Optimal Maintenance Time for Repairable Systems Under Two Types of Failures

Abstract

Determination of preventive maintenance is an important issue for systems under degradation. A typical maintenance policy calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, failures are modeled according to a non homogeneous Poisson process. A perfect preventive maintenance restores the system to the as good as new condition. The motivation for this article was a maintenance data set related to power switch disconnectors. Two different types of failures could be observed for these systems according to their causes. The major difference between these types of failures is their costs. Assuming that the system will be in operation for an infinite time, we find the expected cost per unit of time for each preventive maintenance policy and hence obtain the optimal strategy as a function of the processes intensities. Assuming a parametrical form for the intensity function, large sample estimates for the optimal maintenance check points are obtained and discussed.

Keywords:

• Log-linear process
• Maximum likelihood estimate
• Minimal repair
• Non homogeneous Poisson process
• Power law process

Mathematics Subject Classification:

• 62N05
• 90B25

Acknowledgments

The research of Enrico A. Colosimo has been partially funded by CNPq (Conselho de Desenvolvimento Científico e Tecnológico) of the Ministry for Science and Technology of Brazil and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais). The research of Gustavo L. Gilardoni has been partially funded by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), CNPq and FINATEC.