New Methods of an Assessment of the Integrated Performance Indicator

Many real-world systems can be modeled by multi-state flow networks (MFNs) and their reliability evaluation features in designing and control of these systems. Considering the maintenance cost constraint makes the problem of reliability evaluation of an MFN more realistic. The maintenance cost associated with an MFN is the total cost of recovering the network from its current state back to its largest state. For a given demand level
$d$
and a maintenance budget limit b, the integrated performance indicator at level (d, b) is defined as the probability of transmitting at least
$d$
units of flow from the source node
$s$
to the sink node
$t$
and satisfying the maintenance budget limit b. It is shown, that the integrated performance indicator at level (d, b) can be computed using either actual (d, b)-MPs or (d – 1, b)-MCs and minimal elements of the set of all capacity vectors for which associated maintenance cost does not exceed the maintenance budget limit b. Moreover, efficient algorithms for determining these extreme capacity vectors of three types are presented.