Preventive maintenance policy for repairable systems

Abstract

This thesis is concerned with the design, reliability analysis and optimal preventive maintenance for repairable system. This thesis is divided into the following three parts. i) A preventive maintenance policy with minimal repair at failure, periodic overhaul and replacement is considered. A model describing the effect of overhaul is proposed and the expected cost rate is obtained under negligible or non-negligible maintenance time. Based on this model, optimal number of overhauls and optimal interval between overhauls for minimizing the expected cost rate over infinite time horizon are determined. Under some mild conditions, a unique optimal maintenance policy exists and a closed form expression for the optimal interval between overhauls is derived when the lifetime of the system follows Weibull distribution. ii) Lifetime distribution and reliability are analyzed for standby systems consisting of units that alternate between operating and standby states periodicall y to inspect and detect failures of standby units. It is assumed that when a unit fails, a minimal repair with negligible repair time is performed. A cumulative exposure model is used to describe the failure time distribution. The method of maximum likelihood is used to estimate the parameters, and specific formulas for Weibull model are obtained. A simulation model is then developed to assess the system reliability based on the estimated lifetime distribution and the method is applied to a high pressure pump system. iii) Optimal designs of three redundant systems (parallel, standby, and k out of n systems) under warranty are considered. The optimal number of redundant units which minimize the expected cost rate is found and the number is shown to be finite and unique. For given inspection interval before expiration of warranty, the optimal number of redundant units is also obtained. The effects of warranty and inspection to the optimal number of redundant units are studied.