Availability and Reliability of a 1-Server System with n Warm Standbys

This paper deals with the availability and reliability of a system with n warm standbys; the operating unit and the standbys all have constant failure rates. The failure rate of a standby depends upon its position in the stack of standbys. The paper describes the model. The Supplement derives the general integral equations for the system; then solves them for the special case of n = 2. The Laplace transforms for the mean down-time of the system and for the mean time to system failure are obtained. The steady-state availability of the system is discussed.