Bayesian analysis of fixed-interval preventive-maintenance models

This article develops methods for making accurate decisions when scheduling preventive maintenance in systems where inter-event times can be modelled by a delayed renewal process or delayed alternating renewal process. A practical application, relating to the reliability and maintenance of a relatively low-level component (valve) in a continuous-process industry over a period of six years is presented to demonstrate and compare the different approaches. Our analyses indicate a cost-effective recommendation for maintenance practice in this context. Our main thrust relates to the use of Bayesian methodology in order to obtain rational, admissible decisions. Particular advances over previous research allow for informative prior distributions, better approximations which lead to improved accuracy, non-negligible downtimes, and general lifetime distributions. General analytic solutions are sought for the simpler models, in order to achieve accuracy and insight. The resulting integrals can only be solved to give an infinite series and one approximation to the required solution is obtained by truncating this series. Two other approximations are developed, based on expansions of the prior predictive and log-posterior distributions. A simulation approach is also developed to include prior information and hence provide alternative approximations to these optimal decisions. With exponential lifetime distributions, the relevant posterior lifetime distributions are non-central Pareto. This simulation is simple to program, compared to the approximations, but requires more computing time. It is accurate and extends easily to situations involving greater complexity. We consider two such extensions, the inclusion of downtimes and Weibull lifetime distributions.