考慮Gamma製程變異數發生變動下之製程能力調整

Abstract

製程能力指標經常被用來衡量製程製造產品符合規格能力，不僅提供品質保證的工具，也是提供品質改善方面的一個方針。自從Motorola公司在1980年代提出6倍標準差觀念後，許多品質工程師質疑為什麼在計算製程能力之前要增加1.5倍標準差的調整。Bothe (2002) 針對此問題，用統計的方法解釋了原因，且說明調整量是按照抽樣數來決定。在計算製程能力指標之前，需要先假設製程為穩態的，也就是在生產過程中平均數和標準差不會改變，但是在實務上製程為動態。當產品品質特性為非常態且變異數未知時，對我們估算製程能力會有什麼影響？本研究將針對產品品質特性符合Gamma分配時，其製程變異數改變時之製程能力調整方法。針對不同的Gamma參數來計算不同的檢定力，在基於Bothe的假設提出修正量。在本研究的最後，我們將利用一個實例來說明當製程品質特性服從Gamma分配並考慮製程變異數發生變動時，應如何調整製程能力指標 。

Process capability indices (PCIs) have been proposed in the manufacturing industry to provide numerical measures on process 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 Six Sigma advocates claim it is necessary to add a 1.5 shift to the average when estimating process capability. Bothe (2002) provided a statistical reason for including such a shift in the process average that is based on the chart’s subgroup size. When calculating the process capability, we have assumed the process is stable (the process mean and variation do not change), but in practice, the process is dynamic. What is the effect on the capability estimates when the process output has a non-normal distribution with process variance change is remained unknown? This research investigates process capability adjustments when process variance change from Gamma distribution, and compares the detection power of difference parameters and subgroup size from Gamma distributions under Bothe’ advises. Finally, we add the adjustment to capability index of non-normal processes. For illustration purpose, an application example is presented.