監控製程的變異對於確保品質的一致是非常重要的。在很多製程上，尤其是半導體生產製程中，製程的總變異通常是由很多原因造成的，因此僅使用一簡單統計量來衡量整體之製程變異常常無法確認變異的來源。
然而，若製程之總變異可分解成由不同的特殊原因所造成的變異數成份(Variance Components)，則管制已分解的變異數成份比管制整體的變異來的更為適當與有效率，因為造成變異的原因不同，不應該放在一起計算，如此將無法知道究竟是哪個主因造成變異的，故應分開來看。
在Nelson(1995)中所提出的，巢式設計(Nested Design)下其變異數經過特殊轉換後，若會服從F分配，則可獲得該變異數之信賴區間的作法，故本研究主要運用此概念探討在單因子隨機效應模型(One-Factor Random Effects Model)、二個隨機因子模型(Two-Factor Random Effects Model)、二因子混合效應模型(Two-Factor Mixed Effects Model)以及巢式與分裂區集模型(Nested and Split-Plot Design Model)下之變異數成份的信賴區間為何以達到管制製程變異的目的。

Monitoring the variances of processes is important to ensure the consistence of quality. In many processes, especially for those in the semiconductor industry, several factors would lead to the variance of overall process. Thus, it is difficult to identify the origin of variances by using one simple statistics to measure the overall process variance.
However, it is more effective and more appropriate to monitor the decomposed variance components rather than the overall variance, if the overall process variance can be decomposed into variance components with associated special causes. Since the causes of variance are different, we cannot calculate the variances as a whole; otherwise, we cannot identify the major cause contributing to the variance, so we should do separately.
Nelson (1995) addressed that with Nested Design, if the variance follows F- statistics after being specially transformed, we can get the confidence intervals of variance. Hence, this study mainly applies this idea to discuss how the confidence interval of variance components with One-Factor Random Effects Model, Two-Factor Random Effects Model, Two-Factor Mixed Effects Mode and Nested and Split-Plot Design Model can reach the goal of controlling the variance of process.

吳宗正 (1994)， 變異數分析理論與應用，台北市華泰書局
Badgwell, T. A., Edgar, T. F., Trachtenberg, l. and Elliott J. K. (1992), “Experimental Verification of a Fundamental Model for Multiwafer Low-pressure Chemical Vapor Deposition of Polysilicon,” Journal of the Electrochemical Society, 139, pp.524-532.
Burdick, R. K. and Graybill, F. A. (1992), Confidence Intervals on Variance Components, Marcel Dekker Inc., New York.
Chang, T. C. and Gan, F. F. (1995), “A Cumulative Sum Control Chart for Monitoring Process Variance,” Journal of Quality Technology, 27, pp. 109-119.
Chang, T. C. and Gan, F. F. (2004), “Shewhart Charts for Monitoring the Variance Components,” Journal of Quality Technology, 36, pp. 293-308.
Davies, O. L. and Goldsmith, P. L. (1980), Statistical Methods in Research and Production, Longman Group Limited, New York, NY, pp.166-167.
Duncan, A. J. (1986), Quality Control and Industrial Statistic, 5th ed. Homewood, IL: R. D. Irwin.
Kim, K. S. and Yum, B. J. (1999), “Controls Charts for Random and Fixed Wafer Location and Measurement Positions,” IEEE Transaction on Semiconductor Manufacturing, 12, pp. 214-228.
Lowry, C. A., Champ, C. W. and Woodall, W. H. (1995), “The Performance of Control Charts for Monitoring Process Variation,” Communications in Statistics- Simulation and Computation, 24, pp.409-437.
MacGregor, J. F. and Harris, T. J. (1993), “The Exponentially Weighted Moving Variance,” Journal of Quality Technology, 25, pp. 106-118.
Montgomery, D. C. (2001), Introduction to Statistical Quality Control, 4th ed. John Wiley & Sons, New York.
Montgomery, D. C. (2005), Design and Analysis of Experiments, 6th ed. John Wiley & Sons, New York.
Nelson, L. S. (1995), “Using Nested Design: II. Confidence Limits for Standard Deviations,” Journal of Quality Technology, 27, pp. 265-267.
Page, E. S. (1954), “Continuous Inspection Schemes,” Biometrics, 41, pp.100-115.
Reynolds, M. R. Jr. and Stoumbos, Z. G. (2004), “Control Charts and the Efficient Allocation of Sampling Resources,” Technometrics, 46, pp. 200-214.
Roberts, S. W. (1959), “Control Chart Tests Based on Geometric Moving Averages,” Technometrics , 1, pp. 239-250.
Houf, R. E. and Berman, D. B. (1988), “Statistical Analysis of Power Module Thermal Test Equipment Performance,” IEEE Transaction on Components, Hybrids, and Manufacturing Technology, 11, pp. 516-520.
Roes, K. C. and Does, R. J. M. (1995), “Shewhart-Type Charts in Nonstandard Situations,” Technometrics, 37, pp. 15-40.
Scheffe, H. (1959), The Analysis of Variance, Wiley New York.
Shewhart, W. A. (1931), Economic Control of Quality of Manufactured Product, Princeton, NJ: Van Nostrand Reinhold Co., (Republished in 1981 by the American Society for Quality Control, Milwaukee, WI).
Woodall, W. H. and Thomas, E. V. (1995), “Statistical Process Control with Several Components of Common Cause Variability,” IEEE Transactions, 27, pp. 757-764.
Yashchin, E. (1994), “Monitoring Variance Components,” Technometrics, 36, pp. 379-393.