在這篇論文，我們主要是建立一個不完美的維護模型，結合了一連續時間的使用率並建立在一個虛擬年齡的模型下所求出的最佳維護策略.
在此論文將楊(2011)的模型從間斷時間的使用率改成連續時間的 等候線模型。實際上，我們知道每一段區間的使用率會受到上一期未完成的組件數量，區間長度以及到達率跟服務率比例的影響。此虛擬時間函數以Liu et al.(1995) 的概念為基礎，此函數可以更容易去分析失敗率因為失敗率函數不會改變。此函數會受到使用率、維護程度而對失敗率產生變化。因此虛擬函數受到這些因子影響後，會使得函數時間曲線回復。所以我們要決定最佳的PM次數及維護的長度在一固定區間的維護模型下，並且探討不同參數的變化對模型產生的影響。

In this study, our purpose is to construct an imperfect maintenance model, which combines utilization with continuous time and based on virtual age function, for computing the minimized expect total cost to decide an optimal policy.
We extend Yang (2010) for utilization to a continuous time Markov chain with queuing model. In practical, we know that utilization of every period will be decided by the service of the units are not completed in the end of last station, the length of the overhaul interval, and the proportion of arrival rate with service rate. Then, the concept of our virtual age function is based on Liu, Makis and Jardine (1995). This function can use to analyze failure time function more easy but it does not change. The utilization and degree of maintenance of the system are both affected by the failure intensity function with a virtual age function. Besides, the virtual age function will also be affected by two improvement factors that are general repair and PM action both restore the function curve to a certain degree. In this thesis, we will determine optimal PM times and general repair length over a finite planning horizon with a periodic replacement model, and show how it varies with parameters.

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