Inspection Times for Stand-by Units

Giovanni Parmigiani
Duke University

May 12 1993

This paper studies optimal timing of inspections for units in cold stand-by. The problem is approached in continuous time. The policies developed adapt optimally to information provided by failures of the main unit and by aging of both the stand-by and main unit.

Results include a general form for the optimal policy, consisting of a recursive relation between successive inspection times, and of a renewal-type integral equation to determine the value of the objective function for a given policy. Further results are derived for the case in which the failure densities describing the process are log-concave. Then the stopping rule is easily characterized. It is also shown that the interval between inspections decrease with time, and tat the optimal schedule is unique. A binary search algorithm for finding the solution is outlined.


reliability , inspection, constrained optimization, nonmarkovian deterioration


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