The calculation of reliability for complex systems

This study develops two programs for the calculation of the reliability of small complex systems. Small Is defined as 10 or less components, 10 or less paths or 10 or less cuts. A method for reducing large systems Is presented with an application.

Both programs are written in VAX/VMS Basic. Program ESPACE enumerates all possible system states. The user inputs the components, their reliabilities and the min cut set. The program determines which states result in system failure from the cut set and sums the reliabilities of those states to find system reliability.

For program ADDON the user inputs component reliabilities and either the min path set or the min cut set. The program manipulates string expressions to produce the terms of the addition theorem, applies the idempotency law (A Intersection A Is A) and calculates the signed terms which are summed to give system reliability.

Systems with common cause failure are not considered.