Joint maintenance and inspection optimization of a k-out-of-n system

Abstract

Redundantly-configured k-out-of-n systems have wide applications in various industries. Even though the reliability and availability of k-out-of-n systems have been studied in the literature, not many models have been proposed for inspection and maintenance optimization of such systems. In addition, for majority of k-out-of-n systems, it is assumed that a failed component is always rectified by replacement, which is not a realistic assumption for many systems in the real world. In this paper, we consider a k-out-of-n system with components whose failures follow a non-homogeneous Poisson process with power law intensity function. The system is periodically inspected, and if the number of failed components in an inspection interval does not exceed n-k+1, the failed components are detected and rectified only at a periodic inspection. However, if the number of failures reaches n-k+1, the system fails and this is when all the failed components are detected and fixed. When a failure is detected, we should decide whether to minimally repair the component or replace it. Thus, two types of optimal decisions should be made simultaneously: obtaining the optimal maintenance action for a failed component and finding the optimal periodic inspection interval for the entire system. We formulate a model to obtain jointly the optimal maintenance actions and the periodic inspection interval which results in the minimum total expected cost of the system over a finite planning horizon. The optimal maintenance decision is the optimal number of minimal repairs that should be performed before a component is replaced. The total cost includes the cost of periodic inspections, the penalty cost for system failures, minimal repairs and replacements of the components, and the penalty cost for the downtime of the components before they get rectified.We then develop a simulation model to obtain the required model parameters. The application of the proposed model is shown in case studies of a 1-out-of-5 (parallel), 2-out-of-5 and 5-out-of-5 (series) systems. The 1-out-of-5 system incurs the smallest optimal total expected cost of inspection and maintenance, while the 5-out-of-5 system incurs the highest optimal cost. The optimal inspection period is the longest for the 5-out-of-5 system, since the greater number of failures provides a greater number of opportunistic inspections, which reduces the need for frequent periodic inspections.

Inspection and maintenance optimisation of multicomponent systems

“…However, the size of the search space is very large in this case. For this reason, this problem, albeit in the context of periodic inspections, has been previously broken down into several stages for maintenance and inspection optimisation for all hard-type components in Stage 1, marginal optimisation of the maintenance decision for each soft-type component in Stage 2 and optimisation of the inspection period for the entire system in Stage 3 [71,126]. Monte-Carlo simulation was used for marginal multi-stage optimisation.…”

“…Bjarnason et al [19,20] consider hidden failures in the context of a k-out-of-n redundant system and develop a joint optimisation model for minimising the total cost of both maintenance and inventory policies. Babishin and Taghipour [86] propose a joint optimisation procedure for minimising the total cost of both periodic and opportunistic inspections and corrective maintenance for a k-out-of-n system with hidden failures. In another article, Babishin and Taghipour [87] consider a k-out-of-n system with hidden failures under both periodic and opportunistic inspections, minimal repair, corrective or preventive replacement and find the optimal joint inspection and maintenance policies, as well as provide expressions for the expected number of system failures in terms of the cost ratio and component failure intensity.…”

“…Bjarnason et al [19,20] consider a joint optimisation model for minimising the total cost of both maintenance and inventory policies for hidden failures in the context of a k-out-of-n redundant system. Babishin and Taghipour [86] propose a joint optimisation procedure for minimising the total cost of both periodic and opportunistic inspections and corrective maintenance for a k-out-of-n system with hidden failures.…”

“…Babishin and Taghipour [87] optimise both maintenance and inspection policies, but only for a k-out-of-n system under periodic inspections. Babishin and Taghipour [71,126] use a three-stage optimisation procedure to obtain optimal inspection policy for hard-type components in Stage 1, optimal maintenance in Stage 2 and optimal periodic inspection interval for soft-type components in Stage 3 using the Monte Carlo simulation. The authors are unaware of any previous models which have attempted to optimise both the maintenance action and the inspection policy under non-periodic inspections.…”

Reliability Calculation for Dormant k-out-of-n Systems with Periodic Maintenance

“…In reference Tutt et al (2009) and ( 2012), risk-informed preventive maintenance optimization was presented. In reference Babishin et al (2016), maintenance inspection optimization of k-out-of-n redundant system was presented. In reference Guo et al (2016), optimization of preventive maintenance interval on the aircraft indicators was presented.…”