A novel three parameters extended weibull distribution with application using engineering data

Abstract

Abstract Weibull distribution is widely used for lifetime modelling in reliability engineering. However, its lack of sufficient tail flexibility often results in poor fit in extreme events. We proposed another three-parameter extension of the Weibull distribution with additional flexibility without sacrificing tractability. We derived and studied its statistical properties, including reliability measures, quantile function, moment, stress-strength, mean waiting time, moment generating function, characteristics function, Rényi entropy, order statistics, mean residual life and mode. We adopted the inverse transform approach in random number generation, and through simulation, we evaluated the performance of the maximum likelihood estimates. The fitness of the distribution was examined using 373/epoxy fatigue fracture dataset and compared with five similar extensions of the Weibull distribution. Our proposed novel distribution fits the data best among the competing models. It is therefore recommended as a better alternative in modelling heavily tailed data due to its flexibility. Future studies could consider other estimation techniques to compare the efficiency and performance of the parameter estimators.