Abstract
Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.
Highlights
In reliability analysis, it is not easy to collect lifetimes on highly reliable products with very long lifetimes, because very few or even no failures may occur within a limited testing time under normal conditions
We considered the statistical inference procedure for the unknown parameters of the power generalized Weibull (PGW)(γ, ], 1) distribution and the acceleration factor (β), when the data are progressive type-II censored from stress partially ALT (SSPALT)
(1) The mean square errors (MSEs) of maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the considered parameters decrease as the sample size increases
Summary
It is not easy to collect lifetimes on highly reliable products with very long lifetimes, because very few or even no failures may occur within a limited testing time under normal conditions. In step-stress ALT, the stress on each unit is not constant but is increased step by step at prespecified times or upon the occurrence of a fixed number of failures. Consider n units are placed on life test, and the experimenter terminates the experiment after a prespecified number of units m ≤ n fail. In conventional type-II censoring schemes do not allow to remove units at points other than the terminal point of the experiment. A generalization of type-II censoring is the progressive type-II censoring It is a method which enables an efficient exploitation of the available resources by continual removal of a prespecified number of surviving test units at each failure time. This paper will concentrate on SSPALTs under progressive type-II censoring
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