隨著科技蓬勃發展，不論是生活中或工程應用中的設備設計皆複雜且精密，但在結構上大致相同，皆由主要零件、功能性零件及僅有輔助作用的輔助型零件所組成。一般來說，主零件及功能性零件間具有相互作用關係，當其中一項失效時，系統便會停止運作。但主零件及輔助型零件之間為另一種情形，當輔助零件失效時，系統雖不會停止運作，卻會單向增加主零件失效的機率，本論文以單向失效相依效應表示。傳統上對於設備零件的失效狀況大多考量零件之間為獨立或相互作用下去研究，並未考量到單向失效相依的情況。故本論文在考量主零件會受輔助零件失效的單向影響下，建構系統零件的期望總成本率模式。模式中，零件每次失效皆以小修進行處理，小修後零件的失效率會回到失效前的狀態。但是零件的失效次數會隨零件退化而愈加頻繁，因此，為減少頻繁失效帶來的小修成本，系統零件會進行置換的動作，在不同的時間置換會帶來不同的置換成本。故本論文在探討單向失效相依效應下系統零件的最佳置換策略與最佳置換時程，使得零件的期望總成本率為最低，並以數值範例分析置換成本對期望成本率之影響。

With the rapid development of technology, the design of equipment in both life and engineering applications becomes more complex and precise, but the structures are similar. Consisting of main component, functional component and auxiliary component. In general, there is an interaction between the main component and the functional component. When one of them fails, the system stops working. However, there is another situation between the main component and the auxiliary component. When the auxiliary component fails, the system will not stop working, but it will increase the probability of the failure of the main component. Traditionally, the failures of components have been considered as independent or interactive, but no one-way failure interaction has been considered. Therefore, this paper constructs the expected total cost rate model of two-components system, which the main component is one-way influenced by the auxiliary component. In this model, each failure of the component is recovered by minimal repairs. But the number of failures will increase more frequently. Therefore, in order to reduce the excessive repair cost, will be performed to bring the component back to the initial condition. This paper investigates the optimal replacement strategy for the system with two components, so that the expected total cost is the minimized, and same numerical examples are used to analyze the impact of replacement cost on the expected total cost rate.

[1] Barlow, R. E. and L. C. Hunter, “Optimum preventive maintenance policies,” Operational Research, 8-1, 90-100 (1960).
[2] Nakagawa, T. and M. Kowada, “Analysis of a system with minimal repair and its application to replacement policy,” European Journal of Operational Research, 12, 176-182 (1983).
[3] Jhang, J. P. and S. H. Sheu, “Opportunity-based age replacement policy with minimal repair,” Reliability Engineering and System Safety, 64, 339-344 (1999).
[4] Chien, Y. H. and S. H. Sheu, “Extended optimal age-replacement policy with minimal repair of a system subject to shocks,” European Journal of Operational Research, 174-1, 169-181 (2006).
[5] Wang, S., Zhang, S., Li, Y., Liu, H. and Z. Peng, “Selective maintenance decision-making of complex systems considering imperfect maintenance,” International Journal of Performability Engineering, 14-12, 2960-2970 (2018).
[6] Berg, R. E. and B. Epstein, “Comparison of age, block and failure replacement policies,” IEEE Transactions on Reliability, 27-1, 25-29 (1978).
[7] Beichelt, F., “A generalized block-replacement policy,” IEEE Transactions on Reliability, 30, 171-172 (1981).
[8] Osaki, S., “Applied stochastic system modeling,” Springer, New York.
[9] Sheu, S. H., “Extended block replacement policy of system subject to shocks,” IEEE Transactions on Reliability, 46, 375-382 (1997).
[10] Nakagawa, T. and S. Mizutani, “A summary of maintenance policies for a finite interval,” Reliability Engineering and System Safety, 94, 89-96 (2009).
[11] 王美崴，「雙元件系統個別與群體置換之比較」，中國工業工程學會學術研討會，2014。
[12] Zhou, Q. and Y. Sun, “Imperfect Maintenance Model Study Based on Reliability Limitation,” MATEC Web of Conferences, 65, 1006 (2016)
[13] Nakade, K. and H. Mikuri, “Optimal maintenance policy of multiple parts with operating cost dependent on repair level,” Journal of Advanced Mechanical Design, Systems and Manufacturing, 10-3 (2016)
[14] Huang, C. H. and C. H. Wang, “A Time-Replacement Policy for Multistate Systems with Aging Components under Maintenance, from a Component Perspective,” Mathematical Problems in Engineering 2019, 9651489 (2019).
[15] Lai, M. T. and Y. C. Chen, “Optimal periodic replacement policy for a two-unit system with failure rate interaction,” The International Journal of Advanced Manufacturing Technology, 29-3, 367-371 (2016).
[16] Cha, J. H. and E. Y. Lee, “An extended stochastic failure model for a system subject to random shocks,” Operations Research Letters, 38, 468-473 (2010)
[17] Wang, Y. and H. Pham, “Modeling the Dependent Competing Risks with Multiple Degradation Processes and Random Shock Using Time-Varying Copulas,” IEEE Transactions on Reliability, 61, 13-22 (2012)
[18] Zhang, N., Fouladirad, M. and A. Barros, “Maintenance of a two dependent component system: a case study,” IFAC-Papers On Line, 49-12, 793-798 (2016)
[19] Fan, M., Zeng, Z., Zio, E. and R. Kang, “Modeling dependent competing failure processes with degradation-shock dependence,” Reliability Engineering and System Safety, 165, 422-430 (2017)
[20] Shen, J. Y. “Reliability analysis for multi-component systems with degradation interaction and categorized shocks” Applied Mathematical Modelling, 56, 487-500 (2018).
[21] Huang, X. Z., Jin, S., He, X. F. and D. He, “Reliability analysis of coherent systems subject to internal failures and external shocks,” Reliability Engineering and System Safety, 181, 75-83 (2019)