考慮製程平均發生偏移下之製程能力評估

Abstract

製程能力指標被用來衡量製程製造產品符合規格的能力，不僅是提供品質保證的工具，也是在品質改善方面一個方針。不過，自從Motorola公司在1980年代提出6個標準差的觀念後，很多統計學家質疑這些提倡6個標準差的人，為什麼他們在衡量製程能力時，會先對製程平均做1.5個標準差的調整。Bothe(2002)針對這個問題，利用管制圖的機制來偵測製程平均發生偏移的情況，發現它隨著不同的抽樣個數可以有不同的調整量，可是Bothe 的研究是在常態的假設下，事實上，非常態的製程在業界是較常發生的。我們針對非常態的情況，探討了三個Non-normal (Gamma, Weibull and Lognormal distributions)的平均連串長度, 發現其對常態假設非常敏感。所以我們針對這三個非常態Gamma分配做詳細的分析,導出在不同非常態分配下應調整的偏移量，並針對非常態適用的Cpk 指標做調整。在論文的最後，我們用一個實例來說明如何在非常態(以Gamma分配為例)的情況下，在考慮製程平均會發生變動的情況下，如何調整製程能力指標Cpk。

Process capability indices have been proposed in the manufacturing industry to provide numerical measures on process reproduction capability, which are effective tools for quality assurance and guidance for process improvement. Motorola, Inc. introduced its Six Sigma quality initiative to the world in the 1980s. Some quality practitioners questioned why the Six Sigma advocates claim it is necessary to add a 1.5 shift to the average when estimating process capability. Bothe (2002) provides a statistical reason for including such a shift in the process average that is based on the chart’s subgroup size. Data in Bothe’ study was assumed to be approximately normally distributed. What effects on capability estimates when the process output has a non-normal distribution? This paper investigates the average run length of three non-normal distributions and calculate the mean shift adjustments and addresses this problem computing reliable estimates for capability index for non-normal process (particularly for gamma distribution) when the statistically adjustments is considered. For illustration purpose, an application example is presented.