The State Variable Approach to System Effectiveness

TLDR: A vector expression for system effectiveness is presented which is formally the same as the expression for availability in the case of a single-function system and which can be extended easily to cover multifunction systems.

Abstract: Expressions are given in the literature for the availability, mean-time-between-failures, mean uptime, and mean downtime for systems consisting of a number of identical modules in redundancy. Using the concept of superstates, vector expressions for these parameters are presented which apply to a system consisting of an arbitrary interconnection of different types of modules. A vector expression for system effectiveness is presented which is formally the same as the expression for availability in the case of a single-function system and which can be extended easily to cover multifunction systems.