Optimization of system reliability in the presence of common cause failures

The redundancy allocation problem is formulated with the objective of maximizing system reliability in the presence of common cause failures. These types of failures can be described as events that lead to simultaneous failure of multiple components due to a common cause. When common cause failures are considered, component failure times are not independent. This new problem formulation offers several distinct benefits compared to traditional formulations of the redundancy allocation problem. For some systems, recognition of common cause failure events is critical so that the overall system reliability estimation and associated design resembles the true system reliability behavior realistically. Since common cause failure events may vary from one system to another, three different interpretations of the reliability estimation problem are presented. This is the first time that mixing of components together with the inclusion of common cause failure events has been addressed in the redundancy allocation problem. Three non-linear optimization models are presented. Solutions to three different problem types are obtained. They support the position that consideration of common cause failures will lead to different and preferred “optimal” design strategies.     

Reliability analysis of cluster-based ad-hoc networks

The mobile ad-hoc wireless network (MAWN) is a new and emerging network scheme that is being employed in a variety of applications. The MAWN varies from traditional networks because it is a self-forming and dynamic network. The MAWN is free of infrastructure and, as such, only the mobile nodes comprise the network. Pairs of nodes communicate either directly or through other nodes. To do so, each node acts, in turn, as a source, destination, and relay of messages. The virtue of a MAWN is the flexibility this provides; however, the challenge for reliability analyses is also brought about by this unique feature. The variability and volatility of the MAWN configuration makes typical reliability methods (e.g. reliability block diagram) inappropriate because no single structure or configuration represents all manifestations of a MAWN. For this reason, new methods are being developed to analyze the reliability of this new networking technology. New published methods adapt to this feature by treating the configuration probabilistically or by inclusion of embedded mobility models. This paper joins both methods together and expands upon these works by modifying the problem formulation to address the reliability analysis of a cluster-based MAWN. The cluster-based MAWN is deployed in applications with constraints on networking resources such as bandwidth and energy. This paper presents the problem's formulation, a discussion of applicable reliability metrics for the MAWN, and illustration of a Monte Carlo simulation method through the analysis of several example networks.     

A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability

This paper describes a Monte-Carlo (MC) simulation methodology for estimating the reliability of a multi-state network. The problem under consideration involves multi-state two-terminal reliability (M2TR) computation. Previous approaches have relied on enumeration or on the computation of multi-state minimal cut vectors (MMCV) and the application of inclusion/exclusion formulae. This paper discusses issues related to the reliability calculation process based on MMCV. For large systems with even a relatively small number of component states, reliability computation can become prohibitive or inaccurate using current methods. The major focus of this paper is to present and compare a new MC simulation approach that obtains accurate approximations to the actual M2TR. The methodology uses MC to generate system state vectors. Once a vector is obtained, it is compared to the set of MMCV to determine whether the capacity of the vector satisfies the required demand. Examples are used to illustrate and validate the methodology. The estimates of the simulation approach are compared to exact and approximation procedures from solution quality and computational effort perspectives. Results obtained from the simulation approach show that for relatively large networks, the maximum absolute relative error between the simulation and the actual M2TR is less than 0.9%, yet when considering approximation formulae, this error can be as large as 18.97%. Finally, the paper discusses that the MC approach consistently yields accurate results while the accuracy of the bounding methodologies can be dependant on components that have considerable impact on the system design.     

A Classification Tree Based Approach for the Development of Minimal Cut and Path Vectors of a Capacitated Network

This paper presents a holistic method that links together Monte-Carlo simulation, exact algorithms, and a data mining technique, to develop approximate bounds on the reliability of capacitated two-terminal networks. The method uses simulation to generate network configurations that are then evaluated with exact algorithms to investigate if they correspond to a network success or failure. Subsequently, the method implements commercially available software to generate a classification tree that can then be analyzed, and transformed into capacitated minimal cut or path vectors. These vectors correspond to the capacitated version of binary minimal cuts & paths of a network. This is the first time that these vectors are obtained from a decision tree, and in this respect, research efforts have been focused on two main directions: 1) deriving an efficient yet intuitive approach to simulate network configurations to obtain the most accurate information; and given that the classification tree method could for some applications provide imperfect or incomplete information without the explicit knowledge of the reliability engineer, 2) understand the relationship between the obtained vectors, and the real capacitated minimal cut & path vectors of the network, and its reliability. The proposed method has been tested on a set of case networks to assess its validity & accuracy. The results obtained show that the technique described is effective, simple, and widely applicable.     

All-terminal network reliability optimization via probabilistic solution discovery

This paper presents a new algorithm that can be readily applied to solve the all-terminal network reliability allocation problems. The optimization problem solved considers the minimization of the network design cost subject to a known constraint on all-terminal reliability by assuming that the network contains a known number of functionally equivalent components (with different performance specifications) that can be used to provide redundancy. The algorithm is based on two major steps that use a probabilistic solution discovery approach and Monte Carlo simulation to generate the quasi-optimal network designs. Examples for different sizes of all-terminal networks are used throughout the paper to illustrate the approach. The results obtained for the larger networks with unknown optima show that the quality of the solutions generated by the proposed algorithm is significantly higher with respect to other approaches and that these solutions are obtained from restricted solution search space. Although developed for all-terminal reliability optimization, the algorithm can be easily applied in other resource-constrained allocation problems.     

Interval-valued availability framework for supplier selection based on component importance

The availability of ageing systems, particularly weapon systems within the Department of Defense, is of significant concern, as budgets tighten and system replacement is infeasible. This work addresses the selection of sole suppliers according to their ability to provide component parts that strengthen availability of the system. We extend a popular multi-criteria decision-making approach, Technique for Order Preferences by Similarity to an Ideal Solution, by (i) considering the availability of individual components as the criteria in the decision problem and (ii) weighting those criteria according to the value of component importance measures while (iii) accounting for uncertainty in underlying reliability and maintainability parameters with interval numbers. An aircraft example illustrates the approach.