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 reliability of repairable systems. Often goodness-of-fit tests are required to check the hypothesis that failure data came from a power-law process model. Three statistics, Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling, are considered for a goodness-of-fit test of a power-law process in the case of failure-truncated data. 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 came from a nonhomogeneous Poisson process with log-linear intensity function. This power comparison is a new result, which can guide in selecting a test statistic and sample size. The power study shows that the tests have acceptable power for some parameter values and the Cramer-von Mises statistic has the highest power for a sample-size ⩾20