目前市面上銷售的產品，因為科技的更新，每過一段時間就會上市新世代同類型的產品，在新世代產品上市一段時間後，舊世代的產品則會下市，這時市面上就沒有舊世代產品存在。當市面上同時存在新舊世代產品時，消費者就會考慮種種因素是否要淘汰舊市代產品更換成新世代產品，這個動作稱作「汰換」。在實務上，產品都具有退化的性質，隨著產品的使用年齡增加，產品的失效率也會隨之增加，因此產品就越來越有可能發生失效，失效會使得產品無法運作。本論文將產品分成兩種形式，第一種為產品是可維修的，當產品發生失效時，採用小修的動作進行維修，使產品恢復正常運作，當產品隨著使用時間的增長，失效的次數也會隨之增加，造成維修成本過高，這時就會採用置換的動作，更換一個全新的產品；第二種為產品是不可維修的，當產品發生失效時，就直接採用置換的動作，換成一個全新的產品。針對這兩種產品形式，在市面上存在新舊世代產品時，尋求汰換為新世代產品的時間，因此建立汰換為新世代產品的數學模型，以最低成本為目標，找出最佳的汰換時間，最後進行數值分析來探討新舊世代產品的相關成本對最佳汰換時間的影響。

Because of updating of technology, the same type of products in new generation will be launched at regular interval. The old generation products currently on the market will no longer be sold after new generation products released for a period of time. Then, there will no old generation products in the market. When there are new and old generation products on the market at the same time, consumers will consider various factors to replace old generation products with new generation products, which is called “switch-over.” In practice, the products are degraded. As the usage increases, the failure rate of these products may increase the opportunity of failure occurs in products then makes products do not work. This paper purposes the products which divided two types. The first one are repairable products, when the products fail, which performing minimal repair to restore the products to normal status. According to the usage increases of products, the number of failures will increase to result in excessive repair costs. Then, we will perform replacement actions to change a new product. The second one is non-repairable product. When the products fail, we will perform replacement actions directly to replace with new products. This paper purposes to find switch-over time for the products which have old and new generation products on the market. Therefore, the mathematical model of switching over to new generation products is established to minimize the total costs and find the optimal switch over time. Finally, the impact of the relative costs of new and old generation products on the switch over time is demonstrated through numerical examples.

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