现代半导体制造中质量控制和评价的关键技术研究
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摘要
如今，在半导体和集成电路制造领域，随着工艺过程、技术和设备的日益复杂，电子元器件产品自身功能的不断完善，以及客户对工艺水平及产品质量要求的不断提高，使得生产过程质量控制和评价技术显得日益重要。同时，越来越多的国内企业为了向国际型企业标准迈进，开始重视质量控制与工艺评价技术。因此，全面实施工艺质量控制与评价技术具有重要意义。
本论文以半导体生产过程中多品种小批量生产过程及多变量生产工艺为主要研究对象，以理论分析及计算机模拟仿真为手段，利用self-starting技术、多元数值积分与极大似然估计等，研究了多品种小批量生产过程中，工艺参数均值和标准偏差的监控，以及如何对多变量生产过程的产品质量和工艺进行评价。本论文同时介绍了基于截尾样本分析供应商所提供的产品质量的方法。本文的研究成果有助于提高产品质量，减少质量缺陷，对提高企业的市场竞争力具有深远的意义。本论文的主要研究内容包括：
1).分析了在多品种小批量生产模式下，实施质量过程控制技术所面对的困难。创新性地提出了多品种生产模式下的质量控制方法——T-K控制图技术，用于检测工艺参数母体均值及标准偏差的波动。该控制图采用一种对样本量要求不高的方法，基于采集的每批样本数据，计算T、K统计量，使得T、K统计量各自相互独立且服从相同分布。该技术具有self-starting特点，无需经历分析用控制图阶段估计母体的分布参数，尤其是T控制图的建立过程与母体标准偏差无关。即便在母体分布参数未知的情况下，只要样本数据达到2批，T-K控制图即可对多品种小批量生产过程实施质量控制。
2).从SPC技术的基本原理出发点，讨论了控制图性能的衡量方法。对平均运行长度的概念、意义及计算方法做出简单介绍。其次对T控制图及K控制图的ARL性能进行了分析。而后分析了self-starting控制图的缺陷，并提出了一种优化方法用于改进具有自启动特点的控制图的ARL性能。结果表明，改进后的Q控制图以及T-K控制图的ARL性能均有明显提升。
3).以单变量工艺为核心简要介绍单变量工序能力指数与工艺成品率的关系，并结合6σ设计评价思路对常规Cpk计算方式进行了改进，提出了一种与成品率具有一一对应关系的等效工序能力指数ECpk。之后沿用这一思想引出基于成品率的多变量工序能力指数MECpk的概念及计算方法，并分析了协方差矩阵对多变量工艺成品率的影响，提出了一种提升工艺成品率的解决思路。最后通过实例详述了多变量工序能力指数的计算过程，通过与其他多变量工序能力指数评价结果对比，验证了MECpk指数的有效性。
4).成品率反映了产品的内在质量和可靠性。从购买者的角度出发，介绍了如何利用产品特性参数的截尾样本数据来评价供应商所提供产品的质量；提出了利用服从截尾正态分布的样本数据推测产品成品率的方法，该方法同时适用于单侧及双侧截尾情况；定量分析了成品率计算结果的置信区间，进而给出了该方法对样本容量的要求。同时，结合半导体产品的实际测试数据介绍了基于截尾数据推测成品率的步骤，并验证了算法有效性。
5).此外，在本课题的研究基础上，开发了质量控制与评价软件系统。该软件包含了质量过程控制与工艺评价功能，涵盖了多种控制图技术和工序能力指数计算方法，而且具有本文所提出的多变量工序能力指数计算模块。
In the field of modern semiconductor and integrated circuit manufacturing, asprocess, technology and equipments are becoming more and more complicated, thefunction of electronic devices is becoming more perfect and users bring morerequirements to process level and product quality.Then, it isnecessary thatthe techniquesof quality control and process evaluation should be paied more attention. At the sametime, in order to keep abreast of time and compete with international companies, domesticcompanies begin to implement techniques of quality management and process evaluation.So, their implement is of important significance.
This dissertation studies some problems of process control and evaluation inmultivariate process and multi-variety and small batch manufacturing system using self-starting technique, multivariate numerical integration and maximum likelihoodestimation and so on through theory and computer simulation analysis. The problemsinclude monitoring process mean and standard deviation of multi-variety and small batchproduction run, and the evaluation of the process and product quality of multivariateprocess. In the meanwhile, the method of evaluation on the quality of product providedby suppliers based on truncated sample is also introduced. These researches can improveprocess products quality and reduce quality defects. It is meaningful to up-grate marketcompetitiveness of enterprise. The main contents are summarized as follows:
1). Fistly, the existing problem of implementing quality control and evaluation inmulti-variety and small batch production runs to monitor process mean and standarddeviation is analyzed. A quality control technique in multi-variety and small batchmanufacturing system, T-K control chart, is proposed constructively. Using this method,the quality manager needn’t collect samples as many as traditional chart. The T or Kstatistics are calculated based on each subgroup, and the statistics of each subgroup areindependent with each other and have an identical distribution. This method adopts self-startingtechnique, and does notrequire PhaseI sample aimingat estimating processmean.Especially, the T-chart does not need the estimation of variance. Even the distributionparameters are unknown, the T-K chart can be used to monitor multi-variety and smallbatch production run as long as there are no less than2subgroups.
2). In the light of the theory of statistical process control, some methods to evaluatethe performance of control chart are discussed. Then, the concept, the significance andthe calculation steps of average run length are introduced. The ARL performance of Tchart and K chart is analyzed. In addition, the shortcoming of self-starting control chart is studied, and a strategy for optimizing theARLperformance of self-staring control chartis proposed. The result reveals that the ARL performance is improved dramatically afterthe optimization.
3). The relationship between the index Cpkand process yield for the case with singlecharacteristic is analyzed. Then an equivalent process capability index ECpkis proposedbased on the idea of six sigma design strategy. ECpkindex has a one-to-onecorrespondence relationship with process yield. Following this idea we develop amultivariate PCI MECpkwhich can be used to evaluate process capability for processeswith multiple characteristics and we also discuss the impact of covariance matrix onprocess yield, fromwhich the authors propose a solution to improve overall process yield.Some illustrative examples are presented to verify the validity of the suggested index invarious cases.
4). It is known that product yield reflects the potential product quality and reliability,which means that high yield corresponds to good quality and high reliability. From theview of consumers, the method of judging the quality of products supplied bymanufacturers based on truncated samples is introduced. This dissertation proposes analgorithm for calculating the parameters of full Gaussian distribution before truncationbased on truncated dataand estimating product yield.The algorithmis proper to both one-side and two-side truncation. The confidence interval of the yield result is derived, andthe effect of sample size on the precision of the calculation result is also analyzed. Finally,the steps for calculating the product yield are offered and the effectiveness of thisalgorithm is verified by an actual instance.
5). In addition, based on the models and algorithms discussed above, the computer-aid quality control and process evaluation software is developed. The software systemincludes the function for statistical process control and process capability evaluation. Thesoftware offers many control charts,process capability indicesand especially the functionfor computing multivariate process capability index proposed in this dissertation.
本论文以半导体生产过程中多品种小批量生产过程及多变量生产工艺为主要研究对象，以理论分析及计算机模拟仿真为手段，利用self-starting技术、多元数值积分与极大似然估计等，研究了多品种小批量生产过程中，工艺参数均值和标准偏差的监控，以及如何对多变量生产过程的产品质量和工艺进行评价。本论文同时介绍了基于截尾样本分析供应商所提供的产品质量的方法。本文的研究成果有助于提高产品质量，减少质量缺陷，对提高企业的市场竞争力具有深远的意义。本论文的主要研究内容包括：
1).分析了在多品种小批量生产模式下，实施质量过程控制技术所面对的困难。创新性地提出了多品种生产模式下的质量控制方法——T-K控制图技术，用于检测工艺参数母体均值及标准偏差的波动。该控制图采用一种对样本量要求不高的方法，基于采集的每批样本数据，计算T、K统计量，使得T、K统计量各自相互独立且服从相同分布。该技术具有self-starting特点，无需经历分析用控制图阶段估计母体的分布参数，尤其是T控制图的建立过程与母体标准偏差无关。即便在母体分布参数未知的情况下，只要样本数据达到2批，T-K控制图即可对多品种小批量生产过程实施质量控制。
2).从SPC技术的基本原理出发点，讨论了控制图性能的衡量方法。对平均运行长度的概念、意义及计算方法做出简单介绍。其次对T控制图及K控制图的ARL性能进行了分析。而后分析了self-starting控制图的缺陷，并提出了一种优化方法用于改进具有自启动特点的控制图的ARL性能。结果表明，改进后的Q控制图以及T-K控制图的ARL性能均有明显提升。
3).以单变量工艺为核心简要介绍单变量工序能力指数与工艺成品率的关系，并结合6σ设计评价思路对常规Cpk计算方式进行了改进，提出了一种与成品率具有一一对应关系的等效工序能力指数ECpk。之后沿用这一思想引出基于成品率的多变量工序能力指数MECpk的概念及计算方法，并分析了协方差矩阵对多变量工艺成品率的影响，提出了一种提升工艺成品率的解决思路。最后通过实例详述了多变量工序能力指数的计算过程，通过与其他多变量工序能力指数评价结果对比，验证了MECpk指数的有效性。
4).成品率反映了产品的内在质量和可靠性。从购买者的角度出发，介绍了如何利用产品特性参数的截尾样本数据来评价供应商所提供产品的质量；提出了利用服从截尾正态分布的样本数据推测产品成品率的方法，该方法同时适用于单侧及双侧截尾情况；定量分析了成品率计算结果的置信区间，进而给出了该方法对样本容量的要求。同时，结合半导体产品的实际测试数据介绍了基于截尾数据推测成品率的步骤，并验证了算法有效性。
5).此外，在本课题的研究基础上，开发了质量控制与评价软件系统。该软件包含了质量过程控制与工艺评价功能，涵盖了多种控制图技术和工序能力指数计算方法，而且具有本文所提出的多变量工序能力指数计算模块。
In the field of modern semiconductor and integrated circuit manufacturing, asprocess, technology and equipments are becoming more and more complicated, thefunction of electronic devices is becoming more perfect and users bring morerequirements to process level and product quality.Then, it isnecessary thatthe techniquesof quality control and process evaluation should be paied more attention. At the sametime, in order to keep abreast of time and compete with international companies, domesticcompanies begin to implement techniques of quality management and process evaluation.So, their implement is of important significance.
This dissertation studies some problems of process control and evaluation inmultivariate process and multi-variety and small batch manufacturing system using self-starting technique, multivariate numerical integration and maximum likelihoodestimation and so on through theory and computer simulation analysis. The problemsinclude monitoring process mean and standard deviation of multi-variety and small batchproduction run, and the evaluation of the process and product quality of multivariateprocess. In the meanwhile, the method of evaluation on the quality of product providedby suppliers based on truncated sample is also introduced. These researches can improveprocess products quality and reduce quality defects. It is meaningful to up-grate marketcompetitiveness of enterprise. The main contents are summarized as follows:
1). Fistly, the existing problem of implementing quality control and evaluation inmulti-variety and small batch production runs to monitor process mean and standarddeviation is analyzed. A quality control technique in multi-variety and small batchmanufacturing system, T-K control chart, is proposed constructively. Using this method,the quality manager needn’t collect samples as many as traditional chart. The T or Kstatistics are calculated based on each subgroup, and the statistics of each subgroup areindependent with each other and have an identical distribution. This method adopts self-startingtechnique, and does notrequire PhaseI sample aimingat estimating processmean.Especially, the T-chart does not need the estimation of variance. Even the distributionparameters are unknown, the T-K chart can be used to monitor multi-variety and smallbatch production run as long as there are no less than2subgroups.
2). In the light of the theory of statistical process control, some methods to evaluatethe performance of control chart are discussed. Then, the concept, the significance andthe calculation steps of average run length are introduced. The ARL performance of Tchart and K chart is analyzed. In addition, the shortcoming of self-starting control chart is studied, and a strategy for optimizing theARLperformance of self-staring control chartis proposed. The result reveals that the ARL performance is improved dramatically afterthe optimization.
3). The relationship between the index Cpkand process yield for the case with singlecharacteristic is analyzed. Then an equivalent process capability index ECpkis proposedbased on the idea of six sigma design strategy. ECpkindex has a one-to-onecorrespondence relationship with process yield. Following this idea we develop amultivariate PCI MECpkwhich can be used to evaluate process capability for processeswith multiple characteristics and we also discuss the impact of covariance matrix onprocess yield, fromwhich the authors propose a solution to improve overall process yield.Some illustrative examples are presented to verify the validity of the suggested index invarious cases.
4). It is known that product yield reflects the potential product quality and reliability,which means that high yield corresponds to good quality and high reliability. From theview of consumers, the method of judging the quality of products supplied bymanufacturers based on truncated samples is introduced. This dissertation proposes analgorithm for calculating the parameters of full Gaussian distribution before truncationbased on truncated dataand estimating product yield.The algorithmis proper to both one-side and two-side truncation. The confidence interval of the yield result is derived, andthe effect of sample size on the precision of the calculation result is also analyzed. Finally,the steps for calculating the product yield are offered and the effectiveness of thisalgorithm is verified by an actual instance.
5). In addition, based on the models and algorithms discussed above, the computer-aid quality control and process evaluation software is developed. The software systemincludes the function for statistical process control and process capability evaluation. Thesoftware offers many control charts,process capability indicesand especially the functionfor computing multivariate process capability index proposed in this dissertation.
引文
[1] John E. Bauer, Grace L. Duffy, Russell T. Westcott. The Quality ImprovementHandbook, Second Edition. U.S.:ASQ Quality Press,2006.
[2] Jensen, W. A., Jones-Farmer, A. L., Champ, C. W. and Woodall, W. H.. Effects ofparameter estimation on control charts properties: a literature review. Journal ofQuality Technology2006,38,349-364.
[3] Capizzi, G. and Masarotto, G.. Practical design of generalized likelihood ratiocontrol charts for autocor-related data. Technometrics2008,50,357-370.
[4]袁普及.基于成组技术的质量控制的研究－SPC在多品种小批量制造中的应用：[硕士学位论文]．南京，南京航空航天大学，2003.
[5] Pearn WL, Kang HY, Lee AHI, Liao MY. Photolithography Control in WaferFabrication Based on Process Capability Indices with Multiple Characteristics.IEEE Transactions on Semiconductor Manufacturing2009;22(3):351–356. DOI:10.1109/TSM.2009.2024851
[6] Chan LK, Cheng SW, Spiring FA. A multivariate measure of process capability.Journal of Modeling and Simulation1991;11:1–11.
[7] Acemoglu D,Verdier T. Property rights, corruption and the allocation of talent: Ageneral equilibrium approach[J]. Economic Journal,1998,108:1381-1403.
[8]贾新章,李京苑.统计过程控制与评价:Cpk/SPC和PPM技术,第一版.北京:电子工业出版社,2004.
[9] C. P. Quesenberry. The effect of sample size on estimated limits for and X controlcharts. Journal of Quality Technology1993;25,237-247.
[10] C. P. Quesenberry. SPC methods for quality improvement. U.S.: Wiley,1997.
[11]Automotive IndustryAction Group,American Society for Quality Control, SupplierQuality Requirements Task Force. Fundamental statistical process control:reference manual. U.S.:AIAG,1991.
[12] Quesenberry CP. SPC Q charts for start-up processes and short or long runs. Journalof Quality Technology1991;23:213-224
[13] Quesenberry, C. P. On properties of Q charts for variables. Journal of QualityTechnology1995;27,184-203.
[14] Zantek PF. Run-length distributions of Q-chart schemes. IIE Transactions2005;37:1037-1045.
[15] Del Castillo E, Montgomery DC. Short-run statistical process control: Q chartenhancements and alternative methods. Quality and Reliability EngineeringInternational1994;10:87-97
[16] He F, Jiang W, Shu L. Improved self-starting control charts for short runs. QualityTechnology and Quantitative Management,2008;5(3):289--308.
[17] G. Nenes, G. Tagaras. The economically designed CUSUM chart for monitoringshort production runs. International Journal of Production Research2006;44(19):1569-1587
[18] Hawkins, D. M. Self-starting CUSUM charts for location and scale. The Statistician1987;36,299-315.
[19] Celano, G., Castagliola, P., Trovato, E. and Fichera, S. Shewhart and EWMA tcontrol charts for short production runs. Quality and Reliability EngineeringInternational2011;27:313–326.
[20] Montgomery DC. Introduction to Statistical Quality Control (5th edn). Wiley: NewYork, NY, U.S.A.,2005
[21] D.R. Bothe,SPCforShortRunProductionRuns,InternationalQualityInstituteInc.,Northville, Michigan,1988.
[22] Lin, S.-Y., Lai, Y.-J. and Chang, S. I. Short-Run statistical process control:multicriteria part family formation. Quality and Reliability EngineeringInternational1997,13:9–24.
[23] Castagliola P, Celano G, Fichera S. Monitoring process variability using EWMA.Handbook of Engineering Statistics, Pham H (ed.). Springer: Berlin,2006;291–325.
[24] Castagliola P. A R-EWMA control chart for monitoring the process range.International Journal of Reliability, Quality, and Safety Engineering2005;12:31–49.
[25] Castagliola, P. and V nnman, K.(2007), Monitoring capability indices using anEWMAapproach. Qual. Reliab. Engng. Int.,23:769–790. doi:10.1002/qre.838
[26] Castagliola, P. and V nnman, K.(2008), Average run length when monitoringcapability indices using EWMA. Qual. Reliab. Engng. Int.,24:941–955. doi:10.1002/qre.940
[27]M.E.EvansandN.F.Hubele,Acasestudyoffamilyformation forstatistical processcontrol in small-batch manufacturing: presentation and discussion with questionsand answers, Society of Manufacturing Engineers, Blue Book Series, Dearborn,Michigan,1993.
[28] D. L. Kimbler and B.A. Sudduth, Using statistical process control with mixed partsin FSM, Proceedings of the Japan-USA Symposium on Flexible Automation, SanFrancisco,1992, pp441-445.
[29] G. F. Koons and J. J. Luner, SPC in low volume manufacturing: a case study, Journalof Quality Technology1991,23,(4),287-295
[30] Quesenberry, C. P. The effect of sample size on estimated limits for X and Xcontrol charts. Journal of Quality Technology1993,25,237-247.
[31] Eugene L. Grant, Richard S. Leavenworth.统计质量控制[M].北京:清华大学出版社,2001
[32] Lothar Sachs.应用统计手册[M].天津:天津科技翻译出版公司,1988
[33]西格蒙哈尔朋.保证科学——质量控制及可靠性导论[M].中国标准出版社,1984.
[34]彼得S.潘得,罗伯特P.纽曼,罗兰R.卡瓦纳.6西格玛管理法[M].机械工业出版社,2001.
[35] J.M.朱兰,小弗兰克M.格里纳.质量计划与分析[M].石油工业出版社,1985.
[36] J.M.朱兰.质量控制手册上[M].上海科学技术文献出版社,1980.
[37] J.M.朱兰.质量控制手册下[M].上海科学技术文献出版社,1980.
[38]森口繁一.新编质量管理的统计学方法[M].机械工业出版社,1988.
[39]田口玄一.质量工程学概论[M].中国对外翻译出版公司,1985.
[40] Kotz S and Johnson N. L., Process Capability Indices, Chapman and Hall,London[M], U.K.,1993a
[41] Bothe D.R., Measuring Process Capability, McGraw-Hill[M], New York,1997
[42] Kotz S. and Lovelace C., Introduction to Process Capability Indices[M], Arnold,London, U.K.,1998
[43] Wheeler, D, J., Beyond Capability Confusion[M], SPC Press, Knoxville, T.N.,1999
[44] Rinne, M. and Mittag, H. J., Prozeβfajigkeitsmessung fur die industrielle Praxis(withEnglish summary)[M], Carl Hanser Verlag Munchen Wien,1999.
[45] W. L. Pearn, S. Kotz, N. L. Johnson. Distributional and inferential properties ofprocess capability indices. Journal of Quality Technology1992;24(4):216–231.
[46] W. Taam, P. Subbaiah, J.W. Liddy.Anote on multivariate capability indices. JournalofApplied Statistics1993;20(3):339--351.
[47] Mohammad R. Niavarani, Rassoul Noorossana, Babak Abbasi. Three NewMultivariate Process Capability Indices. Communications in Statistics-Theory andMethods Vol.41, Iss.2,2012
[48] F.K. Wang, J.C. Chen. Capability Index using Principal Components Analysis.Quality Engineering1998;11(1):21-27.
[49] R.L. Shinde, K.G. Khadse. Multivariate process capability using principalcomponent analysis. Quality and Reliability Engineering International2009;25(1):69–77.
[50] N.F. Hubele, H. Shahriari, C.S. Cheng.“A Bivariate Process Capability Vector, inStatistics and Design in Process Control” in Statistical Process Control inManufacturing edited by J. B. Keats, and D. C. Montgomery. Marcel Dekker, NY:299-310.1991
[51] H. Shahriari, N.F. Hubele, F.P. Lawrence. A Multivariate Process Capability Vector.Proceedings of the4th Industrial Engineering Research Conference1995. pp.303-308.
[52] Chen, H.,1994,“A Multivariate Process Capability Index over a Rectangular SolidTolerance Zone”, Statistica Sinica,4, pp.749-758.
[53] Chan, L. K., Cheng, S. W., Spiring, F. A.(1991). A multivariate measure of processcapability. Int. J. Model. Simul.11:1–6.
[54] Wang, F. K., Du, T. C. T.(2000). Using principal component analysis in processperformance for multivariate data. Omega. Int. J. Manage. Sci.28:185–194.
[55] Pearn, W. L., Chen, K. S.,(2002). One-sided capability indices CPU and CPL:decision making with sample information. Int. J. Qual. Reliab. Manage.19(3):221–245.
[56] Bothe DR. A capability study for an entire product. ASQC Quality CongressTransactions, Nashville, TN, vol.46,1992;172--178.
[57] W. L. Pearn, J.-J. H. Shiau, Y. T. Tai and M. Y. Li. Capability Assessment forProcesses with Multiple Characteristics:AGeneralization of the Popular Index Cpk.Quality and Reliability Engineering International2011;27(8):1119–1129.
[58] Chen, K. S., Pearn, W. L. and Lin, P. C., Capability measures for processes withmultiple characteristics. Qual. Reliab. Engng. Int.(2003),19:101–110.
[59] Boyles RA. The Taguchi capability index. Journal of Quality Technology1991;23:17--26.
[60] Pearn, W. L., Wu, C. H. and Tsai, M. C.(2012), A Note on “Capability Assessmentfor Processes with Multiple Characteristics: A Generalization of the Popular IndexCpk”. Qual. Reliab. Engng. Int.. doi:10.1002/qre.1295
[61] Perakis, M. and Xekalaki, E., On the Implementation of the Principal ComponentAnalysis–Based Approach in Measuring Process Capability. Qual. Reliab. Engng.Int.(2011). doi:10.1002/qre.1260
[62] M. Schoonhoven, M. Riaz and R. J M M Does. Design and Analysis of ControlCharts for Standard Deviation with Estimated Parameters. Journal of qualitytechnology2011,43(4):307-334.
[63] Wu, Chien-wei.An Overview of Theory and Practice On Process Capability Indicesfor Quality Assurance. International Journal of Production Economics.2009.117(2):338-359.
[64] J. C. Lee, H. N. Hung, W. L. Pearn and T. L.Kueng. On the distribution of theestimated process yield index Spk. Qual. Reliab. Engng. Int.(2002),18:111–116.
[65] Peter Olofsson, Mikael Andersson. Probability, Statistics, and Stochastic Processes,2nd Edition. U.S.: Wiley,2012.
[66] R.E. Walpole, R.H. Myers, S.L. Myers, and K. Ye. Probability&Statistics forEngineers&Scientists (8th edn). Prentice Hall: NJ,U.S.A.,2006
[67]王兆军,巩震,邹长亮等. ARL计算方法综述.数理统计与管理,2011.30(3):467-497.
[68] James C. Fua, Fred A. Spiringa and Hansheng Xieb. On the average run lengths ofquality control schemes using a Markov chain approach. Statistics&ProbabilityLetters,2002.56(4):369–380.
[69] D. Brook and D. A. Evans. An Approach to the Probability Distribution of CusumRun Length. Biometrika,1972.59(3):539-549.
[70] Zhang, L., Chen, G. and Castagliola, P. On t and EWMA t charts for monitoringchanges in the process mean. Quality and Reliability Engineering International2009,25:933–945.
[71] Johnson, N. L., Kotz, S., and Balakrishnan, N. Continuous Univariate Distributions(Volume2)2nd edition, John Wiley&Sons, New York, U.S.A.,2005.
[72] Yum, B.-J. and Kim, K.-W.(2011), A bibliography of the literature on processcapability indices:2000–2009. Qual. Reliab. Engng. Int.,27:251–268. doi:10.1002/qre.1115
[73] Thomas Pyzdek, Paul Keller. The Six Sigma Handbook, Third Edition[M]. NewYork: McGraw-Hill Professional,2010
[74] Z. Drezner. Computation of the Trivariate Normal Integral. Mathematics ofComputation1994;63:289–294.
[75] Z. Drezner and G. O. Wesolowsky. On the Computation of the Bivariate NormalIntegral. Journal of Statistical Computation and Simulation1989;35:101–107.
[76] A. Genz. Numerical Computation of Rectangular Bivariate and Trivariate Normaland t Probabilities. Statistics and Computing2004;14(3):251–260.
[77] A. Genz and F. Bretz. Numerical Computation of Multivariate t Probabilities withApplication to Power Calculation of Multiple Contrasts. Journal of StatisticalComputation and Simulation1999;63:361–378.
[78] A. Genz and F. Bretz. Comparison of Methods for the Computation of Multivariatet Probabilities. Journal of Computational and Graphical Statistics2002;11(4):950–971.
[79] R.L. Plackett. A reduction formula for normal multivariate integrals. BiometrikaTrust1954;41(3):351360.
[80] T.L. Sultan. An acceptance chart for raw materials of two correlated properties.QualityAssurance1986;12:70--72.
[81] J.-N. Pan and C.-Y. Lee. New capability indices for evaluating the performance ofmultivariate manufacturing processes. Quality and Reliability EngineeringInternational2010;26:3–15.
[82]P.L. GoethalsandB.R. Cho.Thedevelopmentofa target-focusedprocesscapabilityindex with multiple characteristics. Quality and Reliability EngineeringInternational2011;27:297–311.
[83] C. W. Wu and W. L. Pearn. Measuring manufacturing capability for couplers andwavelength division multiplexers. The International Journal of AdvancedManufacturing Technology2005;25:533–541.
[84] Mo PH. Corruptionand economic growth. Journal of Comparative Economics,2001,29:66-79.
[85] Wen Lea Pearn, H. N. Hung, N. F. Peng etal. Testing process precision for truncatednormal distributions. Microelectronics Reliability,2007,47(12):2275-2281.
[86] Kane VE. Process capability indices. Journal of Quality Technology,1986,18:41--52.
[87] Kotz S, Johnson NL. Process capability indices—A review,1992–2000. Journal ofQuality Technology,2002,34(1):1--19.
[88] Rose-Ackerman S. Redesigning the State to Fight Corruption: Transparency,Competition and Privatization. Public Policy for Private Sector. Washington,DC.:World Bank,1996.
[89] Liang Tao, Jia Xinzhang. An empirical formula for yield estimation from singlytruncated performance data of qualified semiconductor devices. Journal ofSemiconductors,2012,33(12):125008-7.
[90] Norman L. Johnson, Samuel Kotz, N. Balakrishnan. Continuous UnivariateDistributions, Volume1, second edition. New York: Wiley-Interscience,1994.
[91] Joseph-Frédéric Bonnans, Jean Charles Gilbert, Claude Lemarechal. Numericaloptimization: Theoretical and practical aspects, second edition. Berlin: Springer-Verlag,2006.
[92] F. Y. Edgeworth. On the Probable Errors of Frequency-Constants. Journal of theRoyal Statistical Society,1908,71(3):499–512.
[93] John W. Pratt. F. Y. Edgeworth and R. A. Fisher on the Efficiency of MaximumLikelihood Estimation. TheAnnals of Statistics,1976,4(3):501–514.
[94] Whitney K. Newey, Daniel McFadden. Handbook of Econometrics, Volume4.Amsterdam: Elsevier Science,1994.
[2] Jensen, W. A., Jones-Farmer, A. L., Champ, C. W. and Woodall, W. H.. Effects ofparameter estimation on control charts properties: a literature review. Journal ofQuality Technology2006,38,349-364.
[3] Capizzi, G. and Masarotto, G.. Practical design of generalized likelihood ratiocontrol charts for autocor-related data. Technometrics2008,50,357-370.
[4]袁普及.基于成组技术的质量控制的研究－SPC在多品种小批量制造中的应用：[硕士学位论文]．南京，南京航空航天大学，2003.
[5] Pearn WL, Kang HY, Lee AHI, Liao MY. Photolithography Control in WaferFabrication Based on Process Capability Indices with Multiple Characteristics.IEEE Transactions on Semiconductor Manufacturing2009;22(3):351–356. DOI:10.1109/TSM.2009.2024851
[6] Chan LK, Cheng SW, Spiring FA. A multivariate measure of process capability.Journal of Modeling and Simulation1991;11:1–11.
[7] Acemoglu D,Verdier T. Property rights, corruption and the allocation of talent: Ageneral equilibrium approach[J]. Economic Journal,1998,108:1381-1403.
[8]贾新章,李京苑.统计过程控制与评价:Cpk/SPC和PPM技术,第一版.北京:电子工业出版社,2004.
[9] C. P. Quesenberry. The effect of sample size on estimated limits for and X controlcharts. Journal of Quality Technology1993;25,237-247.
[10] C. P. Quesenberry. SPC methods for quality improvement. U.S.: Wiley,1997.
[11]Automotive IndustryAction Group,American Society for Quality Control, SupplierQuality Requirements Task Force. Fundamental statistical process control:reference manual. U.S.:AIAG,1991.
[12] Quesenberry CP. SPC Q charts for start-up processes and short or long runs. Journalof Quality Technology1991;23:213-224
[13] Quesenberry, C. P. On properties of Q charts for variables. Journal of QualityTechnology1995;27,184-203.
[14] Zantek PF. Run-length distributions of Q-chart schemes. IIE Transactions2005;37:1037-1045.
[15] Del Castillo E, Montgomery DC. Short-run statistical process control: Q chartenhancements and alternative methods. Quality and Reliability EngineeringInternational1994;10:87-97
[16] He F, Jiang W, Shu L. Improved self-starting control charts for short runs. QualityTechnology and Quantitative Management,2008;5(3):289--308.
[17] G. Nenes, G. Tagaras. The economically designed CUSUM chart for monitoringshort production runs. International Journal of Production Research2006;44(19):1569-1587
[18] Hawkins, D. M. Self-starting CUSUM charts for location and scale. The Statistician1987;36,299-315.
[19] Celano, G., Castagliola, P., Trovato, E. and Fichera, S. Shewhart and EWMA tcontrol charts for short production runs. Quality and Reliability EngineeringInternational2011;27:313–326.
[20] Montgomery DC. Introduction to Statistical Quality Control (5th edn). Wiley: NewYork, NY, U.S.A.,2005
[21] D.R. Bothe,SPCforShortRunProductionRuns,InternationalQualityInstituteInc.,Northville, Michigan,1988.
[22] Lin, S.-Y., Lai, Y.-J. and Chang, S. I. Short-Run statistical process control:multicriteria part family formation. Quality and Reliability EngineeringInternational1997,13:9–24.
[23] Castagliola P, Celano G, Fichera S. Monitoring process variability using EWMA.Handbook of Engineering Statistics, Pham H (ed.). Springer: Berlin,2006;291–325.
[24] Castagliola P. A R-EWMA control chart for monitoring the process range.International Journal of Reliability, Quality, and Safety Engineering2005;12:31–49.
[25] Castagliola, P. and V nnman, K.(2007), Monitoring capability indices using anEWMAapproach. Qual. Reliab. Engng. Int.,23:769–790. doi:10.1002/qre.838
[26] Castagliola, P. and V nnman, K.(2008), Average run length when monitoringcapability indices using EWMA. Qual. Reliab. Engng. Int.,24:941–955. doi:10.1002/qre.940
[27]M.E.EvansandN.F.Hubele,Acasestudyoffamilyformation forstatistical processcontrol in small-batch manufacturing: presentation and discussion with questionsand answers, Society of Manufacturing Engineers, Blue Book Series, Dearborn,Michigan,1993.
[28] D. L. Kimbler and B.A. Sudduth, Using statistical process control with mixed partsin FSM, Proceedings of the Japan-USA Symposium on Flexible Automation, SanFrancisco,1992, pp441-445.
[29] G. F. Koons and J. J. Luner, SPC in low volume manufacturing: a case study, Journalof Quality Technology1991,23,(4),287-295
[30] Quesenberry, C. P. The effect of sample size on estimated limits for X and Xcontrol charts. Journal of Quality Technology1993,25,237-247.
[31] Eugene L. Grant, Richard S. Leavenworth.统计质量控制[M].北京:清华大学出版社,2001
[32] Lothar Sachs.应用统计手册[M].天津:天津科技翻译出版公司,1988
[33]西格蒙哈尔朋.保证科学——质量控制及可靠性导论[M].中国标准出版社,1984.
[34]彼得S.潘得,罗伯特P.纽曼,罗兰R.卡瓦纳.6西格玛管理法[M].机械工业出版社,2001.
[35] J.M.朱兰,小弗兰克M.格里纳.质量计划与分析[M].石油工业出版社,1985.
[36] J.M.朱兰.质量控制手册上[M].上海科学技术文献出版社,1980.
[37] J.M.朱兰.质量控制手册下[M].上海科学技术文献出版社,1980.
[38]森口繁一.新编质量管理的统计学方法[M].机械工业出版社,1988.
[39]田口玄一.质量工程学概论[M].中国对外翻译出版公司,1985.
[40] Kotz S and Johnson N. L., Process Capability Indices, Chapman and Hall,London[M], U.K.,1993a
[41] Bothe D.R., Measuring Process Capability, McGraw-Hill[M], New York,1997
[42] Kotz S. and Lovelace C., Introduction to Process Capability Indices[M], Arnold,London, U.K.,1998
[43] Wheeler, D, J., Beyond Capability Confusion[M], SPC Press, Knoxville, T.N.,1999
[44] Rinne, M. and Mittag, H. J., Prozeβfajigkeitsmessung fur die industrielle Praxis(withEnglish summary)[M], Carl Hanser Verlag Munchen Wien,1999.
[45] W. L. Pearn, S. Kotz, N. L. Johnson. Distributional and inferential properties ofprocess capability indices. Journal of Quality Technology1992;24(4):216–231.
[46] W. Taam, P. Subbaiah, J.W. Liddy.Anote on multivariate capability indices. JournalofApplied Statistics1993;20(3):339--351.
[47] Mohammad R. Niavarani, Rassoul Noorossana, Babak Abbasi. Three NewMultivariate Process Capability Indices. Communications in Statistics-Theory andMethods Vol.41, Iss.2,2012
[48] F.K. Wang, J.C. Chen. Capability Index using Principal Components Analysis.Quality Engineering1998;11(1):21-27.
[49] R.L. Shinde, K.G. Khadse. Multivariate process capability using principalcomponent analysis. Quality and Reliability Engineering International2009;25(1):69–77.
[50] N.F. Hubele, H. Shahriari, C.S. Cheng.“A Bivariate Process Capability Vector, inStatistics and Design in Process Control” in Statistical Process Control inManufacturing edited by J. B. Keats, and D. C. Montgomery. Marcel Dekker, NY:299-310.1991
[51] H. Shahriari, N.F. Hubele, F.P. Lawrence. A Multivariate Process Capability Vector.Proceedings of the4th Industrial Engineering Research Conference1995. pp.303-308.
[52] Chen, H.,1994,“A Multivariate Process Capability Index over a Rectangular SolidTolerance Zone”, Statistica Sinica,4, pp.749-758.
[53] Chan, L. K., Cheng, S. W., Spiring, F. A.(1991). A multivariate measure of processcapability. Int. J. Model. Simul.11:1–6.
[54] Wang, F. K., Du, T. C. T.(2000). Using principal component analysis in processperformance for multivariate data. Omega. Int. J. Manage. Sci.28:185–194.
[55] Pearn, W. L., Chen, K. S.,(2002). One-sided capability indices CPU and CPL:decision making with sample information. Int. J. Qual. Reliab. Manage.19(3):221–245.
[56] Bothe DR. A capability study for an entire product. ASQC Quality CongressTransactions, Nashville, TN, vol.46,1992;172--178.
[57] W. L. Pearn, J.-J. H. Shiau, Y. T. Tai and M. Y. Li. Capability Assessment forProcesses with Multiple Characteristics:AGeneralization of the Popular Index Cpk.Quality and Reliability Engineering International2011;27(8):1119–1129.
[58] Chen, K. S., Pearn, W. L. and Lin, P. C., Capability measures for processes withmultiple characteristics. Qual. Reliab. Engng. Int.(2003),19:101–110.
[59] Boyles RA. The Taguchi capability index. Journal of Quality Technology1991;23:17--26.
[60] Pearn, W. L., Wu, C. H. and Tsai, M. C.(2012), A Note on “Capability Assessmentfor Processes with Multiple Characteristics: A Generalization of the Popular IndexCpk”. Qual. Reliab. Engng. Int.. doi:10.1002/qre.1295
[61] Perakis, M. and Xekalaki, E., On the Implementation of the Principal ComponentAnalysis–Based Approach in Measuring Process Capability. Qual. Reliab. Engng.Int.(2011). doi:10.1002/qre.1260
[62] M. Schoonhoven, M. Riaz and R. J M M Does. Design and Analysis of ControlCharts for Standard Deviation with Estimated Parameters. Journal of qualitytechnology2011,43(4):307-334.
[63] Wu, Chien-wei.An Overview of Theory and Practice On Process Capability Indicesfor Quality Assurance. International Journal of Production Economics.2009.117(2):338-359.
[64] J. C. Lee, H. N. Hung, W. L. Pearn and T. L.Kueng. On the distribution of theestimated process yield index Spk. Qual. Reliab. Engng. Int.(2002),18:111–116.
[65] Peter Olofsson, Mikael Andersson. Probability, Statistics, and Stochastic Processes,2nd Edition. U.S.: Wiley,2012.
[66] R.E. Walpole, R.H. Myers, S.L. Myers, and K. Ye. Probability&Statistics forEngineers&Scientists (8th edn). Prentice Hall: NJ,U.S.A.,2006
[67]王兆军,巩震,邹长亮等. ARL计算方法综述.数理统计与管理,2011.30(3):467-497.
[68] James C. Fua, Fred A. Spiringa and Hansheng Xieb. On the average run lengths ofquality control schemes using a Markov chain approach. Statistics&ProbabilityLetters,2002.56(4):369–380.
[69] D. Brook and D. A. Evans. An Approach to the Probability Distribution of CusumRun Length. Biometrika,1972.59(3):539-549.
[70] Zhang, L., Chen, G. and Castagliola, P. On t and EWMA t charts for monitoringchanges in the process mean. Quality and Reliability Engineering International2009,25:933–945.
[71] Johnson, N. L., Kotz, S., and Balakrishnan, N. Continuous Univariate Distributions(Volume2)2nd edition, John Wiley&Sons, New York, U.S.A.,2005.
[72] Yum, B.-J. and Kim, K.-W.(2011), A bibliography of the literature on processcapability indices:2000–2009. Qual. Reliab. Engng. Int.,27:251–268. doi:10.1002/qre.1115
[73] Thomas Pyzdek, Paul Keller. The Six Sigma Handbook, Third Edition[M]. NewYork: McGraw-Hill Professional,2010
[74] Z. Drezner. Computation of the Trivariate Normal Integral. Mathematics ofComputation1994;63:289–294.
[75] Z. Drezner and G. O. Wesolowsky. On the Computation of the Bivariate NormalIntegral. Journal of Statistical Computation and Simulation1989;35:101–107.
[76] A. Genz. Numerical Computation of Rectangular Bivariate and Trivariate Normaland t Probabilities. Statistics and Computing2004;14(3):251–260.
[77] A. Genz and F. Bretz. Numerical Computation of Multivariate t Probabilities withApplication to Power Calculation of Multiple Contrasts. Journal of StatisticalComputation and Simulation1999;63:361–378.
[78] A. Genz and F. Bretz. Comparison of Methods for the Computation of Multivariatet Probabilities. Journal of Computational and Graphical Statistics2002;11(4):950–971.
[79] R.L. Plackett. A reduction formula for normal multivariate integrals. BiometrikaTrust1954;41(3):351360.
[80] T.L. Sultan. An acceptance chart for raw materials of two correlated properties.QualityAssurance1986;12:70--72.
[81] J.-N. Pan and C.-Y. Lee. New capability indices for evaluating the performance ofmultivariate manufacturing processes. Quality and Reliability EngineeringInternational2010;26:3–15.
[82]P.L. GoethalsandB.R. Cho.Thedevelopmentofa target-focusedprocesscapabilityindex with multiple characteristics. Quality and Reliability EngineeringInternational2011;27:297–311.
[83] C. W. Wu and W. L. Pearn. Measuring manufacturing capability for couplers andwavelength division multiplexers. The International Journal of AdvancedManufacturing Technology2005;25:533–541.
[84] Mo PH. Corruptionand economic growth. Journal of Comparative Economics,2001,29:66-79.
[85] Wen Lea Pearn, H. N. Hung, N. F. Peng etal. Testing process precision for truncatednormal distributions. Microelectronics Reliability,2007,47(12):2275-2281.
[86] Kane VE. Process capability indices. Journal of Quality Technology,1986,18:41--52.
[87] Kotz S, Johnson NL. Process capability indices—A review,1992–2000. Journal ofQuality Technology,2002,34(1):1--19.
[88] Rose-Ackerman S. Redesigning the State to Fight Corruption: Transparency,Competition and Privatization. Public Policy for Private Sector. Washington,DC.:World Bank,1996.
[89] Liang Tao, Jia Xinzhang. An empirical formula for yield estimation from singlytruncated performance data of qualified semiconductor devices. Journal ofSemiconductors,2012,33(12):125008-7.
[90] Norman L. Johnson, Samuel Kotz, N. Balakrishnan. Continuous UnivariateDistributions, Volume1, second edition. New York: Wiley-Interscience,1994.
[91] Joseph-Frédéric Bonnans, Jean Charles Gilbert, Claude Lemarechal. Numericaloptimization: Theoretical and practical aspects, second edition. Berlin: Springer-Verlag,2006.
[92] F. Y. Edgeworth. On the Probable Errors of Frequency-Constants. Journal of theRoyal Statistical Society,1908,71(3):499–512.
[93] John W. Pratt. F. Y. Edgeworth and R. A. Fisher on the Efficiency of MaximumLikelihood Estimation. TheAnnals of Statistics,1976,4(3):501–514.
[94] Whitney K. Newey, Daniel McFadden. Handbook of Econometrics, Volume4.Amsterdam: Elsevier Science,1994.
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