一般市面上的產品隨著使用時間增加皆無可避免失效的情形發生，而其原因可歸為兩個面向，分別為產品本身內部的自然退化以及來自外部的隨機衝擊，且無論導致產品失效的原因為何，當失效發生時需執行小修使其回到失效前狀態，因此為了避免產品失效次數增加進而導致產品效能不穩定或是造成成本上的負擔，需在某時刻執行置換使總成本最小化。而隨著科技發展日新月異，市面上推出許多新產品、零件以及機器設備具有自我恢復的能力，使其受到衝擊時可以減少衝擊所帶來之附加成本。然而此些具有自我恢復力之產品雖可減緩衝擊之影響，當決定置換為此類型之產品時所需額外付出之成本也相對較高。在過去探討置換策略相關的文獻中，鮮少以具自我恢復力之產品作為研究對象，因此本論文針對以下三種退化產品(1)僅考慮內部退化之產品、(2)在隨機衝擊下不具自我恢復力之產品以及(3)在隨機衝擊下具自我恢復力之產品建立成本模式，並以數值範例分析比較三者最佳置換策略之差異，且進一步探討自我恢復力之價值。

Generally, products on the market are unavoidable to fail as time passes. It can be attributed to two main reasons, which are the internal deterioration and the external random shocks. No matter the reason of the failure, minimal repair is performed to restore the products back to the operating state. Therefore, the replacement is needed to avoid the unstable performance and the cost burden which are caused by the increasing failure times. With the ever-changing technology, many new products on the market have the capability of resilience, which can reduce the additional cost for the random shocks. However, although these kinds of products can mitigate the impact of shocks, the extra cost for performing the replacement is also higher. In the past literature, they only considered the replacement strategy under the random shocks, but the concept of resilience has hardly been considered. As a result, this paper establishes a cost model for the following three deteriorating products:(1) The internal deterioration product, (2) The deteriorating product without resilience under random shocks and (3) The deteriorating product with resilience under random shocks. In addition, this paper compared the optimal replacement strategies for three deteriorating products. Finally, some numerical examples are given to explored the value of resilience.

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