Reliability Redundancy Allocation Problem Research Articles

An improved particle swarm optimization algorithm for reliability-redundancy allocation problem with mixed redundancy strategy and heterogeneous components

The reliability–redundancy allocation problem (RRAP) has been intensively studied to identify the optimal system design under several constraints, so as to maximize the system reliability as much as possible. Recently, the mixed redundancy strategy where both active redundant components and cold standby components can be simultaneously used by a subsystem has been introduced into the RRAP, leading to a more superior result than that of a subsystem with either active redundancy strategy or cold standby strategy. Nevertheless, in the existing studies, all the components deployed in a subsystem have to be homogeneous even if the mixed redundancy strategy is chosen. The strong premise is released in this paper by introducing heterogeneous components into the RRAP. The resulting optimization problem is resolved by proposing an improved particle swarm optimization (PSO) algorithm with stochastic perturbation nature. The efficiency of the proposed algorithm has been demonstrated by conducting a set of comparative studies on three benchmark problems. As observed in our study, the design flexibility introduced by our method can always yield a greater system reliability than that of the state-of-the-art methods. Most importantly, we also reveal that the switching reliability has significant influence on the optimal system configuration.

Type-2 fuzzy reliability–redundancy allocation problem and its solution using particle-swarm optimization algorithm

In this paper, the fuzzy multi-objective reliability redundancy allocation problem (FMORRAP) is proposed, which maximizes the system reliability while simultaneously minimizing the system cost under the type 2 fuzzy uncertainty. In the proposed formulation, the higher order uncertainties (such as parametric, manufacturing, environmental, and designers uncertainty) associated with the system are modeled with interval type 2 fuzzy sets (IT2 FS). The footprint of uncertainty of the interval type 2 membership functions (IT2 MFs) accommodates these uncertainties by capturing the multiple opinions from several system experts. We consider IT2 MFs to represent the subsystem reliability and cost, which are to be further aggregated using extension principle to evaluate the total system reliability and cost according to their configurations, i.e., series parallel and parallel series. We proposed a particle swarm optimization (PSO) based novel solution approach to solve the FMORRAP. To demonstrate the applicability of two formulations, namely, series parallel FMORRAP and parallel series FMORRAP, we performed experimental simulations on various numerical data sets. The decision makers/system experts assign different importance to the objectives (system reliability and cost), and these preferences are represented by sets of weights. The optimal results are obtained from our solution approach, and the Pareto optimal front is established using these different weight sets. The genetic algorithm (GA) was implemented to compare the results obtained from our proposed solution approach. A statistical analysis was conducted between PSO and GA, and it was found that the PSO based Pareto solution outperforms the GA.

Efficient reliability–redundancy allocation with uniform importance measure in presence of correlated failure

ABSTRACTThe problem of designing optimal system architecture (including the redundancy level and the corresponding reliability of each component) which maximizes reliability through resource constraints has been attracted increasing attention in recent years. In this paper, a hybrid method in which an effective co-evolutionary particle swarm optimization combined with harmony search algorithm is proposed to solve the reliability–redundancy optimization problem in the presence of correlated component failures. Another main objective which is considered is decreasing the role of critical component in system reliability. So two different scenarios for reliability–redundancy optimization problem were investigated. The first scenario is reliability–redundancy optimization in the presence of correlation between subsystem failures and the second scenario is considering the multi-objective reliability redundancy allocation problem where the reliability of the system and the uniformity of importance measure of each subsystem are considered as two different objectives. To show the effectiveness of the proposed method, numerical results of some sample systems are illustrated. In addition, some numerical results of two different types of RRAP are reported. The obtained simulation results show that the proposed approach is better in comparison of previously reported in the recent literature.

A novel boundary swarm optimization method for reliability redundancy allocation problems

A new methodology called boundary simplified swarm optimization (BSO) is proposed by integrating a novel self-boundary search (SBS) and a two-variable update mechanism (UM2) to improve simplified swarm optimization (SSO) in solving mixed-integer programing problems that include both discrete and continuous variables. To balance the exploration and exploitation ability, the proposed SBS is implemented to update the current best solution (called gBest) based on the boundary conditions and analytical calculations to enhance the exploitation ability of gBest; the UM2 updates the solutions (called non-gBest) that are not gBest to fix the over-exploration of the SSO, in which all variables need to update without exploiting the information of the neighborhood area. The performance of the proposed BSO is ascertained by comparing the results with existing algorithms using four reliability redundancy allocation benchmark problems in the existing literature.

Multiple-Objective Optimization and Design of Series-Parallel Systems Using Novel Hybrid Genetic Algorithm Meta-Heuristic Approach

In this study, we develop a new meta-heuristic-based approach to solve a multi-objective optimization problem, namely the reliability-redundancy allocation problem (RRAP). Further, we develop a new simulation process to generate practical tools for designing reliable series-parallel systems. Because the RRAP is an NP-hard problem, conventional techniques or heuristics cannot be used to find the optimal solution. We propose a genetic algorithm (GA)-based hybrid meta-heuristic algorithm, namely the hybrid genetic algorithm (HGA), to find the optimal solution. A simulation process based on the HGA is developed to obtain different alternative solutions that are required to generate application tools for optimal design of reliable series-parallel systems. Finally, a practical case study regarding security control of a gas turbine in the overspeed state is presented to validate the proposed algorithm.

Multi-objective optimization of reliability–redundancy allocation problem with cold-standby strategy using NSGA-II

The reliability–redundancy allocation problem (RRAP) involves the selection of components reliability and redundancy levels, with the aim of maximizing system reliability. Generally, RRAPs are formulated with the assumption of active redundancy strategy. In this paper, the problem is formulated by considering a cold-standby strategy. In most practical cases, complicated decision-making problems are encountered due to the presence of several conflicting objectives such as maximizing system reliability and simultaneously minimizing the total cost, weight or volume of the systems. Therefore, it is essential to consider these conflicting criteria as the main objectives of the optimization problem. Hence, in this paper, a bi-objective RRAP is developed. The proposed mathematical model is developed for three benchmark problems and solved by using a multi-objective evolutionary algorithm (NSGA-II). In order to calculate the exact reliability values for the problems, a recently introduced Markov-based approach is used. The results indicate that, in comparison with recent studies, the proposed NSGA-II shows superior performance and leads to better results in all benchmark problems. In other words, for each problem, a variety of structures are presented which outperform the best active structure and at least one structure is obtained that outperforms the best standby one in the literature.

Genetic Algorithm Based Approach for Reliability Redundancy Allocation Problems in Fuzzy Environment

This paper presents the use of genetic algorithm to solve reliability redundancy allocation problem of complicated system in fuzzy environment. Generally, this problem has been formulated as single objective integer non-linear programming problem with several resource constraints. In this paper, the reliability of each component as well as other parameters related to the problem is considered to be fuzzy valued. In this work, the corresponding constrained optimization problem has been transformed to crisp constrained optimization problem using defuzzification of fuzzy number. Here, widely known Yager ranking Index has been used for defuzzification of fuzzy number. The Big-M penalty function technique has been used to transform the constrained optimization problem into an unconstrained optimization problem. The converted problem has been solved with the help of real coded genetic algorithm. To illustrate the proposed methodology, a numerical example has been considered and solved. To study the performance of the proposed genetic algorithm, sensitivity analyses have been done graphically.

Optimal reliability design of a system with k-out-of-n subsystems considering redundancy strategies

This study presents new reliability models for k-out-of-n systems using a structured continuous-time Markov chain. The approach makes it comfortable to identify the characteristics of the lifetime of the system, such as reliability and expected lifetime. To demonstrate the advantage, the analysis results of them for the multi-spectral camera system, which is the only payload of Korea multi-purpose satellite-2 as an example of a real system. Furthermore, existing studies on a k-out-of-n system with standby redundancy has provided the approximated reliability for it. In this paper, it is confirmed that the approximation error could have an effect on the reliability design for a system. Moreover, new versions of reliability optimization problems, redundancy allocation problem (RAP) and reliability-redundancy allocation problem(RRAP), are proposed. In order to maximize system reliability, they further determine the redundancy strategy, either active or standby redundancy for each k-out-of-n subsystem from the traditional problems. A parallel genetic algorithm is proposed for an RRAP modeled by nonlinear mixed integer programming.

A hybrid Jaya algorithm for reliability–redundancy allocation problems

ABSTRACTThis article proposes an efficient improved hybrid Jaya algorithm based on time-varying acceleration coefficients (TVACs) and the learning phase introduced in teaching–learning-based optimization (TLBO), named the LJaya-TVAC algorithm, for solving various types of nonlinear mixed-integer reliability–redundancy allocation problems (RRAPs) and standard real-parameter test functions. RRAPs include series, series–parallel, complex (bridge) and overspeed protection systems. The search power of the proposed LJaya-TVAC algorithm for finding the optimal solutions is first tested on the standard real-parameter unimodal and multi-modal functions with dimensions of 30–100, and then tested on various types of nonlinear mixed-integer RRAPs. The results are compared with the original Jaya algorithm and the best results reported in the recent literature. The optimal results obtained with the proposed LJaya-TVAC algorithm provide evidence for its better and acceptable optimization performance compared to the original Jaya algorithm and other reported optimal results.

Particle Swarm Optimization with Intelligent Mutation for Nonlinear Mixed-Integer Reliability-Redundancy Allocation

As improving system reliability in a basic system has been always one of the important concerns in reliability engineering; many studies have been developed in this regard. In this paper, a novel intelligent PSO (PSO-IM) is proposed. In suggested approach two different types of mutation operator, which controlled by Fuzzy controller, are applied to standard PSO for finding the best solution of reliability-redundancy allocation problems (RRAP). Also a heuristic inertia weight equation is introduced in our proposed PSO-IM. The main objective of our solution is to achieve maximum reliability in a basic system with acceptable redundancy allocation subject to cost, weight, volume. The proposed method (PSO-IM) significantly improves the search ability of basic PSO and finds the maximum reliability in comparison with previous works.

A robust reliability redundancy allocation problem under abnormal external failures guided by a new importance measure

Besides inherent failures under normal conditions studied by classical reliability engineering, systems may also be subject to abnormal external failures, whose probabilities are hard, if not impossible, to predict, such as failures caused by natural disasters (e.g. earthquakes, floods, and tornados) and malicious attacks. Thus, abnormal external failures need to be considered when designing a system, as in reliability redundancy allocation problem. To deal with the uncertainty of abnormal external failures and based on robust optimization, this research proposes a multi-objective optimization approach that can simultaneously maximize system reliability under both normal and the worst cases of abnormal external failures for redundancy allocation problem. Since the amount of abnormal external failures is usually unknown, the worst case for each possible amount of abnormal external failures needs to be identified first. For this purpose, a new importance measure that can quantify the importance of a subset of system components with arbitrary cardinality is proposed. We also revise a widely used multi-objective evolutionary algorithm, multi-objective probabilistic solution discovery algorithm, to deal with the complexity of redundancy allocation problem. The merits of the revised algorithm are demonstrated by extensive experiments.

Multi-objective Reliability-Redundancy Allocation Problem with Interval Type-2 Fuzzy Uncertainty

The multiobjective reliability redundancy allocation problem (MORRAP) aims to ensure high system reliability in the presence of optimally redundant components. This is one of the most important design considerations for system designers. Due to the associated uncertainty in component parameters, precise computations of overall system reliability, cost, and weight, etc., are difficult during design time. Hence, these parameters are befitting to be modeled as fuzzy quantities. As type-1 fuzzy numbers have limitations in representing higher order uncertainties, so this paper models the component parameters viz., reliability, cost, and weight with interval type-2 fuzzy numbers. Thus, we propose a novel formulation of MORRAP, termed as interval type-2 fuzzy multiobjective optimization problem (IT2FMORRAP). A popular multiobjective evolutionary algorithm, viz., nondominated sorting genetic algorithm II, is used to solve the proposed IT2FMORRAP, for which we have developed two novel algorithms in this paper. Numerical examples are included to demonstrate the solution approach. On comparing the outcomes with earlier results, we have found that the proposed IT2FMORRAP outperforms classical as well as other type-1 fuzzy-number-based approaches.

A bi-objective multi-period series-parallel inventory-redundancy allocation problem with time value of money and inflation considerations

A large number of existing research studies on reliability redundancy allocation problems do not take into consideration the time value of the money and the inflations costs associated with the component inventories. In this study, we formulate a multi-component multi-period series-parallel inventory redundancy allocation problem (SPIRAP) as a mixed-integer nonlinear mathematical model where: (a) the costs are calculated by considering the time value of money and inflation rates; and (b) the total warehouse capacity to store the components, the total budget to purchase the components and the truck capacity are subject to constraints. The primary goal in this study is to find the optimal order quantity of the components for each subsystem in each period such that the total inventory costs are minimized and the system reliability is maximized, concurrently. A controlled elitism non-dominated ranked genetic algorithm (CE-NRGA), a NSGA-II, and a multi-objective particle swarm optimization (MOPSO) are presented to solve the proposed SPIRAP. A series of numerical examples are used to demonstrate the applicability and exhibit the efficacy of the procedures and algorithms. The results reveal that the CE-NRGA outperforms both NSGA-II and MOPSO.

Reliability–redundancy allocation problem considering optimal redundancy strategy using parallel genetic algorithm

To maximize the reliability of a system, the traditional reliability–redundancy allocation problem (RRAP) determines the component reliability and level of redundancy for each subsystem. This paper proposes an advanced RRAP that also considers the optimal redundancy strategy, either active or cold standby. In addition, new examples are presented for it. Furthermore, the exact reliability function for a cold standby redundant subsystem with an imperfect detector/switch is suggested, and is expected to replace the previous approximating model that has been used in most related studies. A parallel genetic algorithm for solving the RRAP as a mixed-integer nonlinear programming model is presented, and its performance is compared with those of previous studies by using numerical examples on three benchmark problems.

A novel strategy for redundant components in reliability--redundancy allocation problems

ABSTRACTThis article presents a new interpretation and formulation of the Reliability–Redundancy Allocation Problem (RRAP) and demonstrates that solutions to this new problem provide distinct advantages compared with traditional approaches. Using redundant components is a common method to increase the reliability of a system. In order to add the redundant components to a system or a subsystem, there are two traditional types of strategies called active and standby redundancy. Recently a new redundancy strategy, called the “mixed” strategy, has been introduced. It has been proved that in the Redundancy Allocation Problem (RAP), this new strategy has a better performance compared with active and standby strategies alone. In this article, the recently introduced mixed strategy is implemented in the RRAP, which is more complicated than the RAP, and the results of using the mixed strategy are compared with the active and standby strategies. To analyze the performance of the new approach, some benchmark problems on the RRAP are selected and the mixed strategy is used to optimize the system reliability in these situations. Finally, the reliability of benchmark problems with the mixed strategy is compared with the best results of the systems when active or standby strategies are considered. The final results show that the mixed strategy results in an improvement in the reliability of all the benchmark problems and the new strategy outperforms the active and standby strategies in RRAP.

A value-driven approach for optimizing reliability-redundancy allocation problem in multi-state weighted k-out-of-n system

This study concentrates on optimizing a multi-state weighted k-out-of-n system consisting of different types of reparable components. An optimization model is developed to decide upon both optimal redundancy allocation and best maintenance activities for reliability allocation. The optimization model is to maximize system reliability and minimize system cost simultaneously. To reach this goal, a financial view has been employed to estimate the system reliability, and combine it with system cost. The proposed model determines the number of each component type in the system, and the maintenance actions and the time at which they should be applied. Also, the model is programmed by MATLAB, and Genetic Algorithm is used to solve a practical case.

A penalty guided stochastic fractal search approach for system reliability optimization

Modern industry requires components and systems with high reliability levels. In this paper, we address the system reliability optimization problem. A penalty guided stochastic fractal search approach is developed for solving reliability allocation, redundancy allocation, and reliability–redundancy allocation problems. Numerical results of ten case studies are presented as benchmark problems for highlighting the superiority of the proposed approach compared to others from literature.

Improved Bat Algorithm for Reliability-Redundancy Allocation Problems

The bat algorithm is a recently proposed meta-heuristic algorithm. Usually in solving the problem of optimization, the position of virtual bats is updated by flying speed, which decreases efficiency of the algorithm and accuracy of the solution. This paper has improved the location update strategy and individual selection strategy of bat algorithm, then puts forward an improved bat algorithm. The algorithm is used to solve three typical reliability-redundancy allocation problems, and the simulation experiment results show that the presented algorithm greatly enhances the computation efficiency, convergence speed and precision of the optimal solution in addressing the problem of reliability redundancy optimization. When compared with the best results reported in the previous literatures, the algorithm achieves a better or equally good optimal solution. It is demonstrated that the proposed algorithm is effective in solving reliability-redundancy allocation problems.

A novel artificial fish swarm algorithm for solving large-scale reliability–redundancy application problem

A novel artificial fish swarm algorithm (NAFSA) is proposed for solving large-scale reliability-redundancy allocation problem (RAP). In NAFSA, the social behaviors of fish swarm are classified in three ways: foraging behavior, reproductive behavior, and random behavior. The foraging behavior designs two position-updating strategies. And, the selection and crossover operators are applied to define the reproductive ability of an artificial fish. For the random behavior, which is essentially a mutation strategy, the basic cloud generator is used as the mutation operator. Finally, numerical results of four benchmark problems and a large-scale RAP are reported and compared. NAFSA shows good performance in terms of computational accuracy and computational efficiency for large scale RAP.

A note on a reliability redundancy allocation problem using a tuned parameter genetic algorithm

This paper presents an improved continuous genetic algorithm (CGA) to optimize the reliability redundancy allocation problem (RRAP) which determines the best redundancy strategies, the number of components, and levels of each subsystem to maximize the system reliability. In this system, both active and cold-standby redundancies can be chosen for individual subsystems. The RRAP belongs to NP-hard problems in the computational complexity theory that is the main reason for employing CGA to solve it. In addition, the response surface methodology (RSM) is used to increase the performance of CGA considering the design of experiments. This algorithm employs a new chromosome so that frees offspring to repair during the evolution process. Considering several numerical examples, the proposed algorithm presents better solutions than the previous studies based on the system reliability. Finally, the conclusion and future research are considered.