Modelling Reliability Data with Finite Weibull or Lognormal Mixture Distributions

This paper presents a reliability analysis study of lifetime data based on Weibull and Lognormal distributions models. The main aim of this study is to compare two finite mixture distributions, Weibull mixture distribution (WMD) and Lognormal mixture distribution (LMD) for modelling heterogeneous survival data sets. This paper also provides the characterization of both WMD and LMD. A comparison of fitted cumulative distribution functions, probability density functions, hazard functions, reliability functions and the mean lifetime is obtained for different distribution models. The expectation-maximization (EM) and Levenberg-Marquardt algorithms are used for estimating the parameters of these mixture models. The goodness of fit is implemented by using different statistical methods such as the Kolmogorov-Smirnov (KS), Akaike’s Information Criteria (AIC) tests and correlation coefficient to show the best fit for modelling survival data. This study give engineers some guidance for selecting the appropriate distribution model