傳統統計製程管制圖均在製程數據服從常態分配且符合獨立性的假設下發展而成。然而，在現今之科技發展迅速的帶動下，許多製程已採用自動化之生產及檢驗方式，但此種方式將導致製程數據間具有高度之自我相關性，若仍以傳統管制圖來監控製程將造成錯誤警報明顯增加。

過去之研究顯示，偵測自我相關製程中之偏移變異，應用殘差管制法具有較佳之效益，但預測模型之參數估計誤差將明顯增加其判斷誤差。而在類神經網路之管制方法上，大多數的學者所提出之方法只能處理單一自我相關係數下之製程，而實際製程之自我相關係數將隨時間或批量之差異而改變。因此，針對不同之自我相關係數下的製程數據，就必須有多個類神經網路才能達到全面性之監控效益。

為了有效改善過去管制方法之缺點，並能正確且快速偵測製程之偏移狀況，本研究以多個不同自我相關係數所獲得之數據，來建構以類神經網路為基之管制法。本研究亦利用類神經網路發展一估計偏移量之系統，當所提管制法偵測出製程發生偏移時，可進一步估計其偏移量，藉以提供資訊給工程人員立即調整製程參數，並使製程能快速地回復到管制狀態內。本研究中，以平均連串長度以及平均絕對誤差百分比作為評估之績效指標。研究顯示，類神經網路管制法之績效較傳統EWMA管制法佳，另外，再以模擬產生之製程數據，驗證本研究所發展的類神經網路管制法確實有實務應用之可行性。

本研究所提出之類神經網路管制法具有三項優良特性，第一、無論製程處於何種程度之自我相關係數下，都能具有良好的偵測效益；第二、所提出之管制程序可有效避免殘差管制法中預測模型之參數估計誤差之缺點。第三、如同傳統管制法，本研究所提出之類神經網路管制法對於平均值向上及向下偏移均具有相同之偵測能力。

In the standard applications of statistical process control, a state of statistical control is identified with a process generating independent and identically distributed random variables. In fact, the assumption of uncorrelated or independent observations is not even approximately satisfied in some manufacturing processes.

A scheme of neural network is based on a function of multiple correlation coefficients instead of single correlation coefficient on traditional control charts. They are used to eliminate disadvantages of control charts and detect the process mean shift quickly and correctly.

The main idea of neural network-based approach is to monitor the process mean shifts and detect process mean shifts and estimate the magnitude of shifts. We use the back-propagation neural network to solve these problems. A process control method will be more effective if the adjusted magnitude can be estimated correctly in this research of process mean changed.

The performance of neural networks are evaluated by the average run lengths (ARL) and mean absolute percent errors (MAPE) using simulation. From simulation data of this model and developed results, the neural network method strongly outperforms EWMA charts and can be wildly adapted to many production processes.

In this study, a neural network-based control method offers three main advantages. First, this method offers good detecting ability for most and most of the processes under any level of autocorrelation coefficient. Second, the proposed control procedures effectively eliminate errors and disadvantages of parameter estimating on residual control chart. Last, neural network control method is capable of detecting process of mean upwards and downward shift as well as traditional control charts.

目錄

摘要 i
英文摘要 iii
誌謝 v
目錄 vi
表目錄 viii
圖目錄 x

一、緒論 1

1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究範圍 2
1.4 研究方法與步驟 3
1.5 論文架構 4

二、文獻探討 6

2.1 傳統統計製程管制法 6
2.2 時間序列模式 8
2.3 自我相關之統計製程管制法 10
2.4 類神經網路在製程管制上之應用 13

三、研究方法 17
3.1 倒傳遞網路 17
3.2 偵測自我相關製程之類神經網路 20
3.2.1 訓練樣本 20
3.2.2 類神經網路之架構 21
3.2.3 訓練樣本的參數組合與產生 22
3.2.4 類神經網路之訓練 25

四、類神經網路之效益評估 27

4.1 評估方法 27
4.2 評估指標 27
4.3 偵測效益之評估結果與比較 29
4.3.1 平均值變化之偵測效益 30
4.3.2 估計平均值偏移量之效益 34
4.4 利用實驗設計給定網路參數 38
4.5 數值範例 44

五、結論 68

參考文獻
1.Adams, B. M., Woodall, W. H. and Superville, C. R., “Discussion,” Technometrics, 36, 19-22 (1994).
2.Alwan, L. C. and Roberts, H. V. “ Time-series modeling for statistical process control,” Journal of Business and Economic Statistics, 6, 87-95 (1988).
3.Box, G.. E. P., Jenkins, G.. M. and MacGregor, J. F.“Some recent advance in forecasting and control, Part II,” Journal of the Royal Statistical Society,Ser.C,23, 158-179 (1974).
4.Chang, S. I., and Aw, C. A. “A neural fuzzy control chart for detection and classify process mean shifts,” International Journal of Production Research, 34, 2265-2278 (1996).
5.Cheng, C. S., “A multi-layer neural network model for detecting changes in the process mean,” Computers and Industrial Engineering, 28, 51-61 (1995).
6.Chiu, C. C., Chen, M. K. and Lee, K. M. “Shifts recognition in correlated process data using a neural network,” International Journal of Systems Science, 32, 137-143 (2001).
7.Cook, D. F., and Chiu, C. C. “Using radial basis function neural networks to recognize shifts in correlated manufacturing process parameters,” IIE Transactions, 30, 227-234 (1998).
8.Cook, D. F., Zobel, C. W. and Nottingam, Q. J. “Utilization of neural networks for the recognition of variance shifts in correlated manufacturing process parameters,” International Journal of Production Research, 39, 17, 3881-3887 (2001).
9.Duncan, A. J., Quality Control and Industrial Statistics, 5, Irwin Book Company, Illinois (1986).
10.Grant, E. L. and Leavenworth., R. S. Statistical Quility Control, McGraw-Hill Book Co., New York (1988).
11.Guo, Y. and Dooley, K. J. “Distinguishing between mean, variance and autocorrelation changes in statistical quality control,” International Journal of Production Research, 33, 497-510 (1995).
12.Harris, T. J., and Ross, W. H. “Statistical process control procedures for correlated observations,” The Canadian Journal of Chemical Engineering, 69, 48-57 (1991).
13.Hush, D. R., Salas, J. M. and Horne, B. G. “Error surfaces for multi-layer perceptrons,” IEEE Transactions on System, Man and Cybernetics, 22, 2 (1992).
14.Hush, D. R. and Horne, B. G. “Progress in supervised neural networks,” IEEE Signal Processing Magazine, January, 8-39 (1993).
15.Hwarng, H. B., and Hubele, N. F. “Back-propagation pattern recognizers for control chart: methodology and performance,” Computers and Industrial Engineering, 24, 219-235 (1993a).
16.Hwarng, H. B., and Hubele, N. F. “ control chart pattern identification through efficient off-line neural network training,” IIE Transactions, 25, 27-40 (1993b).
17.Hwarng, H. B., “Detecting process mean shift in the presence of autocorrelation: a neural-network based monitoring scheme,” International Journal of Production Research, 42, 573-595 (2004).
18.Johnson, R. A. and Bagshaw, M. “The effect of serial correlation on performance of CUSUM tests,” Technometrics, 16, 103-112 (1974).
19.Johnson, R. A. and Bagshaw, M. Continous univariate distribution, John Wiley&Sons, New York (1994).
20.Lin, W. W. and Adams, B. M. “Combined control charts for forecast-based monitoring schemes,” Journal of Quality Technology, 28, 289-301 (1996).
21.Lucas, J. M. and Crosier, R. B. “Fast intitial response for CUSUM quility-control schemes: give your CUSUM a head start,” Technometrics, 24, 199-205 (1982).
22.Lu, C. W. and Reynolds, M. R. “Control charts for monitoring the mean and variance of autocorrelated processes,” Journal of Quality Technology, 31, 259-274 (1999).
23.Lu, C. W. and Reynolds, M. R. “Cusum charts for monitoring an autocorrelated process,” Journal of Quality Technology, 33, 316-334 (2001).
24.Lucas, J. M., “Combined Shewhart-CUSUM quality control schemes,” Journal of Quality Technology, 14, 51-59 (1982).
25.Montgomery, D. C., Introduction to Statistical Quality Control, Wiley, New York (1991).
26.Montgomery, D. C., and Mastrangelo, C. M. “Some statistical process control methods for auto-correlated data,” Journal of Quality Technology, 23, 3, 179-193 (1991).
27.Page, E. S., “Continuous inspection schemes,” Biometrika, 41, 100-115 (1954).
28.Pugh, G. A., “Synthetic neural networks for process control,” Computers and Industrial Engineering, 17, 24-26 (1989).
29.Pugh, G. A., “A comparison of neural networks to SPC charts,” Computers and Industrial Engineering, 21, 253-255 (1991).
30.Roberts, S. W., “Control chart tests based on geometric moving average,” Technometrics, 1, 239-250(1959).
31.Vasilopous, A. V. and Stamboulis, A. P. “Modification of control chart limits in the presence of data correlation,” Journal of Quality Technology, 10, 1, 20-30 (1978).
32.Wang, T. Y. and Chen, L. H. “Mean shifts detection and classification in multivariate process: a neural-fuzzy approach” Journal of Intelligent Manufacturing, 13, 211-221 (2002).
33.Wardell, D. G., Moskowitz, H. and Plante, R. D. “Control charts in the presence of data correlation,” Management Science, 38, 1084-1105 (1992).
34.Wardell, D. G., Moskowitz, H. and Plante, R. D. “Run-length distributions of special-cause control charts for correlated processes,” Technometrics, 36, 3-7 (1994).
35.Wardell, D. G., Moskowitz, H. and Plante, R. D. “Run-length distributions of residual control charts for correlated processes,” Journal of Quality Technology, 26, 308-317 (1994).
36.Western Electric Company, Statistical Quality Control Handbook, Western Electric Co. Inc., Indianapolis, Indiana (1958).
37.Zhang, N. F., “Detection capability of residual control chart for stationary process data,” Journal of Applied Statistics, 24, 475-492 (1997).
38.Zhang, N. F., “A statistical control chart for stationary process data,” Technometrics, 40, 24-38 (1998).
39.吳聰宏，「類神經網路應用在品質管制中相關性製程數據之管制」，元智大學工業工程研究所碩士論文，1994。
40.許玉潔，「一個新自相關性製程監控方法之研究」，交通大學統計研究所碩士論文，2001。
41.鄭春生、鄭靜彥，「以類神經網路辨識製程個別值數據之平均值、變異數及相關性的變化」，品質學報，6，29-43 (1999)。
42.萬維君，「應用類神經網路於製程平均值變化之偵測及參數之估計」，元智大學工業工程研究所碩士論文，2001。