An additive modified Weibull distribution

●A new five-parameter modified Weibull distribution is proposed.●The new model is very flexible to model the bathtub-shaped hazard rate data.●Many properties and the estimation of parameters of the new model are discussed.●Two well-known data sets are used for illustrating the superiority of the new model.

A new five-parameter lifetime distribution with increasing, decreasing and bathtub-shaped hazard function is proposed in this paper. An important property of the new distribution is that it is very flexible to model the bathtub-shaped hazard rate data. For a bathtub-shaped hazard rate with sharp change in the initial and wear-out phase, the new distribution can provide a better fit than many other modified Weibull distributions. The properties of the new distribution including moments, order statistics and the Weibull type probability plot (WPP) are studied. The estimation of parameters is discussed by using the method of maximum likelihood. Finally, the superiority of the proposed distribution and its four-parameter sub-model are tested by analyzing two well-known lifetime data sets.