Performance analysis and optimization of a cold standby system subject to δ-shocks and imperfect repairs

This paper analyzes and optimizes the economic performance of a cold standby system subject to δ-shocks and imperfect repairs. Specially, the system consists of two components with different reliability characteristics. It is assumed that shocks arrive according to a Poisson process. When a component is active during operation, it will fail whenever the interarrival time between successive shocks is less than a threshold influenced by the number of repairs performed on this component. For reliability analysis, geometric process models are utilized to characterize the lifetime and repair time of the active component subject to δ-shocks and imperfect repairs. Using the supplementary variable method, some reliability measures of the system are obtained. Moreover, an explicit expression for the long-run cost per unit time is derived to quantify the system's economic performance. Finally, the optimal repair policy is determined based on this economic performance measure, and a sensitivity analysis is conducted to provide managerial insights for the efficient operation of such a system.