Published: 2008-12-09
ISBN:
ISSN: 1650-3686 (print), 1650-3740 (online)
Purpose: This work proposes an innovative control chart of the Weibull percentiles using Bayesian estimators supported by bootstrap methods.
Approach: The chart offers two main advantages.
On one side; the estimation procedure is able to effectively integrate both the experimental and the technological information exploiting some specific Bayesian estimators.
On the other side; the bootstrap techniques allow to capitalize the experimental information provided by few samples.
Findings: The performance of the control chart has been investigated by means of a large Monte Carlo study.
Value of the paper: The paper presents a control chart for Weibull percentiles; where few alternative charts can be found.
Statistical Process Control; non-Normal control charts; Bayesian inference; Weibull distribution; Bootstrap methods
Bajgier; S.M. (1992); “The use of bootstrapping to construct limits on control charts”; Proc. Decision Science Institute; San Diego; CA; 1611–1613
Canavos; G.C.; Tsokos; C.P.; (1972); “Bayesian Concepts for the Estimation of Reliability in the Weibull Life-Testing Model”; International Statistical Review; 40(2); 153 160
Canavos; G.C.; Tsokos; C.P.; (1973); “Bayesian Estimation of Life Parameters in the Weibull Distribution”; Operations Research; 21(3); 755-763
Carlin; B.P.; Gelfand; A.E. (1991); “A Sample Reuse Method for Accurate Parametric Empirical Bayes Confidence Intervals”; Journal of the Royal Statistical Society. Series B; 53(1); 189-200
Erto; P. (1982); “New Practical Bayes estimators for the 2-parameters Weibull distributions”; IEEE Transactions on Reliability; 31(2); 194-197
Erto P.; (2005); “Integration of technological and statistical knowledge for reliability control”; Proc. 55th Session of International Statistical Institute; Sydney; Australia
Erto; P.; Giorgio; M. (1996); “Modified Practical Bayes Estimators”; IEEE Transactions on Reliability; 45(1); 132-137
Erto; P.; Lanzotti; A. (1990); “A Bayesian approach to the statistical control of the reliability of a flexible manufacturing system” (in Italian); Proc. of the Annual Conf.; AIRO ‘90; Models and methods for decision support; Sorrento; Italy; 31-45
Erto; P.; Pallotta; G. (2006); “A Bayesian Cumulative Memory Control Chart for Weibull Processes”; Proc. 9th QMOD Conference; Liverpool; UK; 300-310
Erto; P.; Pallotta; G. (2007); “A new control chart for Weibull technological processes”; Quality Technology and Quantitative Management; 4(4); 553-567
Erto; P.; Rapone; M. (1984); “Non-informative and Practical Bayesian confidence bounds for reliable life in the Weibull model”; Reliability Engineering; 7; 181-191
Erto; P.; Pallotta; G. and Park; S.H. (2008); “An Example of Data Technology Product: a Control Chart for Weibull Processes”; International Statistical Review (available at http://www.blackwell-synergy.com/doi/abs/10.1111/j.1751-5823.2008.00043.x)
Johnson; L.; Kotz; S. and Balakrishnan; N. (1994); Continuous univariate distributions; 2nd edition; Wiley; New York
Kanji; G.K. and Arif; O.H. (2001); “Median rankit control chart for Weibull distribution”; Total Quality Management; 12(5); 629-642
Laird; N.M.; Louis; T.A. (1987); “Empirical Bayes confidence intervals based on bootstrap samples”; Journal of American Statistical Association; 82; 739-750
Nichols; M.D.; Padgett; W.J. (2005); “A Bootstrap Control Chart for Weibull Percentiles”; Quality and Reliability Engineering International 22(2); 141-151
Padgett; W.J.; Spurrier; J.D. (1990) Shewhart-type charts for percentiles of strength distributions. Journal of Quality Technology; 22(4); 283-288
Park; S.H. (1996); Robust design and analysis for quality engineering; London; Chapman & Hall.
Seppala; T.; et al. (1995); “Statistical Process Control via the Subgroup Bootstrap”; Journal of Quality Technology 27(2); 139-153
Shapiro; S.S. (1990); How to Test Normality and Other Distributional Assumptions; ASQC Quality Press; Milwaukee
Shore; H. (2004); “Non-normal populations in quality applications: a revisited perspective”; Quality and Reliability Engineering International; 20; 375-382
Smith; R.L.; Naylor; J.C.; (1987). “A Comparison of Maximum Likelihood and Bayesian Estimators for the Three- Parameter Weibull Distribution”; Applied Statistics; 36(3); 358-369
Steiner; S.H.; MacKay R.J. (2001); “Detecting Changes in the Mean from Censored Lifetime Data”; Lenz ; H.J. and Wilrich; P.T.; Frontiers in Statistical Quality Control; Physica-Verlag; 275-289
Wood; M.; Kaye; M.; Capon; N.; (1999); “The Use of Resampling for Estimating Control Charts Limits”; Journal of the Operational Research Society 50(6); 651-659
Xie; M.; Goh; T. N. and Ranjan P. (2002); “Some effective control chart procedures for reliability monitoring”; Reliability Engineering and System Safety; 77; 2; 143-150
Zhang; L.; Chen; G. (2004); “EWMA charts for monitoring the mean of censored Weibull lifetimes”; Journal of Quality Technology; 36(3); 321-328
