Xbar與R管制圖的聯合經濟統計設計應用在自相關資料上

The Joint Economic Statistical Design of Xbar and R Control Charts for Autocorrelated Data

10.6840/cycu200700506

柯佳甫

韋伯分配 ； 窮舉法 ； 自相關的資料 ； X 與R 管制圖 ； 經濟統計性設計 ； Autocorrelated data ； ‾X and R control charts ； Weibull distribution ； Economic-statistical design ； Grid search method

中原大學工業工程研究所學位論文

2007年

碩士

陳慧芬

英文

本論文研究探討在Costa以及Chen他們架構下的Xbar 與R管制圖的聯合經濟統 計設計。根據成本模型，我們假設品質特性測量值是服從自相關的時間序列模式 且系統在製程管制內時間服從韋伯分配。當我們設計一個管制圖時，必須決定四 個設計參數：樣本數n、抽樣間隔時間 h、X 管制圖上下限的距離因素 k1及R管 制圖上下限的距離因素 k2。 然而現在有非常多的文獻在探討資料是服從獨立性假設下之經濟統計設計 管制圖與自相關性資料管制圖，但是卻很少有文獻是研究上述兩種概念的結合。 因此，本論文探討上述兩種概念的結合情形。 在本論文中，我們是使用蒙地卡羅模擬在窮舉法下去找尋最佳的設計參數使 得每小時的期望成本為最低。我們同時也去做關於自相關性、不同程度的期望值 和變異數偏移及不同的韋伯參數下的敏感度分析。根據實驗結果，當自相關性呈 現正相關性的增加時，我們發現樣本數n、抽樣間隔時間h以及每小時的期望成本 會增加，但是管制上下限的距離因素k1及k2降低了。當平均數位移增加時，樣本 數n和抽樣間隔時間h及管制上下限的距離因素k2降低，管制上下限的距離因素k1 及每小時的期望成本會增加。當變異數位移增加時，樣本數n和抽樣間隔時間h 及管制上下限的距離因素k1降低，管制上下限的距離因素k2及每小時的期望成本 會增加。當韋伯比例參數λ1增加時，n、h及k1降低， k2及每小時的期望成本增加。 但是在平均數與變異數偏移量為(1,2)時， k1及每小時的期望成本降低，n、h及 k2增加。

In this thesis, we consider the joint economic–statistical design ‾X and R control charts which is based on the framework of the Costa and Chen et al. According to the cost model we assume that the quality characteristic are autocorrelated and the in–control time follows the Weibull distribution. There are four design parameters : the sample size n, sampling interval h and the control limit factors k1 and k2 are determined to design control charts ‾X and R, respectively. At present, most literatures research either the economic–statistical design in which the data is satisfying independent assumption or the control chart in which the data is satisfying autocorrelated. But there are a few literatures in researching of the combination of these two concepts. Consequently, we investigate these combined themes in this thesis. In this thesis, we use the grid search method by Monte Cario simulation to find the optimal design parameters to minimize the expected cost per hour. We also perform the sensitivity analysis to study the effects of autocorrelation, the amount of shift in mean and variance and the Weibull scale parameters. As the result, when the autocorrelation increases positively and then we would find that the sample size n and the sampling interval h increase, but control limit factors k1 and k2 decrease. The expected hourly cost increases by the autocorrelation either positively and nagetively increase. When the amount shift of mean increases, n, h and k2 decrease and k1 and the expected hourly cost increase. When the amount shift of variance increases, n, h and k1 decrease and k2 and the expected hourly cost increase. When 1 increase, n, h and k1 decrease and k2 and the expected hourly cost increase, but in the shift of the combination ( , )=(1,2), k1 decrease and n, h ,k2 and the expected hourly cost increase.

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