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k ‐step stage life testing
Author(s) -
Laumen Benjamin,
Cramer Erhard
Publication year - 2021
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12227
Subject(s) - censoring (clinical trials) , weibull distribution , exponential distribution , accelerated life testing , mathematics , estimator , exponential function , extension (predicate logic) , statistics , maximum likelihood , computer science , mathematical analysis , programming language
The model of stage life testing proposed in Laumen and Cramer (2019b) is extended from two to k stages. It is illustrated that this model can be seen as an extension of progressive censoring with fixed censoring times as well as of simple step stress testing. Extending the first model, the new approach allows to incorporate information from progressively censored units subject to additional life testing. On the other hand, simple step stress modeling is generalized in the sense that only parts of the units under test are put on another stress level whereas the others remain on the initial level. The model is further studied for exponential lifetimes assuming a cumulative exposure model. We obtain the exact (conditional) distribution of the maximum likelihood estimators which is applied to construct (exact) confidence intervals for the distribution parameters. Finally, we investigate the situation of Weibull distributed lifetimes on the initial stage. The study is supplemented by illustrative simulations.