Optimal maintenance/replacement policies under the number-of-shock model

Abstract

This thesis is concerned with replacement problems both under the "Number-of-Shock" model and the number-of-shock model with preventive maintenance. In the number-of-shock model, it is assumed that shocks occur to a facility in accordance with a Poisson process, that the probability of the facility``s surviving a shock is dependent upon the cumulative number of shocks, and that the facility is under continuous review for shock occurrence. Revenew generated by facility operations, preventive replacement cost, and failure replacement charge are considered for the analyses of the replacement policies. Under the number-of-shock model, it is shown that the "Control Number Rule", which replaces either upon failure or when the cumulative number of shocks reach a control number, whichever comes first, is the optimal policy maximizing the longrun expected profit per unit of time. In addition, the shock probabilities are formulated under the cumulative damage model and fatal shock threshold mode. In comparison among the age replacement rule, cumulative damage replacement rule and control number rule, the cumulative damage replacement rule is found most profitable, while the age replacement rule least profitable. These results imply that replacement rules based on shock characteristic guarantee the higher facility performance. Finally, assuming that in the number-of-shock model the intensity parameter of the shock arrival process can be affected by preventive maintenance, joint problems of preventive maintenance and replacement are discussed.