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k‐step stage life testing

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  • Benjamin Laumen
  • Erhard Cramer

Abstract

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.

Suggested Citation

  • Benjamin Laumen & Erhard Cramer, 2021. "k‐step stage life testing," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 203-233, May.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:2:p:203-233
    DOI: 10.1111/stan.12227
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    References listed on IDEAS

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    1. Balakrishnan, N. & Kateri, M., 2008. "On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2971-2975, December.
    2. N. Balakrishnan & G. Iliopoulos, 2010. "Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 89-109, July.
    3. Debashis Samanta & Debasis Kundu & Ayon Ganguly, 2018. "Order Restricted Bayesian Analysis of a Simple Step Stress Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-221, November.
    4. Iliopoulos, G. & Balakrishnan, N., 2009. "Conditional independence of blocked ordered data," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1008-1015, April.
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