Some Problems of Tradeoff When the Standby Units and Operating Units of a Redundant System Have Different Probabilities of Success

This note considers a redundant system in which the standby units may have a different probability of success than the operating units for a given mission profile. A model is developed so that one can calculate the system reliability for the mission. Furthermore, for the case where reliabilities (probabilities of mission success) of the standby units can be related to the cost of these units, a tradeoff study is made in a few special cases to determine the optimum number of standby components (in the sense of maximizing system reliability) to be installed when there is a fixed sum of money available for the installation of standby units.