Failure data analysis with extended Weibull distribution

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 by Marshall and Olkin (1997). It has 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. The model characterization based on the Weibull Probability Plot (WPP) is studied in this article. The WPP for actual data set can be concave, convex, or likely S-shaped. A procedure is provided for parameter estimation based on WPP. In addition, the maximum likelihood estimation is also presented. An example is shown to illustrate the procedure and application.