雙配方製程之無母數衰變模型與剩餘壽命預測

Abstract

在工業應用中工廠機台零件之特性或效能會隨著使用時間而逐漸老化，當老化至某一程度時，會導致機台故障或對產品產生巨大影響；因此預測機台故障時間點是個十分重要的議題。目前文獻上之衰變模型是根據執行相同配方下所量測到之衰變資料而建立的，但實際工廠應用所蒐集之衰變資料，可能執行了不只一種配方，而不同配方對零件之老化速率未必相同。在本論文中，將針對兩種不同配方依序交錯執行時所得到之衰變資料來建立無母數衰變模型，並應用於零件剩餘壽命之預測上。本論文以函數型資料分析為基礎，使用Chiou et al. (2014) 所提之多變量函數主成分分析之概念，將Zhou et al. (2011) 建構於單配方主成分分析之衰變模型推廣至建構於雙配方主成分分析之衰變模型，並利用此模型來預測使用中之零件的剩餘壽命分配。

In many manufacturing processes, the quality characteristics or process performance degrades as machine parts age with time and the impact of the degradation could be significant when the aging reaches the failure threshold. Therefore, how to predict the failure time is an important issue. Most existing degradation models were proposed for processes operating under one recipe; however, sometimes the degradation data are collected for a process that operates under more than one recipe and different recipes may have different aging rates. In this paper, considering a process that operates two recipes alternately, we first propose a nonparametric degradation model that can be estimated from a set of historical degradation data via a two-function functional principal component analysis (FPCA) proposed in Chiou et al. (2014). Then we extend the Bayes estimation method proposed in Zhou et al. (2011) to our two-recipe situation to obtain a posterior distribution of a future degradation value as well as the residual useful life (RUL) distribution of a new part. In the end, by plugging the previously established two-function FPCA degradation model, we obtain an empirical Bayes estimate of the RUL distribution.