統計製程管制第一階段分析之新策略

Abstract

針對統計製程管制第一階段分析，本論文提出並研究一次只剔除一個最極端的管制外樣本點的作法，稱之為“OAAT”法。模擬研究顯示，「OAAT」法可大幅降低假警報之發生，克服了現行每次剔除所有管制外樣本之作法會造成丟棄大量穩定樣本的重大缺點。文中亦建議一個何時檢查製程之新策略，亦即檢查管制外之樣本以尋找其發生原因之適合時機。在製程由不穩定到穩定過程中，此策略可節省大量時間與金錢。為陳述此新法，本文使用最常用的Shewhart平均值管制圖。文中對以下三種方法加以研究：（一）使用傳統方法控制個別假警報率，（二）使用Bonferroni 法控制整體假警報率，（三）以逐次P值法控制假發現率。文中應用「OAAT」作法於上述三種方法並藉模擬研究以真、假警報數之期望值來評估比較其表現。

The purpose of this paper is to propose and study a new OAAT procedure for Phase I analysis in statistical process control that only discards the most extreme sample at a time. Our simulation study demonstrates that the OAAT procedure reduces dramatically the occurrences of false alarms. It can overcome the drawback that the practice of discarding all beyond-limits samples at each iteration of chart construction throws away too many in-control samples. We also suggest a new strategy on when to inspect the process to look for assignable causes for samples signaling out-of-control alarms. The new strategy may save tremendous amount of time and money in bringing the process to in-control state. The most popular Shewhart Xbar Chart is used for illustrating the new procedure. Three methods of detecting out-of-control samples are studied: (i) the traditional method that controls the individual false alarm rate; (ii) the Bonferroni method that controls the overall false alarm rate; (iii) a sequential p-value method that controls the false discovery rate. We apply the OAAT procedure to the three methods. The performance of the proposed schemes is evaluated and compared in terms of the expected number of false alarms and the expected number of true alarms via simulation studies.