[en] In this paper, we present Shewhart type Z ̅ and S2 control charts for monitoring individual or joint shifts in the scale and shape parameters of a Weibull distributed process. The advantage of this method is its ease of use and flexibility for the case where the process distribution is Weibull, although the method can be applied to any distribution. We illustrate the performance of our method through simulation and the application through the use of an actual data set. Our results indicate that Z ̅ and S2 control charts perform well in detecting shifts in the scale and shape parameters. We also provide a guide that would enable a user to interpret out-of-control signals.
Research Center/Unit :
Centre for Quantitative Methods and Operations Management
Disciplines :
Business & economic sciences: Multidisciplinary, general & others
Author, co-author :
Faraz, Alireza ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie
Saniga, Erwin
Heuchenne, Cédric ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie
Language :
English
Title :
Shewhart Control Charts for Monitoring Reliability with Weibull Lifetimes
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Bibliography
Weibull W,. A statistical distribution function of wide applicability. Journal of Applied Mechanics 1951; 18: 293-296.
Weibull W,. References on Weibull Distribution. FTL A Report, Forsvarets Teletekniska Laboratorium, Stockholm, 1977.
Fok SL, Mitchell BC, Smart J, Marsden BJ,. A numerical study on the application of the Weibull theory to brittle materials. Engineering Fracture Mechanics 2001; 68: 1171-1179.
Basu B, Tiwari D, Kundu D, Prasad R,. Is Weibull distribution the most appropriate statistical strength distribution for brittle materials? Ceramics International 2009; 35: 237-246.
Durham SD, Padgett WJ,. Cumulative damage model for system failure with application to carbon fibers and composites. Technometrics 1997; 39: 34-44.
Padgett WJ, Spurrier JD,. Shewhart-type charts for percentiles of strength distributions. Journal of Quality Technology 1990; 22: 283-288.
Padgett WJ, Durham SD, Mason AM,. Weibull analysis of the strength of carbon fibers using linear and power law models for the length effects. Journal of Composite Materials 1995; 29: 1873-1884.
Keshavan MK, Sargent GA, Conrad H,. Statistical analysis of the hertzian fracture of pyrex glass using the Weibull distribution function. Journal of Materials Science 1980; 15: 839-844.
Murthy DNP, Xie M, Jiang R,. Weibull Models, Wiley series in probability and statistics. John Wiley and Sons, Hoboken, New Jersy, 2004. ISBN 0-471-36092-9
Bai DS, Choi IS,. X and R Control Charts for Skewed Populations. Journal of Quality Technology 1995; 27: 120-131.
Ramalhoto MF, Moaris M,. Shewhart control charts for the scale parameter of a Weibull control variable with fixed and variable sampling intervals. Journal of Applied Statistics 1999; 26: 129-160.
Nichols PR, Padgett WJ,. A bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International 2006; 22: 141-151.
Pascual F, Zhang H,. Monitoring the Weibull shape parameter by control charts for the sample range. Quality and Reliability Engineering International 2011; 27: 15-25.
Villanueva D, Feijõo A, Pazos JL,. Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment. Resources 2013; 2: 370-384.
Abramowitz M, Stegun IA, (eds.). Error Function and Fresnel Integrals, Ch. 7 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972; 297-309.
Saniga EM,. Economic statistical control chart designs with an application to X and R charts. Technometrics 1989; 31: 313-320.
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