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The purpose of this paper is to introduce an efficient algorithm based on a non-linear accepting threshold to solve the redundancy allocation problem (RAP) considering multiple redundancy strategies. In addition to the components reliability, multiple redundancy strategies are simultaneously considered to vary the reliability of the system. The goal is to determine the optimal selection of elements, redundancy levels and redundancy strategy, which maximizes the system reliability under various system-level constraints.

The mixed RAP considering the use of active and standby components at the subsystem level belongs to the class of NP-hard problems involving selection of elements and redundancy levels, to maximize a specific system performance under a given set of physical and budget constraints. Generally, the authors recourse to meta-heuristic algorithms to solve this type of optimization problem in a reasonable computational time, especially for large-size problems. A non-linear threshold accepting algorithm (NTAA) is developed to solve the tackled optimization problem. Numerical results for test problems from previous research are reported and analyzed to assess the efficiency of the proposed algorithm.

The comparison with the best solutions obtained in previous studies, namely: genetic algorithm, simulated annealing, memetic algorithm and the particle swarm optimization for 33 different instances of the problem, demonstrated the superiority of the proposed algorithm in finding for all considered instances, a high-quality solution in a minimum computational time.

Considering multiple redundancy strategies helps to achieve higher reliability levels but increases the complexity of the obtained solution leading to infeasible systems in term of physical design. Technological constraints must be integrated into the model to provide a more comprehensive and realistic approach.

Designing high performant systems which meet customer requirements, under different economic and functional constraints is the main challenge faced by the manufacturers. The proposed algorithm aims to provide a superior solution of the reliability optimization problem by considering the possibility to adopt multiple redundancy strategies at the subsystem level in a minimum computational time.

A NTAA is expanded to the RAP considering multiple redundancy strategies at the subsystem level subject to weight and cost constraints. A procedure based on a penalized objective function is developed to encourage the algorithm to explore toward the feasible solutions area. By outperforming well-known solving technique, the NTAA provides a powerful tool to reliability designers of complex systems where different varieties of redundancies can be considered to achieve high-reliability systems.

The purpose of this paper is to study the relationship between reported sigma levels and actual failure rates (FRs) of gamma-distributed processes. The added complexity of the non-normality behavior of the gamma distribution is analyzed for the case of the cycle time (CT) of a real procurement process from the oil and gas industry. Then, recommendations and guidelines for the application of Six Sigma methodology for the case study are proposed.

Sensitivity analysis is conducted to study the relationship between gamma distribution parameters and FRs considering different quality levels. Then, adjustments for implementing Six Sigma programs for gamma processes are proposed. These adjustments consist of first determining the appropriate probability distribution, the standard CT and the due date, followed by setting performance zones and improvement strategies on target gamma parameters that yield the minimal FR.

For gamma-distributed processes, simply reporting the sigma level is not sufficient to capture the main characteristics of the process. These characteristics include process FR, mean setting, shape, spread and amount of variation reduction (i.e. improvement effort) required. That is why caution must be exercised when dealing with one-sided non-normal quality characteristics such as CT.

To the authors’ knowledge, this is the first time that the Six Sigma performance has been evaluated for gamma processes to analyze the link between Six Sigma FRs and gamma distribution parameters leading to the development of a modified Six Sigma methodology for non-normal processes.

Reconfiguration mechanisms lead to the design of robust manufacturing systems which have the capability to allow the service continuity, in the presence of a failure, on the basis of a minimal degradation of performances. In this paper, a stochastic model is proposed to assess and to analyze the availability of reconfigurable systems whose equipments are subject to random failures. To distinguish between the normal behavior and the degraded one, the production rate is used as a performance measure. An availability model that takes into account the performance degradation is developed. Close form solutions of the steady‐state availability and the production rate of a reconfigurable system are calculated. Two optimization problems dealing with reconfigurable systems are also addressed. The paper considers a series system consisting of N stochastically independent components. Different technologies are assumed to be available for each component. The following design problems are studied: find the configuration, which allows maximizing the production rate of the system under resource constraints; and find the configuration that allows to reach some predetermined level of production rate at minimal cost. The design model of the first problem leads to mixed linear programming, while the design model of the second problem leads to integer linear programming. A numerical procedure is developed to solve both problems.

The purpose of this paper is to apply a recent kind of neural networks in a reliability optimization problem for a series system with multiple‐choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget and weight. The problem is formulated as a non‐linear binary integer programming problem and characterized as an NP‐hard problem.

The design of neural network to solve this problem efficiently is based on a quantized Hopfield network (QHN). It has been found that this network allows one to obtain optimal design solutions very frequently and much more quickly than other Hopfield networks.

For systems more complex than series systems considered in this paper, the proposed approach needs to be adapted. The QHN‐based solution approach can be applied in many industrial systems where reliability is considered as an important design measure, e.g. in manufacturing systems, telecommunication systems and power systems.

The paper develops a new efficient method for reliability optimization. The most interesting characteristic of this method is related to its high‐speed computation, since the practical importance lies in the short computation time needed to obtain an optimal or nearly optimal solution for large industrial problems.

The purpose of this paper is to extend the optimal design problem of series manufacturing production lines to series‐parallel lines, where redundant machines and in‐process buffers are both included to achieve a greater production rate. The objective is to maximize production rate subject to a total cost constraint.

An analytical method is proposed to evaluate the production rate, and an ant colony approach is developed to solve the problem. To estimate series‐parallel production line performance, each component (i.e. each set of parallel machines) of the original production line is approximated as a single unreliable machine. To determine the steady state behaviour of the resulting non‐homogeneous production line, it is first transformed into an approximately equivalent homogeneous line. Then, the well‐known Dallery‐David‐Xie algorithm (DDX) is used to solve the decomposition equations of the resulting (homogenous) line. The optimal design problem is formulated as a combinatorial optimisation one where the decision variables are buffers and types of machines, as well as the number of redundant machines. The effectiveness of the ant colony system approach is illustrated through numerical examples.

Simulation results show that the analytical approximation used to estimate series‐parallel production lines is very accurate. It has been found also that ant colonies can be extended to deal with the series‐parallel extension to determine near‐optimal or optimal solutions in a reasonable amount of time.

The model and the solution approach developed can be applied for optimal design of several industrial systems such as manufacturing lines and power production systems.

The paper presents an approach for the optimal design problem of series‐parallel manufacturing production lines.

The purpose of this paper is to formulate a new problem of the optimal design of a series manufacturing production line system, and to develop an efficient heuristic approach to solve it. The optimal design objective is to maximize the efficiency subject to a total cost constraint.

To estimate series production line efficiency, an analytical decomposition‐type approximation is used. The optimal design problem is formulated as one of combinatorial optimization where the decision variables are buffers and types of machines. This problem is solved by developing and demonstrating a problem‐specific ant system algorithm. Numerical examples illustrate the effectiveness of the algorithm.

It has been found that this algorithm can always find near‐optimal or optimal solutions quickly. The approach developed in this paper for manufacturing lines can be adapted for power systems and telecommunication systems.

The paper presents a new approach for the optimal design of buffered series production lines. This optimization approach aims at selecting both the machines and the levels of buffers. The paper also develops an efficient solution approach based on the ant system meta‐heuristic.