Reference optimality criterion for planning accelerated life testing

Xu, Ancha; Tang, Yincai

doi:10.1016/j.jspi.2015.06.002

Cited by 12 publications

(6 citation statements)

References 31 publications

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“…This is approach is explored more thoroughly in Xu and Tang. 24 Another approach for log-location-scale families, to include the SEV, is to minimize the volume of a posterior credible region, averaged over the prior distribution. A large sample approximation to the posterior covariance matrix was given by Hong et al 19 ; they give the approximation (using our notation)…”

Section: Optimality Criteriamentioning

confidence: 99%

Bayesian D‐optimal design for life testing with censoring

Taylor

Rigdon

Pan

et al. 2022

Quality & Reliability Eng

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The assumption of normality is usually tied to the design and analysis of an experimental study. However, when dealing with lifetime testing and censoring at fixed time intervals, we can no longer assume that the outcomes will be normally distributed. This generally requires the use of optimal design techniques to construct the test plan for specific distribution of interest. Optimal designs in this situation depend on the parameters of the distribution, which are generally unknown a priori. A Bayesian approach can be used by placing a prior distribution on the parameters, thereby leading to an appropriate selection of experimental design. This, along with the model and number of predictors, can be used to derive the D‐optimal design for an allowed number of experimental runs. This paper explores using this Bayesian approach on various lifetime regression models to select appropriate D‐optimal designs in regular and irregular design regions.

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Section: Optimality Criteriamentioning

confidence: 99%

Bayesian D‐optimal design for life testing with censoring

Taylor

Rigdon

Pan

et al. 2022

Quality & Reliability Eng

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“…Yuan et al pointed out that it was questionable to assume the mutual independence for the model parameters, and the elicitation of the prior distribution for each model parameter was practically difficult. Some other studies suggested to specify the prior distributions of some approximately mutually independent parameters, which are the reparameterization of the model parameters.…”

Section: Bayesian Design Of the Adaptive Planmentioning

confidence: 99%

“…The large‐sample approximation to parameters θ Δ is utilized to reduce the computational burden. Large‐sample approximation has been used in many studies of Bayesian ALT designs, such as Zhang and Meeker, Xu and Tang, Yuan et al, Hong et al, and Ma and Meeker . The accuracy of the approximation has been verified to be reasonable if the sample size is not very small.…”

Section: Bayesian Design Of the Adaptive Planmentioning

confidence: 99%

“…Under the Bayesian framework, we consider the variance of the Bayesian estimator of t p ( ξ U ). Following Zhang and Meeker and Xu and Tang, the posterior mode is used as the Bayesian estimator.…”

Section: Numerical Examplementioning

confidence: 99%

“…For the purpose of effectively using test resources to obtain failure information, many researchers have been dedicated to designing optimum plans with 2 stress levels. At the same time, Yang pointed out that although optimum plans were statistically optimal, they were sensitive to the misspecification of planning information, because only 2 stress levels were used.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Designing adaptive accelerated life tests using Bayesian methods

Xiang

Yang

Shen

2017

Quality & Reliability Eng

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The traditional constant‐stress accelerated life test may encounter the problem of no or a few failures at the low stress level, if the test is stopped after a fixed period. Insufficient failures usually make it difficult to estimate reliability characteristics and to discover design deficiencies of the product. To mitigate the problem, the adaptive plan is designed based on Bayesian methods in this study. Under the constraints of test facilities, test units, time, and cost, the adaptive plan is optimized according to the criterion of minimizing the preposterior variance of the logarithm of a quantile of the lifetime distribution at the use condition. Large‐sample approximation is applied to reduce the computational burden. Genetic algorithm is adopted to determine the optimal design of the adaptive plan. Finally, a numerical example is given to demonstrate the advantages of the proposed adaptive plan.

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Bayesian optimal life‐testing plan under the balanced two sample type‐II progressive censoring scheme

Mondal

Bhattacharya

Pradhan

et al. 2020

Appl Stoch Models Bus & Ind

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Joint progressive censoring schemes are quite useful to conduct comparative life‐testing experiment of different competing products. Recently, Mondal and Kundu (“A New Two Sample Type‐II Progressive Censoring Scheme,” Commun Stat‐Theory Methods; 2018) introduced a joint progressive censoring scheme on two samples known as the balanced joint progressive censoring (BJPC) scheme. Optimal planning of such progressive censoring scheme is an important issue to the experimenter. This article considers optimal life‐testing plan under the BJPC scheme using the Bayesian precision and D‐optimality criteria, assuming that the lifetimes follow Weibull distribution. In order to obtain the optimal BJPC life‐testing plans, one needs to carry out an exhaustive search within the set of all admissible plans under the BJPC scheme. However, for large sample size, determination of the optimal life‐testing plan is difficult by exhaustive search technique. A metaheuristic algorithm based on the variable neighborhood search method is employed for computation of the optimal life‐testing plan. Optimal plans are provided under different scenarios. The optimal plans depend upon the values of the hyperparameters of the prior distribution. The effect of different prior information on optimal scheme is studied.

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Reference optimality criterion for planning accelerated life testing

Cited by 12 publications

References 31 publications

Bayesian D‐optimal design for life testing with censoring

Bayesian D‐optimal design for life testing with censoring

Designing adaptive accelerated life tests using Bayesian methods

Bayesian optimal life‐testing plan under the balanced two sample type‐II progressive censoring scheme

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