自我相關殘差管制圖模型選取之研究

Model Selection for Autocorrelated Residual Control Charts

潘浙楠(Jen-Nan Pan)；席嘉澤(Chi-Tse His)；陳曉倩(Sheau-Chiann Chen)

指數加權移動平均管制圖 ； 累和管制圖 ； 模型選取準則 ； CUSUM control chart ； EWMA control chart ； information criterion ； model order selection

品質學報

16卷4期（2009 / 08 / 31）

245 - 260

繁體中文

隨著電腦科技的日新月異及生產過程在自動化技術不斷改進下，蒐集製程資料的間隔時間已大幅縮短，使得樣本間存在著高度自我相關性。因此，若將此類資料以傳統的管制圖進行監控極易產生誤判，而導致不必要的成本浪費。近年來已有多位學者藉由不同統計模型的選取準則協助廠商選擇正確的時間數列模型，這些準則依其不同統計模型，大致可分爲具有漸進有效性（如AIC和AICC）與一致性（如BIC與SIC）之準則兩大類，另有學者提出結合前述兩類優點之WIC準則。基於上述模型選取準則各有其適用性，因此本研究著重於不同樣本數情形下，如何利用適當的準則選取正確的統計模型。結果顯示WIC準則較爲穩健，這可作爲業界在處理自我相關製程資料與監控時的重要參考。

When the process data are correlated, one should first select a suitable model to fit the data and then use the traditional control charts to monitor the change of residual. The effectiveness of using residual control charts depend crucially on the appropriateness of the model selected. In this paper, several order-selection criteria including AICC (bias-corrected Akaike's information criterion), BIC (Akaike's Bayesian modification of AIC), and WIC (Weighted average Information Criterion) are used to select the model order when the process data follows a time series model like ARMA (Auto-Regressive and Moving Average). The performances of these criteria are further demonstrated by simulation under different sample size as well as a numerical example. The results show that the performances of model selection using WIC are more robust than other criteria such as AIC, AICC, BIC and SIC.

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