An out of n system is down (at time , say) due to the failure of at least r of its components. Each component is made up of t equally reliable parts assembled in parallel. All parts are assumed to function independently of one another. Three different policies are described for inspecting and repairing the parts of one component after another until all (or some) of the failed components are identified (and fixed). It is assumed that a less reliable part is cheaper to repair than a more reliable one. It is shown that in order to minimize the expected total cost of necessary repairs, for each of the three policies, the weakest component should be inspected first, then the second weakest and so on. It is also shown that the closer the optimal order is followed (in a specific sense described by a partial ordering on the set of permutations of ) the less is the expected cost that will be incurred.
