Two preventive replacement strategies for systems with protective auxiliary parts subject to degradation and economic dependence

In many engineering systems, except for the critical parts fulfilling the main functions, there exist some parts equipped to protect the critical parts and enhance their reliabilities. Failures of these protective parts (named as auxiliary parts) do not halt the system directly like the critical parts. Dependence between the critical and auxiliary parts is commonly observed but has seen limited research. In this paper, we study systems with a critical subsystem and a protective auxiliary subsystem subject to degradation and economic dependence. For such systems, two preventive replacement models are presented. Model I allows the two subsystems to be replaced separately while Model II provides a joint replacement strategy. The long-run average cost of the system is derived by the technique of semi-regenerative process. Thereafter, the optimization problem is formulated with the objective of determining the optimal inspection period and preventive replacement thresholds that minimize the long-run average cost of each model. A numerical study of a boring tool equipped with a damper as the auxiliary subsystem is provided to demonstrate the proposed method. Finally, sensitivity analysis on the cost parameters is conducted, based on which the two proposed maintenance models are compared and their application conditions are discussed.