Burr分配於Cpk信賴區間之評估探討

A Study of Capability Interval for Cpk Capability Index Through Burr Distribution.

許力文(Li-Wen Hsu)

指導教授 ： 陳雲岫

元智大學/工程學院/工業工程與管理學系/碩士(2011年)

摘要

製程能力指標為製程品質管制主要的工具之一，大多數的論文都是在常態假設下去進行製程能力指標信賴區間之分析，鮮少針對非常態資料來作探討。
本研究主要是根據製程能力指標Cpk值，分別選定母體為常態或非常態時之母體平均數(μ)和母體標準差(σ)，將資料對應至Burr分配後，再經由兩種不同方式來求算出製程能力指標Cpk之(1-α)×100%信賴區間，利用製程能力指標Cpk信賴區間之覆蓋率、平均寬度與標準差來探討常態與非常態資料之製程能力指標Cpk信賴區間之差異，以及比較兩種求算信賴區間方法之成效。
研究結果顯示製程能力指標Cpk之高、中、低值對信賴區間之覆蓋率並無顯著影響。樣本數越多則製程能力指標Cpk信賴區間之覆蓋率越高，而信賴區間之平均寬度與標準差越小。本研究的計算信賴區間方法二在常態分配與非常態分配之資料所得到的覆蓋率皆高於計算方法一，但方法一之信賴區間平均寬度與標準差皆小於方法二。

關鍵字

製程能力指標 ； Burr分配

並列摘要

Process capability index (Cpk) is one of the tools in statistical process control to evaluate the process quality. The constructing of confidence interval of Cpk, usually, is assumed the normality assumption of the population. However non-normal data observed frequently in the real process. In this research, we study the performance of confidence interval of Cpk under a Burr distribution. First, we use a set of real data to fit a Burr distribution and obtain the estimates of parameters. Second, we use two different methods to compute confidence interval of Cpk by simulated data, and study Cpk the coverage, average width and standard deviation of the confidence interval of Cpk. The simulation results show that the value of Cpk has little affection larger samples sizes will result on the coverage rate. Also, smaller standard deviation of estimated Cpk, shorter average confidence interval width, and confidence interval coverage rate increase. The method two obtain the confidence interval coverage rate is higher than method one. But The method one result smaller standard deviation of estimated Cpk and shorter average confidence interval width.

並列關鍵字

Process capability index ； Burr distribution

參考文獻

1.Bissell, A . F., “How reliability is your capability index,” Applied Statistics, Vol. 39,No.3, pp. 331-341, 1990.

2.Burr, I. W., “Cumulative frequency functions,” Annals of Mathematical Statistics, Vol. 13, pp. 215-232, 1942.

3.Burr, I. W., “Parameters for a general system of distributions to match a grid of α3 and α4,” Communications in Statistics, 2, pp. 1-21, 1973.

4.Burr, I. W., Peter J. CislakSource, “On a general system of distributions: I. Its curve-shape characteristics; II. The sample median,” Journal of the American Statistical Association, Vol. 63, No. 322, pp. 627-635., 1968.

5.B. Abbasi, S. Z. Hosseinifard, M. Abdollahian, “On the estimating burr XII distribution parameters,” Seventh International Conference on Information Technology, 2010.