More goodness-of-fit tests for the power-law process

The power-law process is often used as a model for reliability growth of complex systems or for reliability of repairable systems. There are many results on estimation and hypothesis testing concerning parameters of the power-law process. Goodness-of-fit tests for the power-law process were presented in Park & Kim (1992) using Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling statistics. This paper considers the same problem using three statistics, Kuiper, Watson and weighted Watson. Tables of critical values for the three statistics are presented and the results of a power study are given under the alternative hypothesis that failure data come from a nonhomogeneous Poisson process with log-linear intensity function. The power study shows that the tests have acceptable power for various parameter values and the Cramer-von Mises Statistics, in Park and Kim (1992), has the highest power among the six statistics. An example from the Cox air conditioning repair data is presented