Title

以分批法估計相關性資料的製程能力指標

Translated Titles

Estimation of Process Capability Indices for Autocorrelated Data Using Batching Methods

DOI

10.6840/cycu200700490

Authors

陳玫均

Key Words

製程能力指標 ; 信賴區間 ; 覆蓋率 ; 時間序列 ; 分批法 ; Confidence Interval ; Coverage Percentage ; Batching Method ; Process

PublicationName

中原大學工業工程研究所學位論文

Volume or Term/Year and Month of Publication

2007年

Academic Degree Category

碩士

Advisor

陳慧芬

Content Language

英文

Chinese Abstract

在此篇論文中,我們應用分批法來建立製程能力指標Cp的信賴區間,而品質特徵測量值服從某未知的自相關時間序列。製程能力指標在製造業被廣泛的運用,在評估量化製程績效上是個常見且易懂的表達方式。目前有很多製程能力指標的信賴區間文獻,但多假設品質特徵測量值是獨立且服從常態分配,但在實務上,這假設不見得成立,因此我們考慮具相關性的品質特徵測量值,且邊際分配可能不是常態分配,使得建立出來的信賴區間更有實務應用價值。 目前研究相關性資料的製程能力指標的文獻,多假設品質特徵測量值服從常態分配(或是近似常態分配),我們選擇其中二篇有提出Cp信賴區間估計法的文獻做比較,其中一篇是利用統計微分方法估計Cp估計量的期望值及變異數,以建立信賴區間;另一篇是假設製程資料只有前m個自相關係數不等於零,應用中央極限定理提出Cp估計量的期望值及變異數,並建立其信賴區間。這兩篇文獻都假設品質特徵值的邊際分配是常態。 本研究利用分批法來估計Cp估計量的變異數,進而提出建立信賴區間的方法。此法邏輯上簡單、不限於邊際分配為常態的假設,且稍加改變即可應用於建立其他製程能力指標,如Cpk、 Cpm等。我們利用三個時間序列來比較本法與上述兩文獻所提出的方法:AR(1), ARMA(1, 1)及ARTA(autoregressive to anything)過程。方法論的績效指標是信賴區間的覆蓋率及一半寬度,覆蓋率約接近指定的信賴水準越好,信賴區間的一半寬度越短越好。實驗結果顯示,分批法有朝設定的信賴度收歛的趨勢,且較其他兩法更具穩健性。

English Abstract

In this thesis, we apply batching method to construct the confidence interval for Cp when the quality characteristic measurements are autocorrelated. Process capability indices are widely used in the manufacturing industries and providing a common and easily understood language for quantifying the performance of a process. Process capability indices have received substantial research attention. Most research assumes that the quality characteristic measurements are independent and normally distributed. However, in practice, the assumptions may not be tenable. It would be more appropriate to assume that quality characteristic measurements are autocorrelated. In the research, we consider the capability index Cp for stationary time series processes. We apply the concept of batching method to construct the confidence interval of Cp and then compare with the other two methods. One uses the method of statistical differentials to obtain the approximate expectation and variance of the estimator Cbp, and then constructs the confidence interval. The other method assumes that only the first m observations have autocorrelations and applies the central limit theorem to show the expectation and variance of the estimator Cbp and then constructs the confidence interval. However, this two methods assume the quality characteristic measurements is normal distribution. We establish the 100(1− )% confidence interval for Cp, in which the variance of the Cp estimator is estimated based on the batching method. The method is easy to implement, simple in logic, and well performed. It can also be applied to other capability indices, like Cpk, Cpm, as long as we have a little change. We compare batching method and the two methods. The performance is compared with the coverage percentage. Batching method shows a convergence rate and it is more reliable and robust when we have large enough sample sizes.

Topic Category 工學院 > 工業工程研究所
工程學 > 工程學總論
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