A new decision theoretic sampling plan for exponential distribution under Type-I censoring

Abstract

In this paper a new decision theoretic sampling plan (DSP) is proposed for Type-I censored exponential distribution. The proposed DSP is based on a new estimator of the expected lifetime of an exponential distribution which always exists, unlike the usual maximum likelihood estimator. The DSP is a modification of the Bayesian variable sampling plan of Lam. An optimum DSP is derived in the sense that it minimizes the Bayes risk. In terms of the Bayes risks, it performs better than Lam’s sampling plan and its performance is as good as the Bayesian sampling plan of Lin, Liang and Haung, although implementation of the DSP is very simple. Analytically it is more tractable than the Bayesian sampling plan of Lin, Liang and Haung, and it can be easily generalized for any other loss functions also. A finite algorithm is provided to obtain the optimal plan and the corresponding minimum Bayes risk is calculated. Extensive numerical comparisons with the optimal Bayesian sampling plan proposed by Lin, Liang and Haung are made. The results have been extended for three degree polynomial loss function and for Type-I hybrid censoring scheme.

Keywords:

• Bayesian sampling plan
• Bayes risk
• Exponential distribution
• Proposed estimator
• Type-I censoring

Acknowledgements

We express our sincere thanks to the referees and the editor for their useful suggestions which led to an improvement over an earlier version of this manuscript.