The Highest & Lowest Reliability Achievable with Redundancy

Often system reliability can be enhanced through the use of redundancy. Redundancy may, however, have a detrimental effect on the statistical relationship of redundant elements. When the components in a redundant system have more than one failure-mode and when failures are s-dependent, it is difficult to assess the reliability of the system. The paper describes the θ-transformation by which the highest and lowest reliability achievable can be determined for a configuration using components with specified reliabilities. As a by-product we become able to pinpoint the statistical relationships that give rise to highest and lowest system reliabilities.