多重抽樣平均數管制圖的經濟性設計

An Economic Design of Multiple Sampling (average)X Charts

廖乃毅(Nai-Yi Liao) ； 李佩熹(Pei-Hsi Lee) ； 童超塵(Chau-Chen Torng)

《品質學報》 15卷4期 (2008/08) Pp. 311-319

摘要

雙次抽樣(平均值)(平均值)X管制圖（Double Sampling (平均值)X charts; DS管制圖）和三次抽樣(平均值)X管制圖（Triple Sampling (平均值)X charts; TS管制圖）統稱為多重抽樣(平均值)X管制圖（Multiple Sampling (平均值)X charts; MS管制圖），MS管制圖的發展能有效的提升製程監控能力，從統計設計觀點來看，TS管制圖在製程監控的成效優於DS管制圖。Duncan的經濟性模型常被用來決定管制圖的最佳設計，並可透過成本與其他管制圖比較製程監控的經濟效益。因此，本研究根據DS管制圖和TS管制圖的製程管制原理，修改Duncan的經濟性模型，並求解最佳的管制圖設計，從最後的成本分析發現，DS管制圖在製程平均數呈現小偏移時表現較TS管制圖佳，當平均數呈現大偏移時，TS管制圖反而比較好。

關鍵字

雙次抽樣平均數管制圖 ； 三次抽樣平均數管制圖 ； 管制圖的經濟性設計

並列摘要

Development of the double sampling (average)X chart (DS chart) and triple sampling (average)X chart (TS chart) can improve performance in process monitoring. Both charts are called as multiple sampling (average)X charts (MS charts). From a statistical viewpoint, TS charts have better performance than DS charts. In order to compare their designs from an economic perspective, we apply Duncan's economical model to control procedures of DS charts and TS charts and then solve their optimal design parameters. Result shows that DS charts have better economic effect than TS charts in small shift process, but the TS charts are more economical than DS charts when the process mean occurs large shift.

並列關鍵字

double sampling (average)X chart ； triple sampling (average)X chart ； economic design of control chart

參考文獻

Chen, Y. K.(2004).Economic design of X control charts for non-normal data using variable sampling policy.International Journal of Production Economics.92(1),61-74.

Chou, C. Y.,Chen, C. H.,Liu, H. R.(2001).Economic design of (average)X charts for non-normally correlated data.International Journal of Production Research.39(9),1931-1941.

Costa, A. F. B.(1994).(average)X charts with variable sample size.Journal of Quality Technology.26(3),155-163.

Costa, A. F. B.(1997).(average)X charts with variable sample size and sampling intervals.Journal of Quality Technology.29(2),197-204.

Daudin, J. J.(1992).Double sampling (average)X charts.Journal of Quality Technology.24(2),78-87.