Configuration determination for k-out-of-n partially redundant systems

The k-out-of-n configuration is a widely adopted structure for partially redundant safety systems. This configuration ensures a high level of reliability and safety with limited financial and space resources. It also facilitates on-line Test and Maintenance (T&M) without having to shut the system down. One question a decision maker needs to answer when adopting k-out-of-n systems is: what is the best configuration for the application, i.e. how many channels in total need to be utilized and among these channels, how many channels need to function simultaneously in order for the system to function. There are various factors to consider in order to make this decision. This paper looks at this problem from a reliability engineers point of view. A quantitative analysis is performed for both unavailability and probability of spurious operation due to independent failure. In particular, the relative gain and/or loss of these quantities that occurs due to changing from one configuration to another are compared through rigorous mathematical analysis. The results provide important information that can be used when choosing system configurations to meet regulatory requirements and financial constraints. The two different configurations for shutdown systems in Nuclear Power Plants, the 2-out-of-3 system and the 2-out-of-4 system, are utilized as an example to illustrate the theoretical results.