Optimal maintenance policy of repairable system with bathtub shaped intensity

The power law process (PLP) and log linear process (LLP) are able to describe the processes with monotonic trend during the operating time. However, these models are not able to describe the processes with a non-monotonic trend such as bathtub shaped intensity. In this paper we proposed the superposed log linear process (S-LLP) for modeling bathtub shaped intensity function. The S-LLP is a nonhomogeneous Poisson process (NHPP) that results from the superposition of two LLP with different parameters. To get the maximum likelihood (ML) estimates, we proposed the three-parameter log-likelihood function evaluated using a genetic algorithm. Also, to obtain approximated confidence intervals, the information matrix and the variance-covariance matrix have been evaluated. The suggested methods are applied to field data from a repairable system.