Stochastic Analysis of a System with Redundant Robots, One Built-in Safety Unit, and Common-Cause Failures

This paper presents reliability and availability analyses of a mathematical model representing a robot-safety system having n-redundant robots and one built-in safety unit with common-cause failures. At least k robots must function successfully for the overall robot system success. The system failure rates and the partially failed system repair rates are assumed constant and the failed system repair time is assumed arbitrarily distributed. Markov and supplementary variable methods were used to develop generalized expressions for state probabilities, system availabilities, reliability, and mean time to failure. Some plots of these expressions are shown.