Minimax surveillance schedules with partial information

An analysis is made of the problem of finding the optimal schedule for checking an operating system which is subject to failure detectable only by inspection of the system. If a cost is attached to each inspection of the system and also to undetected failure, then there exists the problem of scheduling inspections to minimize total costs. This problem also exists for the surveillance inspection of stored goods subject to deterioration with time. Previous work by Barlow and Hunter gives the optimal schedules for two special cases — when the failure distribution of the units is known to be exponential, and when it is known to be uniform. Derman has obtained the minimax schedule, that is, the schedule which minimizes the maximum possible expected cost for the case where the failure distribution is entirely unknown. This paper assumes that the location of one percentile of the failure distribution of the units is known, and is concerned with the optimal use of this partial information. The minimax schedule is obtained for the case where the operation is to continue until either a failure is detected, or a stipulated time has elapsed, and comparisons are made with Derman' s results for an unknown distribution.