本研究最主要的目的為利用退化資料幫助預測產品未來失效機率並建構預測區間。這些失效機率的預測區間可以提供決策者決定備料數量或是維修時間的參考。如果決策者可以較準確地預測產品未來失效機率，那麼備料數量可以減少或是維修時間不會過早或是過晚，庫存成本或是維修預算也可以相對降低。我們使用累積失效機率來評估產品表現，並透過區間量化可能的預測誤差。

退化資料可以想成為一條條退化路徑或是隨機過程，在此我們考慮了隨機效果的退化路徑模型。當退化路徑的係數超過兩個，且彼此相依的情況，一般常見的做法為假設多變量常態分佈。但實際情況常會發現這樣假設不成立。本研究主要的貢獻為結合關連結構模型來幫助建立多變量分布函數，而得到失效機率的估計，藉由自助法建構預測區間。
我們將我們提出的方法應用到國道路面糙度的資料上。

In this study, the main goal is estimating failure probability of future products with degradation data and constructing prediction intervals. According to these prediction intervals, decision maker may utilize the bounds of prediction intervals to decide how many spare parts are needed or when to maintain
the products. If they can precisely predict the failure probability of products, they may be able to keep an appropriate stock level or maintain products at appropriate time. This may reduce the inventory cost or maintenance budget. We use cumulative failure rate to monitor the performance of components of the products. The possible prediction error is evaluated by an interval.

Degradation data can be described by degradation paths or stochastic processes. Here we consider the random effect degradation path model. When coefficients of a path are more than two and correlated, a general procedure is assuming a multivariate normal distribution of the coefficients. However this assumption may be violated in real case. The contribution of our work is that we combine Copula model to construct multivariate distribution function and estimate the failure probability. The prediction intervals are constructed through bootstrap approach. We apply our proposed methodologies to roughness degradation data of highway pavement.

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