Reliability and performance analysis of multi-state systems based on analytical load flow considerations

The last three decades have been marked by the advent of various analytical and simulation algorithms, enhanced for the reliability evaluation of multi-state systems. Though the latter are widely believed to be the most applicable to realistic systems, they impose a greater degree of computational burden. Consequently, they have been outshone, especially in structural optimization, redundancy allocation and maintenance optimization problems. On the flip side, analytical techniques are constrained by their various unique limitations. Prominent amongst these being, inapplicability to multiple output systems with competing demand and reliance on the enumeration of system path or cut sets prior to analysis. The development, therefore, of a single approach that addresses these limitations is desirable. In this paper, the fact that most engineering systems satisfy the flow conservation principle and can be regarded as multi-state flow networks is exploited. An analytical algorithm that efficiently derives all the possible system performance levels and uses basic probability algebra to estimate their probabilities of occurrence is developed. The algorithm is enhanced to support systems with flow losses, Common-Cause Failures (CCF), and minimal system reconfigurations. These attributes, as applied to two case studies, ensure the limitations of existing techniques are overcome.