A TSST of the reliability function for exponential failure model using type II censored data with minimum cost of experimentations

Abstract

This paper considers a class of an efficient 'two-stage shrinkage testimator' (TSST) of 'reliability function' of 'exponential distribution', and the class uses additional information which can be obtained from the past practices, and in the form of past initial estimates (λ0) about the unknown parameter λ. The TSST is dependent upon a convenient shrinking factor, conventional estimators, the 'right censored plan' of sj 'ordered observations' of a variable sample of 'size' Sj and by developing five 'testing regions' for screening the 'closeness' of λ0 to λ by different 'criteria'. The computations of 'bias', 'mean squared error', 'expected sample size' and 'relative efficiency' show that the behaviour of the class of 'TSST' is almost similar to existing testimators and better than classical and similar estimators in several properties, for different constants and variables involved in it. Throughout the paper an application to a 'life time' problem is provided to illustrate applicability of the 'TSST' and expressions that are obtained from it. The behaviour of the developed 'TSST' and the significant comparative results offer some useful and sufficient insights for researchers to continue in the 'TSST' direction, and give adequate reasons for experimenters/practitioners to use 'TSST' in their applications.