On partial ordering and tests of the generalized new better than used class of life distributions

Two generalized classes of the concept ‘new better than used’, namely the new better than used in failure rate and the new better than used in average failure rate classes of life distributions are considered. The relations between these three classes are established through the partial ordering of the tail heaviness. Two test statistics for the generalized classes based on the empirical distributions are derived and their exact distributions are investigated. The distributions of these statistics are tabulated for some small samples. The power of the tests is studied for some common distributions in reliability modelling