Bounds on the availability function

Abstract

The report deals with the problem of computing the availability function for an alternating renewal process with exponential failure times and general repair times. General expressions giving upper and lower bounds on the availability are derived, as well as an estimate of the error. Several of the bounds with greatest practical consequence are worked out and illustrated for a gamma repair distribution with any integer shape parameter. The case of constant repair is compared to the case of gamma repair with a large shape parameter. Finally, some simulation results using a log normal repair distribution are compared to the gamma results, suggesting that a gamma distribution can be used in lieu of a log normal for purposes of computing the availability function. (Author)