The mean function of a repairable system that is subjected to an imperfect repair policy

Abstract

A repairable system can be simply characterized as a system which is repaired rather than replaced after a failure. In many practical situations, the mean function of a repairable system depends on several explanatory variables referred to as covariates that are time dependent. The mean function is an important figure that represents the expected number of failures up to a certain time. In this article, a repairable policy is proposed by using auxiliary stochastic processes which describe behaviors of these covariates and various properties are derived using the proposed policy. A general method to assess indirectly the mean function of a repairable system by using information on these covariates is also discussed.

Keywords:

• Brownian motion
• counting process
• cumulative intensity function
• controllable covariate
• gamma process
• intensity function
• maximum liklihood
• non-homogeneous Poisson process
• decreasing failure rate
• uncontrollable covariate