Finding the MTBF of repairable systems by reduction of the reliability block diagram

Abstract

Systems consisting of units with independent failures and with adequate repair facilities to initiate the repair of any unit when it fails are considered. Such systems can be assumed to be made up of independently operating units. The representation by reliability block diagrams of how successful operation of such a system is determined by the successful operation of its constituent units is well known. In the same way that reliability block diagrams can be reduced to find the reliability of a non-maintained system, the reliability block diagram of a system of independent units can be reduced to find the availability of the repairable system. Using the same reduction procedure, the MTBF of the system can be found in terms of the MTBF and availability of the individual units. The formulae for reducing the different basic connections of blocks are derived. However, the reduction procedure applies only to systems of the series-parallel type; the method of extending it to systems that would be series-parallel if some unit were replaced either by a short circuit or by an open circuit is discussed.