保固為售貨公司對於購買產品的顧客的一個擔保。在產品的保固期內，若此產品在正常的使用情況下，而導致產品不能使用或損壞，售貨公司必須無條件的將損壞的產品修理至正常甚至更換新的產品給顧客。而保固維修資料即在產品保固期內，所收集到要求免費維修的損壞產品紀錄。保固維修的資料庫建立容易，很多公司建立此資料庫通常是想使用其訊息達到對於產品品質的早期監控，對於維修所需更換的產品元件備料的預測，以及建立對於不同的ODM商所製造的產品元件品質的評估與獎懲程序。但由於保固維修資料庫為求建立方便，導致資料庫中可能會有銷售延遲與回報延遲之問題。這樣的延遲問題常常導致無法正確得到產品真正的失效時間，造成分析上的困難。

在過去的研究中，褶積模型通常被應用來解決有延遲問題的保固維修資料。但是往往很少有研究，同時考慮銷售延遲與回報延遲的問題。在本研究中，當回報延遲時間無法從保固維修資料庫中得到，我們提供了一個新的方法用來估計回報時間的分佈。若資料收集有銷售延遲與回報延遲的問題時，我們亦建立了可靈活描述產品失效率的參數模型來解決這樣的問題。

使用我們所建立的參數模型可以得到產品未來的失效率與其預測區間。而利用模型所預測出來的失效率，可以提供給廠商作為參考，以達到早期監控產品的品質、備料的預測、以及對於ODM商的獎懲程序。研究中我們也提供了一個新的圖形工具—“失效率匯總監控圖”，利用此圖形工具我們可以初步快速與容易的偵測出品質較為不好的產品。

A warranty is a guarantee between a manufacturer and a consumer which requires the manufacturer to rectify failures that occurred in non-human factors within certain time. Most companies maintain warranty databases for purposes of warranty expense forecasting and the ODM (Original Design Manufacturers) penalty program. The warranty database may have the sales lag and report lag problems. These problems cause the difficulty of failure time analysis which the real interest is the failure time after the customer starts to use the product.

In certain literature, the convolution models were applied to the warranty database with the lag time problem. However, not much research has been done for the problem that the data have two types of lag at the same time. In this study, we propose a new method which are used to estimate the report lag distribution, when the report lag time are not recorded in the warranty databases. We also build a flexible parametric model which describes the failure rate of field data that are collected with sales lag and report lag and predicts the future failure rate with uncertainty limits.

Finally, we use the predicted failure rate to estimate the required spare parts, to indicate the possible quality outbreak for early warning and suggest a ODM penalty rule. A new graphical tool, aggregate failure-rate monitor plot, is proposed for the surveillance of product quality.

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