Efficient decomposition method for reliability analysis of coherent discrete systems

Abstract

For the purpose of reliability analysis, the performance of many systems is modelled as a function of discrete component states. Examples include infrastructure networks such as transportation networks, power distribution networks, and water pipeline networks. For such systems, it is common to model performance of a component by a few states rather than by a continuous measure (e.g., a roadway has 100%, 50%, or 10% of its normal traffic capacity).

Most system reliability methods (SRMs) (e.g., surrogate modelling and adaptive sampling) are developed for systems with continuous component events. They often leverage an assumption that a system state transitions smoothly with respect to component states. This assumption does not hold for systems with discrete component events, in which a change in state of a single component can incur a drastic change in system state. Such non-smoothness, and the fact that the system performance function might only take on a small number of values, make it challenging to infer trends of system state with change in component states.

Another distinctive characteristic of systems with discrete component events is that they often consist of a large number of components. Luckily, for these systems, the increased dimensionality is less critical than for systems described by continuous input random variables. This is because in discrete systems, it is easier to decompose system events by exploiting minimal cut-sets and link-sets. The use of these minimal sets does not confine the application to binary-state systems. In multi-state systems, their definition can be generalized to refer to the most concise representations of component states that characterize failure or survival events.

This study presents an efficient decomposition method for reliability analysis of systems with discrete component events. To achieve efficiency, we impose the assumption that the system performance is coherent, i.e., worsening component states does not improve the system state, and improving component states does not worsen it. To handle general systems, we also propose a strategy for identifying the minimal sets, which applies to any coherent system. The proposed algorithm is applied to evaluate an example system with costly performance functions: a transportation network evaluated by traffic assignment optimization.