自我恢復力之概念啟發於生物機制，意即當生物受到之衝擊時，之後，在一定時間內恢復至健康狀態。近年來關於自我恢復力之概念已在電機、航太與運輸等其他工程領域中受到越來越多的關注，如金屬化薄膜電容、具有自我修復之材料等等。傳統上，對於系統設備的失效大多定義為受到的衝擊超過界限值，鮮少針對在系統具備自我恢復力之前提下探討相應之維修或置換策略。故本論文在線性退化系統具備自我恢復力之情況下，以系統退化狀態與置換門檻取代傳統失效率來描述系統狀態，並建構系統的期望成本率模式。模式中，系統不只受到自身退化影響，也面臨外在隨機衝擊，造成系統狀態效能越來越差，為了減少日益變差之系統效能所造成額外成本，所以當系統狀態退化至某一門檻時進行系統置換的動作。根據期望成本率模式，本論文進一步探討退化系統在不同狀態與外在隨機衝擊之下之最佳置換時機與成本模式，以及當忽略系統自我恢復力之置換策略對最佳置換門檻與期望總成本率之影響。

The concept of self-healing is initiated from biology mechanism, which means a creature will recover to healthy status while suffering shocks. In the recent year, self-healing has attracted much attention in engineering field. For instance, metalized thin film capacitors repair electrical conductivity to avoid short and the self-resilience material for airplanes repairs the damaged surface by themselves. Traditionally, the failures of systems have been considered as suffering random shocks only, but no damage self-healing phenomenon has been considered. Therefore, this paper constructs an expect total cost rate model for a linear-deteriorating system, which has self-healing capability under random shocks. In this model, the system performance is affected by not only degradation but also random shocks. In order to reduce the excessive cost caused by worse performance, system will be replaced while the system status exceeds a replacement threshold. This paper investigates the optimal replacement strategy for the linear-deteriorating system with self-healing under random shocks, so that the expected total cost rate is minimized. Finally, some numerical examples are given to analyze the impact of the self-healing capability on the expected total cost rate.

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