製程能力指標Cpm之近似不偏估計量

An Approximately Unbiased Estimator of Process Capability Index Cpm

陳靜怡(Ching-Yi Chen)

指導教授 ： 彭文理

國立交通大學/管理學院/工業工程與管理系所/碩士(2016年)

摘要

製程能力指標廣泛地用來評估製程產出產品是否符合規格要求的一個重要工具，其不僅可提供品質保證，也可提供一個方針於品質改善。在各式各樣的指標中，Cpm被視為高科技製造產業中用來衡量製程損失最普遍的指標之一，但其估計量為一個偏誤估計量，因此，本篇研究提出一個修正係數來求得Cpm的近似不偏估計量，這使得業界使用者能夠精確的評估製程。本篇論文利用Matlab軟體中的曲線擬合工具來求Cpm指標的近似不偏估計量。然而，製程參數 μ 和 σ 為未知，所以無法計算求得修正因子中的ξ，因此，我們利用複式抽樣方法求出參數的估計量。

關鍵字

製程能力指標 ； 近似不偏估計 ； 曲線擬合工具 ； 複式抽樣

並列摘要

Process capability indices (PCIs) have been extensively used to determine whether the process products meet the specifications limits, and they can provide decisions for quality assurance problems and guide a principal for improving process quality. Among various indices, Cpm is one popularly used index because it provides a measure on the process loss, but the estimator of it is biased. Thus, this thesis, proposes a correction factor to obtain the approximately unbiased estimator. The curve fitting by the computer program Matlab is adapted to obtain the correction factor. Since the process parameters μ and σ are unknown in the correction factor, bootstrap method can be used to estimate them.

並列關鍵字

process capability index ； approximately unbiased estimator ； curve fitting ； bootstrap

參考文獻

Kotz S, Johnson NL (1993) Process capability indices. Chapman & Hall, London.

Boyles, R. A. (1991) The Taguchi capability index. Journal of Quality Technology, 23, 17–26.

Zimmer L. S, Hubele NF (1997) Quantiles of the sampling distribution of Cpm. Qual Eng 10:309–329.

Zimmer L. S, Hubele NF, Zimmer WJ (2001) Confidence intervals and sample size determination for Cpm. Qual Reliab Eng Int 17:51–68.

Vännman K (1997) Distribution and moments in simplified form for a general class of capability indices. Comm St-Th 26(1):159–179.