A Bayesian Estimation of Reliability Measures of Stepwise Exponential Distribution System

Abstract

This paper presents an analysis method for reliability measures of a system with step changes in failure and repair rates. Both failure and repair time have exponential functions of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various kinds of equipment. This paper deals with the system having components in a series arrangement. Bayesian statistics are used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of several reliability measures: (1) failure and repair rates, (2) mean time to failure, (3) mean time to repair, (4) reliability function and (5) availability. A sample problem is given to illustrate the methodology. Bayesian estimation of the stepwise exponential distribution model is useful in the planning predictive maintenance of equipment.