On Optimal Progressive Censoring Schemes from Models with U-Shaped Hazard Rate: A Comparison between Conventional and Fuzzy Priors

This paper explores the optimal censoring schemes from models with U-shaped hazard rates (USHRs) using Bayesian methods. Topp-Leone (TL) distribution has been considered as a special case. We have used conventional and fuzzy priors for the estimation. Further, the symmetric and asymmetric loss functions have been considered for the estimation. Since the Bayes estimators (BEs) for the parameters of the TL distribution cannot be derived in the closed form, we have used Quadrature method (QuM), Lindley’s approximation (LinA), Tierney and Kadane’s approximation (TKA), and Gibbs sampler (GiS) for the approximate estimation of the parameters. We also considered the different techniques to compare various progressive censoring schemes on the basis of their information contents and hence reported the optimal censoring schemes under Bayesian framework. The performance of the different BEs has been compared on the basis of a simulation study. A real-life example has been considered for the illustration.