Establishment of the optimal time interval between periodic inspections for redundant systems

For redundant systems with periodic inspections, the establishment of the optimal time interval between inspections that maximize availability and minimize costs is a challenging issue. This paper develops a model to analyze the reliability and determine the optimal interval between inspections of redundant systems subjected to periodic inspections. It uses discrete time Markov Chains to define the transition probabilities between the state of the systems and the costs related with each state. To optimize the time between inspections, the total cost per cycle was minimized using the Markov Chain properties followed by a numerical search technique. Four models of systems are analyzed and numerical examples for systems comprised of two and three components are presented: Model I - Active redundancy without component repair; Model II - Active redundancy with component repair; Model III - Standby redundancy without component repair and Model IV - Standby redundancy with component repair. The main advantage of the model used in this paper is the inclusion of costs for unavailability and production losses through the definition of the downtime costs that penalize the model when the system fails. This model can also be extended and generalized to determine the optimal interval between inspections in systems with active or inactive redundancies and with n components.