Unavailability equations for k-out-of-n systems

This paper updates and extends earlier published analytical results for the unavailabilities (probabilities of failure on random demand) of redundant standby systems with k-out-of-n logic. Such systems are mostly used in safety and protection systems and are subject to latent and detectable failures. Latent failures are detected by periodic tests and repaired immediately after discovery. Many potential failure and error modes are included in the formalism. Interesting relations between two approaches are pointed out. Both consecutive and staggered testing schemes are evaluated, and methods for including certain common cause failures in the analyses are pointed out.