臺灣博碩士論文加值系統

田口方法廣泛地運用於參數設計，參數設計的目的乃是找出控制因子的水準，使得在該水準之品質特性值對雜訊因子之變異不敏感。為了達成這個目標，田口利用直交表設計實驗，以最小的時間和資源來獲得最佳化的設計參數。他利用訊號雜訊比來衡量品質績效，並對訊號雜訊比作變異數分析，以決定顯著因子之水準。在變異數分析中利用向上合併誤差法來估計誤差項之變異數，並使用F值等於4之準則來判定顯著因子。田口方法廣泛地運用在製造過程中，使其品質特性值對雜訊因子不敏感。即便如此，田口方法卻成了統計學者批判與討論的主題。
本研究藉由探討田口方法之型I錯誤的風險，延續這種批判與討論。型I錯誤的風險乃是將不顯著之因子誤判為顯著因子的概率。對各種靜態品質特性值利用直交表進行模擬分析。在本研究中，假設品質特性值呈常態分佈且具有相同的平均值與標準差。因此，所有的因子均不顯著之虛無假設是真的。然而模擬結果顯示所有的直交表，其型I錯誤的風險卻非常高，而造成參數設計之錯誤決策。因此，本研究之結論為田口方法不是參數設計的有效方法。本研究建議用更簡單且更有效的其他方案。

Taguchi method is a widely used approach for parameter design. The overall goal of parameter design is to find settings of the controllable factors so that the response is least sensitive to variations in the noise variables, while still yielding an acceptable mean level of the response. To achieve this goal, Taguchi utilizes an orthogonal array (OA) to obtain dependable information about the design parameter with minimum time and resources. Then, he adopts signal-to-noise (S/N) ratio as a quality measure evaluate performance. In the statistical analysis of S/N ratio, analysis of variance (ANOVA) is performed to determine significant factor effects. In ANOVA, Taguchi suggests pooling-up technique to obtain an estimate of error variance and adopts F value of four to decide significant factor effects. Taguchi method has widespread applications upstream in manufacturing to fine-tune a process in such a manner that the output is insensitive to noise factors. Nevertheless, this method was the subject of discussion and much debate among statisticians in different platforms. This research proposes an extension to ongoing research by investigating the alpha risk of Taguchi method, or the probability of identifying insignificant factors as significant, with mostly used OAs for different type static quality characteristics (QCH) using simulation. In this research, it is assumed that all QCH values are normally distributed with the same mean and standard deviation. Consequently, the null hypothesis that all factors are identified as insignificant is true. However, simulation results reveal that the alpha risk is very high with all OAs, which may provide erroneous conclusions in parameter design.

Table of Contents
Acknowledgment i
Chinese Abstract ii
English Abstract iii
Table of Contents iv
List of Figures vi
List of Tables vii
Chapter 1 INTRODUCTION 1
1.1 Taguchi’s definition of quality 2
1.2 Taguchi’s orthogonal arrays 4
1.3 Taguchi’s signal-to-noise ratio 6
1.4 Taguchi’s parameter design 7
1.5 Motivation and research objectives 9
Chapter 2 LITERATURE REVIEW 11
2.1 Review and critique of orthogonal arrays 11
2.1.1. Two-level orthogonal arrays 11
2.1.2. Three-level orthogonal arrays 12
2.1.3. Mixed-level orthogonal arrays 13
2.1.4. Four-and five-level orthogonal arrays 14
2.2 Critique of signal-to-noise ratio 16
2.3 Critique of parameter design 18
Chapter 3 RESEARCH METHODOLOGY 21
3.1 Research assumptions 21
3.2 Simulation approach 22
3.3 Deciding number of pooled-up columns and 5 % significance level 24
Chapter 4 ALPHA RISK WITH TWO-LEVEL OAs 26
4.1 Pooling-up technique and F test with two-level OAs 26
4.2 The alpha risk for S/N ratio 27
4.2.1 The alpha risk for S/N ratio at four 27
4.2.2 alpha risk for S/N ratio at 5 % significance level 33 4.3 The alpha risk for a standardized QCH 37
4.4 Summary of alpha risk with two-level OAs 44
Chapter 5 ALPHA RISK WITH THREE-LEVEL OAs 46
5.1 Pooling-up and F test with three-level OAs 46
5.2 The alpha risk for S/N ratio 47
5.2.1 The alpha risk for S/N ratio at four 47
5.2.2 alpha risk for S/N ratio at 5 % significance level 51
5.3 The alpha risk for a standardized QCH 54
5.4 Summary of alpha risk with three-level OAs 56
Chapter 6 ALPHA RISK WITH MIXED-LEVEL OA 58
6.1 Pooling-up and F test with mixed-level OAs 58
6.2 The alpha risk for S/N ratio 60
6.2.1 The alpha risk for S/N ratio at four 60
6.2.2alpha risk for S/N ratio at 5 % significance level 61
6.3 The alpha risk for a standardized QCH 63
6.4 Summary of alpha risk results 64
Chapter 7 CONCLUSIONS AND FUTURE RESEARCH 66
7.1 Conclusions 66
7.2 Future research 67
Appendix A 68
Appendix B 74
References 86

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