Calculation of the expected number of failures for a repairable asset system

The expected number of failures is the essential element in cost analysis for a repairable system in engineering asset management. A renewal process is typically used for modelling a repairable system with perfect repairs while a nonhomogeneous Poisson process can be used to model a repairable system with minimal repair. An asset system with imperfect repair will be restored to the state which is somewhere between as bad as old and as good as new. While imperfect repairs are more realistic, it is more challenging to calculate the expected number of failures. In this chapter, we propose an imperfect reparable system assuming decreasing restoration levels conditional on the previous repair actions. Compared with a popular imperfect repairable system settings which assumes a constant discount restoration level after the first failure occurrence, our decreasing restoration levels model may better represent the actual repair-restoration patterns for many asset systems. The likelihood function of the newly proposed model is derived and the model parameters can be estimated based on historical failure time data. We adopt a cumulative hazard function based Monte Carlo simulation approach to calculate the expected number of failures for the newly proposed reparable system model. This new simulation algorithm is demonstrated on both simulated and real data and compared to a popular existing model under a Weibull distribution setting. An advantage of our simulation algorithm is that a bootstrap version confidence band on the estimated expected number of failures can easily be constructed. The modelling and simulation results in the chapter can be used for the development of an engineering reliability analysis and asset management decision making tool.