本文提出一個新型態的貨批檢驗機制，整合指數加權移動平均(Exponentially Weighted Moving Average, EWMA)法與製程能力指標Cpk。製造業廠商時常透過製程能力指標來評估品質績效以及評選供應商。文獻中基於製程能力指標Cpk的單次驗收計畫已經被提出來，雖然操作簡單但其只考量當前貨批品質水準，而忽略掉先前貨批的檢測結果，無法有效率地判斷貨批品質。本文提出的計畫透過EWMA統計量可以同時考慮當期樣本的品質表現以及前期樣本的表現，以期能有效地判定製造過程產出品質水準是否符合要求。
本文提出之貨批檢驗機制主要針對服從常態分配且具雙邊規格界限之品質特性。傳統分析方法大多假設樣本來自獨立過程，然而連續製造所產生的資料量可能具有相關性或是自我相關，故若把具自我相關性的樣本當作來自獨立過程的樣本可能會誤導分析結果。因此，本文除了提出針對獨立性資料，對於資料具自我相關性之情形也提出修正的貨批品質判定機制。
檢驗機制需透過統計準則以及品質表現來決定所需樣本數以及接受或拒絕該貨批的基準。機制的建立不僅要最小化買賣雙方的風險，還要考慮到抽樣檢測的經濟性，本檢驗機制所需的參數設定可以透過建立最佳化模型求得，目標函數為最小化所需的平均樣本數，限制式為保障生產者以及消費者所能承擔的風險。經比較結果顯示，所提出的貨批品質判定機制在相同的品質水準及風險要求下，可提供較經濟的貨批驗收判定結果，最後，除了將檢驗所需之樣本數及判定標準整理成表格外，也透過案例分析來說明所提出機制的操作流程。

In this thesis, a new variables quality inspection scheme based on the process capability index Cpk using the exponentially weighted moving average (EWMA) statistic is developed. Process capability indices are widely used in the manufacturing industries for process performance assessment and supplier selection. The single sampling plan based on the index Cpk has been proposed in past literature. Although single sampling schemes are easy to be implemented, they only consider the current lot and overlook the past information. This proposed inspection scheme considers the quality of the current lot as well as the proceeding lots through the EWMA statistics. The EWMA statistic is the weighted average of all past and current sample information and has been applied for quality control in detecting small shifts.
The proposed inspection scheme assumes that the quality characteristic follows the normal distribution and has two-sided specification limits. Traditional methods assume the data is from independent process. However, it is viewed as a common case that the autocorrelated observations are generated. Process data in continuous manufacturing may be correlated or self-dependent. It may mislead the results through applying the basic capability indices to autocorrelated processes and treating them as independent processes. Thus, we not only propose an inspection scheme for independent data but also develop an inspection scheme for autocorrelated data.
Inspection schemes use statistical principles to determine the sample size and the criteria for accepting or rejecting a lot based on the quality of a sample. The construction of an inspection scheme should not only minimize the risks involved in the sampling procedure itself but also be economical for the inspection for the products. The scheme parameters are determined by minimizing the sample number required for inspection with two constraints specified by the producer and the consumer. A comparative study is conducted to examine the performance of the proposed inspection scheme and the existing sampling plans. The proposed inspection scheme can be adopted to determine whether the process performance meets the yield standards and leads to a reliable decision. An illustrative example is also provided to demonstrate the operating procedure of applying the proposed scheme.

摘要 I
ABSTRACT II
TABLE OF CONTENTS IV
LIST OF TABLES VI
LIST OF FIGURES VIII
CHAPTER1. INTRODUCTION 1
1.1. RESEARCH BACKGROUND AND MOTIVATION 1
1.2. RESEARCH PURPOSE 4
1.3. RESEARCH ASSUMPTIONS AND LIMITATIONS 5
1.4. RESEARCH STRUCTURE 6
CHAPTER2. LITERATURE REVIEW 8
2.1. ACCEPTANCE SAMPLING PLANS 8
2.2. PROCESS CAPABILITY ANALYSIS 10
2.3. EXPONENTIALLY WEIGHTED MOVING AVERAGE STATISTIC 14
2.4. PROCESS CAPABILITY ANALYSIS WITH AUTOCORRELATED DATA 17
CHAPTER3. AN EWMA-BASED QUALITY INSPECTION SCHEME FOR INDEPENDENT DATA 22
3.1. SCHEME DESIGN AND OPERATING PROCEDURES 22
3.2. ACCEPTANCE AND REJECTION CRITERIA 24
3.3. SCHEME PARAMETERS AND MODEL CONSTRUCTION 25
3.4. ANALYSIS AND APPLICATION 26
CHAPTER4. AN EWMA-BASED QUALITY INSPECTION SCHEME FOR AUTOCORRELATED DATA 32
4.1. INDEX FOR DATA FROM AN MA(1) PROCESS 32
4.2. INDEX FOR DATA FROM AN AR(1) PROCESS 33
4.3. SCHEME PARAMETERS AND MODEL CONSTRUCTION 33
4.3.1. For MA(1) Process 33
4.3.2. For AR(1) Process 35
4.4. ANALYSIS AND APPLICATION 36
CHAPTER5. ANALYSIS AND DISCUSSIONS 51
5.1. SAMPLE SIZE COMPARISON 51
5.2. SMOOTHING FACTOR SELECTION 53
5.3. AN ILLUSTRATIVE EXAMPLE 53
CHAPTER6. CONCLUSIONS AND FUTURE WORK 59
6.1. CONCLUSIONS 59
6.2. FUTURE WORK 60
REFERENCES 62

1. Aslam, M., Azam, M., and Jun, C. H. (2015) A New Lot Inspection Procedure Based on Exponentially Weighted Moving Average, International Journal of Systems Science, 46(8), 1392-1400.
2. Bissell, A. F. (1990) How Reliable is Your Capability Index?, Journal of the Royal Statistical Society. Series C (Applied Statistics), 39(3), 331-340.
3. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (2008) Time Series Analysis: Forcasting and Control, (4th ed.), Wiley.
4. Boyles, R. A. (1991) The Taguchi Capability Index, Journal of Quality Technology, 23(1), 17-26.
5. Chou, Y. M., Owen, D. B., and Borego, S. A. (1990) Lower Confidence Limits on Process Capability Indices, Journal of Quality Technology, 22(3), 223-229.
6. Dodge, H. F. and Romig, H. G. (1929) A Method of Sampling Inspection, The Bell System Technical Journal, 8(10), 613–631.
7. Duncan, A. J. (1986) Quality Control and Industrial Statistics, (5th ed.), Irwin.
8. Franklin, L. A. and Wasserman, G. S. (1992) a. A Note on the Conservative Nature of the Tables of Lower Confidence Limits for Cpk, with a Suggested Correction, Communications in Statistics:Simulation and Computation, 21(4), 1165-1169.
9. Franklin, L. A. and Wasserman, G. S. (1992) b. Bootstrap Lower Confidence Limits for Capability Indices, Journal of Quality Technology, 24, 196-210.
10. Hunter, J. S. (1989) A Point Plot Equivalent to Shewhart Chart with Western Electric Rules, Quality Engineering, 2, 13-19.
11. Kalgonda, A. A., Koshti V. V., and Ashokan, K. V. (2011) Exponentially Weighted Moving Average Control Chart, Asian Journal of Management Research, 2(1), 253-263.
12. Kotz, S. and Lovelace, C. R. (1998) Process Capability Indices in Theory and Practice, (1st ed.), Hodder Education Publishers.
13. Kushler, R. and Hurley, P. (1992) Confidence Bounds for Capability Indices, Journal of Quality Technology, 24(4), 188-195.
14. Lucas, J. M. and Saccucci, M. S. (1990) Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements, Technometrics, 32(1), 1-29.
15. Lundkvist, P., Vännman, K. and Kulchci, M. (2012) A Comparison of Decision Methods for Cpk When Data are Autocorrelated, Quality Engineering, 24(4), 460-472.
16. Kalwani, M. U. and Narayandas, N. (1995) Long-Term Manufacturer-Supplier Relationships: Do They Pay off for Supplier Firms?, Journal of Marketing, 39(1), 1-16.
17. Mathew, T., Sebastian, G., and Kurian, K. M. (2007) Generalized Confidence Intervals for Process Capability Indices, Quality and Reliability Engineering International, 23(4), 471-481.
18. Montgomery, D. C. (2009) Introduction to Statistical Quality Control, (6th ed.), Wiley.
19. Nagata, Y., and Nagahata, H. (1994) Approximation Formulas for the Confidence Intervals of Process Capability Indices, Okayama Economic Review, 25, 301-314.
20. Noorossana, R. (2002) Short Communication Process Capability Analysis in the Presence of Autocorrelation, Quality and Reliability Engineering International, 18(1), 75-77.
21. Patel, A. K. and Divecha, J. (2011) Modified Exponentially Weighted Moving Average (EWMA) Control Chart for an Analytical Process Data, Journal of Chemical Engineering and Materials Science, 2(1), 12-20.
22. Pearn, W. L. and Chen, K. S. (1997) Multiprocess Performance Analysis: A Case Study, Quality Engineering, 10(1), 1-8.
23. Pearn, W. L., Kotz, S., and Johnson, N. L. (1992) Distributional and Inferential Properties of Process Capability Indices, Journal of Quality Technology, 24(4), 216-231.
24. Pham, H. (2006) Handbook of Engineering Statistics, (1st ed.), Springer.
25. Roberts, S. W. (1959) Control Chart Tests Based on Geometric Moving Averages, Technometrics, 1, 239-250.
26. Schilling, E. G. and Neubauer, D. V. (2008) Acceptance Sampling in Quality Control, (2nd ed.), Marcel Dekker Inc.
27. Shore, H. (1997) Process Capability Analysis when Data are Autocorrelated, Quality Engineering; 9(4), 615–625.
28. Wallgren, E. (2001) Confidence Limits for The Process Capability Index Cpk for Autocorrelated Quality Characteristics, Frontiers in Statistical Quality Control 6, (1st ed.), Heidelberg: Physica-Verlag.
29. Wallgren, E. (2007) Essays on Capability Indices for Autocorrelated Data, Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences 25, Uppsala.
30. Zhang, N. F. (1998) Estimating Capability Indices for Autocorrelated Data, Journal of Applied Statistics, 25(4), 559-574.
31. Zhang, N. F., Stenback, G. A. and Wardrop, D. M. (1990) Interval Estimation of Process Capability Index Cpk, Communications in Statistics-Theory and Methods, 19, 4455-4470.