晶圓造流程中設立許多量測站以監控各產品參數是否符合規格，然而受限於檢測機台數量有限而產品需求增加，如何合理降低抽樣頻率且能維持品質，乃是一重要的議題。探討降低抽樣樣本數或抽樣頻率的文獻雖多，但多由統計角度制訂抽樣決策，並未將成本因素納入。本研究目的即為建立成本導向的抽樣頻率統計決策架構，經由貝式決策分析建立對總期望成本函數，對於品質水準穩定之產品，在品質成本與抽樣成本間相互權衡，以最小總期望損失決策目標，以求得適當之抽樣頻率。實證中則將抽樣頻率統計決策架構應用於晶圓製造廠中，對單一量測站依其良率優劣，決定抽樣頻率，另一方面則建立由歷史資料推論貝式決策所需相關資訊的方法。實證結果顯示產品良率為影響抽樣頻率決策最重要的因素，並提出量率穩定與否亦為抽樣頻率決策的重要依據。因此建議未來研究方向需納入系統平均可運作時間(mean time between failure)於決策架構中。

A number of inspection and measurement stations are set in the fabrication process to assure that the quality of wafer meets the specific requirements. Due to the limitation of inspection machine capacities, reducing sampling frequency to save capacity under the acceptable quality level becomes important. However, reaserchs about sampling plan usually focus on statistical aspect rather than economic aspect. In this study, we developed a cost-based heuristic for statistically determining the sampling frequency in wafer fab based on the Baye's decision analysis. The expected loss funciton is derived by integrating the loss of inspected and the loss of non-inspected lots. We aimed to determine the optimal sampling frequency that minimize the expected loss by trading-off between sampling costs and the quality loss. An empirical study is practiced with data from a wafer fab to validate the strucure and find out the crucial issue in reducing sampling frequency decision. As the resaults, we concluded that failure probability of population is the pivotal factor in sampling frequency decision. However,MTBF, the length between to assignable cause, is another keypoint. Thius, we suggested that further study should develop the distribution of MTBF from existing data in fabs or develop the method to monitor random cause and assignable cause separately.

[1] Barbara M. J. and Paul V. D., "of clinical efficacy-Cost-effectiveness calculations in the Diagnosis and treatment of hypertensive renovascular disease " The New England Journal of Medicine, vol 293, no. 5, p.216-221 (1975).[2] Duncan, A. J., "economic design of X-bar charts used to maintain current control of a process " American Statistical Association Journal, Jun, p.228-241 (1956).[3] Duncan N., and Lewicki A. M., "do we gain from the sixth stool guaiac?" The New England Journal of Medicine, vol. 293, no. 5, p.226-228 (1975).[4] Fink R. L., and Margavio T. M., "models for single sample acceptance sampling plans, no Inspection, and 100 percent inspection" Decision Sciences, vol. 25, no. 4, p625-645 .[5] Guenther W. C., Sampling Inspection in Statistical Quality Control, Macmillan Publishing Company, New York (1977).[6] Hald A., "s single sampling attribute plans for continuous prior distributions" Technometrics, vol. 10, no. 4, p.667-683 (1968).[7] Hsu I. S., "cost model for skip-lot non-destructive sampling" IEEE Transactions on Reliability, vol. R-28, no. 4, p.289-291 (1979).[8] Kane V. E., "capability indices" Journal of Quality Technology, vol. 18, no. 1, p.41-51 (1986).[9] Kushler R. H., and Hurley P., "bounds for capability indices" Journal of Quality Technology, vol. 24, no. 4, p.188-195 (1992).[10] Liebesman B. S., and Saperstein B., "Proposed Attribute Skip-Lot Sampling Program" Journal of Quality Technology, vol. 15, no. 3, p.130-140 (1983).[11] Lorenzen T. J. and Vance L. C., "economic design of control charts: a unified approach" Technometrics, vol. 28, no. 1, p.3-10 (1986).[12] Montgomery, D. C., Introduction to Statistical Quality Control, 2nd ed., John Wiley, New York (1991).[13] Norman Gaither, Production and Operating Management, 7-th ed., Wadsworth publishing company (1996).[14] Nurani R. K., Akella R., and Strojwas A. J., "line defect sampling methodology in yield management: an integrated framework" IEEE Transactions on Semiconductor Manufacturing, vol. 9, no. 4, p.506-515 (1996).[15] Perry R. L., "lot sampling plans" Journal of Quality Technology, vol. 5, no. 3, p.123-130 (1973).[16] Phelps R. I., "lot destructive sampling with Baye's inference" IEEE Transactions on Reliability, vol. R-31, no. 2, p. 191-193 (1982).[17] Sainfort F., "generalized ROC analysis" Evaluation of Medical Technologies, vol. 11, No. 3, p.208-220 (1993).[18] Simon French, Decision theory - an introduction to the mathematics of rationality, Ellis Horwood Limited (1993).[19] Wang Z, Gielen G., and Sansen W., "Fault Detection and the Selection of Measurements for Analog Integrated Circuits" IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, vol. 17, no. 9, p.862-872 (1998).