires less computation time. Once the system structure is changed, one needs to re-evaluate reliability of the altered part of the system using FT analysis. The FT analysis was developed in 1961 by H.A. Watson, who worked in the Bell Telephone Laboratories [7]. It is commonly used to predict reliability of the complicated system in many fields, such as nuclear plants, chemical works, pipelines, control systems, and power systems [8]-[10]. In the area of the power engineering, the FT analysis was used to perform the reliability assessment of electric elements, transmission system [11], supervisory control and data acquisition (SCADA) [12], special protection system [13], communication system in the distribution automation [14, 15], and substation control system [16].For the reliability assessment of protection system, Kjolle et al. provides a comparative review [17]. Meeuwsen presented the influence of protection system failures and preventive maintenance on protection systems using Markov models 1Hong et al.: Fuzzy Fault-Tree Analysis to Assess Reliability of Protection SystemPublished by The Berkeley Electronic Press, 2008in distribution systems [18]. Wang and Thorp proposed a method to determine optimal locations for protection system enhancement [19]. A random search algorithm based on power system heuristics was given for fast rare-event simulation of consecutive relaying malfunctions in bulk power systems [19]. A nonsequential Monte Carlo simulation approach was used to implement the stochastic properties of contingencies, protective response and protection system failures by Yu and Singh [20]. Moreover, the mechanism and scheme of protection system were analyzed on their contribution to the cascading outages after a fault occurs [21].Measurement and statistic will cover uncertainties in many engineering problems. When using the FT analysis, the unavailability, which includes uncertainty, of an element will be employed to assess unavailability of the whole system. In this paper, fuzzy set theory is used for expressing the uncertainty in the FT. More specifically, the unavailability is considered as a fuzzy set and is in terms of a triangular membership function.This paper uses the FT analysis with uncertainty to assess the reliability of a protection system for a switchyard. Not only the reliability of subsystems and system can be attained, but also the measures of importance of fault events can be attained.The problem will be described in Sec. II. Then the fuzzy set and the FT analysis will be introduced in Sec. III. Studied results of the protection system of a 345kV switchyard serving as an example will be provided in Sec. IV. Conclusions will be given in Sec. V.II. P ROBLEM D ESCRIPTIONA 345kV switchyard in the 3rd nuclear power plant in Taiwan serves as an example in this paper. The 345kV switchyard is composed of a 1-1/2 buses structure, which connects two generators and four 345kV transmission lines. The diagram of the switchyard is shown in Figure 1.Figure 1 Switchyard Structure DAPENG #1DAPENG #2DAPENG #3LONGQI 2International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 4, Art. 1/ijeeps/vol9/iss4/art1The switchyard has 11 SF 6 breakers named from BR01 through BR11. There are five functions in the protection system in order to protect generator, bus and transmission line. If any fault happens, the protection system will be active and enable the breakers to trip. The five functions are (i) bus protection, (ii) transmission line protection, (iii) breaker failure protection, (iv) generator backup protection and (v) remote trip protection. This paper uses the FT analysis to assess the reliability of this protection system incorporating these 5 functions. The mathematical background is provided first below.III. M ATHEMATICAL B ACKGROUND3.1 Fuzzy SetThe unavailability of an element actually should be updated regularly according to the operation conditions. However, reliability study is a planning issue for a long-term consideration. Hence, the unavailability of the element becomes uncertain. The uncertainty is treated as the fuzzy set. The triangular membership function in the fuzzy set is used to express each relevant parameter in this paper. That is,μA (x 2) = 1 and μA (x 1) = μA (x 3) = 0whereμA (x ) = the membership function of fuzzy set Ax 1 = the lower bound of xx 2 = the x with membership value of onex 3 = the upper bound of xIn this paper, the α-cut (level) is used for representing the fuzzified degree. A fuzzy set with an α-cut means that a smaller x domain with respect to the membership values higher than α is considered. For triangular fuzzy sets, fuzzy arithmetic operations are equivalent to the corresponding interval arithmetic operations for each α-cut [22]. A fuzzy set with the α-cut can be represented mathematically as:()],[21ααααa a A x A == (1)where a 1 and a 2 represent the lower and upper limits (with membership value of α) of x , respectively.3Hong et al.: Fuzzy Fault-Tree Analysis to Assess Reliability of Protection SystemPublished by The Berkeley Electronic Press, 2008For the basic arithmetic operations, Eqs. (2) and (3) can be attained:],[2211ααααααb a b a B A ++=+ (2)],[2211ααααααb a b a B A ××=× (3)3.2 Fault Tree AnalysisThe protection system of a switchyard is composed of many different elements. In this paper, the most commonly used probabilistic model for the element, i.e., the conventional two-state model, will be used.The FT analysis is a logic and diagrammatic method for assessing reliability of a system. The critical elements affecting the reliability should also be identified first. In this paper, failure of a protection system is called as a top event ; failure of a function (defined in Sec. 2) is named as a sub-top event and failure of an element is called a fault event .Any FT consists of a finite number of minimum cut sets (MCSs), which are unique for the (sub-) top event [7]. In other words, a (sub-) top event includes finite MCSs. The (sub-) top event can be written in the general form as follows:(Sub-)TOP Event (4)∑==ki i MCS 1whereMCS i = the i-th minimum cut set.k = the number of minimum cut sets.3.3 Measures of ImportanceOne significant quantity in the reliability assessment is the so called “measures of importance” [22]. It provides the “influence measure” of a fault event (element) to the top event. The measures of importance can be regarded as the sensitivity of a fault event with respect to the top event. A larger measure of importance indicates the corresponding fault event is more important compared to other events. The measures of importance in an uncertain environment considering the fuzzy unavailability can be achieved by Fuzzy Importance Measure (FIM) [23].Let Top_event =f (U 1, U 2, …, U i-1, U i , U i+1, …, U n ) be the unavailability of the top event. The symbol U i is the unavailability for the i-th element. If the i-th element is fully unavailable, then the unavailability of the top event becomes()n i i Ui U U U U U f event Top ,, ,1 ,,,_11211L L +−== (5)4International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 4, Art. 1/ijeeps/vol9/iss4/art1If the i-th element is fully available, then the unavailability of the top event becomes()n i i Ui U U U U U f event Top ,, ,0 ,,,_11210L L +−== (6)Then[]01_,_===Ui Ui i event Top event Top ED FIM (7)whereFIM i = index of FIM for element iED = Euclidean distance between two fuzzy setsMore specifically, let ED[A,B] be the Euclidean distance between two fuzzy setsA and B. ED[A, B] is defined as follows:[]()()5.010222211,∑=⎥⎦⎤⎢⎣⎡−+−=αααααααb a b a B A ED (8)where and are defined in Equation (1).,1αa ,2αa α1b α2bIV . C ASE S TUDY - R ESULTS AND D ISCUSSIONS4.1 Overall FT TreeFailure of the 345kV switchyard, as shown in Figure 1, is considered as the top event in this paper. Any failure of the 5 protection functions (defined in Sec. 2) will lead to the top event. Failure of the whole protection system (top event) is made up of the failure of the five functions (the sub-top events defined in Sec.3.2). The relationship between the top event and 5 sub-top events is shown in Figure 2.5Hong et al.: Fuzzy Fault-Tree Analysis to Assess Reliability of Protection SystemPublished by The Berkeley Electronic Press, 2008In the protection system, the elements, influencing the top event, include breaker, relay, DC power for control and communication, etc. The fuzzy unavailability (x 2, the x with membership value of one, defined in Sec. 3.1) for each fault event is provided in Table I [11, 24]. The upper and lower bounds of x are the deviation of ±30% from x 2, respectively.T ABLE I U NA V AILABILITIES OF E LEMENTSElements No. Fault event Unavailability x 2Breaker 1 SF 6 circuit breaker 150×10-6Relay 2 Relay 87 fault 100×10-6 3 Relay 50BF fault 100×10-6 4 Relay 86BF fault 100×10-6 5Relay 50 fault 100×10-6 6Relay 21 fault 100×10-6 7Relay 2 fault 100×10-6 8Relay 87 malfunction 100×10-6 9Relay 50BF malfunction 100×10-6 10Relay 86BF malfunction 100×10-6 11Relay 50 malfunction 100×10-6 12Relay 21 malfunction 100×10-6 13Relay 2 malfunction 100×10-6 Digitalrelay 14 Digital relay fault200×10-6 15 Digital relay malfunction 100×10-6 DC power 16 DC power50×10-6 Optical fiber 17 Optical fiber equipment fault10×10-6 18 Optical fiber communication fault 100×10-6 Microwave 19Microwave equipment fault 200×10-620 Microwave communication fault 100×10-66International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 4, Art. 1/ijeeps/vol9/iss4/art14.2 Five Sub-top EventsThe function of bus protection is designed for protecting bus 1 and bus 2. Figure 3 illustrates the FT for the bus protection. In the viewpoint of this function alone, the sub-top event is the bus protection failure. If a bus has an abnormal condition, it should be isolated (2nd layer in Figure 3). The bus isolation is achieved by breakers (BR01, BR04, BR07 and BR10 for bus 1) and isolation action (3rd layer in Figure 3). The isolation action consists of the main protection and backup protection (4th layer in Figure 3). Both main protection and backup protection require differential relays (items 2 and 8 defined in Table I) and DC power (item 16 defined in Table I). Hence, any failure of differential relays or DC power will result in the main/backup protection failure. If both main and backup protections fail, then the isolation action fails. Furthermore, if any breaker or isolation action fails, the bus isolation will fail. Bus isolation failure for either bus 1 or 2 will lead to the bus protection failure.A FT of the transmission line protection is illustrated in Figure 4. When only this function is considered, the sub-top event is transmission line protection failure. Each transmission line has the same protective function including phase protection or grounding protection incorporating with breakers. Each transmission line has its own dedicated breakers (BR10 and BR11 for DAPENG #1, BR09 and BR08 for DAPENG #2, BR06 and BR05 for DAPENG #3, BR03 and BR02 for LONGQI). The line protection failure may result from phase protection, grounding protection or breaker failures. Two protective equipments and communications perform the protective function.The FT of the breaker failure protection is depicted in Figure 5. If only this function is considered, the failure of the breaker failure protection is defined as the sub-top event. There are 11 SF 6 breakers, each of which has a protective function, in the switchyard. Figure 6 is the diagrammatic FT for the generator backup protection. The generator backup protection failure is the sub-top event in this case. If MW generation cannot be transferred into buses, the protection function will isolate the generators to keep them safe. Moreover, the remote tripping is conducted using two breakers and communications, as shown in Figure7. Failure of the remote trip protection is the sub-top event for this function. Each transmission line has its remote trip protection.7Hong et al.: Fuzzy Fault-Tree Analysis to Assess Reliability of Protection SystemPublished by The Berkeley Electronic Press, 2008Figure 3 Fault-tree of Bus Protection8International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 4, Art. 1/ijeeps/vol9/iss4/art1Figure 4 Fault-tree of Transmission Line Protection9Published by The Berkeley Electronic Press, 2008Figure 5 Fault-tree of Breaker Failure Protection10/ijeeps/vol9/iss4/art1Figure 6 Fault-tree of Generator Backup Protection Published by The Berkeley Electronic Press, 200811Figure 7 Fault-tree of Remote Trip Protection4.3 Reliability of Protection SystemAfter the above sub-FTs are constructed, all sub-FTs are transferred into MCSs by Boolean operations. The unavailabilities of fault events shown in Table I are used for the MCSs in order to calculate fuzzy unavailability of each sub-top event. Table II illustrates the reliabilities of the top event and each sub-top event. The reliability is in terms of fuzzy unavailability which provides a possible range with membership. The strongest function with the smallest unavailability and the weakest function with the largest unavailability are the remote trip protection and the breaker failure protection, respectively. The corresponding failure rates and annual downtimes, transformed from x2 (see appendix), are also shown in the 5th and 6th columns of Table II./ijeeps/vol9/iss4/art1124.4 Fuzzy Importance MeasureThe FIM of fault events is calculated by Eq. (7). For example, Table III shows the FIMs of the bus protection. The elements (16, 2 and 8) in Figure 3 denote DC power, relay 87 fault and relay 87 malfunction, defined in Table I, respectively. Because they are at the same level as shown in Figure 3, these three elements have the same FIMs (4.581378E-03), as shown in Table III. On the other hand, the element 1 (BR10, 07, 04 and 01), as shown in Figure 3, is the SF6 breaker defined in Table I. The SF6 breaker has a higher level compared with the previous elements. Hence, SF6 breaker has a larger FIM (1.555635E+01). Table IV illustrates FIMs of all elements with respect to the top event. It is found that SF6 breaker and relays (50, 86, 21 and 2) are crucial.T ABLE II R ELIABILITIES OF T OP E VENT AND S UB-T OP E VENTSTop event and Sub-top eventUnavailability(×10-3)Failure rate(times/year)Equivalentannualdowntime(hours/year) x2UpperboundLowerboundProtection systemfailure 7.940840 10.32330 5.558377 15.96632×10-3 69.56 Bus protection failure 1.200183 1.560284 0.840082 2.40229×10-3 10.51 Transmission lineprotection failure 1.200778 1.561207 0.840350 2.40348×10-3 10.52 Breaker failureprotection failure 6.600000 8.580000 4.620000 13.25840×10-3 57.82 Generator backupprotection failure 2.390000 3.107000 1.673000 4.78763×10-3 20.94 Remote trip protectionfailure 0.600389 0.780603 0.420175 1.20126×10-3 5.26T ABLE III FIMs OF B US P ROTECTIONFault events FIMsSF6 circuit breaker 1.555635E+01Protection relay malfunction (87)4.581378E-03Protection relay fault (87) 4.581378E-03DC power 4.581378E-0313 Published by The Berkeley Electronic Press, 2008T ABLE IV FIMs OF P ROTECTION S YSTEMFault events FIMsSF6 circuit breaker 1.555635E+01Protection relay malfunction (50) 1.555635E+01Protection relay fault (50BF) 1.555635E+01Protection relay malfunction (50BF) 1.555635E+01Protection relay fault (86BF) 1.555635E+01Protection relay malfunction (86BF) 1.555635E+01Protection relay fault (50) 1.555635E+01Protection relay fault (21) 1.555635E+01Protection relay malfunction (21) 1.555635E+01Protection relay fault (2) 1.555635E+01Protection relay malfunction (2) 1.555635E+01DC power 1.555635E+01Digital relay fault 5.529250E-03Protection relay malfunction (87) 4.581378E-03Digital relay malfunction 5.529250E-03Optical fiber communication fault 5.529250E-03Microwave equipment fault 2.527657E-03Protection relay fault (87) 4.581378E-03Microwave communication fault 2.527657E-03Optical fiber equipment fault 5.529250E-03V. C ONCLUSIONSIn this paper, reliability of the protection system for a switchyard was assessed using the fault-tree analysis with fuzzy unavailability. It could be achieved by the minimum cut sets using Boolean operation and fuzzy arithmetic operations. The unavailability of a system was then transformed to the failure rate and the downtime. The planner may know the possible range of reliability with fuzziness. The measure of importance for the fault event was also identified using Fuzzy Importance Measure (FIM). A 345kV switchyard in the 3rd nuclear power plant in /ijeeps/vol9/iss4/art114Taiwan served as an example in this paper. From the simulation results, it could be found that the strongest and weakest functions were the remote trip protection and the breaker failure protection, respectively. Moreover, it was found that SF6 breaker, relays (50, 86, 21 and 2) and DC power were crucial considering FIMs.AppendixFor reliability assessment, one needs to attain the unavailability data of the fault events and then compute the unavailability of the system using Equation (4). Finally, the annual down time of the system can be evaluated from the unavailability as follows:Annual downtime = unavailability ×8760(hr/year) (A-1)The failure rate λ can be obtained by solving Eq. (A-2):Unavailability = 1 + TITI ⋅−⋅−λλ1)exp( TI=1 year (A-2)Equation (A-2) can be derived as follows: Assume that States 1 and 2 for an element are in the UP and DOWN conditions, respectively. Let the initial probability for State 1 be unity. Then the probability for State 1 at time t is exp(-t λ). The definition of unavailability for State 2 is the corresponding probability, i.e., 1- exp(-t λ). For a given test interval TI, the average unavailability for State 2 can be obtained byUnavailability = ∫−−TI dt t TI 0))exp(1(1λ = 1 + TITI ⋅−⋅−λλ1)exp(VI. R EFERENCES[1] R. Billinton, M. Fotuhi-Firuzabad, L. Bertling, “Bibliography on the Application of Probability Methods in Power System Reliability Evaluation 1996-1999,” IEEE Power Engineering Review, Vol. 21, No. 8, pp. 56-56, 2001.[2] ISA-TR84.00.02-2002, The Instrumentation, Systems, and Automation Society(ISA), 2002.15Published by The Berkeley Electronic Press, 2008[3] I EEE guide for selecting and using reliability predictions based on IEEE 1413,IEEE Std 1413.1-2002.[4] Y. Dutuit, and A. Rauzy, “Efficient Algorithms to Assess Component andGate Importance in Fault Tree Analysis,” Reliability Engineering and System Safety, V ol. 72, No. 2, pp. 213-222, 2001.[5] L. Xing, K. N. Fleming, and W. T. 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故障树分析法和模糊集理论在堆垛机故障诊断中的应用廖伦彪;杨丰;张宝;杨涛;吕婷【摘要】利用故障树分析(Fault Tree Analysis)技术对堆垛机进行可靠性分析时,因缺乏数据而无法准确获得部件失效概率.为此,结合专家的语言判断和模糊集理论(Fuzzy Set Theory),提出了一种基于故障树分析技术和模糊集理论的堆垛机故障诊断方法.该方法根据堆垛机操作人员的经验,获取专家在堆垛机部件失效概率上的主观评判;采用模糊集理论将专家的主观语言表述模糊化处理,转化成客观的失效可能性数值;结合堆垛机主接触器模块故障诊断实例,验证了该方法的可行性.结果表明:该方法可以有效解决因数据缺乏导致部件失效概率不确定问题,为堆垛机的故障诊断和维护决策提供了帮助.【期刊名称】《烟草科技》【年(卷),期】2014(000)007【总页数】4页(P17-20)【关键词】故障树分析;堆垛机;专家语言;模糊集;失效概率;故障诊断【作者】廖伦彪;杨丰;张宝;杨涛;吕婷【作者单位】四川烟草工业有限责任公司绵阳分厂,四川省绵阳市高新区飞云大道中段373号 621000;西南科技大学信息工程学院,四川省绵阳市涪城区青龙大道中段59号 621010;四川烟草工业有限责任公司绵阳分厂,四川省绵阳市高新区飞云大道中段373号 621000;西南科技大学信息工程学院,四川省绵阳市涪城区青龙大道中段59号 621010;西南科技大学信息工程学院,四川省绵阳市涪城区青龙大道中段59号 621010【正文语种】中文【中图分类】TB114堆垛机是烟草行业自动化立体仓库的核心设备之一，发生故障时会直接影响到生产作业的正常进行。
故障树分析（Fault Tree Analysis，FTA）技术作为经典的诊断方法之一，能够对设备做出全面、系统的可靠性评估，并且已成功运用于堆垛机的故障诊断［1-2］。
传统的FTA 需要对底事件的失效概率做出精确求解，然而在实际中由于许多新型复杂装备系统处于全寿命周期的前期阶段，难以确定系统元器件的故障概率，也无法获得足够的实验数据和现场数据。
信息安全风险评估是对信息风险加以识别、评估并作出综合分析的过程，是科学地分析和理解信息系统在保密性、完整性、可用性等方面所面临的风险，并在减少、转移、规避等风险控制方法之间做出决策的过程。
近年来，国内外信息安全风险评估的研究工作取得突飞猛进的进展，各种评估方法层出不穷，大大缩短了评估所花费的时间、资源，提高了评估的效率，改善了评估的效果。
无论何种方法，基本上都遵循了风险评估流程，只是在具体实施手段和风险计算方面有所不同，其共同的目标都是找出组织信息资产面临的风险及其影响，以及目前安全水平与组织安全需求之间的差距，本文对信息安全风险评估中比较典型的几种方法进行介绍和剖析。
1层次分析法层次分析法是美国运筹学家萨蒂（T.L.Saaty）于20世纪70年代初提出的一种定性与定量分析相结合的多准则决策分析方法。
其基本思想是在决策目标的要求下，将决策对象相对于决策标准的优劣状况进行两两比较，最终获得各个对象的总体优劣状况，为决策和评选优先级别提供依据。
层次分析法通过构造风险矩阵评价总体风险，在风险评估的实际应用中是一种行之有效、可操作性强的方法，其应用性也较为灵活，既适用于机构信息安全风险的自评估，也适用于专门提供安全服务组织的他评估。
但此方法不适合分析风险因素较多的多层次结构模型，另外风险因素比较时专家经验不同易出现一致性检验不符合的情况。
2故障树分析法故障树分析模型是由美国Bell电话试验室的Waston H.A.于1961年提出的，作为分析系统可靠性的数学模型，现已成为比较完善的系统可靠性分析技术。
故障树分析法是一种“下降形”的、演绎的逻辑分析方法，既可以用于定性的情况下，也可以用于定量的情况下。
不仅可以分析由单一构件所引起的系统故障，也可以分析多个构件不同模式故障所产生的系统故障情况。
该方法遵循从结果找原因的原则，即在前期预测和识别各种潜在风险因素的基础上，沿着风险产生的路径，运用逻辑推理的方法，求出风险发生的概率，并最终提出各种控制风险因素的方案。
阐述基于模糊可靠性故障树分析的优势本文主要针对船用齿轮箱，分析齿轮箱结构型式，建立基于模糊可靠性故障树分析模型，利用蒙特卡洛算法在传统故障树分析基础上进行封装，并使用VC++、MAT-LAB混合编程，仿真船用齿轮箱系统，以分析船用齿轮箱的失效型式。
1 基于模糊可靠性故障树分析的优势在船用齿轮箱失效型式分析中，应用基于模糊可靠性故障树对其进行分析，较传统故障树分析方法中的工作及故障状态，深化产品的工作状态，能够对产品可靠性作出正确的评价。
在船用齿轮箱失效型式分析中，应用基于模糊可靠性故障树分析方法，可以降低获取事件发生概率准确值的难度，用精确值表示事件发生概率，不再是传统的不二向量分析方法，可以运用贝叶斯网络模型，以此来描述船用齿轮箱系统内各部件间相互的关系，并得出系统可靠性指标，验证模型有效性；还可以运用模糊理论，分析船用齿轮箱可靠性，在给定统一失效概率计算方法的前提下，从而得出齿轮箱的可靠性参数；同时也能够采用蒙特卡罗方法来编制一定的计算机程序，统计出可靠性参数，绘制相关参数曲线，提高船用齿轮箱失效分析的效率，提升船用齿轮箱的可靠性。
2 构建齿轮箱故障树2.1 故障树中的事件船用齿轮箱故障树构建中，应该以不能正常工作齿轮箱来作为顶事件，然后再通过分析、研究齿轮箱故障原因，找出引起齿轮箱失效各级底事件，之后可以将其简归纳，形成故障树。
在故障树中，对于故障树顶事件中主要可以包括由离合器打滑、润滑系统失效、关键部件失效组成；故障树中间事件中主要包括摩擦片失效、工作油孔堵塞、油质不合格以及油温过高、轴承失效、轴断裂等事件组成；故障树底事件主要可包括安装精度低、轴承装配不好、齿距偏差、机械磨损、疲劳失效、箱体铸造缺陷、塑性变形、腐蚀、轴加工精度不高等事件组成。
2.2 定性、定量分析故障树故障树分析中，应用数字仿真技术，对其进行定性及定量分析。
在定性分析中，其主要任务就是找出产生顶事件的所有故障模式，并求故障树全部最小割集。
模糊故障树分析方法在HACCP中的应用研究王开义1，2，赵春江2※，张方田2（1．北京工业大学计算机学院，北京100022；2．国家农业信息化工程技术研究中心，北京100097）摘要：HACCP（Hazard Analysis and Critical Control Point)称为“危害分析与关键控制点",HACCP是一个复杂的系统工程，对于农产品加工企业或食品企业而言，制定一个产品的HACCP计划有很大的难度,特别是对于关键控制点的正确选取更需要领域专家的帮助。
本文介绍了故障树分析方法在HACCP体系第一原则和第二原则上的应用，并引入模糊数学理论中的模糊算法和非模糊化方法与故障树分析方法相结合，分别适用于HACCP计划的制定和HACCP计划的变更，并可根据该方法开发出制定HACCP计划的软件工具，使得HACCP计划的制定趋于简单化和自动化。
关键词:危害分析与关键控制点（HACCP);故障树分析方法;模糊算法；非模糊化方法0 引言：HACCP称为“危害分析与关键控制点”。
其强调的是在生产过程中通过预防使可能发生的食品安全危害降低到最低限度，而不是靠事后检验产品的安全性。
采用HACCP原理预防农产食品的不安全危害,已成为农产品生产加工企业全过程质量安全控制技术发展的新趋势[1］.目前的农产品生产加工企业绝大多数是中小型企业，而这些农产品加工企业在实施HACCP过程中无一例外地面临着技术、人才、资金等方面的困难[2］，因为HACCP管理体系涉及到食品工艺学、微生物学、化学和物理学、质量控制和危险性评估等多方面的专业知识［3]。
国内外很多研究人员一直致力于研究简单化、自动化、智能化的HACCP实施方法与工具[4］［5］［6］。
这些研究成果多数针对某一个特定的产品（如：鱼罐头等),通过对多个企业实施HACCP的大量实践数据进行危害分析，挖掘危害分析及关键控制点的规律，进而为新实施该产品HACCP体系的企业提供技术支持.但是,目前应用效果还不能满足实际需求，现实中人们还是采用传统的方法，借鉴专家的经验并结合企业的实际情况来实施HACCP.本研究结合近些年来开发农业企业HACCP管理软件的工程实践,探索利用故障树理论、模糊数学理论来降低HACCP实施难度的方法。
