製程良率分析於單變量與多變量剖面資料｜國立臺灣科技大學博碩士論文系統

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研究生：	Yeneneh Tamirat Negash Yeneneh - Tamirat Negash
論文名稱：	製程良率分析於單變量與多變量剖面資料 Process Yield Analysis for Single and Multivariate Profiles
指導教授：	王福琨 Fu-Kwun Wang
口試委員:	陳建良 James C.Chen 林則孟 James T. Lin 歐陽超 Chao Ou-Yang 王孔政 Kung-Jeng Wang
學位類別：	博士 Doctor
系所名稱：	管理學院 - 工業管理系 Department of Industrial Management
論文出版年：	2015
畢業學年度：	103
語文別：	英文
論文頁數：	185
中文關鍵詞：	剖面資料、製程良率、雙邊規格、單邊規格、自我相關、比率檢定統計量、多重比較方法
外文關鍵詞：	profiles, process–yield index, one-sided specifications, two-sided specifications, autocorrelation, ratio test statistic, multiple comparisons with the best
相關次數：	點閱：213 下載：6
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在許多工業應用中，若製程或產品的品質的特徵是由一個反應變數和一個或多個解釋變數的關係以函數來解釋之，則稱為剖面資料。單一的剖面資料可能包含數百或數千剖面。確保具有剖面資料的製程良率是非常重要的任務。
本論文提出製程良率分析於剖面資料及其供應商選擇的應用研究。本研究包含了八個議題的研究成果，在第二章是處理傳統製程良率於資料具相關性的研究。第三章和第四章處理製程良率於剖面資料具自我相關與剖面資料間具自我相關的研究。在剖面資料遵循自相相關回歸模型AR(1)下得到近似製程能力指標的信賴下界。第五章中提出於單邊製程規格線性剖面資料時,互相獨立常態分配下的新指標和及常態分配下的新指標和，這些指標可以提升製程產出的精確度。此外建構近似常態分配的兩個指標和。第七章與第八章是線性剖面於雙邊製規格和單邊規格時,以比率檢定統計量為基礎的指標，來比較兩個供應商的製程良率,有比率檢定統計的統計性質與提供在特訂的檢定力和信心水準下剖面資料數量的計算。第九章是利用多重比較方法對於多個供應商( )的製程良率評選。最後是結論以及對於未來研究的建議。

In many industrial applications, the quality of a process or product can be characterized by a functional relationship between a response variable and one or more explanatory variables which is referred to as profile. A single profile may contain hundred or thousand data points. Assuring the process capability for profiles to meet the requirement is a very important task.
This dissertation presents contributions within the field of process yield analysis, profile monitoring, and process selection for profiles. Eight papers one in each chapter are incorporated in this dissertation. In Chapter 2 the distribution for the process-yield index Spk is developed for autocorrelated process data. Thus, the lower confidence bound can be easily obtained for decision making. The aim of Chapters 3 and 4 is to evaluate the process yield for autocorrelation between profiles and correlation within a profile respectively. We derive an approximate lower confidence bound for the process-yield index SpkA;AR(1) when linear profiles follow an autoregressive model AR(1). In Chapter 5 two new indices CTpuA and CTplA for mutually independent normality and two new indices CTpuA;pc and CTplA;pc for multivariate normality are proposed to measure the process capability for multivariate linear profiles with one-sided specifications. These indices can provide an exact measure of the process yield. The approximate normal distributions for CTpuA and CTplA are constructed. Chapters 6 & 7 propose the ratio test statistic based on the process yield index to compare two suppliers for linear profiles with two-sided and one-sided specification limits respectively. The statistical properties of the ratio test statistic are presented. Critical values of the tests are calculated to determine the selection decisions. The number of profiles required for a designated selection power and confidence level is also investigated. Chapters 8 and 9 propose the multiple comparisons with the best method based on the process-yield index to tackle process selection problem among K (k>=2) alternatives. The power analysis is conducted. The required numbers of profiles for different power levels are also provided. Finally, the achievement and contributions of this dissertation are summarized in Chapter 10.

Table of Content
摘要                                                      i
Abstract                                              ii
Acknowledgement                                              iii
Table of Content                                      v
List of Figures                                              viii
List of Tables                                              ix
Chapter 1                                              1
Introduction                                              1
1.1 Process Capability                                      1
1.2 Profile Analysis and Applications                      2
1.3 Process Capability Indices for Profiles              4
1.4 Research Objectives                                      8
1.4.1 Specific Objectives                              8
1.5 Organization                                      9
References                                              11
Chapter 2                                              14
Lower Confidence Bound for Process-Yield Index
with Autocorrelated Process Data                              14
Abstract                                              14
2.1 Introduction                                      14
2.2 Process-Yield Index with Autocorrelated Process Data      16
2.3 Simulation Study                                      20
2.4 Illustrative Examples                              29
2.5 Conclusion                                              32
References                                              32
Chapter 3                                              35
Process Yield Analysis for Autocorrelation between
Linear Profiles                                              35
Abstract                                              35
3.1 Introduction                                      35
3.2 Process-yield Index and Lower Confidence Limit      37
3.3 Simulation Study                                      41
3.4 Illustrative Example                              44
3.5 Conclusion                                              49
References                                              50
Appendix                                              51
Chapter 4                                              56
Process Yield Analysis for Linear Within-Profile
Autocorrelation                                              56
Abstract                                              56
4.1 Introduction                                      56
4.2 Process-Yield Index for Within-Profile Autocorrelation    59
4.3 Simulation Study                                      63
4.4 Illustrative Example                              67
4.5 Conclusion                                              68
References                                              68
Appendix:                                              70
Chapter 5                                              73
Process Yield for Multivariate Profiles with One-Sided
Specifications                                              73
Abstract                                              73
5.1 Introduction                                      73
5.2 Process Yield Indices for Multivariate Linear Profiles    75
5.2.1 Mutually Independent Normality Case              75
5.3.2 Multivariate Normality Case                      81
5.3 Simulation Study                                      83
5.4 Illustrative Examples                              90
5.5 Conclusions and Future Research                      93
References                                              94
Chapter 6                                              96
Implementing the Ratio Test Statistic to Compare Two
Suppliers for Linear Profiles                              96
Abstract                                              96
6.1 Introduction                                      96
6.2 Review on the Process-Yield Index for Linear Profiles     97
6.3 Proposed Method                                      99
6.3.1 Statistical Properties of the Ratio Test Statistic      99
6.3.2 Testing Cases                                      102
6.3.3 The Number of Profiles Required                      106
6.4 Comparison Study                                      107
6.5 Illustrative Examples                              109
6.6 Conclusion                                              112
References                                              112
Chapter 7                                              114
Process Selection for Linear Profiles with One-Sided
Specifications Based on the Ratio Test Statistic      114
Abstract                                              114
7.1 Introduction                                      115
7.2 Process Yield Indices for Linear Profiles with
One-Sided Specifications                              116
7.3 Supplier Selection Procedure                      121
7.3.1 Ratio Test Statistic                              121
7.3.2 Selection Determination                              124
7.3.3 The number of Profiles Required                      129
7.4 Illustrative Examples                              131
7.5 Conclusion                                              133
References                                              133
Appendix:                                              134
Chapter 8                                              137
Multiple Comparisons with the Best for Supplier
Selection with Linear Profiles                              137
Abstract                                              137
8.1 Introduction                                      137
8.2 The Process-Yield Index SpkA for Linear Profiles      139
8.3 An MCB Method for Supplier Selection              141
8.4 Performance Analysis                              143
8.4.1 Statistical Power Analysis                      143
8.4.2 The Number of Profiles Required                      146
8.4.3 Simulation Study                                      148
8.5 Illustrative Examples                              149
8.6 Summary and Concluding Remarks                      152
References                                              152
Chapter 9                                              154
Multiple Comparisons with the Best for Process Selection
for Linear Profiles with One-Sided Specifications      154
Abstract                                              154
9.1 Introduction                                      154
9.2 The Process-Yield Indices for Linear Profiles
with One-Sided Specifications                              155
9.3 An MCB Method for Supplier Selection              158
9.4 Performance Analysis                              160
9.4.1 Power Analysis                                      160
9.4.2 The Number of Profiles Required                      161
9.5 Illustrative Example                              164
9.6 Conclusion                                              165
References                                              166
Chapter 10                                              168
Conclusion and Future Study                              168
10.1 Conclusion                                              168
10.2 Future Study                                      170
Brief Introduction of the Author                      171

                                

Chapter 1
References

1.Juran, J.M., Quality control handbook. 3 ed. 1974, New York: McGraw-Hill.
2.Kane, V.E., Process capability indices. Journal of Quality Technology, 1986. 18(1): p. 41-52.
3.Hsiang, T.C. A tutorial on quality control and assurance—the Taguchi methods. in ASA Annual Meeting. 1985. Las Vegas Nevada, USA.
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5.Boyles, R.A., Process capability with asymmetric tolerances. Communications in Statistics-Simulation and Computation, 1994. 23(3): p. 615-635.
6.Clements, J.A., Process capability calculations for non-normal distributions. Quality progress, 1989. 22(9): p. 95-97.
7.Constable, G. and J. Hobbs. Small samples and non-normal capability. in ASQC Quality Congress Transactions. 1992.
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9.Pearn, W. and K. Chen, Estimating process capability indices for non‐normal pearsonian populations. Quality and Reliability Engineering International, 1995. 11(5): p. 386-388.
10.Kotz, S. and N.L. Johnson, Process capability indices. 1993: CRC Press.
11.Pearn, W. and S. Kotz, Encyclopedia and handbook of process capability indices: a comprehensive exposition of quality control measures. 2006: World Scientific Hackensack, NJ.
12.Shore, H., Process capability analysis when data are autocorrelated. Quality Engineering, 1997. 9(4): p. 615-626.
13.Zhang, N.F., Estimating process capability indexes for autocorrelated data. Journal of Applied Statistics, 1998. 25(4): p. 559-574.
14.Wallgren, E., Confidence limits for the process capability index C pk for autocorrelated quality characteristics, in Frontiers in Statistical Quality Control 6. 2001, Springer. p. 312-331.
15.Wallgren, E., A generalization of the Taguchi capability index for data generated by a first order moving average process. Statistical Mtehods, 2001. 3(1): p. 1-16.
16.Noorossana, R., Process capability analysis in the presence of autocorrelation. Quality and Reliability Engineering International, 2002. 18(1): p. 75-77.
17.Vännman, K. and M. Kulahci, A model‐free approach to eliminate autocorrelation when testing for process capability. Quality and reliability engineering international, 2008. 24(2): p. 213-228.
18.Lovelace, C.R., et al., Lower confidence limits for process capability indices Cp and Cpk when data are autocorrelated. Quality and Reliability Engineering International, 2009. 25(6): p. 663-700.
19.Sun, J., S. Wang, and Z. Fu, Process capability analysis and estimation scheme for autocorrelated data. Journal of Systems Science and Systems Engineering, 2010. 19(1): p. 105-127.
20.Lundkvist, P., K. Vännman, and M. Kulahci, A comparison of decision methods for C pk when data are autocorrelated. Quality Engineering, 2012. 24(4): p. 460-472.
21.Noorossana, R., A. Saghaei, and A. Amiri, Statistical analysis of profile monitoring. Vol. 865. 2011: John Wiley & Sons.
22.Montgomery, D.C., Statistical Quality Control: A Modern Introduction. 2013, Singapore: Wiley.
23.Woodall, W.H., Current research on profile monitoring. Production, 2007. 17(3): p. 420-425.
24.Jin, J. and J. Shi, Feature-preserving data compression of stamping tonnage information using wavelets. Technometrics, 1999. 41(4): p. 327-339.
25.Kang, L. and S.L. Albin, On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 2000. 32(4): p. 418-426.
26.Walker, E. and S.P. Wright, Comparing curves using additive models. Journal of Quality Technology, 2002. 34(1): p. 118-129.
27.Gupta, S., D. Montgomery, and W. Woodall, Performance evaluation of two methods for online monitoring of linear calibration profiles. International Journal of Production Research, 2006. 44(10): p. 1927-1942.
28.Amiri, A., W.A. Jensen, and R.B. Kazemzadeh, A case study on monitoring polynomial profiles in the automotive industry. Quality and Reliability Engineering International, 2010. 26(5): p. 509-520.
29.Paynabar, K. and J. Jin, Characterization of non-linear profiles variations using mixed-effect models and wavelets. IIE Transactions, 2011. 43(4): p. 275-290.
30.Chang, S.I., et al., Statistical process control for monitoring nonlinear profiles: a six sigma project on curing process. Quality Engineering, 2012. 24(2): p. 251-263.
31.Parker, P.A., et al. A single-vector force calibration method featuring the modern design of experiments. in 39 th AIAIA Aerospace Sciences Meeting and Exhibit, Reno Nevada. 2001.
32.Eyvazian, M., et al., Phase II monitoring of multivariate multiple linear regression profiles. Quality and Reliability Engineering International, 2011. 27(3): p. 281-296.
33.Chou, S.H., Quality engineering applications on single and multiple nonlinear profiles, in Industrial and Manufacturing Systems Engineering. 2014, Kansan State: Manhattan, Kansas.
34.Shahriari, H. and M. Sarrafian. Assessment of process capability in linear profiles. in Proceedings of the 6th International Industrial Engineering Conference, Tehran, Iran (in Farsi). 2009.
35.Zahra Hosseinifard, S. and B. Abbasi, Evaluation of process capability indices of linear profiles. International Journal of Quality & Reliability Management, 2012. 29(2): p. 162-176.
36.Hosseinifard, S.Z. and B. Abbasi, Process capability analysis in non normal linear regression profiles. Communications in Statistics-Simulation and Computation, 2012. 41(10): p. 1761-1784.
37.Ebadi, M. and H. Shahriari, A process capability index for simple linear profile. International Journal of Advanced Manufacturing Technology, 2013. 64(5-8): p. 857-865.
38.Wang, F.K., A Process Yield for Simple Linear Profiles. Quality Engineering, 2014. 26(3): p. 311-318.
39.Wang, F.K. and Y.C. Guo, Measuring process yield for nonlinear profiles. Quality and Reliability Engineering International, 2014. 30(8): p. 1333-1339.
40.Ebadi, M. and A. Amiri, Evaluation of process capability in multivariate simple linear profiles. Scientia Iranica, 2012. 19(6): p. 1960-1968.
41.Wang, F.K., Process yield for multivariate linear profiles. Quality Technology and Quantitative Management, 2014(in press).
42.Albing, M., Contributions to process capability indices and plots, in Mathematics. 2008, Luleå University of Technology: Sweden.
43. Wang, F.K., Process yield analysis for a process with profiles. Working Paper, National Taiwan University of Science and Technology, Taipei, Taiwan, 2015.

Chapter 2
References

1.Boyles, R.A., Process capability with asymmetric tolerances. Communications in Statistics-Simulation and Computation, 1994. 23(3): p. 615-635.
2.Montgomery, D.C., Statistical Quality Control: A Modern Introduction. 2013, Singapore: Wiley.
3.Psarakis, S. and G. Papaleonida, SPC procedures for monitoring autocorrelated processes. Quality Technology and Quantitative Management, 2007. 4(4): p. 501-540.
4.Scagliarini, M., Estimation of C p for autocorrelated data and measurement errors. Communications in Statistics-Theory and Methods, 2002. 31(9): p. 1647-1664.
5.Shore, H., Process capability analysis when data are autocorrelated. Quality Engineering, 1997. 9(4): p. 615-626.
6.Zhang, N.F., Estimating process capability indexes for autocorrelated data. Journal of Applied Statistics, 1998. 25(4): p. 559-574.
7.Wallgren, E., Confidence limits for the process capability index C pk for autocorrelated quality characteristics, in Frontiers in Statistical Quality Control 6. 2001, Springer. p. 312-331.
8.Wallgren, E., A generalization of the Taguchi capability index for data generated by a first order moving average process. Statistical Mtehods, 2001. 3(1): p. 1-16.
9.Noorossana, R., Process capability analysis in the presence of autocorrelation. Quality and Reliability Engineering International, 2002. 18(1): p. 75-77.
10.Vännman, K. and M. Kulahci, A model‐free approach to eliminate autocorrelation when testing for process capability. Quality and Reliability Engineering International, 2008. 24(2): p. 213-228.
11.Lovelace, C.R., et al., Lower confidence limits for process capability indices Cp and Cpk when data are autocorrelated. Quality and Reliability Engineering International, 2009. 25(6): p. 663-700.
12.Sun, J., S. Wang, and Z. Fu, Process capability analysis and estimation scheme for autocorrelated data. Journal of Systems Science and Systems Engineering, 2010. 19(1): p. 105-127.
13.Lundkvist, P., K. Vännman, and M. Kulahci, A comparison of decision methods for Cpk when data are autocorrelated. Quality Engineering, 2012. 24(4): p. 460-472.
14.Lee, J., et al., On the distribution of the estimated process yield index Spk. Quality and Reliability Engineering International, 2002. 18(2): p. 111-116.
15.R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. 2012, ISBN 3-900051-07-0.

Chapter 3

References
1.Kang, L. and S.L. Albin, On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 2000. 32(4): p. 418-426.
2.Woodall, W.H., Current research on profile monitoring. Production, 2007. 17(3): p. 420-425.
3.Noorossana, R., A. Saghaei, and A. Amiri, Statistical analysis of profile monitoring. Vol. 865. 2011: John Wiley & Sons.
4.Chuang, S.C., et al., A framework for nonparametric profile monitoring. Computers & Industrial Engineering, 2013. 64(1): p. 482-491.
5.Ghahyazi, M.E., S.T.A. Niaki, and P. Soleimani, On the monitoring of linear profiles in multistage processes. Quality and Reliability Engineering International, 2014. 30(7): p. 1035-1047.
6.Li, Z. and Z. Wang, An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles. Computers & Industrial Engineering, 2010. 59(4): p. 630-637.
7.Noorossana, R., M. Eyvazian, and A. Vaghefi, Phase II monitoring of multivariate simple linear profiles. Computers & Industrial Engineering, 2010. 58(4): p. 563-570.
8.Noorossana, R., A. Vaghefi, and M. Dorri, Effect of non‐normality on the monitoring of simple linear profiles. Quality and Reliability Engineering International, 2011. 27(4): p. 425-436.
9.Zhang, Y., et al., Control charts for monitoring linear profiles with within‐profile correlation using Gaussian process models. Quality and Reliability Engineering International, 2014. 30(4): p. 487-501.
10.Kazemzadeh, R., R. Noorossana, and A. Amiri, Phase II monitoring of autocorrelated polynomial profiles in AR (1) processes. Scientia Iranica Transaction E: Industrial Engineering, 2010. 17(1): p. 12-24.
11.Noorossana, R., A. Amiri, and P. Soleimani, On the monitoring of autocorrelated linear profiles. Communications in Statistics—Theory and Methods, 2008. 37(3): p. 425-442.
12.Soleimani, P., R. Noorossana, and A. Amiri, Simple linear profiles monitoring in the presence of within profile autocorrelation. Computers & Industrial Engineering, 2009. 57(3): p. 1015-1021.
13.Shahriari, H. and M. Sarrafian. Assessment of process capability in linear profiles. in Proceedings of the 6th International Industrial Engineering Conference, Tehran, Iran (in Farsi). 2009.
14.Zahra Hosseinifard, S. and B. Abbasi, Evaluation of process capability indices of linear profiles. International Journal of Quality & Reliability Management, 2012. 29(2): p. 162-176.
15.Hosseinifard, S.Z. and B. Abbasi, Process capability analysis in non normal linear regression profiles. Communications in Statistics-Simulation and Computation, 2012. 41(10): p. 1761-1784.
16.Ebadi, M. and H. Shahriari, A process capability index for simple linear profile. International Journal of Advanced Manufacturing Technology, 2013. 64(5-8): p. 857-865.
17.Wang, F.K., A Process Yield for Simple Linear Profiles. Quality Engineering, 2014. 26(3): p. 311-318.
18.Wang, F.K. and Y.C. Guo, Measuring process yield for nonlinear profiles. Quality and Reliability Engineering International, 2014. 30(8): p. 1333-1339.
19.Shore, H., Process capability analysis when data are autocorrelated. Quality Engineering, 1997. 9(4): p. 615-626.
20.Zhang, N.F., Estimating process capability indexes for autocorrelated data. Journal of Applied Statistics, 1998. 25(4): p. 559-574.
21.Wallgren, E., Confidence limits for the process capability index Cpk for autocorrelated quality characteristics, in Frontiers in Statistical Quality Control 6. 2001, Springer. p. 312-331.
22.Wallgren, E., A generalization of the Taguchi capability index for data generated by a first order moving average process. Statistical Methods, 2001. 3(1): p. 1-16.
23.Noorossana, R., Process capability analysis in the presence of autocorrelation. Quality and Reliability Engineering International, 2002. 18(1): p. 75-77.
24.Vännman, K. and M. Kulahci, A model‐free approach to eliminate autocorrelation when testing for process capability. Quality and Reliability Engineering International, 2008. 24(2): p. 213-228.
25.Lovelace, C.R., et al., Lower confidence limits for process capability indices Cp and Cpk when data are autocorrelated. Quality and Reliability Engineering International, 2009. 25(6): p. 663-700.
26.Sun, J., S. Wang, and Z. Fu, Process capability analysis and estimation scheme for autocorrelated data. Journal of Systems Science and Systems Engineering, 2010. 19(1): p. 105-127.
27.Lundkvist, P., K. Vännman, and M. Kulahci, A comparison of decision methods for C pk when data are autocorrelated. Quality Engineering, 2012. 24(4): p. 460-472.
28.Boyles, R.A., Brocess capability with asymmetric tolerances. Communications in Statistics-Simulation and Computation, 1994. 23(3): p. 615-635.
29.R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. 2012, ISBN 3-900051-07-0.
30.Croarkin, C. and P. Tobias, NIST/SEMATECH e-handbook of statistical methods. NIST/SEMATECH. Available online: http://www. itl. nist. gov/div898/handbook, 2010.
31.Lee, J., et al., On the distribution of the estimated process yield index Spk. Quality and Reliability Engineering International, 2002. 18(2): p. 111-116.

Chapter 4
References

1.Woodall, W.H., Current research on profile monitoring. Production, 2007. 17(3): p. 420-425.
2.Noorossana, R., A. Saghaei, and A. Amiri, Statistical analysis of profile monitoring. Vol. 865. 2011: John Wiley & Sons.
3.Noorossana, R., A. Vaghefi, and M. Dorri, Effect of non‐normality on the monitoring of simple linear profiles. Quality and Reliability Engineering International, 2011. 27(4): p. 425-436.
4.Kang, L. and S.L. Albin, On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 2000. 32(4): p. 418-426.
5.Noorossana, R., A. Amiri, and P. Soleimani, On the monitoring of autocorrelated linear profiles. Communications in Statistics—Theory and Methods, 2008. 37(3): p. 425-442.
6.Kazemzadeh, R., R. Noorossana, and A. Amiri, Phase II monitoring of autocorrelated polynomial profiles in AR (1) processes. Scientia Iranica Transaction E: Industrial Engineering, 2010. 17(1): p. 12-24.
7.Jensen, W.A., J.B. Birch, and W.H. Woodall, Monitoring correlation within linear profiles using mixed models. Journal of Quality Technology, 2008. 40(2): p. 167-183.
8.Jensen, W.A. and J.B. Birch, Profile monitoring via nonlinear mixed models (vol 41, pg 18, 2009). Journal of Quality Technology, 2009. 41(3): p. 321-321.
9.Amiri, A., W.A. Jensen, and R.B. Kazemzadeh, A case study on monitoring polynomial profiles in the automotive industry. Quality and Reliability Engineering International, 2010. 26(5): p. 509-520.
10.Soleimani, P., R. Noorossana, and A. Amiri, Simple linear profiles monitoring in the presence of within profile autocorrelation. Computers & Industrial Engineering, 2009. 57(3): p. 1015-1021.
11.Qiu, P., C. Zou, and Z. Wang, Nonparametric profile monitoring by mixed effects modeling. Technometrics, 2010. 52(3).
12.Narvand, A., P. Soleimani, and S. Raissi, Phase II monitoring of auto-correlated linear profiles using linear mixed model. Journal of Industrial Engineering International, 2013. 9(1): p. 1-9.
13.Zhang, Y., et al., Control charts for monitoring linear profiles with within‐profile correlation using Gaussian process models. Quality and Reliability Engineering International, 2014. 30(4): p. 487-501.
14.Shahriari, H. and M. Sarrafian. Assessment of process capability in linear profiles. in Proceedings of the 6th International Industrial Engineering Conference, Tehran, Iran (in Farsi). 2009.
15.Zahra Hosseinifard, S. and B. Abbasi, Evaluation of process capability indices of linear profiles. International Journal of Quality & Reliability Management, 2012. 29(2): p. 162-176.
16.Hosseinifard, S.Z. and B. Abbasi, Process capability analysis in non normal linear regression profiles. Communications in Statistics-Simulation and Computation, 2012. 41(10): p. 1761-1784.
17.Ebadi, M. and H. Shahriari, A process capability index for simple linear profile. International Journal of Advanced Manufacturing Technology, 2013. 64(5-8): p. 857-865.
18.Wang, F.K., A process yield for simple linear profiles. Quality Engineering, 2014. 26(3): p. 311-318.
19.Wang, F.K. and Y.C. Guo, Measuring process yield for nonlinear profiles. Quality and Reliability Engineering International, 2014. 30(8): p. 1333-1339.
20.Shore, H., Process capability analysis when data are autocorrelated. Quality Engineering, 1997. 9(4): p. 615-626.
21.Zhang, N.F., Estimating process capability indexes for autocorrelated data. Journal of Applied Statistics, 1998. 25(4): p. 559-574.
22.Wallgren, E., Confidence limits for the process capability index Cpk for autocorrelated quality characteristics, in Frontiers in Statistical Quality Control 6. 2001, Springer. p. 312-331.
23.Wallgren, E., A generalization of the Taguchi capability index for data generated by a first ordermoving average process. Statistical Mtehods, 2001. 3(1): p. 1-16.
24.Noorossana, R., Process capability analysis in the presence of autocorrelation. Quality and Reliability Engineering International, 2002. 18(1): p. 75-77.
25.Vännman, K. and M. Kulahci, A model‐free approach to eliminate autocorrelation when testing for process capability. Quality and Reliability Engineering International, 2008. 24(2): p. 213-228.
26.Lovelace, C.R., et al., Lower confidence limits for process capability indices Cp and Cpk when data are autocorrelated. Quality and Reliability Engineering International, 2009. 25(6): p. 663-700.
27.Sun, J., S. Wang, and Z. Fu, Process capability analysis and estimation scheme for autocorrelated data. Journal of Systems Science and Systems Engineering, 2010. 19(1): p. 105-127.
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32.Schabenberger, O. and F.J. Pierce, Contemporary statistical models for the plant and soil sciences. 2010, Boca Raton: CRC press.

Chapter 5
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23.Pearn, W.L., C. Wu, and M. Tsai, A note on “capability assessment for processes with multiple characteristics: a generalization of the popular index Cpk”. Quality and Reliability Engineering International, 2013. 29(2): p. 159-163.
24.Noorossana, R., M. Eyvazian, and A. Vaghefi, Phase II monitoring of multivariate simple linear profiles. Computers & Industrial Engineering, 2010. 58(4): p. 563-570.
25.R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. 2012, ISBN 3-900051-07-0.
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Chapter 6
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1.Kang, L. and S.L. Albin, On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 2000. 32(4): p. 418-426.
2.Noorossana, R., A. Saghaei, and A. Amiri, Statistical analysis of profile monitoring. Vol. 865. 2011: John Wiley & Sons.
3.Woodall, W.H., Current research on profile monitoring. Production, 2007. 17(3): p. 420-425.
4.Soleimani, P., A. Narvand, and S. Raissi, Online monitoring of auto correlated linear profiles via mixed model. International Journal of Manufacturing Technology and Management, 2013. 27(4): p. 238-250.
5.Adibi, A., D.C. Montgomery, and C.M. Borror, Phase II monitoring of linear profiles using a P-value approach. International Journal of Quality Engineering and Technology, 2014. 4(2): p. 97-106.
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9.Ebadi, M. and H. Shahriari, A process capability index for simple linear profile. International Journal of Advanced Manufacturing Technology, 2013. 64(5-8): p. 857-865.
10.Hosseinifard, S.Z. and B. Abbasi, Process capability analysis in non normal linear regression profiles. Communications in Statistics-Simulation and Computation, 2012. 41(10): p. 1761-1784.
11.Nemati Keshteli, R., et al., Functional process capability indices for circular profile. Quality and Reliability Engineering International, 2014. 30(5): p. 633-644.
12.Zahra Hosseinifard, S. and B. Abbasi, Evaluation of process capability indices of linear profiles. International Journal of Quality & Reliability Management, 2012. 29(2): p. 162-176.
13.Wang, F.K., Measuring the process yield for circular profiles. Quality and Reliability Engineering International, 2013, DOI: 10.1002/qre.1614.
14.Wang, F.K., A process yield for simple linear profiles. Quality Engineering, 2014. 26(3): p. 311-318.
15.Wang, F.K., Measuring the process yield for simple linear profiles with one‐sided specification. Quality and Reliability Engineering International, 2014. 30(8): p. 1145-1151.
16.Wang, F.K. and Y.C. Guo, Measuring process yield for nonlinear profiles. Quality and Reliability Engineering International, 2014. 30(8): p. 1333-1339.
17.Chou, Y.M., Selecting a better supplier by testing process capability indices. Quality Engineering, 1994. 6(3): p. 427-438.
18.Daniels, L., et al., Using confidence intervals to compare process capability indices. Quality Engineering, 2004. 17(1): p. 23-32.
19.Hubele, N.F., A. Berrado, and E.S. Gel, A Wald test for comparing multiple capability indices. Journal of quality technology, 2005. 37(4): p. 304-307.
20.Lin, C.J. and W.L. Pearn, Process selection for higher production yield based on capability index Spk. Quality and Reliability Engineering International, 2010. 26(3): p. 247-258.
21.Pearn, W.L. and C. Wu, Supplier selection critical decision values for processes with multiple independent lines. Quality and Reliability Engineering International, 2013. 29(6): p. 899-909.
22.Wu, C.W., M.Y. Liao, and T.T. Yang, Efficient methods for comparing two process yields–strategies on supplier selection. International Journal of Production Research, 2013. 51(5): p. 1587-1602.
23.Wang, F.K., The difference test statistic for two suppliers with linear profiles. Quality and Reliability Engineering International, 2014, DOI: 10.1002/qre.1726.
24.R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. 2012, ISBN 3-900051-07-0.

Chapter 7
References
1.Woodall, W.H., Current research on profile monitoring. Production, 2007. 17(3): p. 420-425.
2.Noorossana, R., A. Saghaei, and A. Amiri, Statistical analysis of profile monitoring. Vol. 865. 2011: John Wiley & Sons.
3.Zahra Hosseinifard, S. and B. Abbasi, Evaluation of process capability indices of linear profiles. International Journal of Quality & Reliability Management, 2012. 29(2): p. 162-176.
4.Wang, F.K., Measuring the process yield for simple linear profiles with one‐sided specification. Quality and Reliability Engineering International, 2014. 30(8): p. 1145-1151.
5.Pearn, W.L., H. Hung, and Y.C. Cheng, Supplier selection for one-sided processes with unequal sample sizes. European Journal of Operational Research, 2009. 195(2): p. 381-393.
6.Pearn, W., et al., An effective powerful test for one-sided supplier selection problem. Journal of Statistical Computation and Simulation, 2011. 81(10): p. 1313-1331.
7.Hsu, Y.C., W. Pearn, and Y.F. Chuang, Sample size determination for production yield estimation with multiple independent process characteristics. European Journal of Operational Research, 2009. 196(3): p. 968-978.
8.Pearn, W.L., C. Wu, and M. Tsai, A note on “capability assessment for processes with multiple characteristics: a generalization of the popular index Cpk”. Quality and Reliability Engineering International, 2013. 29(2): p. 159-163.
9.Pearn, W.L., et al., An extension of the product acceptance determination for one‐sided process with multiple characteristics. Quality and Reliability Engineering International, 2013. 29(2): p. 277-284.
10.Pearn, W. and C. Wu, Supplier selection for multiple characteristics processes with one-sided specifications. Quality Technology and Quantitative Management, 2013. 10(1): p. 133-139.
11.Yum, B.J. and K.W. Kim, A bibliography of the literature on process capability indices: 2000–2009. Quality and Reliability Engineering International, 2011. 27(3): p. 251-268.
12.Spiring, F., Exploring process capability with Mathematica. Quality and Reliability Engineering International, 2011. 27(3): p. 369-387.
13.Grau, D., New process capability indices for one-sided tolerances. Quality Technology and Quantitative Management, 2009. 6(2): p. 107-124.
14.Grau, D., On the choice of a capability index for asymmetric tolerances. Quality Technology & Quantitative Management, 2010. 7(3): p. 301-319.
15.Grau, D., Process yield, process centering and capability indices for one-sided tolerance processes. Quality Technology and Quantitative Management, 2012. 9(2): p. 153-170.
16.Maiti, S.S., M. Saha, and A.K. Nanda, On generalizing process capability indices. Journal of Quality Technology and Quantitative Management, 2010. 7(3): p. 279-300.
17.Parchami, A. and M. Mashinchi, Testing the capability of fuzzy processes. Quality Technology and Quantitative Management, 2009. 6(2): p. 125-136.
18.Wang, F.K., Supplier selection for multiple linear profiles with one‐sided specifications. Quality and Reliability Engineering International, 2014.
19.R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. 2012, ISBN 3-900051-07-0.
20.Amiri, A., C. Zou, and M.H. Doroudyan, Monitoring correlated profile and multivariate quality characteristics. Quality and Reliability Engineering International, 2014. 30(1): p. 133-142.

Chapter 8
References

1.Kang, L. and S.L. Albin, On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 2000. 32(4): p. 418-426.
2.Lin, C.J. and W.L. Pearn, Process selection for higher production yield based on capability index Spk. Quality and Reliability Engineering International, 2010. 26(3): p. 247-258.
3.Woodall, W.H., Current research on profile monitoring. Production, 2007. 17(3): p. 420-425.
4.Dickson, G.W., An analysis of vendor selection systems and decisions. 1996.
5.Olhager, J. and E. Selldin, Supply chain management survey of Swedish manufacturing firms. International Journal of Production Economics, 2004. 89(3): p. 353-361.
6.Hsu, B.M., C.Y. Chiang, and M.H. Shu, Supplier selection using fuzzy quality data and their applications to touch screen. Expert Systems with Applications, 2010. 37(9): p. 6192-6200.
7.Zhang, X., C. Lee, and S. Chen, Supplier evaluation and selection: a hybrid model based on DEAHP and ABC. International Journal of Production Research, 2012. 50(7): p. 1877-1889.
8.Lin, C.J. and W.L. Pearn, Group selection for production yield among k manufacturing lines. Journal of Statistical Planning and Inference, 2011. 141(4): p. 1510-1518.
9.Lin, C.J. and H.H. Kuo, Multiple comparisons with the best for supplier selection. Quality and Reliability Engineering International, 2014. 30(7): p. 1083-1092.
10.Pearn, W.L. and C. Wu, Supplier selection critical decision values for processes with multiple independent lines. Quality and Reliability Engineering International, 2013. 29(6): p. 899-909.
11.Tai, Y.T., W.L. Pearn, and S.K. You, An effective test for supplier selection evaluation with multiple characteristics. Journal of Testing and Evaluation, 2011. 39(6): p. 1165-1173.
12.Hosseinifard, S.Z. and B. Abbasi, Process capability analysis in non normal linear regression profiles. Communications in Statistics-Simulation and Computation, 2012. 41(10): p. 1761-1784.
13.Zahra Hosseinifard, S. and B. Abbasi, Evaluation of process capability indices of linear profiles. International Journal of Quality & Reliability Management, 2012. 29(2): p. 162-176.
14.Ebadi, M. and A. Amiri, Evaluation of process capability in multivariate simple linear profiles. Scientia Iranica, 2012. 19(6): p. 1960-1968.
15.Ebadi, M. and H. Shahriari, A process capability index for simple linear profile. International Journal of Advanced Manufacturing Technology, 2013. 64(5-8): p. 857-865.
16.Wang, F.K., A process yield for simple linear profiles. Quality Engineering, 2014. 26(3): p. 311-318.
17.Wang, F.K. and Y.C. Guo, Measuring process yield for nonlinear profiles. Quality and Reliability Engineering International, 2014. 30(8): p. 1333-1339.
18.Horrace, W.C. and P. Schmidt, Multiple comparisons with the best, with economic applications. Journal of Applied Econometrics, 2000. 15(1): p. 1-26.
19.R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. 2012, ISBN 3-900051-07-0.
20.Noorossana, R., M. Eyvazian, and A. Vaghefi, Phase II monitoring of multivariate simple linear profiles. Computers & Industrial Engineering, 2010. 58(4): p. 563-570.

Chapter 9
References

1.Zahra Hosseinifard, S. and B. Abbasi, Evaluation of process capability indices of linear profiles. International Journal of Quality & Reliability Management, 2012. 29(2): p. 162-176.
2.Wang, F.K., Measuring the process yield for simple linear profiles with one‐sided specification. Quality and Reliability Engineering International, 2014. 30(8): p. 1145-1151.
3.Pearn, W.L., H. Hung, and Y.C. Cheng, Supplier selection for one-sided processes with unequal sample sizes. European Journal of Operational Research, 2009. 195(2): p. 381-393.
4.Pearn, W., et al., An effective powerful test for one-sided supplier selection problem. Journal of Statistical Computation and Simulation, 2011. 81(10): p. 1313-1331.
5.Hsu, Y.C., W. Pearn, and Y.F. Chuang, Sample size determination for production yield estimation with multiple independent process characteristics. European Journal of Operational Research, 2009. 196(3): p. 968-978.
6.Pearn, W.L., C. Wu, and M. Tsai, A note on “capability assessment for processes with multiple characteristics: a generalization of the popular index Cpk”. Quality and Reliability Engineering International, 2013. 29(2): p. 159-163.
7.Pearn, W.L., et al., An extension of the product acceptance determination for one‐sided process with multiple characteristics. Quality and Reliability Engineering International, 2013. 29(2): p. 277-284.
8.Yum, B.J. and K.W. Kim, A bibliography of the literature on process capability indices: 2000–2009. Quality and Reliability Engineering International, 2011. 27(3): p. 251-268.
9.Grau, D., New process capability indices for one-sided tolerances. Quality Technology and Quantitative Management, 2009. 6(2): p. 107-124.
10.Grau, D., On the choice of a capability index for asymmetric tolerances. Quality Technology & Quantitative Management, 2010. 7(3): p. 301-319.
11.Grau, D., Process yield, process centering and capability indices for one-sided tolerance processes. Quality Technology and Quantitative Management, 2012. 9(2): p. 153-170.
12.Maiti, S.S., M. Saha, and A.K. Nanda, On generalizing process capability indices. Journal of Quality Technology and Quantitative Management, 2010. 7(3): p. 279-300.
13.Parchami, A. and M. Mashinchi, Testing the capability of fuzzy processes. Quality Technology and Quantitative Management, 2009. 6(2): p. 125-136.
14.Pearn, W. and C. Wu, Supplier selection for multiple characteristics processes with one-sided specifications. Quality Technology and Quantitative Management, 2013. 10(1): p. 133-139.
15.Wang, F.K., Supplier selection for multiple linear profiles with one‐sided specifications. Quality and Reliability Engineering International, 2014.
16.Wang, F.K., Y. Tamirat, and Y.S. Tsai, Process selection for linear profiles with one‐sided specifications based on the ratio test statistic. Quality and Reliability Engineering International, 2014.
17.R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. 2012, ISBN 3-900051-07-0.
18.Amiri, A., A. Zand, and D. Soudbakhsh. Monitoring simple linear profiles in the leather industry (a case study). in Proceedings of the 2nd International Conference on Industrial Engineering and Operations Management, Kuala Lumpur, Malaysia, January. 2011.

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