A k-out-of-n:G system and a system with components subject to soft and hard failures are both inspected non-periodically. For
the k-out-of-n system, components fail “silently” (i.e. are hidden), and the entire system fails when (n-k+1)st component fails. For
the system with hard-type and soft-type components, hard failures cause system failure, while soft failures are hidden and do not
cause immediate failure of the system, but still reduce its reliability. Every system failure allows for an opportunistic inspection
of hidden soft-type components in addition to the scheduled inspections. The available maintenance types are replacement and
minimal repair. For hard-type components, the maintenance decision is determined by the optimal age before replacement. For the
soft-type components with hidden failures, we do not know their age, and so decide on the appropriate type of maintenance using
the optimal number of minimal repairs before replacement. The hidden nature of soft-type component failures precludes the use of
a tractable analytic expression, so we use simulation and genetic algorithm (GA) to jointly optimise the non-periodic policies on
maintenance and inspection and to ensure these incur minimal expected total cost over a finite planning horizon. Due to increasing computational complexity associated with the number of inspections and maintenance policies to be evaluated, the genetic
algorithm presents a promising method of optimisation for complex multicomponent systems with multiple decision parameters.
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.
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