Reliability Allocation Problem Research Articles

A hybrid cuckoo search and genetic algorithm for reliability–redundancy allocation problems

Solving reliability and redundancy allocation problems via meta-heuristic algorithms has attracted increasing attention in recent years. In this study, a recently developed meta-heuristic optimization algorithm cuckoo search (CS) is hybridized with well-known genetic algorithm (GA) called CS–GA is proposed to solve the reliability and redundancy allocation problem. By embedding the genetic operators in standard CS, the balance between the exploration and exploitation ability further improved and more search space are observed during the algorithms’ performance. The computational results carried out on four classical reliability–redundancy allocation problems taken from the literature confirm the validity of the proposed algorithm. Experimental results are presented and compared with the best known solutions. The comparison results with other evolutionary optimization methods demonstrate that the proposed CS–GA algorithm proves to be extremely effective and efficient at locating optimal solutions.

Reliability Allocation of Underwater Experiment System Based on Particle Swarm Optimization

The problem of system reliability allocation is often solved by direct search method. The shortage, which affects the application of this method, is the large calculation amount of complex system architecture. Particle Swarm Optimization (PSO) is a popular and bionic algorithm based on the social behavior associated with bird flocking for optimization problems. The particle swarm optimization, which attracted the interest of researchers. In this paper, a kind of PSO algorithm is proposed to solve underwater experimental system reliability problems. In addition, the reliability of the system model is established as well, the model is numerically simulated by PSO algorithm and examples are provided. The results show that compared to other algorithms, PSO has a better adaptability and can solve the optimal solution more stably without the precocious weakness, which is more suitable for reliability optimization of a system underwater with a more complex structure.

Fuzzy Multi-Objective Software Reliability Redundancy Allocation Based on MEDA-BFA Algorithm

Software reliability allocation problem is a major problem in engineering design practices. A fuzzy multi-objective software reliability allocation model is established by analyzing the software redundancy architecture and considering some fuzzy factors to reliability. Then, the MEDA-BFA algorithm is proposed based on estimation of distribution to solve software reliability redundancy allocation problem. Finally, experimental results show that the proposed intelligence algorithm can solve multi-objective software reliability allocation effectively and correctly, can help decision makers decide between software reliability and cost.

Complex componential approach for redundancy allocation problem solved by simulation-optimization framework

This article addresses the problem of redundancy and reliability allocation in the operational dimensioning of an automated production system. The aim of this research is to improve the global reliability of the system by allocating alternative components (redundancies) that are associated in parallel with each original component. By considering a complex componential approach that simultaneously evaluates the interrelations among sub-systems, conflicting goals, and variables of different natures, a solution for the problem is proposed through a multi-objective formulation that joins a multi-objective elitist genetic algorithm with a high-level simulation environment also known as simulation optimization framework.

Design and Routine Test Optimization of Modern Protection Systems With Reliability and Economic Constraints

This paper approaches the topic of protection system reliability from an economic point of view by 1) designing an optimal modern protective relay based on a prescribed level of reliability subject to economic constraints and 2) determining optimal routine test intervals by balancing the cost of routine tests and losses due to relay failure. This paper proposes a method that enables the designer to optimally select hardware and software components of a digital protective relay to gain the highest possible overall reliability with a restricted budget. This design can be viewed as a reliability and redundancy allocation problem for which a new easy-to-implement algorithm is proposed. In contrast to the existing literature that views the problem of routine test interval optimization solely from a reliability viewpoint, this paper proposes an optimization procedure for determining optimal test intervals. The optimization objective function consists of three terms: cost of routine tests, losses due to relay unresponsiveness, and losses due to relay maloperation. The value of the objective function is calculated based on a new, simple, and comprehensive Markov model. Illustrative numerical examples clarify the application of the proposed methods and demonstrate their effectiveness in achieving an optimum for both cases.

Reliability Allocation Problem in Series-Parallel Systems

Reliability optimization is an important step in industrial systems design. In order to develop a reliable system, designers may introduce different redundant technologies with the same functionality in parallel. In this paper, each technology is assumed to be composed of series components. The obtained configuration belongs to the series-parallel systems. The presented tool is for the design or the improvement of such systems, in order to minimize the system cost with a reliability constraint. The aim is to find the reliability to allocate to each component in order to minimize the total cost, such that the global system reliability verifies a minimal level constraint. This problem is known to be NP-hard. In this paper, a metaheuristic approach, based on the Ant Colony Optimization technics (ACO), is used in order to improve an existing approach. The experimental results, based on randomly generated instances, outperform the one of previous method dedicated to this problem.

Evolutionary optimization technique for multi-state two-terminal reliability allocation in multi-objective problems

This article presents a newly developed evolutionary algorithm for solving multi-objective optimization models for the design of multi-state two-terminal networks. It is assumed that for each network component, a known set of functionally equivalent component types (with different performance specifications) can be used to provide redundancy. Furthermore, the reliability behavior of the network and its components can have a range of states varying from perfect functioning to complete failure; that is, a multi-state behavior. Thus, the new algorithm allows solving the multi-objective optimization case of the reliability allocation problem for general multi-state two-terminal networks. The optimization routine is based on three major steps that use an evolutionary optimization approach and Monte Carlo simulation to generate a Pareto optimal string of probabilistic solutions to these problems. Examples for different multi-state two-terminal networks are used throughout the article to illustrate the approach. The results obtained for test cases are compared with other proposed methods to show the accuracy of the algorithm in generating approximate Pareto optimal sets for problems with a large solution space.

Model based Binary Decision Diagrams for Complex Networks Reliability Optimization

This paper presents an efficient approach that can be applied to solve the redundancy reliability allocation problem. The optimization problem considers optimization of the system design reliability (respectively: the cost of the allocation) subject to constraints on resources (target system reliability, costs and weights). The algorithm is based on three major steps that use- (1) a depth first search to determine 2-terminal reliability minimal paths, (2) a binary decision diagrams to compute the network reliability and (3) a procedure to find the solution to the optimizing problem. Examples for different networks are used to testify the usefulness of the method so we present some comparison tests

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.

Allocating repairable system’s reliability subject to minimal total cost — An integer programming approach

Reliability allocation problem is commonly treated using a closed-form expression relating the cost to reliability. A recent approach has introduced the use of discrete integer technique for un-repairable systems. This research addresses the allocation problem for repairable systems. It presents an integer formulation for finding the optimum selection of components based on the integer values of their Mean Time to Failure (MTTF) and Mean Time to Repair (MTTR). The objective is to minimize the total cost under a system reliability constraint, in addition to other physical constraints. Although, a closed-form expression relating the cost to reliability may not be a linear; however, in this research, the objective function will always be linear regardless of the shape of the equivalent continuous closed-form function. An example is solved using the proposed method and compared with the solution of the continuous closed-form version. The formulation for all possible system configurations, components and subsystems are also considered.

Series-parallel Systems Design: Reliability Allocation

Reliability optimization is one of the most important steps in industrial systems design. We consider a system composed of different technologies, with the same functionality, in parallel. We assume that each technology is composed of components in series. The purpose is to allocate the reliability of each component in order to minimize the total cost, with a minimal reliability level for the system. In most of the studies, components reliability is assumed to be a decision variable which may be any real value between zero and one. In reality, only a finite number of components, with the same function in a system, are available on the market. Then, components reliability must be chosen among a finite set of values. In our previous works, we proposed a decision tool for the design of parallel-series systems. We present in this paper a pseudopolynomial algorithm for the reliability allocation problem in series-parallel structures. Associating this algorithm with the previous one, we are able to solve reliability and redundancy allocation problems in more complex systems like series-parallel-series and parallel-series-parallel structures.

Reliability allocation problem in a series–parallel system

Abstract In order to improve system reliability, designers may introduce in a system different technologies in parallel. When each technology is composed of components in series, the configuration belongs to the series–parallel systems. This type of system has not been studied as much as the parallel–series architecture. There exist no methods dedicated to the reliability allocation in series–parallel systems with different technologies. We propose in this paper theoretical and practical results for the allocation problem in a series–parallel system. Two resolution approaches are developed. Firstly, a one stage problem is studied and the results are exploited for the multi-stages problem. A theoretical condition for obtaining the optimal allocation is developed. Since this condition is too restrictive, we secondly propose an alternative approach based on an approximated function and the results of the one-stage study. This second approach is applied to numerical examples.

Optimal Reliability Allocation Problem for a Modular Software System

This paper addresses the problem of optimal selection of components for a modular software system that is built by assembling a set of Commercial Off-The-Shelf (COTS) components and/or independent programs developed within the organization. For each module more than one alternative component is available and the same alternative can be purchased at a higher price if greater reliability is desired. It is also assumed that redundant component can be added in the modules to achieve fault tolerance. Now the problem is how to select the components, so as to maximize the system reliability. The first optimization model proposed in this paper maximizes the system reliability incorporating redundancy at component level with budgetary constraints. In the second model the issue of compatibility among alternatives available for different modules, is accounted for. Numerical illustrations are provided to demonstrate the models developed in this paper.

Integrated optimal reliable design, production, and maintenance planning for multipurpose process plants

In multipurpose process plants, which are characterized by sharing different resources (equipment, manpower etc.) for production, unplanned equipment shutdown could affect the timely production of products and hence process profitability. Many approaches have been proposed to ensure high equipment availability by combining design, production, and scheduling frameworks with a maintenance optimization framework. In these approaches, the initial reliability characteristics of equipment, which also determine equipment availability, are considered fixed by problem definition. In this work, a combined design, production and maintenance planning formulation for multipurpose process plants is extended to incorporate the reliability allocation problem at the design stage. A simultaneous optimization framework is presented that addresses the problem of optimal allocation of reliability among equipment simultaneously with the selection of process configuration, production and maintenance planning for multipurpose process plants at the design stage. This framework provides the designer with the opportunity to select the initial reliability of equipment at the design stage by balancing the associated costs with its impact on the design and the availability in the operational stage. The overall problem is formulated as a mixed integer linear programming (MILP) model, and its applicability is demonstrated using a number of examples.

Application of genetic algorithm for reliability allocation in nuclear power plants

Abstract Reliability allocation is an optimization process of minimizing the total plant costs subject to the overall plant safety goal constraints. Reliability allocation was applied to determine the reliability characteristics of reactor systems, subsystems, major components and plant procedures that are consistent with a set of top-level performance goals; the core melt frequency, acute fatalities and latent fatalities. Reliability allocation can be performed to improve the design, operation and safety of new and/or existing nuclear power plants. Reliability allocation is a kind of a difficult multi-objective optimization problem as well as a global optimization problem. The genetic algorithm, known as one of the most powerful tools for most optimization problems, is applied to the reliability allocation problem of a typical pressurized water reactor in this article. One of the main problems of reliability allocation is defining realistic objective functions. Hence, in order to optimize the reliability of the system, the cost for improving and/or degrading the reliability of the system should be included in the reliability allocation process. We used techniques derived from the value impact analysis to define the realistic objective function in this article.

Determination of design alternatives and performance criteria for safety systems in a nuclear power plant via simulated annealing

Abstract This study presents an efficient methodology that derives design alternatives and performance criteria for safety functions/systems in commercial nuclear power plants. Determination of the design alternatives and intermediate-level performance criteria is posed as a reliability allocation problem. The reliability allocation is performed in a single step by means of the concept of two-tier noninferior solutions in the objective and risk spaces within the top-level probabilistic safety criteria (PSC). Two kinds of two-tier noninferior solutions are obtained: desirable design alternatives and intolerable intermediate-level PSC of safety functions/systems. The weighted Chebyshev norm (WCN) approach with an improved Metropolis algorithm in simulated annealing is used to find the two-tier noninferior solutions. This is very efficient in searching for the global minimum of the difficult multiobjective optimization problem (MOP) which results from strong nonlinearity of a probabilistic safety assessment (PSA) model and nonconvexity of the problem. The methodology developed in this study can be used as an efficient design tool for desirable safety function/system alternatives and for the determination of intermediate-level performance criteria. The methodology is applied to a realistic streamlined PSA model that is developed based on the PSA results of the Surry Unit 1 nuclear power plant. The methodology developed in this study is very efficient in providing the intolerable intermediate-level PSC and desirable design alternatives of safety functions/systems.

Reliability and redundancy apportionment using crisp and fuzzy multiobjective optimization approaches

Abstract The reliability of a multistage system with several components in each stage can be improved either by using more reliable components, or by adding redundant components in parallel in any stage. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting goals. For example, in the reliability based design of a system, the designer may be required to maximize the reliability and minimize the cost, weight or volume. This work considers the problem of reliability allocation for multistage systems with components having time-dependent reliability. Two multiobjective optimization techniques are presented, coupled with heuristic procedures, to solve the mixed integer nonlinear programming problems. A generalization of the problem in the presence of vague information results in an ill-structured reliability apportionment problem. The solution of such multiobjective problems is also presented in the present work using the techniques of fuzzy optimization.

Lagrange multiplier method for optimal reliability allocation in a series system

The Lagrange multiplier method has been used employing several analytical cost-reliability curves to solve the problem of optimal reliability allocation for a series system subject to a single cost constraint. It is found that some cost curves yield simple and straightforward exact computation, while other cost curves are relatively difficult for computational purposes.

Geometric programming method for optimal reliability allocation for a series system subject to cost constraint

The geometric programming method has been used to solve the problem of optimal reliability allocation for a series system subject to cost constraint. There is only one cost vs reliability curve, viz. that of Tillman et al., which is in a posynomial form and hence is used to formulate the cost constraint. A numerical example is given to illustrate the technique.

Interactive Optimization of System Reliability Under Multiple Objectives

This paper considers a multiobjective reliability allocation problem for a series system with time-dependent reliability. The method determines the most preferable reliability allocation and preventive maintenance schedule. The problem is multiobjective nonlinear mixed-integer. The decision making procedure is based on interactive optimization and a nonlinear programming algorithm. The method is illustrated by a numerical example.