探討多變量非常態製程之管制圖監控績效

Performance Study of Statistical Monitoring to the Multivariate Control Chart with Non-Normality Manufacturing Effects

伍詩涵(Szu-Han Wu)

指導教授 ： 陳雲岫

元智大學/工程學院/工業工程與管理學系/碩士(2008年)

摘要

管制圖是統計品質管制中重要的工具，一般狀況管制圖通常是在常態假設下利用管制圖進行監控，若直接以管制圖監控非常態製程，將會造成製程監控與製程能力指標判斷的錯誤。
本研究探討多變量管制圖監控二維變量非常態製程之績效，首先模擬出二維非常態製程資料，再應用多變量常態性轉換法，將多變量非常態製程轉換至常態，並以P-P圖與卡方機率圖作常態性分析與檢定，再以Hotelling’s 管制圖進行監控，分析製程之平均連串長度ARL0。另外也探討當二維非常態分配製程產生偏移時，製程同時產生偏移與一個維度製程的偏移情況，分析平均連串長度ARL1在此兩種偏移情形之差異。
研究中針對不同的樣本數、相關係數進行模擬。結果顯示樣本數越大， 管制圖製程監控績效較佳；相關係數越高影響製程績效較大，當製程產生偏移時，相關係數對於製程一個維度偏移的影響較大。由模擬結果中顯示，以Hotelling’s 管制圖監控經多變量常態性轉換後的非常態分配製程績效，其製程的誤警率會因而降低。

關鍵字

多變量管制圖 ； 多變量常態性轉換法 ； 二維Gamma分配模擬演算法 ； 平均連串長度

並列摘要

Monitoring process by using control chart is one of the primary techniques in statistical process control (SPC). Basically, most of control charts function well when the underlying distribution of inspected characteristics follows normal. If the underlying distribution deviates from normal, it may cause a serious mistake of judgment in monitoring the capability of manufacturing.
In this research, we discuss the performance of a multivariate control chart when the inspected 2 correlated variables is non-normal distributed. Firstly, we simulate a set of non-normal two-dimension manufacturing data, then, the simulated data is transformed to normal data by the Multivariate transformation method. We assure the distribution of the transformed data by these data under which the P-P plot and chi-square probability plot. The average of run length (ARL) of the Hotelling’s T 2 control chart is treated as our performance index in this study. We also discuss various conditions with the shift of process mean which in one or two dimensions. The ARLs under those conditions are calculated and compared.
In our experiments, we compare the vary of ARL under different combination of sample sizes and correlation. The results show that the performance of T 2 control chart gets better with the increasing of sample sizes, regardless of the correlation and shape parameter of Gamma distribution. The manufacturing effects increase with the increasing of correlation. The affection of performance is higher with a larger correlation. When the process is out of control, the study shows that effect of correlation to the process is relatively higher when the shift of only in single-mean occurs dimension. Also, the simulation study reveals that false alarm rate of manufacturing effects of Hotelling’s control chart is decreased after a multivariate normal transformation is applied to the process.

並列關鍵字

Multivariate control chart ； Multivariate normal transformation method ； two-dimension Gamma distribution algorithm ； Average run length.

參考文獻

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