Limiting availability of a one-unit system backed by a spare under repair or preventive maintenance

Abstract

We consider a one-unit system under continuous monitoring, aided by an identical spare unit and serviced by a facility that performs repair on a failed unit or preventive maintenance on a recalled unit making it as good as new. We assume instantaneous commencement of service and installation to operation. We find the distribution of the system up time and down time when life-, recall- and service-times have arbitrary probability density functions. Hence, we obtain the limiting availability of the system. Also, we compute the servicing cost per unit time to determine whether preventive maintenance is preferable over a repair only model.