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Failure data analysis with extended Weibull distribution. (English) Zbl 1121.62090

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.

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

Citations:

Zbl 0888.62012

Software:

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References:

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