Maximum likelihood estimation from interval censored recurrent event data

In this paper, we consider the recurrent failures of several repairable units, which can only be observed at periodic inspection times. A unit is not aging over the period between a failure and its detection. The failure times are interval censored by the periodic assessment times. The observed data consists of censoring intervals of failure times and the unobserved data are the actual ages of the units at the failure times. We formulate the likelihood function and use several iterative algorithms to find the maximum likelihood estimate (MLE) of the parameters. The complete Expectation–Maximization (EM) algorithm, the EM gradient, full Newton–Raphson (NR), and the Simplex method are used. We derive recursive equations to calculate the expected values required in the algorithms. We estimate the parameters for four failure datasets, assuming that the failures follow a non-homogeneous Poisson process (NHPP). Three datasets are obtained from a hospital for the components of general infusion pump, and the fourth dataset is simulated. Since the estimation could take a long time, we compare the performance of the algorithms in terms of the required number of iterations to converge, the total execution time, and the precision of the estimated parameters. We also use Monte Carlo and Quasi-Monte Carlo simulation as the substitutes for the recursive procedures in the Expectation step of the EM gradient and compare the results.