Theory for Optimum Accelerated Censored Life Tests for Weibull and Extreme Value Distributions

Nelson, Wayne; Meeker, William Q.

doi:10.2307/1268710

Cited by 80 publications

(56 citation statements)

References 8 publications

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“…Most previous work on optimal design of ALT assumes that the life distribution is either exponential or Weibull (see Ahmad (2010), Ahmad et al (1994), Chernoff (1953Chernoff ( , 1962, Ehrenfeld (1962), Islam and Ahmad (1994), Meeker (1984), Meeker and Escobar (1998), Meeker and Nelson (1975), Nelson (1990), Nelson and Meeker (1978), Park and Yum (1996), Yum and Choi (1989), Seo and Yum (1991)). The Burr type XII, Burr type III, Normal and lognormal models have also been used (see Ahmad and Islam (1996), Ahmad et al (2006), Meeker (1984), Nelson and Kielpinski (1976)).…”

Section: The Proposed Model and Test Methodsmentioning

confidence: 99%

“…Solving (27) and (28)  are determined by using the method described by Nelson and Meeker (1978). It can also be determined by a two-step procedure.…”

Section: Optimization Methodsmentioning

confidence: 99%

“…One is the continuous inspection that results in exact failure times (see Chernoff (1962), Meeker (1984), Meeker and Nelson (1975), Nelson (1990), Nelson and Meeker (1978)). The other is the periodic inspection in which test units are inspected for failure at predetermined points in time.…”

Section: Introductionmentioning

confidence: 99%

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Planning Accelerated Life Tests for Burr Type X Failure Model with Type I Censoring

Ahmad¹,

Khan²,

Khan³

2013

JSTA

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In this paper, we discuss the optimal accelerated life test plans for Burr type X distribution with log-linear model under periodic inspection and Type I censoring. We obtain the maximum likelihood estimators, the Fisher information and the asymptotic covariance matrix of the maximum likelihood estimators. Accelerated life test is optimized with respect to the low test stress and the proportion of test units allocated to the low test stress for given shape parameter. The asymptotic variance of the maximum likelihood estimator of qth quantile at the design stress is derived as an optimality criterion with equally spaced inspection times and the optimal allocation of units for two stress levels are determined. Optimality results show that the asymptotic variance of qth quantile at the design stress is insensitive to the number of inspection times and to misspecifications of guessed failure probabilities at design and high test stresses. Procedures for planning an accelerated life test, including selection of sample size, have been discussed through an example.

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Section: The Proposed Model and Test Methodsmentioning

confidence: 99%

“…Solving (27) and (28)  are determined by using the method described by Nelson and Meeker (1978). It can also be determined by a two-step procedure.…”

Section: Optimization Methodsmentioning

confidence: 99%

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Planning Accelerated Life Tests for Burr Type X Failure Model with Type I Censoring

Ahmad¹,

Khan²,

Khan³

2013

JSTA

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“…As suggested in [5], the planning values can be given in terms of convenient quantities such as failure probabilities at the highest and use stress levels, respectively. As suggested in [12] and [13] information for planning values can be obtained from previous experience with similar products and materials or engineering judgment.…”

Section: Previous Workmentioning

confidence: 99%

Strategy for Planning Accelerated Life Tests With Small Sample Sizes

Meeker

2010

IEEE Trans. Rel.

Self Cite

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Previous work on planning accelerated life tests has been based on large-sample approximations to evaluate test plan properties. In this paper, we use more accurate simulation methods to investigate the properties of accelerated life tests with small sample sizes where large-sample approximations might not be expected to be adequate. These properties include the simulated s-bias and variance for quantiles of the failure-time distribution at use conditions. We focus on using these methods to find practical compromise test plans that use three levels of stress. We also study the effects of not having any failures at test conditions and the effect of using incorrect planning values. We note that the large-sample approximate variance is far from adequate when the probability of zero failures at certain test conditions is not negligible. We suggest a strategy to develop useful test plans using a small number of test units while meeting constraints on the estimation precision and on the probability that there will be zero failures at one or more of the test stress levels. AbstractPrevious work on planning accelerated life tests has been based on large-sample

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“…그리고 커패시터의 경우에는 전량 수입에 의존하고 있 어 정확하게 수명을 예측하여 최적의 교체주기를 판단하는 것은 경제성 측면에서 매우 중요한 일이다. 일반적으로 철도 차량 부품의 가속수명시험에 대한 연구는 1962 년에 Chernoff에 의해 시작된 이래 Singpurwalla [4] , Nelson [5] , Miller-Nelson [6] , Bai [7] 등에 의해 단계적 스트레스의 축적에 따른 수명 예측 연구가 진행되었으며, Hobbs [8] 등은 복합 가속시험을 …”

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Acceleration Life Prediction of the Capacitor on a Traction Inverter for a High-Speed Train

Maeng

Jung²

2015

Journal of the Korean Society of Manufacturing Technology Engin

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ARTICLE INFO ABSTRACTArticle history:The aim of this study is to develop a technique for the accelerated life test of the capacitor in a propulsion control device of a traction inverter used for a high-speed train. Using this technique, the accelerated life test can possibly estimate the life cycle of a capacitor under various temperature conditions and irregularly applied voltage. The accelerated life test is conducted for the capacitor of the traction inverter. The common proceedings of this test are selection of failure mechanism, determination of accelerated stress, range determination of the accelerated stress, determination of the test condition, and distribution and determination of the sample. From this result, the continuous applied voltage was not considered for the acceleration factors anymore. Therefore, the final result having an acceleration factor of 9.4 (= 13,626/1,445) was observed. Furthermore, the life-shortening acceleration effect for the irregular applied voltage condition can be applied to various situations. . 그리고 커패시터의 경우에는 전량 수입에 의존하고 있 어 정확하게 수명을 예측하여 최적의 교체주기를 판단하는 것은 경제성 측면에서 매우 중요한 일이다. 일반적으로 철도 차량 부품의 가속수명시험에 대한 연구는 1962 년에 Chernoff에 의해 시작된 이래 Singpurwalla [4] , Nelson [5] , Miller-Nelson [6] , Bai [7] 등에 의해 단계적 스트레스의 축적에 따른 수명 예측 연구가 진행되었으며, Hobbs [8] 등은 복합 가속시험을

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Theory for Optimum Accelerated Censored Life Tests for Weibull and Extreme Value Distributions

Cited by 80 publications

References 8 publications

Planning Accelerated Life Tests for Burr Type X Failure Model with Type I Censoring

Planning Accelerated Life Tests for Burr Type X Failure Model with Type I Censoring

Strategy for Planning Accelerated Life Tests With Small Sample Sizes

Acceleration Life Prediction of the Capacitor on a Traction Inverter for a High-Speed Train

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