A new modified Weibull distribution

We introduce a new lifetime distribution by considering a serial system with one component following a Weibull distribution and another following a modified Weibull distribution. We study its mathematical properties including moments and order statistics. The estimation of parameters by maximum likelihood is discussed. We demonstrate that the proposed distribution fits two well-known data sets better than other modified Weibull distributions including the latest beta modified Weibull distribution. The model can be simplified by fixing one of the parameters and it still provides a better fit than existing models.