近年來，品質在所多產品上扮演一個重要且必要的角色，而統計製程管制(SPC)為監控品質最重要的統計工具之一，因此SPC中的管制圖也被廣泛的應用在品質管制上。如果管制圖中的三個管制參數(抽樣的樣本數、抽樣間隔和管制界線係數)至少有一個在製程監視過程是變動的，此種管制圖便屬於動態管制圖的範疇。隨著電腦科技的進步，有越來越多的學者投入研究動態管制圖，並且發現動態管制圖大部分都表現的比其相對的靜態管制圖來的好。
本文中，我們使用CUSUM管制圖並使用貝氏(Bayesian)的方法去最小化每單位時間平均成本的動態抽樣策略，而我們所採取的動態抽樣策略是根據系統會變成管制外事前機率的大小來考慮下一時刻是否要進行抽樣。我們將會展示如何藉由考慮其修理費用、抽樣費用及品質的損失的費用去找到最佳的決策：「何時應該要繼續製程但不抽樣」、「何時該繼續製程且抽樣」以及「何時又該停止製程」。最後，我們將會舉一個例子說明如何使用我們所提出之方法。

Recently, quality plays an important and necessary role in many products. The most important statistical tool for quality control in manufacturing is the statistical process control (SPC), so control charts are used widely. A control chart is called dynamic if at least one of the three chart parameters, namely, sample size, sampling interval, and locations of control limits, are allowed to change in progress. Because the improvement in computers, more and more researchers study dynamic charts, and find they normally perform better than the corresponding static charts.
In this paper, we consider the sampling scheme for the cumulative sum control chart using a Bayesian approach in minimizing the average cost per unit time. It gives a dynamic system in which inspection frequency is allowed to vary according to the prior probability that the system will be out of control when producing the next item. We will show how to obtain the optimal solutions, in which one decides when to keep producing without inspection, when to keep producing with inspection, and when to stop the process by considering the trade-off between repair costs, inspection costs, and the quality cost. An example is given to illustrate the proposed procedure.

REFERENCES
Annadi, H. P., Keats, J. B., Runger, G. C., and Montgomery, D. C. (1995). An Adaptive Sample Size CUSUM Control Chart. International Journal of Production Research, 33, 1605-1616.
Bellman, R. (1957). Dynamic Programming. Princeton University Press,Princeton, New Jersey.
Bather, J. A. (1963). Control Charts and the Minimization of Costs. Journal of the Royal statistical Society –Series B, 25, 49-80.
Costa, A. F. B. (1994). Charts with Variable Sample Size. Journal of Quality Technology, 26, 155-163.
Costa, A. F. B. (1997). Charts with Variable Sample Size and Sampling Intervals. Journal of Quality Technology, 29, 197-204.
Costa, A. F. B. (1999a). Charts with Variable Parameters. Journal of Quality Technology, 31, 408-416.
Costa, A. F. B. (1999b). AATS for the Charts with Variable Parameters. Journal of Quality Technology, 31, 455-458.
Croasdale, P. (1974). Control Charts for a Double-Sampling Scheme Based on Average Production Run Lengths. International Journal of Production Research, 12, 585-592.
Daudin, J.J. (1992). Double-Sampling Charts. Journal of Quality Technology, 24, 78-87.
Das, T. K., Jain, V., and Gosavi, A. (1997). Economic Design of Double- Sampling- Interval Policies for Charts With and Without Run Rules. IIE Transactions, 29, 497-506.
Girshick, M. A. and Rubin, H. (1952). A Bayes Approach to a Quality Control Model. Ann. Math. Stat., 23,114-125.
Prabhu, S. S., Montgomery, D. C., and Runger, G. C. (1994). A Combined Adaptive Sample Size and Sampling Interval Control Scheme. Journal of Quality Technology, 26, 164-176.
Prabhu, S. S., Montgomery, D. C., and Runger, G. C. (1995). A Design Tool to Evaluate Average Time to Signal Properties of Adaptive charts. Journal of Quality Technology, 27, 74-83.
Prabhu, S. S., Runger, G. C., and Keats, J. B. (1993). An Adaptive Sample Size Chart. International Journal of Production Research, 31, 2895-2909.
Reynolds, M. R., Jr. (1995).Evaluating Properties of Variable Sampling Interval Control Charts. Sequential Analysis, 14, 59-97.
Reynolds, M. R., Jr., Amin, R. W., and Arnold, J. C. (1990). CUSUM Charts with Variable Sampling Intervals. Technometrics, 32, 371-384.
Reynolds, M. R., Jr., Amin, R. W., Arnold, J. C., and Nachlas, J. A. (1988). Charts with Variable Sampling Intervals. Technometrics, 30, 181-192.
Reynolds, M. R., Jr. and Arnold, J. C., (1989). Optimal One-Sided Shewhart Control Charts with Variable Sampling Intervals. Sequential Analysis, 8, 51-77.
Reynolds, M. R., Jr., Arnold, J. C., and Baik, J. W. (1996). Variable Sampling Interval Charts in the Presence of Correlation. Journal of Quality Technology, 28, 12-30.
Runger, G. C. and Montgomery, D. C. (1993). Adaptive Sampling Enhancements for Shewhart Control Charts. IIE Transactions, 25, 41-51.
Runger, G. C. and Pignatiello, J. J., Jr. (1991). Adaptive Sampling for Process Control. Journal of Quality Technology, 23, 135-155.
Tagaras, G. (1994). A Dynamic Programming Approach to the Economic Design of Charts. IIE Transactions, 26, 48-56.
Tagaras, G. (1996). Dynamic Control Charts for Finite Production Runs. European Journal of Operational Research, 91, 38-55.
Tagaras, G. (1998). A Survey of Recent Developments in the Design of Adaptive Control Charts. Journal of Quality Technology, 30, 212-231.
Taguchi, G. and Wu, Y. (1985). Introduction to Off-Line Quality Control. Central Japan Quality Control Association, Japan.
Taylor, H. M. (1965). Markovian Sequential Replacement Process. Ann. Math. Stat., 36, 1677-1694.
Taylor, H. M. (1967). Statistical Control of a Gaussian Process. Technometrics, 9 , 29-41.