隨著現今科技的蓬勃發展，不論是生活中或者工廠中所使用到的設備都愈加精密複雜，因此若遇到系統失效情況，急需立即維修，使其回復至原先狀態，降低設備停擺帶來的風險。然而，隨著系統使用率及年齡的增加，導致失效情形越加頻繁，使得維修成本提高，因此，需考慮置換系統，使維修成本與置換成本取得平衡，以求得最佳置換時程。但過去皆以失效率來描述系統失效情形，此作法於現實生活中應用較不為真實，其原因為在不同環境下，系統失效的情況皆不一樣，不單只需考量系統本身狀態，更須加以評估外在溫度、濕度、壓力等各種對系統產生衝擊的狀況，因此本文針對失效過程以系統承受力及衝擊量作探討，根據不同系統承受力與衝擊量的組合下，將其失效過程分為卜瓦松過程和非齊次卜瓦松過程，隨後以數值分析探討在不同組合下系統之最佳置換時程，以達到最低期望總成本率。

With the rapid progress of technology, the devices used in life or factories are more and more sophisticated. Therefore, if the systems fail, maintenance is performed immediately to restore the systems back to the operating condition and reduce the risks by systems downtime. However, as the system’s age or usage increases, the number of failures increases and the maintenance cost increases accordingly. Hence, replacement action might be performed to balance the replacement cost and the maintenance cost to obtain the optimal replacement time. But the failure rate was used to describe the failure process in the past, which is not an appropriate application in reality. Because the situations of system failures change according to different environments. It is not only to consider the status of the systems, but also to take the temperature, humidity, pressure, and external shocks into account. Therefore, this paper explores the failure process with bearing capacity of the systems and the strength of the random shocks. Considering these two factors, the failure process of the system can be classifies into Poisson process and non-homogeneous Poisson process. Based on these processes, the optimal replacement time of the system can be derived. Finally, some numerical examples are given to explore the optimal replacement time of different combinations to minimize the expected total cost rate.

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