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Inspection Times for Stand-by Units
Journal of Applied Probability
Vol. 31, No. 4 (Dec., 1994), pp. 1015-1025
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215325
Page Count: 11
You can always find the topics here!Topics: Lagrangian function, Optimal policy, System failures, Differential equations, Objective functions, Scheduling, Uniqueness, Mathematical procedures
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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 ageing of both the stand-by and the 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 logconcave. Then the stopping rule is easily characterized. It is also shown that the interval between inspections decreases with time, and that the optimal schedule is unique. A binary search algorithm for finding the solution is outlined.
Journal of Applied Probability © 1994 Applied Probability Trust