A New Decision Theoretic Sampling Plan for Exponential Distribution under Type-I Censoring

TL;DR

This paper introduces a new decision theoretic sampling plan for Type-I censored exponential distributions, offering a simpler, more analytically tractable approach with improved performance over previous plans, and adaptable to various loss functions.

Contribution

A novel decision theoretic sampling plan based on a new estimator, which is simpler, more versatile, and performs better than existing Bayesian plans for censored exponential data.

Findings

The proposed DSP outperforms Lam's sampling plan in Bayes risk.

It matches the performance of the Bayesian plan by Lih, Lin, and Hsu, with simpler implementation.

The plan is adaptable to different loss functions and censoring schemes.

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 \cite{Lam:1994}. 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 \cite{LLH:2002}, although implementation of the DSP is very simple. Analytically it is more tractable than the Bayesian sampling plan of \cite{LLH:2002}, 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 \cite{LLH:2002} are made. The results have been extended for three degree polynomial loss function and for Type-I hybrid censoring scheme.