A new probabilistic model with mixed-state failure rates: Modeling time-to-event scenarios in reliability and music engineering

We consider and implement a new contemporary and state-of-the-art probabilistic model with optimal data modeling capabilities. We call the present probabilistic model a new beta power flexible Weibull distribution. It is obtained by using the flexible Weibull distribution together with the new beta power transformed method. The flexibility of the new model is explored visually. The visual inspection shows that the proposed model captures many important forms (or shapes) of its density and hazard rate function. For the new beta power flexible Weibull distribution, the point estimators are derived mathematically and numerically (using practical data sets). Additionally, simulation studies are also exercised to show that these point estimators are efficient and consistent. Ultimately, three data sets are taken into account to certify the optimality and relevance of the new model. Among the data sets, the first two applications are picked from reliability engineering and the third data set is observed from music engineering. Regarding the fitting of these three data sets, taking into consideration for statistical tests, it is distinguished that the new model persistently outstrips the rival distributions.