On suitability of modified Weibull extension distribution in modeling product lifetimes and reliability

Abstract

The Weibull distribution (WD) is an important lifetime model. Due to its prime importance in modeling life data, many researchers have proposed different modifications of WD. One of the most recent modifications of WD is Modified Weibull Extension distribution (MWEM). The MWEM has been shown better in modeling lifetime data as compared to WD. However it comparison with other modifications of WD, in modeling product lifetimes and reliability, is missing in the current literature. We have attempted to bridge up this gap. The Bayesian methods have been proposed for the analysis under non-informative (uniform) and informative (gamma) priors. Since the Bayes estimates for the model parameters were not available in closed form, the Lindley’s approximation (LA) has been used for numerical solutions. Based on detailed simulation study and real life analysis, it has been concluded that Bayesian methods performed better as compared to maximum likelihood estimates (MLE) in estimating the model parameters. The MWEM performed better than eighteen other modifications of WD in modeling real datasets regarding electric and mechanical components. The reliability and entropy estimation for the said datasets has also been discussed. The estimates for parameters of MWEM were quite consistent in nature. In case of small samples, the performance of Bayes estimates under ELF and informative prior was the best. However, in case of large samples, the choice of prior and loss function did not affect the efficiency of the results to a large extend.