基因演算法應用於管制圖經濟模式最佳參數設計之研究

The Application of Genetic Algorithm to the Economic Design of Control Charts

黃崑濱(Kun-Bin Haung)

指導教授 ： 鄭春生 ； 蕭育如

元智大學/工程學院/工業工程與管理學系/碩士(1997年)

摘要

在傳統上，管制圖之設計都只是考慮到統計層面，其注重於樣本大小的
選擇及管制界限，用來偵測製程是否落於管制界限中，然而都忽略了管
制圖的經濟層面，例如﹕消除可歸屬原因的成本、抽樣及檢驗成本、調
查管制外相關訊息成本、製程在管制中或管制外的利潤、產生不良品所
造成的成本損失 (不合格品遭顧客退回的損失) 等。根據經濟層面來設
計管制圖之步驟稱為管制圖之經濟設計。管制圖經濟模式之設計是指要
決定下列三個參數：(1) 抽樣樣本大小，(2)抽樣間隔，(3) 管制界限。

過去有關管制圖經濟模式之最佳參數設計之研究，由於牽涉太多數學公
式而須以近似方法求解。本研究主要的目的是要以基因演算法的求解觀
念，運用於管制圖經濟模式之最佳參數的求解，我們以田口方法找出基
因演算法中較佳參數水準的組合。本研究以 -R管制圖之設計及 管制圖
加入警告界限兩種模式來驗證。研究結果顯示基因演算法之求解品質與
傳統方法相似或可優於傳統方法。

關鍵字

管制圖經濟模式 ； 基因演算法 ； 田口方法

並列摘要

Traditionally, control charts have been designed with respect
to statistical criteria only. This usually involves selecting
the sample size and control limits such that the power of the
test to detect a particular shift in the quality characteristic
and the type I error probability are equal to specified values.

The design of a control chart has economic consequences in that
the costs of sampling and testing, costs associated with
investigating out-of-control signals and possibly correcting
assignable causes, and costs of allowing nonconforming units
to reach the consumer are all affected by the choice of the
control chart parameters.

This research applies the genetic algorithm to determining the
parameters in the economic design of control charts. Taguchi*s
design experiment is employed to determine some important
parameters of genetic algorithm. The performances of the
genetic algorithm are verified using the economic design of
x-bar-R control charts and x-bar control charts with warming
limits. The results show that the genetic algorithm performs
as well as or better than traditional methods.

並列關鍵字

economic of control charts ； genetic algorithm ； Taguchi*s design experiment

參考文獻

Arnold, B. F., and E. V. Collani, "Economic process control," Statistica Neerlandica, 41, 89-97(1987).

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

Chiu, W. K., and K. C. Cheung, "An economic study of -charts with warning limits," Journal of Quality Technology, 9 (4), 166-171 (1977).

Chung, K. J., "A simplified procedure for the economic design of charts," International Journal of Production Research, 28, 1239-1246 (1990).

Chung, K. J., "Economic designs of attribute control charts for multiple assignable causes," Optimization, 22, 775-786 (1991).