Bayesian Sampling Plan for the Exponential Distribution with Generalized Type-I Hybrid Censoring Scheme

This paper discusses Bayesian sampling plan when the lifetime of the experimental units follows an exponential distribution and the data are generalized Type-I hybrid censored. Here, we adopt a decision-theoretic approach, and the Bayesian decision function is derived under a general loss function. Based on the Bayesian decision function, the Bayesian sampling plan (BSP) has been obtained. Further, for the conjugate prior distribution, the closed-form Bayes decision rule has been provided under the quadratic decision loss. It is noticed that for higher-degree polynomial loss functions, closed-form Bayes decision function cannot be obtained analytically. To address this limitation, we discuss a numerical approach to obtain Bayes decision function for other forms of the loss functions. As an illustration, we consider fifth-degree polynomial loss function to obtain the optimum BSP. Optimum BSPs under different scenarios have been reported.