On renewal increasing mean residual life distributions: An age replacement model with hypothesis testing application

We study the life distribution of an operating device through the notion of mean residual life. The device is experiencing a random number of shocks governed by a homogeneous Poisson process, and a new U-statistic test procedure is introduced to test the hypothesis of that the life is exponentially distributed against the alternative that the life distribution is the life distribution has renewal increasing mean residual property.