Optimizing the Spare Unit Ordering Strategies for Replacement Under Constrained Availability From a Mathematical Perspective

This article investigates the optimal ordering policies of spare parts for preventive replacement of a single component deteriorating system in this article. The operational system suffers from a deterioration process and is also subject to random shocks during its service, where discrete shocks are categorized into fatal ones and nonfatal ones. To preventing the catastrophic losses resulting from degraded failures or shock incurred failures, a spare unit for replacement is ordered at some time between the system's initial operation and its undesirable failure. The average cost rate with lower-limit constrained availability is minimized to seek the optimal spare unit ordering time, in which the Kuhn-Tucker necessary condition is satisfied. As a comparison strategy, the expected cost effectiveness defined as the ratio of system availability to average cost rate is maximized to dynamically adjust the optimum ordering time of the spare unit. Numerical experiments are designed to validate the existence and uniqueness of the joint optimal spare unit ordering and preventive replacement policies, as well sensitivity analysis of critical parameters are conducted.