Modeling failure data by 3-parameter Weibull distribution models

Many models with three parameters have been developed based on extension or generalization of the Weibull distribution. These models include modified Weibull, Weibull extension, extended Weibull and others. Seven such models are discussed in this paper, in addition to a generalization of the exponential distribution, and a flexible Weibull model with two parameters. These models are more flexible than the usual 2-parameter Weibull, and they are useful for modeling lifetime/failure data with different behaviors such as decreasing, increasing, bathtub-shaped, or even upside-down bathtub-shaped failure rate. In this paper, a procedure for selecting an optimal model for lifetime data analysis is presented based on the plots on Weibull probability paper (WPP). An example is provided to illustrate the procedure and the usefulness of these models. This procedure serves as a guideline for reliability engineers and statisticians when dealing with data modeling.