Zhang, Tieling; Xie, Min Failure data analysis with extended Weibull distribution. (English) Zbl 1121.62090 Commun. Stat., Simulation Comput. 36, No. 3, 579-592 (2007). Summary: A three-parameter distribution, called extended Weibull distribution, is investigated in this article. This model is generated by a method of introducing an additional parameter into a family of distributions of A. W. Marshall and I. Olkin [Biometrika 84, No. 3, 641–652 (1997; Zbl 0888.62012)]. It has the two-parameter Weibull distribution as a special case. One of the merits of this distribution is that the hazard-rate can be increasing, decreasing, or initially increasing, then decreasing and eventually increasing. A model characterization based on the Weibull Probability Plot (WPP) is studied in this article. The WPP for an actual data set can be concave, convex, or likely S-shaped. A procedure is provided for parameter estimation based on WPP. In addition, maximum likelihood estimation is also presented. An example is shown to illustrate the procedure and applications. Cited in 26 Documents MSC: 62N05 Reliability and life testing 62N02 Estimation in survival analysis and censored data 62A09 Graphical methods in statistics 90B25 Reliability, availability, maintenance, inspection in operations research Keywords:extended Weibull distribution; hazard-rate function; Weibull probability plot Citations:Zbl 0888.62012 Software:SPLIDA PDFBibTeX XMLCite \textit{T. Zhang} and \textit{M. Xie}, Commun. Stat., Simulation Comput. 36, No. 3, 579--592 (2007; Zbl 1121.62090) Full Text: DOI References: [1] Burnham , K. P. , Anderson , D. R. ( 1998 ).Model Selection and Inference–A Practical Information-Theoretic Approach. New York : Springer-Verlag , pp. 21 – 29 , 43 – 74 . · Zbl 0920.62006 [2] Cancho V. G., Journal of Applied Statistical Science 8 pp 227– (1999) [3] DOI: 10.1080/02664760500165008 · Zbl 1121.62373 · doi:10.1080/02664760500165008 [4] DOI: 10.1109/24.765929 · Zbl 04552915 · doi:10.1109/24.765929 [5] DOI: 10.1109/TR.2002.805788 · doi:10.1109/TR.2002.805788 [6] DOI: 10.1093/biomet/84.3.641 · Zbl 0888.62012 · doi:10.1093/biomet/84.3.641 [7] Meeker , W. Q. , Escobar , L. A. ( 1998 ).Statistical Methods for Reliability Data. New York : John Wiley & Sons , pp. 383 – 385 . · Zbl 0949.62086 [8] DOI: 10.1109/24.406570 · Zbl 04527630 · doi:10.1109/24.406570 [9] DOI: 10.1109/24.229504 · Zbl 0800.62609 · doi:10.1109/24.229504 [10] DOI: 10.2307/1269735 · Zbl 0900.62531 · doi:10.2307/1269735 [11] DOI: 10.1002/047147326X · Zbl 1047.62095 · doi:10.1002/047147326X [12] DOI: 10.1002/0471725234 · doi:10.1002/0471725234 [13] DOI: 10.1109/TR.2005.853036 · doi:10.1109/TR.2005.853036 [14] DOI: 10.1016/S0951-8320(02)00022-4 · doi:10.1016/S0951-8320(02)00022-4 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.