A nearly optimal inspection policy for a two-component series system

The purpose of this paper is to determine a nearly optimal inspection sequence for a series system consisting of two components subject to gradual deterioration and whose failures are not self-announcing and can be detected only through inspection.

The problem is tackled in the context of condition-based maintenance (CBM) with a maintenance model in the class of the control-limit policies for which the maintenance decision is made following inspection by comparison of the deterioration level to critical thresholds. A mathematical model is developed to express the total expected cost per time unit as a function of the inspection instants.

For any given series system composed of two components with known critical deterioration threshold levels, and for any given set of costs related to inspection, inactivity due to failure, and preventive and corrective replacements of each component, a nearly optimal inspection sequence of the system is derived such as the total expected cost is reduced.

Due to the complexity of the cost model with the inspection instants (×1, ×2, ×3, …) being the decision variables, it has not been possible to derive the optimal solution. A quasi-optimal sequence of inspection times is derived along with the corresponding total average cost per time unit.

In many practical situations in which CBM is implemented, a tradeoff between inspection costs and inactivity and replacement costs has to be balanced when determining the intervals between successive inspections at which the degradation level of the components should be assessed and compared to predetermined critical threshold levels. Inspecting too often would increase inspection costs but in the same time it would also increase the probability to avoid a failure and end up with a preventive replacement, whereas not inspecting often enough would increase the probability to end up with a failure increasing replacement and inactivity costs.

While the inspection problem has been largely treated for single component systems, inspection policies become much more complex when considering multi-component systems. A two-component series system is considered in this paper.