A new decision theoretic sampling plan for type-I and type-I hybrid censored samples from the exponential distribution

TL;DR

This paper introduces a new decision theoretic sampling plan for censored exponential data that simplifies computation and performs comparably or better than existing Bayesian plans in terms of Bayes risk.

Contribution

It proposes a novel DSP based on a reliable estimator, offering easier computation for complex loss functions and comparable performance to Bayesian plans.

Findings

The proposed DSP matches the Bayesian sampling plan in Bayes risk.

It outperforms existing sampling plans in terms of Bayes risk.

Easier to compute for higher degree polynomial and non-polynomial loss functions.

Abstract

The study proposes a new decision theoretic sampling plan (DSP) for Type-I and Type-I hybrid censored samples when the lifetimes of individual items are exponentially distributed with a scale parameter. The DSP is based on an estimator of the scale parameter which always exists, unlike the MLE which may not always exist. Using a quadratic loss function and a decision function based on the proposed estimator, a DSP is derived. To obtain the optimum DSP, a finite algorithm is used. Numerical results demonstrate that in terms of the Bayes risk, the optimum DSP is as good as the Bayesian sampling plan (BSP) proposed by \cite{lin2002bayesian} and \cite{liang2013optimal}. The proposed DSP performs better than the sampling plan of \cite{Lam1994bayesian} and \cite{lin2008-10exact} in terms of Bayes risks. The main advantage of the proposed DSP is that for higher degree polynomial and non-polynomial loss functions, it can be easily obtained as compared to the BSP.