Multi-sample progressive Type-I censoring of exponentially distributed lifetimes

Abstract

In this paper, we introduce the multi-sample progressive Type-I censoring model where $k\ge 2$ independent progressively Type-I censored experiments are conducted. The main objective is the derivation of the exact distribution of the maximum likelihood estimator (MLE) of the scale parameter when the lifetimes are exponentially distributed. The presented results provide also an alternative proof for the exact distribution of the MLE in the situation of a single progressively Type-I censored sample. Further, we use this result to construct exact confidence intervals for the scale parameter. In particular, the required stochastic monotonicity of the MLE is shown.

Keywords:

• Progressive Type-I censoring
• multi-sample progressive Type-I censoring
• exponential distribution
• B-spline convolutions

Acknowledgment

The authors are grateful to two anonymous reviewers for comments and suggestions which led to an improved version of the manuscript.