可修復系統失效數據之分析與預測

Abstract

一個可以精確的預測產品可靠度的方法不僅可以降低供應與需求間的不確定性，並可依此模式改進產品及降低成本。現有的可修復系統失效數據分析與預測方法有三個缺點：（1）需要完整的系統失效資料，不完整的失效資料需要相當複雜的統計方法才能處理；（2）需要大量的歷史資料，歷史資料若不足則不能分析，否，或分析與預測的結果會不準確；（3）幾乎很少考慮到失效數據的季節效果，因此分析與預測的結果可能不夠精準。因此，本研究針對上述三個缺點提出三種新的分析與預測方法。三種方法在蒐集失效數據方面皆只需要單位時間的測試量與失效數即可。第一種方法為利用灰色系統理論（grey system theory）建構可修復系統預測模式，此方法只需少量的歷史資料即可預測可修復系統的失效率；第二種方法為利用季節性自我迴歸移動平均整合模式（Seasonal Autoregressive Integrated-Moving Average Models ; 簡稱SARIMA模式）構建可靠度分析與預測模式，此方法具有比現有常用之指數平滑法與ARIMA模式更能考慮到失效數據的季節效果的優點；第三種為結合SARIMA模式與類神經網路構建出一個新的可靠度分析與預測模式，此方法結合了SARIMA模式與類神經網路的優點，可分析具有趨勢與季節性的資料並同時兼顧長短期的預測及需要少量的歷史資料。本研究最後以一個可修復系統的實例來說明所提三種方法的可行性及較現有方法優越之處。

A precise product reliability prediction model can provide useful information enhance product quality and reduce product cost for manufacturers. Current analyzing and forecasting methods have following three drawbacks: first, complete failure data is required. Otherwise, statistical methods must be employed for analyzing the incomplete field data. Second, a large amount of historical failure data is required. Third, the seasonal effect of failure data was not considered by almost all existing methods. This study proposes three methods for analyzing and predicting reliability for repairable systems. The proposed methods require only number of units and number of repairs in unit time to predict the failure data. The first method utilizes grey system theory to construct a new predictive model for failure data. This model can forecast system’s reliability with just few historical data. The second method utilizes the seasonal autoregressive integrated-moving average（SARIMA）model to build the predictive model for failure data. The second model considers the seasonal effect of the field failure data. The third method constructs the predictive model by combining SARIMA model and neural network model. The third model can not only analyze the trends and seasonal vibration of the data, but also forecast the short and long term reliability of the system using only a small amount of historical data. Finally, a real case of the repairable system is presented to illustrate the feasibility and effectiveness of the proposed methods.