MODELING AND COMPARISON OF MAXIMUM LIKELIHOOD AND MEDIAN RANK REGRESSION METHODS WITH FRÉCHET DISTRIBUTION

In reliability analysis researchers, commonly model failure times with the lifetime distributions. In this article, we have considered the Fréchet distribution as a lifetime model. Often risk managers must make decisions after only a few failures. Thus, an important question is how to estimate the parameters of Fréchet distribution for extremely small sample sizes and Type-I censored data. The life test data are almost always from Type-I censored tests because plan dictates the time at which the test will finish. The study compares the two methods of estimation maximum likelihood estimation and median rank regression by fitting Fréchet distribution parameters. Also, we have conducted a simulation study to empirically investigating the performance of the proposed methods and its properties. Moreover, the comparison of Maximum Likelihood and Median rank regression estimation methods are made by using Type-I censoring. Finally, the application of these methods is discussed by considering the real data for time to breakdown of an insulating fluid between electrodes at a voltage of 34kV. The reliability of insulating fluid is modelled through Fréchet distribution.