A Bayesian reliability model for repairable systems: an application to software data

A commonly used definition of a repairable system (Ascher and Feingold, 1984) states that this is a system which, after failing to perform one or more of its functions satisfactorily, can be restored to fully satisfactory performance by any method other than replacement of the entire system. It is very obvious that most systems in the real world, such as automobiles, aircrafts or computers are designed to be repaired rather than replaced upon failure. The use of a Bayesian procedure allows the system reliability to be estimated by combining failure data of current stage with data of previous stages and prior information to be introduced into the inferential procedure. We present new models for the estimation of times between failures or numbers of failures in a given time. These models are non-parametric regression models based on Poisson failure counts and exponential inter-failure times, respectively. We construct a Bayesian inference method for our models using a Markov Chain Monte Carlo (MCMC) sampling. We evaluate our Bayesian reliability models through an application to real software data.