Study on effect of left-truncated data rate on ML estimation for power law process

This paper used parameter estimation to analyze left-truncated and right-censored failure time data from multiple repairable systems. The systems were identical; the failure occurrence followed a Non-Homogeneous Poisson Process (NHPP) and the intensity rate function followed a power law function. Maximum Likelihood (ML) method was used to estimate the function parameters. Two scenarios were considered. In the first scenario, it was assumed that there were no failures between the operation starting time and the observation starting time points. In the second one, left-truncation was considered and thus the possibility of failure occurrence existed between the operation starting time and the observation starting time points. The parameters estimated from these scenarios were compared to the real input parameters in the data generation to show the importance of the truncation information.