Optimal periodic inspection programs for randomly failing equipment

There have been many analyses made of models for equipment inspection, i. e ., where a system may suffer a bre.akdowfl, ~ut such an event is only discovered by an inspection. Most analyses as· ~ume t~at the tIme to failure follows a negative exponential law which implies that only periodic mspectlOn programs need b~ considered. Another model which has been analyzed by Barlow, Hunter, and Proschan finds the optimal program of inspections when the equipment reliability function is of gener.al form , but a particular los: function is given. In this paper we find the optimal pe riodic in· spectlOn program for systems whICh do not have negative exponential reliability functions . These programs have the virtue of simplicity even though they may not be optimal in an absolute sense. Besides the periodic inspection programs, we derive results for random inspection programs.