Reliability and redundancy apportionment using crisp and fuzzy multiobjective optimization approaches

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.     

Integrating reliability optimization into chemical process synthesis

The growing need to achieve high availability for large integrated chemical process systems demands higher levels of system reliability at the operational stage. In these circumstances, it has become critical to consider the reliability aspects of a system and its components at the design stage. Traditional reliability/availability analysis methods and maintenance optimization frameworks, commonly applied at the design stage, are limited in their application, as in most of these methods the designer is required to specify the process system components, their connectivity and their reliabilities a priori. As a result, these traditional methods do not provide the flexibility to reconfigure a process or select initial reliabilities of equipment in a way that maximizes the inherent plant availability at the design stage. In this paper, we developed an optimization framework by combining the reliability optimization and process synthesis challenges and the combined optimization problem is posed as a mixed integer non-linear programming optimization problem. The proposed optimization framework features an expected profit objective function, which takes into account the trade-off between initial capital investment and the annual operational costs by supporting appropriate estimation of revenues, investment cost, raw material and utilities cost, and maintenance cost as a function of the system and its component availability. The effectiveness and usefulness of the proposed optimization framework is demonstrated for the synthesis of the hydrodealkylation process (HDA) process.     

基于自适应点估计和最大熵原理的结构体系多构件可靠度分析

准确而高效地求解结构体系中多个构件的可靠度水准对结构维护和优化具有重要意义,目前已有学者将蒙特卡洛法和响应面法用于此类可靠度分析。然而,蒙特卡洛法所需结构分析次数取决于失效概率的量级,通常计算成本较高。而响应面法的所需结构分析次数取决于杆件数量,当其数量较多时同样有较高的成本。鉴于此,该文提出了一种基于自适应点估计和最大熵原理的结构体系多构件可靠度分析方法,其所需的结构重分析次数上限与杆件数量无关,计算过程简便无需迭代。首先,通过引入自适应交叉项判定和双变量降维近似模型求解各杆件的前四阶矩;然后,根据各杆件的前四阶矩,采用最大熵原理求解各杆件的可靠度指标;最后,通过多个算例对比了蒙特卡洛法、响应面法和建议方法的精度和效率。结果表明建议方法所需的结构重分析次数远少于蒙特卡洛法和响应面法,实现过程简便,且精度能够满足工程要求。     

Spreadsheet modeling of optimal maintenance schedule for components in wear-out phase

This paper addresses a method for determining the optimum maintenance schedule for components in the wear-out phase. The interval between maintenance for the components is optimized by minimizing the total cost. This consists of maintenance cost, operational cost, downtime cost and penalty cost. A decision to replace a component must also be taken when a component cannot attain the minimum reliability and availability index requirement. Premium solver platform, a spreadsheet-modeling tool, is utilized to model the optimization problem. Constraints, which are the considerations to be fulfilled, become the director of this process. A minimum and a maximum value are set on each constraint so as to give the working area of the optimization process. The optimization process investigates n-equally spaced maintenance at an interval of Tr. The increase in operational and maintenance costs due to the deterioration of the components is taken into account. This paper also performs a case study and sensitivity analysis on a liquid ring primer of a ship's bilge system.     

A multi-objective discrete reliability optimization problem for dissimilar-unit standby systems

A new methodology for the reliability optimization of a k dissimilar-unit nonrepairable cold-standby redundant system is introduced in this paper. Each unit is composed of a number of independent components with generalized Erlang distributions of lifetimes arranged in a series–parallel configuration. We also propose an approximate technique to extend the model to the general types of nonconstant hazard functions. To evaluate the system reliability, we apply the shortest path technique in stochastic networks. The purchase cost of each component is assumed to be an increasing function of its expected lifetime. There are multiple component choices with different distribution parameters available for replacement with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system to minimize the initial purchase cost of the system, maximize the system mean time to failure, minimize the system variance of time to failure, and also maximize the system reliability at the mission time. The goal attainment method is used to solve a discrete time approximation of the original problem.      

Intelligent interactive multiobjective optimization method and its application to reliability optimization

In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designer's preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designer's preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five different value functions simulating the designer in the solution evaluation process. The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems.     

Economic design of a circular consecutive--out-of-:F system with -step Markov dependence

A circular consecutive-k-out-of-n:F system consists of n components arranged along a circular path. The system fails if and only if at least k consecutive components in the system fail. The system reliability, the expected system life, and the expected number of failures are obtained under the assumption that the failure rate of a component depends on the number of consecutive failed components that follow it. A procedure to find the optimal k and a simulation procedure to search the near-optimal k are proposed with illustrative numerical examples. An expected cost per unit time is considered as the objective function to be minimized.     

Joint layout,pipe size and hydraulic reliability optimization of water distribution systems

A multicriteria maximum-entropy approach to the joint layout, pipe size and reliability optimization of water distribution systems is presented. The capital cost of the system is taken as the principal criterion, and so the trade-offs between cost, entropy, reliability and redundancy are examined sequentially in a large population of optimal solutions. The novelty of the method stems from the use of the maximum-entropy value as a preliminary filter, which screens out a large proportion of the candidate layouts at an early stage of the process before the designs and their reliability values are actually obtained. This technique, which is based on the notion that the entropy is potentially a robust hydraulic reliability measure, contributes greatly to the efficiency of the proposed method. The use of head-dependent modelling for simulating pipe failure conditions in the reliability calculations also complements the method in locating the Pareto-optimal front. The computational efficiency, robustness, accuracy and other advantages of the proposed method are demonstrated by application to a sample network.     

Transmission cost allocation based on use of reliability margin under contingency conditions

A reliability-based method for allocating the cost of transmission networks is presented. The cost of a transmission line is divided into two components. The first component corresponds to a part of the line capacity, which is used under normal conditions. The second component corresponds to a portion of the line capacity, which is only used under contingency conditions. The latter is the part that market agents use to calculate the reliability benefit charges of the line. In the proposed method, a probabilistic index is defined based on single-contingency analysis, which measures the reliability margin of each line for each transaction. Furthermore, the cost components associated with capacity use and reliability benefit charges are determined based on the actual reliability margin of lines. This method can be used to provide an equitable means for allocating the cost of transmission network among users of a bilateral market model. The proposed method is illustrated in a small power system as well as the 24-bus IEEE-RTS, and its conceptual and computational feasibility are demonstrated.     

Component choice for managing risk in engineered systems with generalized risk/cost functions

The constrained optimization of resource allocation to minimize the probability of failure of an engineered system relies on a probabilistic risk analysis of that system, and on ‘risk/cost functions’. These functions describe, for each possible improvement of the system's robustness, the corresponding gain of reliability given the considered component or management factor to be upgraded. These improvements can include, for example, the choice of components of different robustness levels (at different costs), addition of redundancies, or changes in operating and maintenance procedures. The optimization model is generally constrained by a maximum budget, a schedule deadline, or a maximum number of qualified personnel. A key question is thus the nature of the risk/cost function linking the costs involved and the corresponding failure-risk reduction. Most of the methods proposed in the past have relied on continuous, convex risk/cost functions reflecting decreasing marginal returns. In reality, the risk/cost functions can be simple step functions (e.g. a discrete choice among possible components), discontinuous functions characterized by continuous segments between points of discontinuity (e.g. a discrete choice among components that can be of continuously increasing levels of robustness), or continuous functions (e.g. exponentially decreasing failure risk with added resources).This paper describes a general method for the optimization of the robustness of a complex engineered system in which all three risk/cost function types may be relevant. We illustrate the method with a satellite design problem. We conclude with a discussion of the complexity of the resolution of this general type of optimization problem given the number and the types of variables involved.     

Optimal design of multi-state weighted k-out-of-n systems based on component design

This paper presents a study on design optimization of multi-state weighted k-out-of-n systems. The studied system reliability model is more general than the traditional k-out-of-n system model. The system and its components are capable of assuming a whole range of performance levels, varying from perfect functioning to complete failure. A utility value corresponding to each state is used to indicate the corresponding performance level. A widely studied reliability optimization problem is the “component selection problem”, which involves selection of components with known reliability and cost characteristics. Less adequately addressed has been the problem of determining system cost and utility based on the relationships between component reliability, cost and utility. This paper addresses this topic. All the optimization problems dealt with in this paper can be categorized as either minimizing the expected total system cost subject to system reliability requirements, or maximizing system reliability subject to total system cost limitation. The resulting optimization problems are too complicated to be solved by traditional optimization approaches; therefore, genetic algorithm (GA) is used to solve them. Our results show that GA is a powerful tool for solving these kinds of problems.     

Strategy and tool development for nuclear power plant design synthesis with measurement of reliability and simplicity

In this work, the conceptual design supporting tools for nuclear power plants have been developed. These tools are made for system synthesis, complexity measure and reliability analysis.This design synthesis program combined with the reliability analysis program accomplishes the system synthesis. This design strategy can reduce mistakes, effort and time. This design tool, based on Prolog language, is applied to the auxiliary feedwater system. A logic based fault tree analysis program (LOFT) is also developed using Prolog language. As LOFT performs symbolic computation during the fault tree analysis, linking with knowledge-base systems is very easy and the partial usage of the program is possible. The importance measure of components obtained from the system reliability analysis and the complexity measure of the system give very important information to the system designer.     

Asymmetric weighted voting systems

The weighted voting system (WVS) studied consists of n units, each of which provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all non-abstaining units. Otherwise, system output is 0. The system input is either 0 or 1. Every unit is characterized by the probability of making decisions 0 and 1 and by probability of abstaining for each input. The system fails if the system output is not equal to its input.In this paper, an asymmetric WVS is suggested in which each voting unit has two weights. The first weight is applied when the unit's decision is 0 and the second weight is applied when the unit's decision is 1. The asymmetry of unit weights allows the WVS designer to take advantage of the knowledge of statistical asymmetry of voting units (asymmetric probabilities of making correct decisions with respect to the input). The paper presents an algorithm for asymmetric WVS reliability evaluation. This algorithm is based on using a universal generating function technique.For a system consisting of voting units with given reliability characteristics, one can maximize the entire system reliability by choosing proper unit weights and threshold value. An algorithm is suggested which finds the optimal unit weights and the threshold. A genetic algorithm is used as the optimization tool. An example is presented in which the superiority of asymmetric WVS over regular symmetric one is demonstrated.     

Optimizing preventive maintenance for mechanical components using genetic algorithms

This paper presents periodic preventive maintenance (PM) of a system with deteriorated components. Two activities, simple preventive maintenance and preventive replacement, are simultaneously considered to arrange the PM schedule of a system. A simple PM is to recover the degraded component to some level of the original condition according to an improvement factor which is determined by a quantitative assessment process. A preventive replacement is to restore the aged component by a new one. The degraded behavior of components is modeled by a dynamic reliability equation, and the effect of PM activities to reliability and failure rate of components is formulated based on age reduction model. While scheduling the PM policy, the PM components within a system are first identified. The maintenance cost and the extended life of the system under any activities-combination, which represents what kind of activities taken for these chosen components, are analyzed for evaluating the unit-cost life of the system. The optimal activities-combination at each PM stage is decided by using genetic algorithm in maximizing the system unit-cost life. Repeatedly, the PM scheduling is progressed to the next stage until the system's unit-cost life is less than its discarded life. Appropriately a mechatronic system is used as an example to demonstrate the proposed algorithm.     

Bayesian reliability analysis of a products of probabilities model for parallel systems with dependent components

In a Bayesian reliability analysis of a system with dependent components, an aggregate analysis (i.e. system-level analysis) or a simplified disaggregate analysis with independence assumptions may be preferable if the estimations obtained from employing these two approaches do not deviate substantially from those derived through a disaggregate analysis, which is generally considered the most accurate method. This study was conducted to identify the key factors and their range of values that lead to estimation errors of great magnitude. In particular, a copula-based Bayesian reliability model was developed to formulate the dependence structure for a products of probabilities model of a simple parallel system. Monte Carlo simulation, regionalised sensitivity analysis and classification tree learning were employed to investigate the key factors. The resulting classification tree achieved favourable predictive accuracy. Several decision rules suggesting the optimal approach under different combinations of conditions were also extracted. This study has made a methodological contribution in laying the groundwork for investigating systems with dependent components using copula-based Bayesian reliability models. With regard to practical implications, this study also derived useful guidelines for selecting the most appropriate analysis approach under different scenarios with different magnitude of dependence.     

Bayesian decision analysis and reliability certification

Reliability certification is set as a problem of Bayesian Decision Analysis. Uncertainties about the system reliability are quantified by assuming the parameters of the models describing the stochastic behavior of components as random variables. A utility function quantifies the relative value of each possible level of system reliability after having been accepted or the opportunity loss of the same level if the system has been rejected. A decision about accepting or rejecting the system can be made either on the basis of the existing prior assessment of uncertainties or after obtaining further information through testing of the components or the system at a cost. The concepts of value of perfect information, expected value of sample information and the expected net gain of sampling are specialized to the reliability of a multicomponent system to determine the optimum component testing scheme prior to deciding on the system's certification. A component importance ranking is proposed on the basis of the expected value of perfect information about the reliability of each component. The proposed approach is demonstrated on a single component system failing according to a Poisson random process and with natural conjugate prior probability density functions (pdf) for the failure rate and for a multicomponent system under general assumptions.     

Maximization of a percentile life of a series system through component redundancy allocation

In a redundancy allocation problem, maximization of system reliability for a specified mission time has been thoroughly studied. Instead, we consider the optimal redundancy which maximizes a percentile life of a series system without violating a cost constraint. A percentile life is the maximum mission time for which system reliability meets at least a specific value. The proposed measure has advantages over regular reliability maximization in fixing warranties or when a system has no clear mission time. Previously, the proposed problem was solved by a heuristic or a genetic algorithm. Because of the infeasibility of finding a close form of percentile life in the redundancy level, we now develop a lexicographic search methodology to obtain an exact optimal solution. A transformed problem is first considered to get an upper bound, which is iteratively used to reduce search space. When any two stages of a system have a precedence relationship based on the cost and lifetime then the search space can be further reduced. The algorithm is general for any continuous increasing lifetime distributions, and can be easily extended for the additional weight and volume constraints.     

A design methodology for the strategic assessment of a product's eco-efficiency

The growing number of manufactured products has given rise to an alarming increase in the volume of industrial waste that is threatening the environment. However, if the various stages of a product are designed to be environmentally sustainable, ecological damage can be minimized, if not eliminated. This paper discusses a methodology that scores the cost, quality and environmental standing of four stages of the life cycle of a product. This is achieved through eight indices, or metrics, which depict the environmental standing of the product. The eight indices cover product cost, product reliability, serviceability and product retirement, among others. A self-learning algorithm is discussed that computes the best and worst values of the indices from a variety of similar products. This enables the designer to build up a comprehensive database of environmental data of a product. When displayed in a radar chart, the indices allow the environmental standing of a product to be quickly assessed, or compared with competitor designs. To emphasize their relative importance, weights may be assigned to the indices. Four case studies are presented and discussed. In the case of the injection-moulded multi-purpose holder, it was found that its reliability could be improved at the expense of manufacturability and retirement options. The eco-indices of 15 specimens of telecommunications paging devices, 13 amp 3-pin electrical plugs and 360 ml moulded drinking cups were computed and plotted on a radar chart. Overall, the analyses revealed that the five models of telecommunications pagers were not designed for end-of-life disposal and that the eco-efficiency of the electrical plugs depended on their country of manufacture, the ones made in the West being more environmentally benign. The drinking cups, on the other hand, illustrate the relative impact of different materials on the environment. The methodology can potentially benefit product designers, manufacturing engineers, sales/marketing personnel, in fact, all who have vested interests in environmentally friendly product design.     

Reliability estimations of components from masked system life data

This paper introduces estimations of reliability values for the individual components in a series system using masked system life data. In particular, we compute the maximum likelihood and Bayes estimates of component reliabilities when the system components have constant failure rates. In obtaining Bayes estimates, it is assumed that the component reliabilities are independent random variables having piecewise linear prior distributions. The model is illustrated for a two-component series. A numerical simulation study is presented to show how one can utilize the present approach to compute estimations of component reliabilities for a practical problem. Further, we investigate the comparison between the maximum likelihood and Bayes estimates, based on the respective percentage errors.