基于对数正态分布的若干非寿险问题
|
摘要
本文在对非寿险精算、控制图研究进展做出综述的基础上,指出将控制图用于非寿险精算风险控制是可行的；给出短期聚合理赔总量的平移对数正态分布近似,并研究平移对数正态分布的概率统计性质及其与短期聚合理赔总量的平移伽玛分布近似的异同；以对数正态分布为理论分布,给出均值-极差联合控制图和指数加权移动平均控制图的控制限表达式、控制限系数表(双侧及单侧两种情况)、控制图的使用步骤及注意事项,并采用平均链长指标评价给出的质量控制图控制效果的好坏；给出反映免赔额及限额损失再保险影响的截尾对数正态分布的参数估计的方法,并结合案例,给出左截尾对数正态分布的拟合步骤和分析。
This paper gives an overview based on the non-life insurance,control charts research progress, point out that the control charts can used for the non-life insurance calculation and risk control is viable; Giving the approximation of parallel move log-normal distribution based on short polymeric claims total, reaching the probability and statistic nature of parallel move log-normal distribution, then comparing with parallel move gamma distribution; Designing the control lines,control lines coefficient table(one-side and double side),the operation steps and matters need attention of mean-range control charts and EWMA control chart based on log-normal distribution,then evaluating the effectiveness of quality control charts use average range length;In the end, giving the estimation of parameter method based on truncated log-normal distribution which can reflect the influence of deductible and quota loss reinsurance, then giving the fit steps and analysis of left truncated log-normal distribution with an example.
This paper gives an overview based on the non-life insurance,control charts research progress, point out that the control charts can used for the non-life insurance calculation and risk control is viable; Giving the approximation of parallel move log-normal distribution based on short polymeric claims total, reaching the probability and statistic nature of parallel move log-normal distribution, then comparing with parallel move gamma distribution; Designing the control lines,control lines coefficient table(one-side and double side),the operation steps and matters need attention of mean-range control charts and EWMA control chart based on log-normal distribution,then evaluating the effectiveness of quality control charts use average range length;In the end, giving the estimation of parameter method based on truncated log-normal distribution which can reflect the influence of deductible and quota loss reinsurance, then giving the fit steps and analysis of left truncated log-normal distribution with an example.
引文
1. ISO 8258, Shewhart Control Charts[S].1991
2. 中华人民共和国国家标准GB/T4091-2001,常规控制图[s].北京：中国标准出版社,2001
3. 美国国家研究委员会.1993.振兴美国数学—90年代的计划[M].北京：世界图书出版公司,1993,111-112
4. 谢志刚,韩天雄.风险理论与非寿险精算[M].天津：南开大学出版社.2000,143-145
5. Burr I.W..The Effect of Non-normality on Constants for X and R Chart[J].Industrial Quality Control.1967,24(5),563-569
6. Schilling E.G. and Nelson P.R..The Effect of Non-normality on the Control Limits of X Charts[J]. Journal of Quality Technology.1976,8(3),183-188
7. Balakrishnan and Kocherlakota. Effect of Non-normality on X Charts:Single Assignable Cause Model[J]. Naval Research Logistics Quarterly.1986,48(3),439-444
8. Chan L.K.,Hapuarachchi K.P. and Macpherson B.D..Robustness of X and R Charts[J].IEEE Transactions on Reliability.1988,37(2),117-123
9. 张洪涛.保险经济学[M].北京：中国人民大学出版社.2006
10. 汪祖杰.现代保险学概论[M].北京：经济科学出版社.2007
11.付菊,徐沈新.保险学概论[M].北京：电子工业出版社.2007
12. MimuroT., Ohsakl M., Yasunaga H.. Four Parameter Evaluation Method of Lateral Transient Response[J]. SAE transactions.1990,99(6),1499-1508
13. 王新军.财产损失保险中损失分布建模的方法性研究[J].统计研究,2002,11,40-43
14. 吴礼斌.基于损失分布的再保险精算模型[J].统计与决策.2004,2,24
15.胡平.非寿险损失分布的精算模型研究[J].时代金融.2006,11,36
16. 施建祥,邬云玲.我国巨灾保险风险证券化研究[J].金融研究.2006,5,103-112
17. 杨星,郭彩琴.我国国债信用风险管理的实证研究[J].预测.2004,23(2),14-17
18. 许端.期权定价公式的概率论推导[J].北京工业大学学报.2004,30(3),382-385
19. 陈万义.非风险中性定价下的欧式期权定价公式[J].数学的实践与认识.2004,34(1),76-79
20.李超杰,何健敏.再装股票期权执行价格最低水平的决定[J].系统工程理论方法应用.2004,13(6),508-511
21. 吴震,杨晓光.信号交叉口右转车道饱和流量研究[J].同济大学学报(自然科学版).2008,36(1),37-41
22.谢涛,邱延峻,蒋泽中.岩石与混凝土界面断裂韧度的分布特性研究[J].岩石力学与工程学报.2004,23(13),2225-229
23.张学雷,王辉,张薇等.土壤系统分类与生物系统分类体系中的多样性特征对比分析[J].土壤学报.2008,45(1),1-8
24.章前,龙兵,邓昭等.昆明市某超市销售收入分析[J].昆明理工大学学报(理工版).2008,33(1),103-104
25.汪明明,周玉文,赵树旗等.降雨量公式的推求方法探讨[J].沈阳建筑大学学报(自然科学版).2008,24(2),274-277
26. 徐天群,陈跃鹏.防洪风险分析中改进的组合分布模型研究[J].数学的实践与认识.2004,34(5),84-90
27. 于洋,孙月静.对数正态分布参数的最大似然估计[J].九江学院学报.2007,6,55-57
28. 夏亚峰,马素丽.对数正态参数估计的损失函风险函数Bayes推断[J].兰州理工大学学报.2008,34(1), 131-133
29. 滕建辅,梁静毅,滕颖.对数正态分布伪随机数的产生与检验[J].天津商学院学报.2007,27(6),1-5
30. Clark Terry L.. Use of Log-normal Distribution for Numerical Calculations of Condensation and Collection[J]. Journal of the Atmospheric Sciences.1976,33(5),810-821
31. Chen G. Generalized Log-normal Distributions with Reliability Application[J]. Computational Statistics& Data Analysis.1995,15(3),309
32. Van Buren M.A.,Watt W.E., Marsalek J.. Application of the Log-normal and Normal Distributions to Stormwater Quality Parameters[J]. Water Research.1997,31(1),95-104
33. Tavassoli Z., Shivani A.,Esmaeilnia. Models of Fragmentation with Power Low Log-normal DistributionfJ]. Physica A:Statistical Mechanics and its Applications.2000,286(1),29-44
34. Yamada, Mitsuru,Nishihara,Akinori. A Log-Normal Distribution Model for Electron Multiplying Detector Signals in Charged Particle Beam Equipments[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences.2003, E86A(12),3276-3282
35. Beeke,Karina. Spectrum Planning-Analysis of Methods for the Summation of Log-normal Distributions[J]. EBU Technical Review.2007,312,145-154
36. Lerche I.. On Log-normal Distributions, Timescales and Basin Analysis Calculations[J]. Computers & Geosciences.1998,24(1),105
37. Simpson I.D., Standish N.. Derivation of the Log-normal Form of Both Section and Spatial Distribution of Particles[J]. Metallography.1977,10(2),149-159
38. Thomas John G.. Determination of log-normal Particle Size Distribution by Dynamic Light Scattering[J]. Journal of Colloid and Interface Science.1987,117(1),187-192
39. 盛聚,谢式千,潘承毅.概率论与数理统计[M].北京：高等教育出版社.2001,83-90
40. 孙志礼,陈良玉.实用机械可靠性设计理论与方法[M].北京：科学出版社.2003
41. Cohen A.C..Estimating the Mean and Variance of Normal Populations from Singly Truncated and Doubly Truncated Samples[J]. Annul of Mathmatica Statistics.1950,21(4),557-569
42. Douglas G Chapman. Estimating the Parameters of a Truncated Gamma Distribution[J]. Annul of Mathmatica Statistics 1956,27(2),498-506
43. Thompson H.R..Truncated Lognormal Distributions:I.Solution by Moments[J]. Biometrika.1951, 38(3-4),414-422
44. Nadarajah, Saralees, Kotz, Samuel. A Truncated Cauchy Distribution[J]. International Journal of Mathematical Education in Science and Technology.2006,37(5),605-608
45. Saralees, Nadarajah,Samuel, Kotz. A Skewed Truncated Cauchy Distribution with Applications in Economics [J]. Applied Economics Letters.2007,14(13),957-961
46. Masoom Ali.M, Saralees, Nadarajah. A Truncated Pareto Distribution[J]. Computer Communications.2006, 30(1),1-4
47. Masoom Ali.M, Saralees, Nadarajah. A Truncated Bivariate Generalized Pareto Distribution [J].Computer Communications.2007,30(8),1926-1930
48. Saralees, Nadarajah, Arjun,K.Gupta. A Skewed Truncated Pearson Type VII Distribution[J].Journal of Japan Statistical Society.2005,35(1),61-71
49. Nadarajah.S,Masoom Ali.M.A Skewed Truncated T Distribution[J]. International Journal of Mathematical Education in Science and Technology.2006,37(5),605-608
50. Coffey C.S, Muller K.E. Properties of Doubly-Truncated Gamma Variables[J]. Communications in Statistics: Theory and Methods.2000,29(4),851-857
51. Ami S.R. Srinivasa Rao. A Note on Derivation of the Generating Function for the Right Truncated Rayleigh Distribution[J]. Applied Mathematics Letters.2006,19(8),789-794
52. Blumenthal.S,Ram.C, Dahiya.Estimating Scale and Truncation Parameters for the Truncated Exponential Distribution with Type-I Censored Sampling [J]. Communications in Statistics-Theory and Methods.2005, 24(1),1-21
53. O'Reilly.F, Rueda.R. Fiducial Inferences for the Truncated Exponential Distribution[J]. Communications in Statistics-Theory and Methods.2007,36(12),2207-2212
54.宋卫星.非正则分布族中参数估计的最高相合阶[J].北京师范大学(自然科学版).2002,38(2),148-155
55.张玲霞,师义民.一维双边截断型分布族中参数函数的经验Bayes估计及其收敛速度[J].纯粹数学与应用数学.1999,15(3),92-98
56.成平,宋卫星.双边截断分布族中的卷积定理与渐近有效性[J].2001,44(4),737-746
57.许勇,师小琳,师义民.NA样本及Linex损失下截断族参数的经验EB估计[J].数学杂志.2004,24(2),124-130
58.张玲霞,师义民.双边截断型分布族参数函数的渐近最优经验Bayes估计[J].数学的实践与认识.2000,30(3),303-309
59.康会光,师义民,许勇.一类单边截断型分布族参数的双侧经验Bayes检验问题[J].工程数学学报.2002,19(2),81-85
60.师义民,赵小山,康会光Linex损失下单边截断型分布族参数的EB估计[J].应用数学.2001,14(3),82-86
61.师义民,许勇.单边截断分布族参数的经验Bayes检验：NA样本情形[J].应用数学.2001,14(4),98-102
62.冯艳,师义民,周巧娟.双边定数截尾情形下指数-威布尔分布参数的Bayes估计[J].系统工程.2006,24(9),117-120
63. Polansky, A. M, Chou Y. M.Mason R. L. Estimating Process Capability Indices for a Truncated Distribution[J].Quality Engineering,1998/9,11(2),257-265
64. Phillips M. D, Cho B. R. Modelling of Optimal Specification Regions[J]. Applied MathematicalModelling, 2000,24(5),327-341
65. Bradley Efron, Robert J.Tibshirani. An Introdution to the Bootstrap[M].Chapman & Hall,1993.
66. Efron B.. Better Bootstrap Confidence Intervals [J]. Journal of the American Statistical Association.1987,85, 79-89
67. Simon J. L.. Resampling:The New Statistics[M].Resampling Statistics.1997
68. QuenodilleMH.Approximate Tests of Correlation in Time-series[J].Journal of Royal Statistical Society Series B.1949,11,68-84
69. TukeyJ.W.. Bias and Confidence in Not-quite Large Samples Abstract [J].Annals of Mathematical Statistics.1958,29,614
70. MillerR.G. The Jackknife-a Review[J].Biometrika.1974,61,1-15
71. Hall P..The Bootstrap and Edgeworth Expansion [M].NewYork:Springer-Verlag Inc..1992
72. Shao J., Tu D..The Jacknife and Bootstrap[M]. New York:Springer-Verlag Inc..1995.
73. Davison A.C.,Hinkley D.V..Bootstrap Methods and Their Application[M].Cambridge:Cambridge University Press.1997.
74. Lahiri S.N..Resampling methodsfor dependentdataM.NewYork:Springer-Verlag Inc..2003.
75.谢益辉,朱钰Bootstrap方法的历史发展和前沿研究[J].统计与信息论坛.2008,23(2),90-96
76. Fahidy T.D..On the Application of a Bootstrapping-resample Technique of Nonparametric Statistics to Electroanalytical Measurements[J] Journal of Electroanalytical Chemistry.2008,615(2),159-164
77. Field, Chris, Robinson, John.Ronchetti, Elvezio. Saddlepoint Approximations for Multivariate M-estimates with Applications to Bootstrap Accuracy[J]. Annals of the Institute of Statistical Mathematics.2008,60(1), 205-224
78. Vishnyakov B.V., Kibzun A.I.. Application of the Bootstrap Method for Estimation of the Quantile Function[J]. Automation and Remote Control.2007,68(11),1931-1944
79. F. Choobineh, D. Branting. A simple Approximation for Semivariace[J]. European Journal of Operations Research.1986,27(5),364-370
80. F. Choobineh, J.L. Ballard.Control Limits of QC charts for Skewed Distributions Using Weighted Variance [J]. IEEE Transactions on Reliability.1987,36(4),473-477
81. Bai D.S., Choi I.S.. X and R Control Charts for Skewed Populations[J]. Journal of Quality Technology. 1995,27(2),120-131
82. Philippe Castagliola. X Control Charts for Skewed Distributions Using Scaled Weighted Variance Method [J]. International Journal of Reliability, Quality and Safety Engineering.2000,7(3),237-252
83. Chang Y.S., Bai D.S.. Control Charts for Positively-skewed Populations with Weighted Standard Deviations[J]. Quality and Reliability Engineering International.2001,17(5),397-406
84. Nelson L. S.. The Shewhart Control Chart-Tests for Special Causes[J].Journal of Quality Technology.1986,16(4),237-239
85. 张公绪,孙静.新编质量管理学(第二版)[M].高等教育出版社.2004,86-87
86. Shewhart W.A.. Economic Control of Quality of Manufactured Product[M].Newyork:D.Van Nostr and Co.Inc..1931,501-505
87. Nelson L.S..The Shewhart Control Chart-Tests for Special Causes[J] Journal of Quality Technology.1984, 16(4),237-239
88. Nelson L.S..The Shewhart X Control Chart [J].Journal of Quality Technology.1985,17(2), a) 114-116
89. ISO 7873:1993, Control Charts for Arithmetic Average with Warning Limits[S].1993
90. ISO 7966:1993, Acceptance Control Charts [S].1993
91. E.S.Page. Continuous Inspection Schemes [J]. Biometrika.1954,41,100-114
92. S.W.Roberts. Control Chart Tests Based on Geometric Moving Averages[J].Technometrics,1959,1,239-250
93. 钟伦燕,韩俊,刘红.统计过程控制(SPC)技术原理和应用[M].北京：电子工业出版社.2001,2-3
94. C.P.Quesenberry. SPC Q Charts for Start-up Processes and Short or Long Runs[J].Journal of Quality Technology.1991 a,23(3),213-214
95. C.P.Quesenberry. SPC Q Charts for a Binomial Parameter. Short or Long Runs[J].Journal of Quality Technology.1991b,23(3),239-246
96. C.P.Quesenberry. SPC Q charts for a Poisson Parameter:Short or long Runs[J].Journal of Quality Technology.1991c,23(3),296-303
97. 张公绪.允许有异常因素的一类新型控制图-选控控制图[J].电子学报.1980,2,1-10
98.张公绪.多因素控制图[J].电子学报.1982,3,31-36
99. Wade M.R.and Woodall W.H.. A review and analysis of cause-selecting control chart[J].Journal of Quality Technology.1993,25 (3),161-169
100. Johnson N.L.. Systems of Frequency Curves Generated by Methods of Translation [J-]. a) Biometrika.1949,33,149-176
101. Bowman K.O. and Shenton L. R..Jhoson's System of Distributions[J].Encyclopedia of Statistical Sciences.1983,4,303-314
102. Hann GJ. and Shaprio S.. Statistical Models in Engineering [M].Jhon Wiley & Sons, New York,NY.1994.
103. Jhonson N.L.,Kotz S.and Balakrishnan N. Continuons Uairaiate Distribution[M].Vol.l. Jhon Wiley & Sons, New York, NY.1994
104. Slifker J.F. and Shapiro S.. The Jhonson System:Selection and Parameter Estimation [J]. Technometrics.1980,22,239-246
105. Stuart A.and Ord J.K.. Kendall's Advanced Theroy of Statistics Vol.1.5thed[M].Oxford Univercity Press.New York,NY.1987
106.卓德保.最佳拟合非正态过程的质量控制[J].系统工程理论方法应用.2004,13(4),372-376
107. Ferrell E. B.. Control Charts for Log-normal Universe [J]. Industrial Quality Control.1958,15,4-6
108. Nelson P.R.. Control charts for Weibull Processes with Standards Given[J]. IEEE Transactions on Reliability.1979,28(4),283-287
109. Cowden D. J.. Statistical Method in Quality Control[M]. Prentice-Hall:Englewood Cliffs, NJ.1957
110. Abel V.. Comments on "Control-limits of QC charts for Skewed Distributions Using Weighted-Variance"[J]. IEEE Transactions on Reliability.1989,38(2),265
111. Chang, Young Soon, Bai, Do Sun. A Multivariate T2 Control Chart for Skewed Populations Using Weighted Standard Deviations [J].Quality and Reliability Engineering International.2004,20(1),31-46
112. Chang and Young Soon. Multivariate CUSUM and EWMA Control Charts for Skewed Populations Using Weighted Standard Deviations[J]. Communications in Statistics:Simulation and Computation.2007,36(4), 921-936
113. Lai K.Cha, Heng J.Cui. Skewness Correction X and R Charts for Skewed Distributions [J]. Naval Research Logistics.2003,50,555-573
114. Cornish E.A. and Fisher R. A..Moments and Cumulants in the Specifications of Distributions[J].Rev Int Stat Inst.1937,4,1-14
115. Pandu R.Tadikamalla, Dana G Popescu. Kurtosis Correction Method for X and R Control Charts for Long-Tailed Symmetrical Distributions[J]. Naval Research Logistics.2007,54,371-383
116. Bajgieh.S.M.,The Use of Bootstrapping to Construct Limits on Control Charts[J]. Proceedings of the Decision Science Institute, San Diego, CA.1992,1611-1613
117. Seppala.T,Moslowttz.H ect, Statistical Process Control via the Subgroup Bootstrap[J]. Journal of Quality Technology.1995,27(2),139-153
118. Liu.R.Y and Tang.J, Control Charts for Dependent and Independent Measurements Based on Bootstrap [J]. Journal of the American Statistical Association 1.1996,1694-1700
119. Steven A. Yourstone,William J. Zimmer.Non-Normality and the Design of Control Charts for AveragesfJ]. Decision Sciences.1992,23(5),1099-1113
120. Michele D.Nichols and Padgett.W.J.A Bootstrap Control Chart for Weibull Percentiles[J].Quality and Reliability Engineering International.2006,22(2),141-151
121. [121] Hotelling H..Multivariate Quality Control-Illustrated by the Air Testing of Sample Bomb Sights[J].Techniques of Statistical Analysis, Eisenhart C, Hastay MW, Wallis WA(eds.).McGraw-Hill:NewYork.1947,111-184
122. Jackson J. E..A User Guide to Principal Components[M]. Wiley:NewYork.1991
123. Woodall W.H..Montgomery D.C..Research Issues and Ideas Instatistical Process Control[J]. Journal of Quality Technology 1999.31,376-386
124. Bersimis S., Psarakis S. and Panaretos J..Multivariate Statistical Process Control Charts:An OverviewfJ]. Quality and Reliability Engineering Intemational.2007,23 (5),517-543
125.刘艳永,孙静,张公绪.多元协方差控制图[J].北京航空航天大学学报.1999,25(1),85-87
126.韩玉启,朱慧明.多元质量特性的贝叶斯均值向量控制图[J].南京理工大学学报.2003,27(5),561-566
127.殷建军,项祖丰,叶力.多元混合分布的EWMA控制图的平均链长[J].浙江工业大学学报.2006,34(1),65-68
128.耿修林.基于主成分原理的多元质量控制图的构造[J].数理统计与管理.2007,26(1),106-111
129. Wardell Don G.Moskowitz Hebert, Plante Robert D.. Run length Distributions of Residual Control Charts forAutocorrelated Processes[J]. Journal of Quality Technology.1994,26(4),310-317
130. Alwan, A.J.,Alwan L.C..Monitoring Autocorrelated Processes Using Multivariate Quality Control Charts[C]. 1994 Proceedings Decision Sciences Institute.1994 Annual Meeting.1994,3,2106-2108
131. Wei Jiang.Multivariate Control Charts for Monitoring Autocorrelated Processes[J]. Journal of Quality Technology.2004,36(4),367-379
132. Jarrett, J.E.,Xia Pan. The Quality Control Chart for Monitoring Multivariate Autocorrelated Processes[J]. Computational Statistics & Data Analysis.2007,51(8),3862-3870
133. Issam B.K., Mohamed L..Support Vector Regression Based Residual MCUSUM Control Chart for Autocorrelated Process[J]. Applied Mathematics and Computation.2008,201(1-2),565-574
134. Philippe Castagliola and Fugee Tsung. Autocorrelated SPC for Non-Normal Situations[J].'Quality and Reliability Engineering International.2005,21(2),131-161
135.孙静.自相关过程的残差控制图[J].清华大学学报(自然科学版).2002,42(6),735-738
136.杨穆尔,孙静.二元自相关过程的残差T2控制图[J].清华大学学报(自然科学版).2006,46(3),403406
137.张敏,何桢.自相关过程的X质量控制图[J].数理统计与管理.2007,26(1),96-100
138.杨穆尔,孙静.多元自相关过程的VAR控制图[J].数理统计与管理.2008,27(2),54-58
139. Jooho Lee, Woo-Joo Kwon. Economic Design of a Two Stage Control Charts Based on Both Performance and Surrogate Variables[J]. Naval Research Logistics.1999,46(8),958-977
140. Fong-Jung Yu,Yun-Shiow Chen. Economic Design of Moving Average Control Charts[J]. Quality Engineering.2005,17(3),391-397
141. Garcia-Diaz J..Carlos, Aparisi Francisco. Economic Design of EWMA Control Charts Using Regions of Maximum and Minimum ARL[J]. Institute of Industrial Engineers.2005,37(11),1011-1021
142. Vommi, Vijaya Babu, Seetala, Murty S.N.. A new Approach to Robust Economic Design of Control ChartsfJ]. Applied Soft Computing Journal.2007,7(1),211-228
143. Huifen Chen,Yuyen Cheng.Non-normality Effects on the Economic-Statistical Design of X Charts with Weibull in-Control Time[J]. European Journal of Operational Research.2007,176(2),986-998
144. Chen Y. K.Economic Design of an Adaptive T2 Control Chart[J]. Journal of the Operational Research Society 2007,58(3),337-345
145. Tagaras G, Nenes G.The Economically Designed Two-Sided Bayesian X Control Chart[J]. European Journal of Operational Research.2007,83(1),263-277
146. Serel D.A.,Moskowitz H..Joint Economic Design of EWMA Control Charts for Mean and Variance [J].European Journal of Operational Research.2007,184(1),157-168
147. Nenes, George; Tagaras, George. An Economic Comparison of CUSUM and Shewhart Charts[J]. Institute of Industrial Engineers.2008,40(2),133-146
148. Zhou Wen-Hui,Zhu Gui-Long. Economic Design of Integrated Model of Control Chart and Maintenance Management[J]. Mathematical and Computer Modelling.2008,47(11-12),1389-1395
149. Antonio F.B.Costa. X Charts with Variable Sample Size[J]. Journal of Quality Technology.1994,26(2), 155-163
150. Antonio F.B.Costa. X Charts with Variable Sample Size and Sampling Interval [J]. Journal of Quality Technology.1997,29(2),197-204
151. Antonio F.B.Costa. Joint X and R Charts with Variable Sample Size and Sampling Interval [J], Journal of Quality Technology.1999,31 (4),387-397
152. Antonio F.B.Costa. AATS for X Chart with Variable Parameters[J]. Journal of Quality Technology.1999,31 (4),455-458
153. Antonio F.B.Costa and Maysa S. De Magalhaes. An Adaptive Chart for Monitoring the Process Mean and Variance[J]. Quality and Reliability Engineering International.2007,23(7),821-831
154. Jesse C. Arnold and Marion R. Reynolds J.R.. CUSUM Control Charts with Variable Sample Size and Sampling Intervals [J]. Journal of Quality Technology.2001,34(1),66-81
155. Zhang Wu Sheng Zhang and Penghui Wang. A CUSUM Control Charts with Variable Sample Size and Sampling Intervals for Monitoring the Process Mean and Variance[J]. Quality and Reliability Engineering International.2007,23(1),157-170
156. Chen Y.K.. An Evolutionary Economic-Statistical Design for VSIX Control Charts Under Non-normality[J]. International Journal of Advanced Manufacturing Technology.2003,22(7-8),602-610
157. Yan-Kwang Chen, Kuo-Ching Chiou. Optimal Design of VSI X Control Charts for Monitoring Correlated Samples[J]. Quality and Reliability Engineering lnternational.2005,21(8),757-768
158. Yan-Kwang Chen, Kun-Lin Hsieh, Cheng-Chang Chang. Economic Design of the VSSI X control Charts for Correlated Data[J]. International Journal of Production Economics.2007,107(2),528-39
159. Lee H.J., Lim T.J., Jang S.C.. VSSI X Control Charts for Processes with Multiple Assignable Causes[C]. 2007 IEEE International Conference on Industrial Engineering and Engineering Management.2007, 1241-1245
160.赵红梅.经济控制界限及其确定方法的研究[J].内蒙古工业大学学报.1999,18(1),69-73
161.王兆军.关于动态质量控制图的设计理论[J].应用概率统计.2002,18(3),316-333
162.王雪松,许世范,巩敦卫.统计过程控制图的优化设计[J].中国矿业大学学报.2000,29(3),297-299
163.王海宇.一种变参数的控制图方法及其稳健分析[J].机械设计与制造.2008,1,9-10
164.张维铭.可变样本容量和抽样区间的质量控制图[J].工程数学学报.2000,17(2),31-36
165.张维铭,刘建斌.可变样本容量的中位值和极差控制图[J].浙江工程学院学报.2001,18(2),88-93
166.刘建斌,张维铭.可变抽样区间的非参数控制图[J].数理统计与管理.2002,21(4),22-27
167.刘建斌,张维铭.可变抽样区间的符号统计量控制图[J].浙江工程学院学报.2002,19(2),75-81
168.张维铭.可变样本容量的质量控制图[J].应用概率统计.2002,18(3),255-261
169.张维铭,刘建斌.可变样本容量和样本区间的联合中位值和极差控制图[J].应用概率统计.2004,20(1),20-26
170.张维铭,刘建斌.可变样本容量和抽样区间的X和R控制图[J].浙江工程学院学报.2004,21(1),30-35
171.吉明明,赵选民,唐伟广.可变抽样区间的非正态EWMA均值控制图[J].系统工程.2006,24(11),114-119
172.李元生.方向数据统计[M].北京：中国科学技术出版社,1998
173.李元生.角度质量控制问题的概率分布[J].中国质量,2001,12,33-34
174.方英,李元生.角度方向-移动向量长度控制图[J].管理学报,2006,3(4),416419
175.方英,李元生.角度平均方向-合向量长度控制图[J].清华大学学报(自然科学版),2006,46(3),407409
176.中国科学院计算中心概率统计组.概率统计计算[M].北京：科学出版社.1983,358-359,363-369,392-399
177.徐钟济.蒙特卡罗方法[M].上海：上海科学技术出版社.1985,60-95,100-118
178.高惠璇.统计计算[M].北京：北京大学大学社.-1995,109-122,149-150
179.王丹,张钰等.截尾分布的极限状态法的可靠度计算[J].机械设计与制造.1999,4,1-2
180. Tippett L.H.C.. On the Extreme Individuals and the Range of Sample Taken from a Normal Population [J].Biometrikal7.1925,364-387
181. Cox D.R.. The Mean and Coefficient of Variation of Range in Small Samples from Non-normal Populations [J]. Biometrika 41.1954,469-481
182. David H. A.. Order Statistics [M].John Wiley & Sons, Inc.1981,33-39
183. Shah S.M., Jaiswal M.C..Estimation of Parameters of Doubly Truncated Normal Distribution from First Four Sample Moments[J]. Annals of the Institute of Statistical Mathematics.1966,18(1),107-111
184.辛士波,李元生.基于自助法的对数正态分布质量控制图[C].第27届中国控制会议论文集(第二册).2008,7,18-21(E1收录)
185.辛士波,李元生.基于尺度赋权方差的EWMA均值控制图[J].数学的实践与认识.2008,38(8),127-132
2. 中华人民共和国国家标准GB/T4091-2001,常规控制图[s].北京：中国标准出版社,2001
3. 美国国家研究委员会.1993.振兴美国数学—90年代的计划[M].北京：世界图书出版公司,1993,111-112
4. 谢志刚,韩天雄.风险理论与非寿险精算[M].天津：南开大学出版社.2000,143-145
5. Burr I.W..The Effect of Non-normality on Constants for X and R Chart[J].Industrial Quality Control.1967,24(5),563-569
6. Schilling E.G. and Nelson P.R..The Effect of Non-normality on the Control Limits of X Charts[J]. Journal of Quality Technology.1976,8(3),183-188
7. Balakrishnan and Kocherlakota. Effect of Non-normality on X Charts:Single Assignable Cause Model[J]. Naval Research Logistics Quarterly.1986,48(3),439-444
8. Chan L.K.,Hapuarachchi K.P. and Macpherson B.D..Robustness of X and R Charts[J].IEEE Transactions on Reliability.1988,37(2),117-123
9. 张洪涛.保险经济学[M].北京：中国人民大学出版社.2006
10. 汪祖杰.现代保险学概论[M].北京：经济科学出版社.2007
11.付菊,徐沈新.保险学概论[M].北京：电子工业出版社.2007
12. MimuroT., Ohsakl M., Yasunaga H.. Four Parameter Evaluation Method of Lateral Transient Response[J]. SAE transactions.1990,99(6),1499-1508
13. 王新军.财产损失保险中损失分布建模的方法性研究[J].统计研究,2002,11,40-43
14. 吴礼斌.基于损失分布的再保险精算模型[J].统计与决策.2004,2,24
15.胡平.非寿险损失分布的精算模型研究[J].时代金融.2006,11,36
16. 施建祥,邬云玲.我国巨灾保险风险证券化研究[J].金融研究.2006,5,103-112
17. 杨星,郭彩琴.我国国债信用风险管理的实证研究[J].预测.2004,23(2),14-17
18. 许端.期权定价公式的概率论推导[J].北京工业大学学报.2004,30(3),382-385
19. 陈万义.非风险中性定价下的欧式期权定价公式[J].数学的实践与认识.2004,34(1),76-79
20.李超杰,何健敏.再装股票期权执行价格最低水平的决定[J].系统工程理论方法应用.2004,13(6),508-511
21. 吴震,杨晓光.信号交叉口右转车道饱和流量研究[J].同济大学学报(自然科学版).2008,36(1),37-41
22.谢涛,邱延峻,蒋泽中.岩石与混凝土界面断裂韧度的分布特性研究[J].岩石力学与工程学报.2004,23(13),2225-229
23.张学雷,王辉,张薇等.土壤系统分类与生物系统分类体系中的多样性特征对比分析[J].土壤学报.2008,45(1),1-8
24.章前,龙兵,邓昭等.昆明市某超市销售收入分析[J].昆明理工大学学报(理工版).2008,33(1),103-104
25.汪明明,周玉文,赵树旗等.降雨量公式的推求方法探讨[J].沈阳建筑大学学报(自然科学版).2008,24(2),274-277
26. 徐天群,陈跃鹏.防洪风险分析中改进的组合分布模型研究[J].数学的实践与认识.2004,34(5),84-90
27. 于洋,孙月静.对数正态分布参数的最大似然估计[J].九江学院学报.2007,6,55-57
28. 夏亚峰,马素丽.对数正态参数估计的损失函风险函数Bayes推断[J].兰州理工大学学报.2008,34(1), 131-133
29. 滕建辅,梁静毅,滕颖.对数正态分布伪随机数的产生与检验[J].天津商学院学报.2007,27(6),1-5
30. Clark Terry L.. Use of Log-normal Distribution for Numerical Calculations of Condensation and Collection[J]. Journal of the Atmospheric Sciences.1976,33(5),810-821
31. Chen G. Generalized Log-normal Distributions with Reliability Application[J]. Computational Statistics& Data Analysis.1995,15(3),309
32. Van Buren M.A.,Watt W.E., Marsalek J.. Application of the Log-normal and Normal Distributions to Stormwater Quality Parameters[J]. Water Research.1997,31(1),95-104
33. Tavassoli Z., Shivani A.,Esmaeilnia. Models of Fragmentation with Power Low Log-normal DistributionfJ]. Physica A:Statistical Mechanics and its Applications.2000,286(1),29-44
34. Yamada, Mitsuru,Nishihara,Akinori. A Log-Normal Distribution Model for Electron Multiplying Detector Signals in Charged Particle Beam Equipments[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences.2003, E86A(12),3276-3282
35. Beeke,Karina. Spectrum Planning-Analysis of Methods for the Summation of Log-normal Distributions[J]. EBU Technical Review.2007,312,145-154
36. Lerche I.. On Log-normal Distributions, Timescales and Basin Analysis Calculations[J]. Computers & Geosciences.1998,24(1),105
37. Simpson I.D., Standish N.. Derivation of the Log-normal Form of Both Section and Spatial Distribution of Particles[J]. Metallography.1977,10(2),149-159
38. Thomas John G.. Determination of log-normal Particle Size Distribution by Dynamic Light Scattering[J]. Journal of Colloid and Interface Science.1987,117(1),187-192
39. 盛聚,谢式千,潘承毅.概率论与数理统计[M].北京：高等教育出版社.2001,83-90
40. 孙志礼,陈良玉.实用机械可靠性设计理论与方法[M].北京：科学出版社.2003
41. Cohen A.C..Estimating the Mean and Variance of Normal Populations from Singly Truncated and Doubly Truncated Samples[J]. Annul of Mathmatica Statistics.1950,21(4),557-569
42. Douglas G Chapman. Estimating the Parameters of a Truncated Gamma Distribution[J]. Annul of Mathmatica Statistics 1956,27(2),498-506
43. Thompson H.R..Truncated Lognormal Distributions:I.Solution by Moments[J]. Biometrika.1951, 38(3-4),414-422
44. Nadarajah, Saralees, Kotz, Samuel. A Truncated Cauchy Distribution[J]. International Journal of Mathematical Education in Science and Technology.2006,37(5),605-608
45. Saralees, Nadarajah,Samuel, Kotz. A Skewed Truncated Cauchy Distribution with Applications in Economics [J]. Applied Economics Letters.2007,14(13),957-961
46. Masoom Ali.M, Saralees, Nadarajah. A Truncated Pareto Distribution[J]. Computer Communications.2006, 30(1),1-4
47. Masoom Ali.M, Saralees, Nadarajah. A Truncated Bivariate Generalized Pareto Distribution [J].Computer Communications.2007,30(8),1926-1930
48. Saralees, Nadarajah, Arjun,K.Gupta. A Skewed Truncated Pearson Type VII Distribution[J].Journal of Japan Statistical Society.2005,35(1),61-71
49. Nadarajah.S,Masoom Ali.M.A Skewed Truncated T Distribution[J]. International Journal of Mathematical Education in Science and Technology.2006,37(5),605-608
50. Coffey C.S, Muller K.E. Properties of Doubly-Truncated Gamma Variables[J]. Communications in Statistics: Theory and Methods.2000,29(4),851-857
51. Ami S.R. Srinivasa Rao. A Note on Derivation of the Generating Function for the Right Truncated Rayleigh Distribution[J]. Applied Mathematics Letters.2006,19(8),789-794
52. Blumenthal.S,Ram.C, Dahiya.Estimating Scale and Truncation Parameters for the Truncated Exponential Distribution with Type-I Censored Sampling [J]. Communications in Statistics-Theory and Methods.2005, 24(1),1-21
53. O'Reilly.F, Rueda.R. Fiducial Inferences for the Truncated Exponential Distribution[J]. Communications in Statistics-Theory and Methods.2007,36(12),2207-2212
54.宋卫星.非正则分布族中参数估计的最高相合阶[J].北京师范大学(自然科学版).2002,38(2),148-155
55.张玲霞,师义民.一维双边截断型分布族中参数函数的经验Bayes估计及其收敛速度[J].纯粹数学与应用数学.1999,15(3),92-98
56.成平,宋卫星.双边截断分布族中的卷积定理与渐近有效性[J].2001,44(4),737-746
57.许勇,师小琳,师义民.NA样本及Linex损失下截断族参数的经验EB估计[J].数学杂志.2004,24(2),124-130
58.张玲霞,师义民.双边截断型分布族参数函数的渐近最优经验Bayes估计[J].数学的实践与认识.2000,30(3),303-309
59.康会光,师义民,许勇.一类单边截断型分布族参数的双侧经验Bayes检验问题[J].工程数学学报.2002,19(2),81-85
60.师义民,赵小山,康会光Linex损失下单边截断型分布族参数的EB估计[J].应用数学.2001,14(3),82-86
61.师义民,许勇.单边截断分布族参数的经验Bayes检验：NA样本情形[J].应用数学.2001,14(4),98-102
62.冯艳,师义民,周巧娟.双边定数截尾情形下指数-威布尔分布参数的Bayes估计[J].系统工程.2006,24(9),117-120
63. Polansky, A. M, Chou Y. M.Mason R. L. Estimating Process Capability Indices for a Truncated Distribution[J].Quality Engineering,1998/9,11(2),257-265
64. Phillips M. D, Cho B. R. Modelling of Optimal Specification Regions[J]. Applied MathematicalModelling, 2000,24(5),327-341
65. Bradley Efron, Robert J.Tibshirani. An Introdution to the Bootstrap[M].Chapman & Hall,1993.
66. Efron B.. Better Bootstrap Confidence Intervals [J]. Journal of the American Statistical Association.1987,85, 79-89
67. Simon J. L.. Resampling:The New Statistics[M].Resampling Statistics.1997
68. QuenodilleMH.Approximate Tests of Correlation in Time-series[J].Journal of Royal Statistical Society Series B.1949,11,68-84
69. TukeyJ.W.. Bias and Confidence in Not-quite Large Samples Abstract [J].Annals of Mathematical Statistics.1958,29,614
70. MillerR.G. The Jackknife-a Review[J].Biometrika.1974,61,1-15
71. Hall P..The Bootstrap and Edgeworth Expansion [M].NewYork:Springer-Verlag Inc..1992
72. Shao J., Tu D..The Jacknife and Bootstrap[M]. New York:Springer-Verlag Inc..1995.
73. Davison A.C.,Hinkley D.V..Bootstrap Methods and Their Application[M].Cambridge:Cambridge University Press.1997.
74. Lahiri S.N..Resampling methodsfor dependentdataM.NewYork:Springer-Verlag Inc..2003.
75.谢益辉,朱钰Bootstrap方法的历史发展和前沿研究[J].统计与信息论坛.2008,23(2),90-96
76. Fahidy T.D..On the Application of a Bootstrapping-resample Technique of Nonparametric Statistics to Electroanalytical Measurements[J] Journal of Electroanalytical Chemistry.2008,615(2),159-164
77. Field, Chris, Robinson, John.Ronchetti, Elvezio. Saddlepoint Approximations for Multivariate M-estimates with Applications to Bootstrap Accuracy[J]. Annals of the Institute of Statistical Mathematics.2008,60(1), 205-224
78. Vishnyakov B.V., Kibzun A.I.. Application of the Bootstrap Method for Estimation of the Quantile Function[J]. Automation and Remote Control.2007,68(11),1931-1944
79. F. Choobineh, D. Branting. A simple Approximation for Semivariace[J]. European Journal of Operations Research.1986,27(5),364-370
80. F. Choobineh, J.L. Ballard.Control Limits of QC charts for Skewed Distributions Using Weighted Variance [J]. IEEE Transactions on Reliability.1987,36(4),473-477
81. Bai D.S., Choi I.S.. X and R Control Charts for Skewed Populations[J]. Journal of Quality Technology. 1995,27(2),120-131
82. Philippe Castagliola. X Control Charts for Skewed Distributions Using Scaled Weighted Variance Method [J]. International Journal of Reliability, Quality and Safety Engineering.2000,7(3),237-252
83. Chang Y.S., Bai D.S.. Control Charts for Positively-skewed Populations with Weighted Standard Deviations[J]. Quality and Reliability Engineering International.2001,17(5),397-406
84. Nelson L. S.. The Shewhart Control Chart-Tests for Special Causes[J].Journal of Quality Technology.1986,16(4),237-239
85. 张公绪,孙静.新编质量管理学(第二版)[M].高等教育出版社.2004,86-87
86. Shewhart W.A.. Economic Control of Quality of Manufactured Product[M].Newyork:D.Van Nostr and Co.Inc..1931,501-505
87. Nelson L.S..The Shewhart Control Chart-Tests for Special Causes[J] Journal of Quality Technology.1984, 16(4),237-239
88. Nelson L.S..The Shewhart X Control Chart [J].Journal of Quality Technology.1985,17(2), a) 114-116
89. ISO 7873:1993, Control Charts for Arithmetic Average with Warning Limits[S].1993
90. ISO 7966:1993, Acceptance Control Charts [S].1993
91. E.S.Page. Continuous Inspection Schemes [J]. Biometrika.1954,41,100-114
92. S.W.Roberts. Control Chart Tests Based on Geometric Moving Averages[J].Technometrics,1959,1,239-250
93. 钟伦燕,韩俊,刘红.统计过程控制(SPC)技术原理和应用[M].北京：电子工业出版社.2001,2-3
94. C.P.Quesenberry. SPC Q Charts for Start-up Processes and Short or Long Runs[J].Journal of Quality Technology.1991 a,23(3),213-214
95. C.P.Quesenberry. SPC Q Charts for a Binomial Parameter. Short or Long Runs[J].Journal of Quality Technology.1991b,23(3),239-246
96. C.P.Quesenberry. SPC Q charts for a Poisson Parameter:Short or long Runs[J].Journal of Quality Technology.1991c,23(3),296-303
97. 张公绪.允许有异常因素的一类新型控制图-选控控制图[J].电子学报.1980,2,1-10
98.张公绪.多因素控制图[J].电子学报.1982,3,31-36
99. Wade M.R.and Woodall W.H.. A review and analysis of cause-selecting control chart[J].Journal of Quality Technology.1993,25 (3),161-169
100. Johnson N.L.. Systems of Frequency Curves Generated by Methods of Translation [J-]. a) Biometrika.1949,33,149-176
101. Bowman K.O. and Shenton L. R..Jhoson's System of Distributions[J].Encyclopedia of Statistical Sciences.1983,4,303-314
102. Hann GJ. and Shaprio S.. Statistical Models in Engineering [M].Jhon Wiley & Sons, New York,NY.1994.
103. Jhonson N.L.,Kotz S.and Balakrishnan N. Continuons Uairaiate Distribution[M].Vol.l. Jhon Wiley & Sons, New York, NY.1994
104. Slifker J.F. and Shapiro S.. The Jhonson System:Selection and Parameter Estimation [J]. Technometrics.1980,22,239-246
105. Stuart A.and Ord J.K.. Kendall's Advanced Theroy of Statistics Vol.1.5thed[M].Oxford Univercity Press.New York,NY.1987
106.卓德保.最佳拟合非正态过程的质量控制[J].系统工程理论方法应用.2004,13(4),372-376
107. Ferrell E. B.. Control Charts for Log-normal Universe [J]. Industrial Quality Control.1958,15,4-6
108. Nelson P.R.. Control charts for Weibull Processes with Standards Given[J]. IEEE Transactions on Reliability.1979,28(4),283-287
109. Cowden D. J.. Statistical Method in Quality Control[M]. Prentice-Hall:Englewood Cliffs, NJ.1957
110. Abel V.. Comments on "Control-limits of QC charts for Skewed Distributions Using Weighted-Variance"[J]. IEEE Transactions on Reliability.1989,38(2),265
111. Chang, Young Soon, Bai, Do Sun. A Multivariate T2 Control Chart for Skewed Populations Using Weighted Standard Deviations [J].Quality and Reliability Engineering International.2004,20(1),31-46
112. Chang and Young Soon. Multivariate CUSUM and EWMA Control Charts for Skewed Populations Using Weighted Standard Deviations[J]. Communications in Statistics:Simulation and Computation.2007,36(4), 921-936
113. Lai K.Cha, Heng J.Cui. Skewness Correction X and R Charts for Skewed Distributions [J]. Naval Research Logistics.2003,50,555-573
114. Cornish E.A. and Fisher R. A..Moments and Cumulants in the Specifications of Distributions[J].Rev Int Stat Inst.1937,4,1-14
115. Pandu R.Tadikamalla, Dana G Popescu. Kurtosis Correction Method for X and R Control Charts for Long-Tailed Symmetrical Distributions[J]. Naval Research Logistics.2007,54,371-383
116. Bajgieh.S.M.,The Use of Bootstrapping to Construct Limits on Control Charts[J]. Proceedings of the Decision Science Institute, San Diego, CA.1992,1611-1613
117. Seppala.T,Moslowttz.H ect, Statistical Process Control via the Subgroup Bootstrap[J]. Journal of Quality Technology.1995,27(2),139-153
118. Liu.R.Y and Tang.J, Control Charts for Dependent and Independent Measurements Based on Bootstrap [J]. Journal of the American Statistical Association 1.1996,1694-1700
119. Steven A. Yourstone,William J. Zimmer.Non-Normality and the Design of Control Charts for AveragesfJ]. Decision Sciences.1992,23(5),1099-1113
120. Michele D.Nichols and Padgett.W.J.A Bootstrap Control Chart for Weibull Percentiles[J].Quality and Reliability Engineering International.2006,22(2),141-151
121. [121] Hotelling H..Multivariate Quality Control-Illustrated by the Air Testing of Sample Bomb Sights[J].Techniques of Statistical Analysis, Eisenhart C, Hastay MW, Wallis WA(eds.).McGraw-Hill:NewYork.1947,111-184
122. Jackson J. E..A User Guide to Principal Components[M]. Wiley:NewYork.1991
123. Woodall W.H..Montgomery D.C..Research Issues and Ideas Instatistical Process Control[J]. Journal of Quality Technology 1999.31,376-386
124. Bersimis S., Psarakis S. and Panaretos J..Multivariate Statistical Process Control Charts:An OverviewfJ]. Quality and Reliability Engineering Intemational.2007,23 (5),517-543
125.刘艳永,孙静,张公绪.多元协方差控制图[J].北京航空航天大学学报.1999,25(1),85-87
126.韩玉启,朱慧明.多元质量特性的贝叶斯均值向量控制图[J].南京理工大学学报.2003,27(5),561-566
127.殷建军,项祖丰,叶力.多元混合分布的EWMA控制图的平均链长[J].浙江工业大学学报.2006,34(1),65-68
128.耿修林.基于主成分原理的多元质量控制图的构造[J].数理统计与管理.2007,26(1),106-111
129. Wardell Don G.Moskowitz Hebert, Plante Robert D.. Run length Distributions of Residual Control Charts forAutocorrelated Processes[J]. Journal of Quality Technology.1994,26(4),310-317
130. Alwan, A.J.,Alwan L.C..Monitoring Autocorrelated Processes Using Multivariate Quality Control Charts[C]. 1994 Proceedings Decision Sciences Institute.1994 Annual Meeting.1994,3,2106-2108
131. Wei Jiang.Multivariate Control Charts for Monitoring Autocorrelated Processes[J]. Journal of Quality Technology.2004,36(4),367-379
132. Jarrett, J.E.,Xia Pan. The Quality Control Chart for Monitoring Multivariate Autocorrelated Processes[J]. Computational Statistics & Data Analysis.2007,51(8),3862-3870
133. Issam B.K., Mohamed L..Support Vector Regression Based Residual MCUSUM Control Chart for Autocorrelated Process[J]. Applied Mathematics and Computation.2008,201(1-2),565-574
134. Philippe Castagliola and Fugee Tsung. Autocorrelated SPC for Non-Normal Situations[J].'Quality and Reliability Engineering International.2005,21(2),131-161
135.孙静.自相关过程的残差控制图[J].清华大学学报(自然科学版).2002,42(6),735-738
136.杨穆尔,孙静.二元自相关过程的残差T2控制图[J].清华大学学报(自然科学版).2006,46(3),403406
137.张敏,何桢.自相关过程的X质量控制图[J].数理统计与管理.2007,26(1),96-100
138.杨穆尔,孙静.多元自相关过程的VAR控制图[J].数理统计与管理.2008,27(2),54-58
139. Jooho Lee, Woo-Joo Kwon. Economic Design of a Two Stage Control Charts Based on Both Performance and Surrogate Variables[J]. Naval Research Logistics.1999,46(8),958-977
140. Fong-Jung Yu,Yun-Shiow Chen. Economic Design of Moving Average Control Charts[J]. Quality Engineering.2005,17(3),391-397
141. Garcia-Diaz J..Carlos, Aparisi Francisco. Economic Design of EWMA Control Charts Using Regions of Maximum and Minimum ARL[J]. Institute of Industrial Engineers.2005,37(11),1011-1021
142. Vommi, Vijaya Babu, Seetala, Murty S.N.. A new Approach to Robust Economic Design of Control ChartsfJ]. Applied Soft Computing Journal.2007,7(1),211-228
143. Huifen Chen,Yuyen Cheng.Non-normality Effects on the Economic-Statistical Design of X Charts with Weibull in-Control Time[J]. European Journal of Operational Research.2007,176(2),986-998
144. Chen Y. K.Economic Design of an Adaptive T2 Control Chart[J]. Journal of the Operational Research Society 2007,58(3),337-345
145. Tagaras G, Nenes G.The Economically Designed Two-Sided Bayesian X Control Chart[J]. European Journal of Operational Research.2007,83(1),263-277
146. Serel D.A.,Moskowitz H..Joint Economic Design of EWMA Control Charts for Mean and Variance [J].European Journal of Operational Research.2007,184(1),157-168
147. Nenes, George; Tagaras, George. An Economic Comparison of CUSUM and Shewhart Charts[J]. Institute of Industrial Engineers.2008,40(2),133-146
148. Zhou Wen-Hui,Zhu Gui-Long. Economic Design of Integrated Model of Control Chart and Maintenance Management[J]. Mathematical and Computer Modelling.2008,47(11-12),1389-1395
149. Antonio F.B.Costa. X Charts with Variable Sample Size[J]. Journal of Quality Technology.1994,26(2), 155-163
150. Antonio F.B.Costa. X Charts with Variable Sample Size and Sampling Interval [J]. Journal of Quality Technology.1997,29(2),197-204
151. Antonio F.B.Costa. Joint X and R Charts with Variable Sample Size and Sampling Interval [J], Journal of Quality Technology.1999,31 (4),387-397
152. Antonio F.B.Costa. AATS for X Chart with Variable Parameters[J]. Journal of Quality Technology.1999,31 (4),455-458
153. Antonio F.B.Costa and Maysa S. De Magalhaes. An Adaptive Chart for Monitoring the Process Mean and Variance[J]. Quality and Reliability Engineering International.2007,23(7),821-831
154. Jesse C. Arnold and Marion R. Reynolds J.R.. CUSUM Control Charts with Variable Sample Size and Sampling Intervals [J]. Journal of Quality Technology.2001,34(1),66-81
155. Zhang Wu Sheng Zhang and Penghui Wang. A CUSUM Control Charts with Variable Sample Size and Sampling Intervals for Monitoring the Process Mean and Variance[J]. Quality and Reliability Engineering International.2007,23(1),157-170
156. Chen Y.K.. An Evolutionary Economic-Statistical Design for VSIX Control Charts Under Non-normality[J]. International Journal of Advanced Manufacturing Technology.2003,22(7-8),602-610
157. Yan-Kwang Chen, Kuo-Ching Chiou. Optimal Design of VSI X Control Charts for Monitoring Correlated Samples[J]. Quality and Reliability Engineering lnternational.2005,21(8),757-768
158. Yan-Kwang Chen, Kun-Lin Hsieh, Cheng-Chang Chang. Economic Design of the VSSI X control Charts for Correlated Data[J]. International Journal of Production Economics.2007,107(2),528-39
159. Lee H.J., Lim T.J., Jang S.C.. VSSI X Control Charts for Processes with Multiple Assignable Causes[C]. 2007 IEEE International Conference on Industrial Engineering and Engineering Management.2007, 1241-1245
160.赵红梅.经济控制界限及其确定方法的研究[J].内蒙古工业大学学报.1999,18(1),69-73
161.王兆军.关于动态质量控制图的设计理论[J].应用概率统计.2002,18(3),316-333
162.王雪松,许世范,巩敦卫.统计过程控制图的优化设计[J].中国矿业大学学报.2000,29(3),297-299
163.王海宇.一种变参数的控制图方法及其稳健分析[J].机械设计与制造.2008,1,9-10
164.张维铭.可变样本容量和抽样区间的质量控制图[J].工程数学学报.2000,17(2),31-36
165.张维铭,刘建斌.可变样本容量的中位值和极差控制图[J].浙江工程学院学报.2001,18(2),88-93
166.刘建斌,张维铭.可变抽样区间的非参数控制图[J].数理统计与管理.2002,21(4),22-27
167.刘建斌,张维铭.可变抽样区间的符号统计量控制图[J].浙江工程学院学报.2002,19(2),75-81
168.张维铭.可变样本容量的质量控制图[J].应用概率统计.2002,18(3),255-261
169.张维铭,刘建斌.可变样本容量和样本区间的联合中位值和极差控制图[J].应用概率统计.2004,20(1),20-26
170.张维铭,刘建斌.可变样本容量和抽样区间的X和R控制图[J].浙江工程学院学报.2004,21(1),30-35
171.吉明明,赵选民,唐伟广.可变抽样区间的非正态EWMA均值控制图[J].系统工程.2006,24(11),114-119
172.李元生.方向数据统计[M].北京：中国科学技术出版社,1998
173.李元生.角度质量控制问题的概率分布[J].中国质量,2001,12,33-34
174.方英,李元生.角度方向-移动向量长度控制图[J].管理学报,2006,3(4),416419
175.方英,李元生.角度平均方向-合向量长度控制图[J].清华大学学报(自然科学版),2006,46(3),407409
176.中国科学院计算中心概率统计组.概率统计计算[M].北京：科学出版社.1983,358-359,363-369,392-399
177.徐钟济.蒙特卡罗方法[M].上海：上海科学技术出版社.1985,60-95,100-118
178.高惠璇.统计计算[M].北京：北京大学大学社.-1995,109-122,149-150
179.王丹,张钰等.截尾分布的极限状态法的可靠度计算[J].机械设计与制造.1999,4,1-2
180. Tippett L.H.C.. On the Extreme Individuals and the Range of Sample Taken from a Normal Population [J].Biometrikal7.1925,364-387
181. Cox D.R.. The Mean and Coefficient of Variation of Range in Small Samples from Non-normal Populations [J]. Biometrika 41.1954,469-481
182. David H. A.. Order Statistics [M].John Wiley & Sons, Inc.1981,33-39
183. Shah S.M., Jaiswal M.C..Estimation of Parameters of Doubly Truncated Normal Distribution from First Four Sample Moments[J]. Annals of the Institute of Statistical Mathematics.1966,18(1),107-111
184.辛士波,李元生.基于自助法的对数正态分布质量控制图[C].第27届中国控制会议论文集(第二册).2008,7,18-21(E1收录)
185.辛士波,李元生.基于尺度赋权方差的EWMA均值控制图[J].数学的实践与认识.2008,38(8),127-132