The modulated power law process (MPLP) is a three-parameter stochastic point process model that can be used to describe the failure times of a repairable system. While the power law process implies that a system is in exactly the same condition just after a repair as it was just before the failure, the MPLP allows for the system to be affected by the failure and repair. We describe an algorithm for obtaining the maximum likelihood estimates (MLEs) of the three model parameters. Asymptotic results are used to give approximate confidence intervals and hypothesis tests for the parameters. A simulation study indicates that the confidence intervals and hypothesis tests have approximately the nominal level.