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Reliability_chap04

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i
1 VR = VRi n
The coefficient of variation for a system of n parallel, uncorrelated, identically distributed elements is smaller than the coefficient of variation of each element.
F = F1 ∪ F2 ∪
–
∪ Fn
n
S = S1 ∩ S 2 ∩
∩ Sn
Assume that all failure events are all statistically independent, we have
P ( S ) = P ( S1 ∩ S 2 ∩
∩ S n ) = ∏ P ( ∩ F2 ∩ S = S1 ∪ S 2 ∪ P ( F ) = P ( F1 ∩ F2 ∩ P ( F ) = Pf
P ( Fi ) = Pfi
–
∩ Fn ∪ Sn
∩ Fn ) = ∏ P ( Fi )
i =1
n
Pf = ∏ Pfi
i =1
n
The probability of failure of the system is smaller than the probability of failure of either component.
4.3 Reliability Bounds for Structural Systems …3
Example 4.5 ~ 4.6 Please refer to the textbook “Reliability of Structures” by Professor A. S. Nowak.
P. 268, Example 9.5 P. 269, Example 9.6
i =1
P ( S ) = 1 − P ( F ) = 1 − Pf
Pf = 1 − ∏ (1 − Pfi )
i =1
n
P ( Si ) = 1 − P ( Fi ) = 1 − Pfi
–
The probability of failure of the system is larger than that of either element.
–
The upper bound is the probability of failure when all elements are statistically independent,or uncorrelated, that is, ρij = 0 . In this case, the system survives only if all the elements survive .
Load
Displacement
Displacement
4.1 Elements and Systems …2
–
In conducting system reliability analysis of structures, it is convenient to distinguish brittle and ductile members by using different symbols. Load
i =1
n
µR = ∑ µR
i =1
n
i
σR =
2 σR ∑
n
i =1
i
–
Consider a special system that has n parallel, uncorrelated, identically distributed elements.
µ R = nµ R
–
i
σ R = nσ R
4.3 Reliability Bounds for Structural Systems …2
4.3.2 Parallel Systems with Positive Correlation
–
For a parallel system with n ductile elements, the bounds on the probability of failure for the parallel system with positive correlation are as follows:
4.2 Reliability of Simple Systems …2
4.2.2 Reliability of Parallel Systems
Consider a parallel system with n perfect ductile elements. Assume that all failure events are all statistically independent.
i i =1
n
–
The lower bound is the probability of failure when all elements are fully correlated, that is, ρij = 1 . In this case, the most unsafe element determines the reliability of the system.
4.3 Reliability Bounds for Structural Systems …4
Homework 7
7.1. Solve the problem 9.2 in text book on P.286 . 7.2. Solve the problem 9.3 in text book on P.286 . 7.3. Solve the problem 9.4 in text book on P.286 . 7.4. Solve the problem 9.5 in text book on P.286 .
4.2.1 Reliability of Series Systems
P
…
P
Consider a series system with n elements. Let Si represent the event “safety of the ith element”, Fi represent the event “failure of the ith element”. S and F represent the events “safety” and “failure” of the system respectively.
Chapter 4
System Reliability Analysis of Structures
4.3 Reliability Bounds for Structural Systems
4.3 Reliability Bounds for Structural Systems …1
4.3.1 Series Systems with Positive Correlation
Example 4.1 ~ 4.4 Please refer to the textbook “Reliability of Structures” by Professor A. S. Nowak.
P. 257, P. 258, P. 261, P. 253,
Example 9.1 Example 9.2 Example 9.3 Example 9.4
–
The upper bound is the probability of failure when all elements are perfectly correlated, that is, ρij = 1 . In this case, the safest element determines the reliability of the system.
End of Chapter 4
–
For a series system with positive correlation between pairs of elements, that is, 0 ≤ ρij ≤ 1 , the probability of failure must satisfy
max Pfi ≤ Pf ≤ 1 − ∏ (1 − Pfi )
∏P
i =1
n
fi
≤ Pf ≤ min Pfi
i
–
The lower bound is the probability of failure when all elements are statistically independent, ρij = 0 . In this case, the system fails only if all the elements fail.
Load
Displacement Brittle member
Displacement Ductile member
Chapter 4
System Reliability Analysis of Structures
4.2 Reliability of Simple Systems
4.2 Reliability of Simple Systems …1
Chapter 4 System Reliability Analysis of Structures
Chapter 4: System Reliability Analysis of Structures
Contents
4.1 Elements and Systems 4.2 Reliability of Simple Systems 4.3 Reliability Bounds for Structural Systems

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Unit 4_Reliability

Unit 4_Reliability

In real testing situations: these imply that
2
Reliability
). X X and s 2 ( X ) s 2 ( X
Advantages of a measure of equivalence: overcome the problem of 1) carry-over effects and 2) situational changes to test takers. Problems with this approach: Increasing the cost of test item development The correlation between alternate forms is confounded by reliability and parallelism (equivalence).
Internal consistency provides an estimate of how related a test is to itself (e.g., are items related to one another). Split-half reliability Cronbach’s alpha (
The 3 types are not substitutable for one another. •____________ – Using the same test on multiple occasions
•____________ – Using alternate forms of a test on the same or different occasions
•____________ – Using one test on one occasion
可靠性测试介绍

可靠性测试介绍


Test Picture
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2.14 FPC side Pull Test
1 名稱: FPC 拉力測試. 2.分類: 2.1 破壞性 FPC side Test 2.2 非破壞性 Machine 3. 條件: 3.1 將FPC拉離PCB. 3.2 0.5kg, 3times, 5s/time 4. 抽樣數: 5個. sketch map 5. 結果判定: 5.1完成相應類別的測試后, 判定 測試結 果是否在規格之內(>1kgf)為判定標准. 5.2完成相應類別的測試后,需進行外觀 及功能測試, 與測試之前進行對比.以是 否發生變化為判定標准.
1
5
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16
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2.13 Passive component Shear Test
1 名稱: 無源元件推力測試. 2. 條件: 將無源元件推離 PCB. 3. 抽樣數: 5個. 4. 結果判定:完成相應類別 的測試后, 判定 測試結果 是否在規格之內 (>200grams)為判定標准.
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2.1 High Temp Storage Test
1 名稱: 高溫儲存測試. 2 條件: 溫度:80+/-2℃; 時間: 0-48-168-500 hrs. 3. 抽樣數: 5 個. 4. 結果判定: 完成每一時間 段的測試后, 需進行外觀 及功能測試, 與測試之前 進行對比.以是否發生變化 為判定標准.
RELIABILITY

RELIABILITY


Assessing Design Reliability: Seven Steps to Prediction
1. Define the product and its functional operation. Use functional block diagrams to describe the systems. Define failure and success in unambiguous terms. 2. Use reliability block diagrams to describe the relationships of the various system elements (e.g. series, parallel, etc.) 3. Develop a reliability model of the system. 4. Collect part and subsystem reliability data. Some of the information may be available from existing data sources. Special tests may be required to acquire other information. 5. Adjust data to fit the special operating conditions of your system. Use care to assure that your “adjustments” have a scientific basis and are not merely reflections of personal opinions. 6. Predict reliability using a mathematical model. 7. Verify your prediction with field data. Modify your models and predictions accordingly.
信度与效度讲义

信度与效度讲义

信度與效度講義信度(Reliability)信度(Reliability)是指衡量工具的正確性(accuracy)或是精確性(precision)。

亦指測驗分數未受測量誤差(errors of measurement)影響的程度。

信度有兩方面的意義，一是穩定性(stability)，一是一致性(consistency)。

穩定性：在不同時間點重複衡量相同的事物或個人，然後比較兩次衡量分數的相關程度。

一致性：一個態度的尺度中，各個項目之間具有一致性或內部同質性。

信度的衡量指標主要有三種：1. 再測信度(Reset Reliability)：不同時間下，相同的研究對象，針對相同的問卷內容作答，得到兩份結果(總分)之相關係數。

曠日費時，較適合Panel Study 。

2. 折半信度(Split Half Reliability)：隨機將問卷題目折半分成兩份，計算這兩份結果之相關係數。

問卷題目內容必須盡量相近。

3. Cronbach ’s α信度：假設k 個題目12(,,,)k X X X 來自同一個概念(T, True)，而各題目之觀察值乃由概念值與誤差項所構成，即2,~(0, );1,2,,;1,2,,.ij i ij ij X T e e i n j k σ=+==其中ij X =第i 個個案在第j 個題目上的觀察值(observation)；i T =第i 個個案之概念值(Construct V alue)，又稱為真實值(True V alue)，無法觀察得到；ij e =誤差項，與真實值無關。

信度的定義：22,2T x Txs r s=?真實分數的變異數信度測量分數的變異數,2(,)(,)(,)(,)x T x Tx TTT x Tx TxC ov X T C ov T T C ov T T C ov T e r s s s s ss e s s s s s+==++===所謂Cronbach ’s α信度，係指每一個個案之概念值(i T )與k 個題目分數總和(1kijj S X==∑)之相關係數平方。