Comparison of cyclic and delayed maintenances for a phased array radar

An antenna of phased array radar (PAR) consists of a large number of individual radiating elements and steers its electromagnetic wave direction by shifting wave phases of these elements. Failed elements have to be detected, diagnosed, localized and replaced at scheduled times to hold a required performance of a radar system. However, the maintenance of an antenna should not be made so frequently, because it interrupts the radar operation and degrades the radar availability. This paper considers two typical policies of cyclic and delayed maintenances for a PAR where a certain number of survival elements is needed to hold a required performance: Failed elements in cyclic maintenance are replaced at periodic times, and those in delayed maintenance are replaced when their number has exceeded a predesignated one. When failures of a PAR antenna elements occur as a Poisson process, the expected costs are obtained and optimal policies for two maintenances which minimize them are analytically discussed.