Review and classification of reliability statistical models exhibiting failure-free life characteristic

In many real-world reliability engineering applications, basic engineering considerations typically result in the need for using a statistical distribution with a failure free life (FFL) parameter. These include the usual failure time models as well as specialized repair time models for maintenance planning, and breakdown voltage models used for voltage endurance studies of electrical insulations. In the domain of quality and reliability engineering, literature in the area of FFL is relatively sparse. In this paper, we proposed a classification structure for the purpose of defining the type of distributions based on considerations of the failure mechanism and distributional structure. From the literature, the three-parameter Weibull distribution has been found to be the most common statistical distribution used when failure free life is considered. Some estimation procedures for the three-parameter Weibull distribution are discussed and a new modified maximum likelihood type approach which leverages on the empirical cumulative distribution function is proposed for subsequent research in this paper.