Diversity in System Reliability following Component Testing

Abstract

There has been substantial attention in the reliability literature to redundancy and diversity of components in system reliability. It is typically argued that, whilst additional components in parallel system structures provide redundancy and increase system reliability, their positive effect may be restricted due to common-cause failures which possibly affect all components of a particular type. This problem can be overcome through a combination of redundancy and diversity, so the use of components of different types, leaving the system less severely affected by possible common-cause failures. There is a second and perhaps even more important reason for aiming at diversity of components, which appears to have received little attention in the literature. One may have only limited information about component reliability, which causes the random functioning of multiple components of one type in a system to be mutually dependent, resulting in possibly higher risk than may be expected without careful consideration of the uncertainties involved.Recently, we have presented Nonparametric Predictive Inference (NPI) for system reliability, with specific focus on so-called voting systems (k-out-of-m systems). In NPI, the reliability of systems is quantified by lower and upper probabilities of system functioning, given binary test results on components, taking uncertainty about component functioning and indeterminacy due to limited test information explicitly into account. In this paper, after a brief overview of results achieved thus far, which include a powerful algorithm for optimal redundancy allocation, we focus on optimal diversity of components related to the limited knowledge about their reliability following test results. It is shown that some level of diversity of components can be beneficial for systems with redundancy, but not for series systems. Throughout this paper attention is restricted to systems with rather basic structures but the lessons learned will certainly also be relevant for more general systems.