為延續企業的競爭優勢，業者亟需能符合成本效益、且能隨時保持高性能狀態的作業系統，因此適當的對系統進行維修置換，將可有效的降低成本以及防止故障的發生。本論文將針對退化系統在執行檢驗工作的條件下提出兩種置換模型，再分別求最佳策略。

首先，針對此兩種置換模型，一旦故障發生，退化系統均必須透過執行檢驗工作才可將其檢查出。而系統所遭遇的故障有兩種，其中包含型-I故障以及型-II故障，我們是以修理的方式排除型-I故障，以直接置換的方式排除型-II故障。在第一種置換模型下，我們設立此退化系統的置換條件為第 次型-I故障或首次型-II故障，視何者先發生即先進行置換。此外，假設故障發生的機率與故障發生的次數有關。然而，即使系統可因型-I故障而修理，但卻會隨機退化，也就是其運作時間將隨機遞減，修理時間將隨機遞增。第二種的退化系統置換模型，我們則是延伸原先第一種置換模型，新增設一置換條件：運作年齡，因此置換條件更換成：運作年齡達到 、或第 次型-I衝擊或首次型-II衝擊，視何者先發生即先進行系統置換。

針對以上兩種置換模型，分別推導出相關長期每單位成本函數，並探討使成本函數最小化的最佳解存在時之條件。本研究可作為類似退化系統或產品在訂定維修置換策略時的參考。

To gain and remain competitive advantage, manufactures require a cost-effective system for maintaining its production machinery in peak operation condition. Repairs and replacements enable us to reduce the operating cost and prevent the occurrence of system failure. In this research we propose two kinds of the replacement models for a deteriorating system with inspections and then find the optimal policy for these two models.

First, a deteriorating system with failures that could only be detected through inspection workfor each of the two replacement models.The system is assumed to have two types of failures including type I failure and failure II failure. Each type I failure, corrected by a minimal. We replace the system when a type II failure occurs.In first replacement model, the system is replaced at the Nth type I failure (minor failure) or first type II failure (catastrophic failure), depending on whichever occurs first. The probability of type I and II failure depends on the number of failures since the last replacement. Such systems can be repaired upon type I failure, but are stochastically deteriorating, that is, the lengths of the operating intervals are stochastically decreasing, whereas the durations of the repairs are stochastically increasing.In the second replacement model, we extend the first one replacement model and add another one replacement condition for the system’s working age. Hence the deteriorating is replaced at the occurrence of the Nth type I failure (minor failure), or the first type II failure (catastrophic failure), or at working age T, whichever occurs first.

For each of the above two models, the unique optimal solution which minimizes the
long-run expected cost per unit of time is determined respectively. This research can be a reference for setting maintenance and replacement policies to analogousdeteriorating systems and product.

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