考慮非中心卡方製程的製程平均發生偏移下之製程能力調整

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的一個方針。不過，自從Motorola公司在1980年代提出6個標準差的觀念後，很多統計學家質疑提倡6個標準差的學者，為什麼在衡量製程能力時需要對製程平均做1.5倍的標準差調整。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 的研究是在常態分配的假設之下，事實上，非常態分配製程在業界是較常發生的。過去的研究也有針對了非常態分配 (伽瑪、韋伯、對數常態分配) 的調整。所以我們針對非常態非中心卡方方配做詳細的分析，導出在不同非常態分配下應調整的偏移量，並針對非常態分配適用的 Cpk 指標做調整。在本研究的最後，以實例來說明如何在非常態分配製程的情況下，在考慮製程平均發生變動的情況下，如何調整製程能力指標 Cpk 。

Process capability indices have been proposed in the manufacturing industry to prove 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 1.5σ shift to the process mean when estimating process capability. Bothe (2002) provides a statistical reason for including such a shift in the process average that is base on the chart’s subgroup size. Data in Bothe’ study was assumed to be approximately normally distributed, but the process output is usually not from approximately normally. Some research is about the PCIs adjustment for process output has a non-normal distribution. This paper investigates the average run length of non-normal distribution, non-central chi-squared distribution, and calculate the mean shift adjustments and addresses this problem computing reliable estimates for capability index Cpk for non-central chi-squared process when the statistically adjustments is considered. For illustration purpose, an application example is presented.