Generalized Renewal Process: Models, Parameter Estimation and Applications to Maintenance Problems

Kijima and Sumita have proposed a stochastic model called the generalized renewal process (GRP) to describe the availability characteristics of repairable systems by introducing the notion of the virtual age of the system. Yanez et al. offer maximum likelihood estimation (MLE) approach for estimating parameters of the GRP models. Due to the complexity of the equations, a close solution is not available, and numerical solutions are proposed with limited success. This paper describes an alternative for calculating the parameters of GRP models using a Genetic Algorithm (GA) approach to solve complex MLE equations. The results using this approach confirm and extend conclusions of the Kijima and Sumita, and Yanez et al. works. Examples of applications of GA have been presented. The paper also concludes that under certain conditions, application of the minimal repair assumption provide a reasonable answer for the availability of repairable units.