應用六倍標準差方法評估製程在變異數會變動情況下的製程能力(I)

Abstract

本計畫預定執行三年，中文摘要分別概述如下： 第一年 計畫名稱：應用六倍標準差方法評估常態製程在變異數會變動情況下的製程能力 中文摘要 製程能力指標是用來衡量製程所製造之產品符合規格的能力，提供對品質計量性的衡量。因此製程能力指標不僅是品質保證也是品質改善的一個工具。Motorola公司在1980年代提出品質改進的六倍標準差方法，但許多統計學家不理解這些提倡六倍標準差的公司，為何他們在衡量製程能力時，要對製程平均做1.5個標準差的調整。Bothe (2002) 針對這個問題，在製程品質特性資料為常態以及變異數不變的條件下，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。事實上，製程之變異數可能是會變動的。因此我們針對製程品質特性資料為常態的情況，在製程平均保持穩定但變異數會變動的情況下，針對常態製程做詳細的分析並針對Cpk 指標做必要的調整。在此研究計畫的最後，我們研究一個實例來說明在常態製程的情況下，當製程變異數發生變動時，如何調整製程能力指標Cpk以對製程能力做出正確的量測。

本計畫預定執行三年，英文摘要分別概述如下： 第一年：Capability Adjustment for Normal Process with Variance Change in Implementing Six Sigma Program 英文摘要 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 1.5σshift 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. Data in Bothe’s study was assumed to be approximately normally distributed and the process variance remained stable. What effects on the capability estimates when the process variance change is remained unknown? This research investigates the detection power of the S2 control chart to the Normal distribution, and calculates the variance change bounds. We address this problem and compute reliable estimates for capability index when the underlying distribution is Normal with variance changes. For illustration purpose, a case study is presented.