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The paper provides for the first time a comprehensive introduction into the mechanisms through which the method of separation achieves risk reduction and into the ways it can be implemented in engineering designs. The concept stochastic separation of critical random events on a time interval, which consists of guaranteeing with a specified probability a specified degree of distancing between the random events, is introduced. Efficient methods for providing stochastic separation by reducing the duration times of overlapping critical random events on a time interval are presented. The paper shows that the probability of overlapping of critical events, randomly appearing on a time interval, is practically insensitive to the distribution of their duration times and to the variance of the duration times as long as the mean of the duration times remains the same. A rigorous proof is presented that this statement is valid even for two random events on a time interval. The paper also provides insight into various mechanisms through which deterministic separation improves reliability and reduces risk. It is demonstrated that the separation on properties is an efficient technique for compensating the drawbacks associated with homogeneous properties. It is demonstrated that improving reliability by including redundancy, improving reliability by segmentation and some of the deliberate weak link techniques and stress limiters techniques for reducing risk are effectively special cases of a deterministic separation. Finally, the paper demonstrates that in a number of cases, the way to extract benefit from the method of separation is to build and analyse a mathematical model based on the method of separation. A comprehensive classification of the discussed methods for stochastic and deterministic separation is also presented. [ABSTRACT FROM AUTHOR]

We propose a framework for analysis and optimization of repairable flow networks by (i) stating and proving the maximum flow minimum flow path resistance theorem for networks with merging flows (ii) a discrete-event solver for determining the variation of the output flow from repairable flow networks with complex topology (iii) a procedure for determining the threshold flow rate reliability for repairable networks with complex topology (iv) a method for topology optimization of repairable flow networks and (v) an efficient algorithm for maximizing the flow in non-reconfigurable flow networks with merging flows. Maximizing the flow in a static flow network does not necessarily guarantee that the flow in the corresponding non-reconfigurable repairable network will be maximized. In this respect, we introduce a new concept related to repairable flow networks: ‘a specific resistance of a flow path’ which is essentially the average percentage of losses from component failures for a flow path from the source to the sink. A very efficient algorithm based on adjacency arrays has also been proposed for determining all minimal flow paths in a network with complex topology and cycles. We formulate and prove a fundamental theorem about non-reconfigurable repairable flow networks with merging flows. The flow in a repairable flow network with merging flows can be maximized by preferentially saturating directed flow paths from the sources to the sink, characterized by the largest average availability. The procedure starts with the flow path with the largest average availability (the smallest specific resistance), and continues by saturating the unsaturated directed flow path with the largest average availability until no more flow paths can be saturated. A discrete-event solver for reconfigurable repairable flow networks with complex topology has also been constructed. The proposed discrete-event solver maximizes the flow rate in the network upon each component failure and return from repair. By maximizing the flow rate upon each component failure and return from repair, the discrete-event solver ensures a larger total output flow during a specified time interval. The designed simulation procedure for determining the threshold flow rate reliability is particularly useful for comparing flow network topologies, and selecting the topology characterized by the largest threshold flow rate reliability. It is also very useful in deciding whether the resources allocated for purchasing extra redundancy are justified. Finally, we propose a new optimization method for determining the network topology combining a maximum output flow rate attained within a specified budget for building the network. The optimization method is based on a branch and bound algorithm combined with pruning the full-complexity network as a way of exploring the possible repairable networks embedded in the full-complexity network. [ABSTRACT FROM AUTHOR]