Bayesian estimation of MTTF for exponential distribution: A Bessel function life testing model

Abstract

In general, failure and repair times for systems and components are thought of as being random in nature and therefore unpredictable. Even though these lifetimes are random, they can be modeled through the use of probability density functions. This paper studied the problem of Bayesian estimation of the mean time to failure (MTTF) when the life times are exponentially distributed. Exponential distribution yields Bessel function model in life testing. Censoring is a distinguishing feature of the field of survival analysis and in this paper we consider Type – II censoring that implies the life tests are terminated after pre-assigned number of failures has been considered. Bayes estimator of the average life has been obtained under LINEX (LINearly-EXponential) loss function. We also obtain corresponding Bayes estimators under squared error loss function (SELF) propounded by Bhattacharya [5] and compare the results from the two loss functions. We propose avenues for extensions of these results for Weibull life testing model.