Control Charts for Monitoring Burr Type-X Percentiles

References

• Ahmad , K. E. , Fakhry , M. E. and Jaheen , Z. F. 1997 . Empirical Bayes estimation of P(Y<X) and characterization of Burr-type X model . Journal of Statistical Planning and Inference , 64 : 297 – 308 .
   Web of Science ®Google Scholar
• Bader , M. G. and Priest , A. M. 1982 . “ Statistical aspects of fiber and bundle strength in hybrid composites ” . In Progress in Science and Engineering Composites , Edited by: Hayashi , T. , Kawata , K. and Umekawa , S. 1129 – 1136 . Tokyo : ICCM-IV .
   Google Scholar
• Bajgier , S. M. 1992 . “ The use of bootstrapping to construct limits on control charts ” . In Proceedings of the Decision Science Institute, San Diego, CA 1611 – 1613 .
   Google Scholar
• Burr , I. W. 1942 . Cumulative frequency functions . Annals of Mathematical Statistics , 13 : 215 – 222 .
   Google Scholar
• Durham , S. D. and Padgett , W. J. 1997 . Cumulative damage models for system strength with application to carbon fibers and composites . Technometrics , 39 : 34 – 44 .
   Web of Science ®Google Scholar
• Efron , B. and Tibshirani , R. J. 1993 . An Introduction to the Bootstrap , New York : Chapman & Hall .
   Google Scholar
• Gunter , B. 1992 . Bootstrapping: How to make something from almost nothing and get statistically valid answers, Part III . Quality Progress , 25 : 119 – 122 .
   Google Scholar
• Hyndman , R. J. and Fan , Y. 1996 . Sample quantiles in statistical packages . American Statistician , 50 : 361 – 365 .
   Web of Science ®Google Scholar
• Ihaka , R. and Gentleman , R. 1996 . R: A language for data analysis and graphics . Journal of Computational and Graphical Statistics , 5 : 299 – 314 .
   Google Scholar
• Jaheen , Z. F. 1995 . Bayesian approach to prediction with outliers from the Burr type X model . Microelectronics Reliability , 35 : 45 – 47 .
   Web of Science ®Google Scholar
• Jaheen , Z. F. 1996 . Empirical Bayes estimation for the reliability and failure rate functions of the Burr type X failure model . Journal of Applied Statistical Science , 3 : 281 – 288 .
   Google Scholar
• Jones , L. A. and Woodall , W. Y. 1998 . The performance of bootstrap control charts . Journal of Quality Technology , 30 : 362 – 375 .
   Web of Science ®Google Scholar
• Kundu , D. and Raqab , M. Z. 2005 . Generalized Rayleigh distribution: Different method of estimations . Computational Statistics & Data Analysis , 49 : 187 – 200 .
   Web of Science ®Google Scholar
• Lio , Y. L. , Chen , D.-G. and Tsai , T.-R. 2011 . Parameter estimations for generalized Rayleigh distribution under progressively type I interval censored data . American Open Journal of Statistics , 1 : 46 – 57 .
   Google Scholar
• Lio , Y. L. and Park , C. 2008 . A bootstrap control chart for Birnbaum-Saunders percentiles . Quality and Reliability Engineering International , 24 : 585 – 600 .
   Web of Science ®Google Scholar
• Lio , Y. L. and Park , C. 2010 . A bootstrap control chart for inverse Gaussian percentiles . Journal of Statistical Computation and Simulation , 80 : 287 – 299 .
   Web of Science ®Google Scholar
• Liu , R. Y. and Tang , J. 1996 . Control charts for dependent and independent measurements based on the bootstrap . Journal of the American Statistical Association , 91 : 1694 – 1700 .
   Web of Science ®Google Scholar
• Mudholkar , G. S. and Srivastava , D. K. 1993 . Exponentiated Weibull family for analyzing bathtub failure-rate data . IEEE Transactions on Reliability , 42 : 299 – 302 .
   Web of Science ®Google Scholar
• Mudholkar , G. S. and Srivastava , D. K. 1995 . The exponentiated Weibull family: A reanalysis of the bus-motor-failure data . Technometrics , 37 : 436 – 445 .
   Web of Science ®Google Scholar
• Nichols , M. D. and Padgett , W. J. 2005 . A bootstrap control chart for Weibull percentiles . Quality and Reliability Engineering International , 22 : 141 – 151 .
   Web of Science ®Google Scholar
• Onar , A. and Padgett , W. J. 2000 . Accelerated test models with the inverse Gaussian distributions . Journal of Statistical Planning and Inference , 89 : 119 – 133 .
   Web of Science ®Google Scholar
• Padgett , W. J. and Spurrier , J. D. 1990 . Shewhart-type charts for percentiles of strength distributions . Journal of Quality Technology , 22 : 283 – 288 .
   Web of Science ®Google Scholar
• R Development Core Team . 2006 . R: A Language and Environment for Statistical Computing , Vienna : R Foundation for Statistical Computing .
   Google Scholar
• Raqab , M. Z. 1998 . Order statistics from the Burr type X model . Computational Mathematical Applications , 36 : 111 – 120 .
   Web of Science ®Google Scholar
• Sartawi , A. and Abu-Salih , M. S. 1991 . Bayesian prediction bounds for the Burr type X model . Communications in Statistics - Theory and Methods , 20 : 2307 – 2330 .
   Web of Science ®Google Scholar
• Seppala , T. , Moskowitz , H. , Plante , R. and Tang , J. 1995 . Statistical process control via the subgroup bootstrap . Journal of Quality Technology , 27 : 139 – 153 .
   Web of Science ®Google Scholar
• Surles , J. G. and Padgett , W. J. 1998 . Inference for P(Y<X) in the Burr type X model . Journal of Statistical Science , 7 : 225 – 238 .
   Google Scholar
• Surles , J. G. and Padgett , W. J. 2001 . Inference for reliability and stress-strength for a scaled Burr type X distribution . Lifetime Data Analysis , 7 : 187 – 200 .
   PubMed Web of Science ®Google Scholar
• Young , G. A. 1994 . Bootstrap: More than a stab in the dark . Statistical Science , 9 : 382 – 415 .
   Web of Science ®Google Scholar