Bayesian sampling plan for the exponential distribution with generalized Type - II hybrid censoring scheme

Abstract

In this paper, a decision-theoretic approach is used to obtain the Bayesian sampling plan (BSP) for the generalized Type-II hybrid censoring scheme when lifetimes of sampled units follow a one-parameter exponential distribution. An efficient loss function is used to decide whether to accept or reject the batch. The BSP is obtained by constructing the closed form of the Bayes decision function. It is observed that the closed form of the Bayes decision function cannot be obtained analytically for any arbitrary loss function. A numerical approach is proposed to determine the optimum BSP for an arbitrary loss function. To illustrate this, we consider a higher degree polynomial loss function and obtain the optimum BSP numerically. Some numerical studies have been conducted to check the performance of the optimum BSP in different cases.

Keywords:

• Bayesian sampling plan
• Bayes risk
• Decision-theoretic approach
• Exponential distribution
• Generalized Type-II hybrid censoring

Acknowledgements

We express our sincere thanks to the Associate Editor and the anonymous reviewers for their valuable comments and suggestions.