Monte carlo estimation for guaranteed-coverage non-normal tolerance intervals

References

• Aitchison , J. and Dunsmore , I.R. 1975 . Statistical Prediction Analysis , Cambridge : Cambridge University Press .
   Google Scholar
• Andradòttir , S. . An Empirical Comparison of Stochastic Approximation Methods for Simulation Optimization . Proceedings of the First Industrial Engineering Research Conference . Edited by: Klutke , G. , Mitta , D.A. , Nnaji , B.O. and Seiford , L.M. pp. 471 – 475 . Noncross, , Georgia : Institute of Industrial Engineers .
   Google Scholar
• > Avramidis A. N. Variance Reduction Techniques for Simulation with Applications to Stochastic Networks Purdue University West Lafayette, Indiana 1993 Ph.D. Thesis, School of Industrial Engineering
   Google Scholar
• DeBrota , D.J. , Dittus , R.S. , Swain , J.J. , Roberts , S.D. , Wilson , J.R. and Venkatraman , S. . Modeling Input Processes with Johnson Distributions . Proceedings of the 1989 Winter Simulation Conference . Edited by: MacNair , E.A. , Musselman , K.J. and Heidelberger , P. Washington, D.C : Institute of Electrical and Electronics Engineers .
   Google Scholar
• Eberhardt , K.R. , Mee , R.W. and Reeve , C.P. 1989 . Computing Factors for Exact Two-Sided Tolerance Limits for a Normal Distribution . Communications in Statistics-Simulation and Computation , 18 : 397 – 413 .
   Web of Science ®Google Scholar
• Guenther , W.C. 1985 . Two-Sided Distribution-Free Tolerance Intervals and Accompanying Sample Size Problems . Journal of Quality Technology , 17 : 40 – 43 .
   Web of Science ®Google Scholar
• Guttman , I. 1970 . Statistical Tolerance Regions: Classical and Bayesian , London : Charles Griffin .
   Google Scholar
• Hashem , S. and Schmeiser , B. 1994 . Algorithm 727: Quantile Estimation Using Overlapping Batch Statistics . ACM Transactions on Mathematical Software , 20 : 100 – 102 .
   Google Scholar
• Hill , I.D. , Hill , R. and Holder , R.L. 1976 . Algorithm AS 99. Fitting Johnson Curves by Moments . Applied Statistics , 25 : 180 – 189 .
   Google Scholar
• Jilek , M. 1981 . A Bibliography of Statistical Tolerance Regions . Statistics , 12 : 441 – 456 .
   Google Scholar
• Jilek , M. and H. 1989 . A Bibliography of statistical Tolerance Regions, II . Statistics , 20 : 165 – 172 .
   Google Scholar
• Johnson , N.L. 1949 . Systems of Frequency Curves Generated by Methods of Translation . Biometrika , 36 : 149 – 176 .
   PubMed Web of Science ®Google Scholar
• Kesten , H. 1958 . Accelerated Stochastic Approximation . Annals of Mathematical Statistics , 29 : 41 – 59 .
   Google Scholar
• Lehmann , E.L. 1983 . Theory of Point Estimation , New York : John Wiley .
   Google Scholar
• Odeh , R.E. and Owen , D.B. 1980 . Tables for Normal Tolerance Limits, Sampling Plans, and Screen-ing , New York : Marcel Dekker .
   Google Scholar
• Owen , D.B. and Hua , Tsunshung A. 1977 . Tables of Confidence Limits on the Tail Area of the Normal Distribution . Communications in Statistics-Simulation and Computation , 6 : 285 – 311 .
   Web of Science ®Google Scholar
• Patel , J.K. 1986 . Tolerance Intervals-a Review . Communications in Staiistics-Theory and Methods , 15 : 2719 – 2762 .
   Web of Science ®Google Scholar
• Polyak , B.T. and Juditsky , A.B. 1992 . Acceleration of Stochastic Approximation by Averaging . SIAM Journal on Control and Optimization , 30 : 838 – 855 .
   Web of Science ®Google Scholar
• Rao , J.N.K. , Subrahmaniam , K. and Owen , D.B. 1972 . Effect of Non-Normality on Tolerance Limits Which Control Percentages in Both Tails of Normal Distribution . Technometrics , 14 : 571 – 575 .
   Web of Science ®Google Scholar
• Robbins , H. and Monro , S. 1951 . A Stochastic Approximation Method . Annals of Mathematical Statistics , 22 : 400 – 407 .
   Google Scholar
• Sacks , J. 1958 . Asymptotic Distributions of Stochastic Approximation Procedures . Annals of Mathematical Statistics , 29 : 373 – 405 .
   Google Scholar
• Schmeiser , B.W. , Avramidis , T.N. and Hashem , S. . Overlapping Batch Statistics . Proceedings of the 1990 Winter Simulation Conference . Edited by: Balci , O. , Sadowski , R. and Nance , R. Piscataway, New Jersey : Institute of Electrical and Electronics Engineers .
   Google Scholar
• Venter , J.H. 1967 . An Extension of the Robbins-Monro Procedure . Annals of Mathematical Statistics , 38 : 181 – 190 .
   Google Scholar
• Wald , A. 1942 . Setting of Tolerance Limits When the Sample Is Large . Annals of Mathematical Statistics , 13 : 389 – 399 .
   Google Scholar
• Wald , A. and Wolfowitz , J. 1946 . Tolerance Limits for a Normal Distribution . Annals of Mathematical Statistics , 17 : 208 – 215 .
   Google Scholar