經由即時監控衰變路徑資料制定最佳維修時程之研究

Abstract

針對一個能經由維修以延長壽命的產品或設備，本論文提出一個由即時監控產品之衰變路徑來決定是否該進行維修以節省成本的策略。為了解產品衰變路徑之特性，我們先以前人所提之函數資料分析方法，利用一組歷史衰變路徑資料為母體衰變路徑建立統計模型，並以馬可夫鏈－蒙地卡羅方法估計模型參數，繼之用此估計出之模型對正在監控中的衰變路徑估計其產品剩餘壽命。我們提出一個很簡單的維修策略，即當所估計之剩餘壽命小於某設定之門檻值即對此產品進行維修。而如何制定即時監控中的衰變路徑之最佳維修門檻，我們再次利用歷史衰變路徑資料，以交叉驗證之每次刪除一條路徑的作法，求出每一條歷史衰變路徑上每一個時間點之估計剩餘壽命；接著以這些資訊模擬維修情境，在不同更換與維修費用比例之下，計算不同門檻值之總成本與總時間，繼而得到單位時間平均成本，並以單位時間平均成本大小來評斷不同門檻值之優劣。如此我們可找出在特定更換與維修費用比例之下，能使單位時間平均成本最小之門檻值。我們由模擬實驗驗證，運用此特定門檻值至別組衰變路徑資料，其單位時間成平均成本與該組資料本身相對應之最小值相當靠近。因此將此特定門檻值運用至即時監控中的衰變路徑是可行的。

In this study, for products or equipment that can prolong their life via certain kind of maintenance, we propose a method to determine whether a product/equipment needs an immediate maintenance for economical reason via real-time monitoring of its degradation path. At each time point of the real-time monitoring, the residual life is estimated by a method presented in Zhou et al. (2014) and compared with a preset threshold. If the estimated residual life is less than the threshold, then perform the maintenance. The method in Zhou et al. (2014) used a set of historical degradation paths to build a statistical model for the degradation path under monitoring by functional data analysis and estimated the model parameters by the Markov chain Monte Carlo method. To determine the appropriate threshold, we first estimate the residual life for each time point we have observed on each of the historical degradation paths by the delete-1 cross-validation method. With this information, we simulate the maintenance scenarios under various threshold candidates. Given the ratio of the replacement and maintenance costs, we calculate the total cost and total time for various threshold candidates. The optimal threshold is the one with the minimum value of the mean cost, which is defined as the ratio of the total cost and the total time. Through a simulation study, it is found that applying the optimal maintenance threshold to other sets of degradation paths only raises the mean cost slightly from that obtained with their own optimal thresholds.