Bayesian modelling and analysis of utility-based maintenance for repairable systems

Abstract

This thesis focuses on modelling and inference for maintenance systems for the purpose of utility optimisation. Providing standardised notation throughout, we first demonstrate the motivation for investigating the problem of modelling and inference for maintenance systems and briefly state the problems which are to be explored. The definitions and terminology, which are also used within the general domains of science and engineering, have been presented in terms of statistical representation. We propose a Bayesian method to optimise the utility of a two phase maintenance system sequentially by dynamic programming method. In particular, the parameters of the failure distribution for the system of interest are analysed within the Bayesian framework. Utility-based maintenance is modelled in several modified models, including imperfect preventive maintenance, time value of money effect in maintenance, maintenance for systems with discrete failure time distributions, maintenance for parallel redundant systems, of which all follow numerical examples. A hybrid approach combining myopic and dynamic programming method is proposed to solve multi-phase maintenance systems. The Bayesian dynamic programming is carried out through the gridding approach to solve the issue arising from nested series of maximisations and integrations over a highly non-linear space. The core of gridding method, the increment is studied extensively. We also utilise and modify the approach proposed by Baker (2006) to analyse the effect of risk aversion on the variability of system in cash flows. The potential generalisation of the current models has been discussed and the future work concerning complicated models and efficient computation methods have also been indicated.