A new extension of the modified Weibull distribution with applications for engineering data

In this study, a novel extension of the three-parameter modified Weibull distribution called the NMW3 distribution is proposed. The NMW3 distribution exhibits increasing or bathtub-shaped hazard rates, which can be beneficial in the context of reliability. The statistical characteristics of the NMW3 distribution are examined, including the difference between the change points of the hazard rate and the mean residual lifetime functions. Additionally, the sensitivities of the parameters and the flatness of the bathtub curve of the NMW3 distribution are discussed. The Weibull probability paper is utilized to characterize plots related to the NMW3 distribution. The parameters of the NMW3 distribution are estimated using both the graphical approach and the maximum likelihood method. Through the analysis of three real data sets, it is demonstrated that the NMW3 distribution outperforms existing extensions of the modified Weibull distributions, highlighting its practical importance. Finally, a reduced distribution of the NMW3 distribution is proposed, and it shows that the reduced distribution has almost the same advantageous characteristics as the NMW3 distribution.