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.

中文翻译：

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k-step阶段寿命测试

Laumen和Cramer（2019b）中提出的舞台寿命测试模型从两个扩展到k阶段。可以看出，该模型可以看作是渐进式审查的扩展，具有固定的审查时间以及简单的逐步压力测试。通过扩展第一个模型，新方法可以合并经过逐步审查的单位的信息，并进行额外的寿命测试。另一方面，从仅将部分被测单元置于另一个应力水平，而将其余部分保持在初始水平的意义上讲，简单的阶跃应力建模是通用的。假设使用累积暴露模型，则需要进一步研究该模型的指数寿命。我们获得最大似然估计量的精确（条件）分布，该分布用于构造（精确）分布参数的置信区间。最后，我们在初始阶段研究了Weibull分布式生命周期的情况。该研究还辅以说明性的模拟。