Economic Design of Control Charts with Burr Distribution for Non-Normal Data under Weibull Failure Mechanism

應用Burr分配處理非常態資料之x bar管制圖經濟性設計於韋伯失效機制下

陳飛龍(Fei-Long Chen) ； 葉卓華(Cho-Hua Yeh)

《工業工程學刊》 23卷3期 (2006/05) Pp. 200-206

https://doi.org/10.29977/JCIIE.200605.0003

摘要

當x bar管制圖被應用去監控製程時，有三項參數應該被定義，包括樣本大小、抽樣間隔與管制界限。在1988年，由Banerjee and Rahim提出，利用變動抽樣間隔相對於固定抽樣間隔方式且在具有韋伯製程失效機制及遞增的危險率之成本模型。然而，當設計管制圖時，經常假設樣本組內的樣本數具有常態分配。這種假設在理論上並不是具有穩定的立場。本篇論文將對於非常態資料在韋伯失效機制下建立x bar管制圖的經濟性設計，最後並以一個Banerjee and Rahim在1988年所使用的例子，說明建構模型的程序。

關鍵字

管制圖 ； 變動抽樣 ； 非常態

並列摘要

When the x bar chart is applied to monitor a manufacturing process, three parameters should be determined: sample size, sampling interval between successive samples, and the control limits for the chart. In 1988, Banerjee and Rahim presented the cost model that used variable sampling intervals as opposed to sampling intervals of fixed length under the process-failure mechanism which follows a Weibull model or some other models having an increased hazard rate. However, when designing control charts, one usually assumes that the measurements in the subgroup are normally distributed. This assumption may not be tenable. This paper develops the economic design of x bar control charts for non-normal data under Weibull shock models. An example is presented to illustrate the solution procedure.

並列關鍵字

control chart ； variable sampling ； non-normal data

參考文獻

Banerjee, P. K,Rahim, M.A.(1988).Economic design of X control charts under weibull shock models.Technometrics.30,407-414.

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Duncan, A. J.(1956).The economic design of X charts used to maintain current control of a process.Journal of the American Statistical Association.51,228-242.

Rahim, M. A.(1985).Economic model of X chart under non-normally and measurement errors.Computers and Operations Research.(Computers and Operations Research).