Parameter estimations in a general hazard rate model using masked data

Abstract

The general hazard rate model is a relevant model to specify the life time distributions in reliability theory and life testing. In this paper, we use masked data to obtain estimations of the unknown parameters included in life time distributions of the individual components belonging to a series system consists of J independent and non-identical components. It is assumed here that the failure rate of component j is general with the form h j ( t)= α j + β j t γ j −1 , j=1,2,…, J, where α j , β j , γ j are non-negative parameters. Maximum likelihood and Bayes estimates of the parameters α j , β j are obtained while γ j are known. Symmetrical triangular prior distributions are assumed for the unknown parameters to be estimated in obtaining the Bayes estimators for these parameters. A large simulation study is done in order to (i) explain how one can utilize the theoretical results obtained and (ii) compare the two procedures used. The problem of estimating the unknown parameters included in increasing linear failure rate model can be obtained as special case by setting γ j =2 for all j=1,2,…, J.