A New Modeling of Periodic Inspection Interval Optimization in Computer System with Failure Interaction

Abstract

The hidden failure is commonly occur in different industries with increasing operational complexity. The component of computers is an example for hidden failure. This component called soft component. In this study two component repairable systems with failure interaction are considered. The failure of these components can be soft or hard. The hard failure causes the system stop, while the soft failure does not, but it increases the system operating costs too. The periodic inspections have a fix cost to system. When the first component fails, it remains in a failed state until the next inspection time. Therefore, if the first component failed in each inspection interval, a down time penalty cost is incurred. The cost is proportional to the elapsed time from failure time to its detection at inspection time. The short inspection interval increases the number of inspection and causes the extra cost for system. As well, long inspection interval causes the greater cost due to long elapsed time between real occurrence of the failure time and the failure detection (penalty cost). On a finite time horizon, the objective of current study is to figure out the optimal inspection interval for the soft failure component to minimize the expected total cost. Therefore, an adapted sample problem is resolved and numerical results are presented.