The problem of testing for a constant failure rate against alternatives with failure rates involving a single change-point is considered. The asymptotic significance level for tests based on maximal score statistics are shown to involve the solution to a first passage time problem for an Ornstein-Uhlenbeck process. An example illustrates the methodology.
"Asymptotic Score-Statistic Processes and Tests for Constant Hazard Against a Change-Point Alternative." Ann. Statist. 13 (2) 583 - 591, June, 1985. https://doi.org/10.1214/aos/1176349540