製程能力指標在合理分群之績效評估

製程能力指標被設計用來量測製程的績效。根據Kotz and Johnson(2002)與Deleryd(1998)指出製程能力研究理論與實務是存在間隙(gap)的，要如何減小間隙並縮減理論與實務間的變異就成為現今極重要之研究課題。到目前為止，製程能力指標估計分配性質大多是基於常態母體且在統計管制之下的單一樣本觀察值，由於抽樣誤差的關係僅利用單一樣本作推論較易導致錯誤的結論，為了提高推論的效率，所以我們必須考量在合理分群(rational subgroup)之下，估計製程能力指標(process capability index)的分配，即對製程能力指標作一統計推論。本文中所用的製程能力指標是根據Taguchi所提出的損失函數(loss function)觀念來衡量製程能力的績效( performance )。在此採用田口方法，一方面期望能在最短時間、最低成本、最少實驗次數、最簡便的分析方法及現有資源條件下，來協助業者達到製程的改進與績效，而目標為降低製造成本，並同時提升原來之品質水準。另一方面也希望能透過田口方法，降低變異、改善品質、提升競爭力。再則，我們考慮在統計品質管制下利用 -Chart、R-Chart、S-Chart的估計量，另外也考慮由Kirmani et al.(1991)、Derman and Ross(1995)提出關於S更好的估計量。最後再利用Patnaik’s(1950)近似卡方分配(Chi-squared distribution)對Cpw(1)、Cpp、Cpmk等製程能力指標作統計推論，以評估製程能力。通常在一般產業，製造業製造過程中檢驗產品所得到的資料，皆為合理分群資料。因此，本文提出有關製程能力指標評估績效的方法，並提供一套簡單評估模式，業者可根據自己產業的特質，選擇合適的指標，套用本文所提供的評估模式，來評估其製程能力，以提昇實用性的價值。

關鍵字

製程能力指標；合理分群；績效評估；損失函數；統計推論

並列摘要

Kotz and Johnson(2002), Deleryd(1998) indicated that there was a gap between theory and practice of process capability studies. Then how to reduce the gap and the variation between the theory and practice of process capability studies has been become a serious problem. Most of results obtained so far regarding the distributional properties of estimated capability indices are based on the assumption of a simple sample of observations from the normally distributed process, which is in-control. To use estimators based on several small subsamples and then interpret the result as if they were based on a single sample may result in incorrect conclusions. For the sake of use past in-control data from subsamples to make decision regarding process capability, the distribution of the estimated capability index with subgrouping should be considered, that is, we construct the statistical inference for the process capability indices. Taguchi used the quadratic loss function to improve the idea that a product imparts no loss only if that product is produced at its target. Taguchi’s philosophy emphasizes the need to have low variability around the target. The use of loss functions in quality assurance settings has grown with the introduction of Taguchi’s philosophy. Theoretical statisticians and economists have for many years used the squared error loss function when making decisions or evaluating decision rules. In this dissertation, we use the Taguchi loss function to evaluate the performance of the process capability indices. We consider estimator that naturally occur when using an -Chart together with a R-Chart or S-Chart in quality control. In addition, we apply a better estimator of σ for moderate large sample size, which was that introduction by Kirmani et al. (1991) and Derman and Ross (1995), respectively, but also to make use of the Patnaik’s(1950) approximation to the central Chi-squared distribution, to construct a procedure lower confidence bounds and hypothesis testing for Cpw(1) and Cpmk when μ=M and also construct a procedure upper confidence bound and hypothesis testing for Cpp to assess the performance for the process capability with subgrouping, respectively. We also develop a simple-to-use method to accurately predict process capability. Whatever method is developed must be computationally simple and easy for an engineer to implement. We know that all the information gathered from the product inspection process in the manufacturing industries can be used as the rational subgroup data in this dissertation. Thus, we have proposed a very simple and highly practical evaluation mode for manufacturers to use. Based on this evaluation mode, manufacturers can choose the most appropriate indices according to the characteristics of their industries.

並列關鍵字

process capability indices ； rational subgroup ； performance evaluation ； loss function ； statistical inference

參考文獻

Abramowitz, M. and Stegun, I. A. (1970). Handbook of Mathematical

Functions with Formulas, Graphs, and Mathematical Tables, Dover

publications, Inc., New York.

Boyles, R. A. (1991). The Taguchi capability index. Journal of Quality

Technology. 23(1), pp. 17-26.

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製程能力指標在合理分群之績效評估

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