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

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.