Abstract:

The Proportional Intensity Model (PIM) extends the classical Proportional Hazard Model (PHM) in order to deal with repairable systems. This paper develops a more general PIM model which uses the imperfect model as baseline function. By using the imperfect model, the effectiveness of repair has been taken into account, without assuming an “as-bad-as-old” or an “as-good-as-new” scheme. Moreover, the effectiveness of other factors, such as the environmental conditions and the repair history, is considered as covariant in this PIM. In order to solve the large number parameters estimation problem, a Bayesian inference method is proposed. The Markov Chain Monte Carlo (MCMC) method is used to compute the posterior distribution for the Bayesian method. The Bayesian Information Criterion (BIC) is employed to perform model selection, namely, selecting the baseline function and remove the nuisance factors in this paper. In the final, a numerical example is provided to demonstrate the proposed model and method.