Stage life testing with random stage changing times

Abstract

In progressive Type-II censoring, it is often claimed that the withdrawn items are further tested under different conditions but a model incorporating this information has not been discussed so far. Introducing the model of Type-II stage life testing, we propose an approach to include information from progressively censored units subject to additional life testing by assuming a cumulative exposure model. Postulating exponentially distributed lifetimes, we establish the exact (conditional) distribution of the maximum likelihood estimators which is applied to construct (exact) confidence intervals for the distribution parameters. Further, we investigate the model with Weibull distributed lifetimes as well as the problem of missing information about the stage of failure. The study is supplemented by illustrative simulations.

Keywords:

• Exact confidence intervals
• EM-algorithm
• exponential distribution
• likelihood inference
• stage life testing
• progressive Type-II censoring
• Weibull distribution

Acknowledgment

The authors are grateful to a reviewer for constructive comments which led to an improved version of the article.