Joint optimal inspection and inventory for a k-out-of-n system

• We model a k-out-of-n system with hidden failures and inventory.
• The system is periodically inspected and the inventory is periodically replenished.
• Failed components are either replaced or minimally repaired.
• A simulation model is developed to calculate the total expected cost.
• The inspection interval and inventory level that minimizes the total cost is found.

PurposeThe objective of this paper is to develop a model, which optimizes jointly the inspection frequency and the inventory level for a k-out-of-n system with repairable components whose failures are hidden.ScopeThe system is periodically inspected to detect failed components, and the components are either minimally repaired or replaced with spares from the inventory. The system fails between periodic inspections if n−k+1 components are down; in that case, all failed components are inspected and rectified if possible. Otherwise, the failed components are rectified at periodic inspections. An emergency spare is ordered at a system failure, if the inventory is empty and all failed components require replacement.MethodologyUsing analytical approach to find the optimal solution is computationally intensive and not practical; a simulation model is developed to solve the problem.ResultsThe proposed model harmonizes the maintenance and inventory policies and finds the joint optimal solution which results in a minimum total cost.ConclusionThe joint optimization model results in a lower cost compared to separate maintenance and inventory optimization models.NoveltyFew joint models for k-out-of-n systems exist, and none of them investigate repairable components whose failures are hidden and follow a non-homogeneous Poisson process.