Identification of process and distribution characteristics by testing monotonic and non-monotonic trends in failure intensities and hazard rates

Statistical tests are developed for testing monotonic and non-monotonic trends in failure data. A procedure is presented, by using a set of six tests as an example, to determine whether a failure process is a renewal process, a homogeneous or a non-homogeneous Poisson process, or none of these. The same tests with different data transformations can also be used for testing the goodness of fit of candidate hazard rates (i.e. distributions) and failure intensities. Several examples illustrate the potential power of these tests and the importance of testing for non-monotonic as well as monotonic trends. The efficiency of these tests is discussed in several special cases.