A design condition for incorporating human judgement into monitoring systems

In safety monitoring, there exists an uncertainty situation in which the sensor cannot detect whether or not the monitored object is in danger. For the uncertainty zone identified by a non-homogeneous safety monitoring system that utilizes two types of sensors with different thresholds, operators or experts are expected to judge whether the real state is safe or dangerous on the basis of additional information from a detailed inspection or other related sensors output. However, the activities for inspection performed by relevant humans may require additional cost and introduce inspection errors. The present article proposes two types of an automatic monitoring system not involving any human inspection or a human–machine (H–M) cooperative monitoring system with inspection. In order to compare the systems, an approach based on the Dempster–Shafer theory is proposed as uncertainty analysis by this theory (it is simpler than by the traditional Bayesian approach). By comparing their expected losses as a result of failed dangerous failures or failed safe failures as well as the inspection errors, the condition is determined under which H–M cooperative systems incorporating human judgements are more effective than automatic monitoring systems.     

An approximation approach for uncertainty quantification using evidence theory

Over the last two decades, uncertainty quantification (UQ) in engineering systems has been performed by the popular framework of probability theory. However, many scientific and engineering communities realize that there are limitations in using only one framework for quantifying the uncertainty experienced in engineering applications. Recently evidence theory, also called Dempster–Shafer theory, was proposed to handle limited and imprecise data situations as an alternative to the classical probability theory. Adaptation of this theory for large-scale engineering structures is a challenge due to implicit nature of simulations and excessive computational costs. In this work, an approximation approach is developed to improve the practical utility of evidence theory in UQ analysis. The techniques are demonstrated on composite material structures and airframe wing aeroelastic design problem.     

A study on group decision-making based fault multi-symptom-domain consensus diagnosis

In the field of fault diagnosis for rotating machines, the conventional methods or the neural network based methods are mainly single symptom domain based methods, and the diagnosis accuracy of which is not always satisfactory. In this paper, in order to utilize multiple symptom domains to improve the diagnosis accuracy, an idea of fault multi-symptom-domain consensus diagnosis is developed. From the point of view of the group decision-making, two particular multi-symptom-domain diagnosis strategies are proposed. The proposed strategies use BP (Back-Propagation) neural networks as diagnosis models in various symptom domains, and then combine the outputs of these networks by two combination schemes, which are based on Dempster–Shafer evidence theory and fuzzy integral theory, respectively. Finally, a case study pertaining to the fault diagnosis for rotor-bearing systems is given in detail, and the results show that the proposed diagnosis strategies are feasible and more efficient than conventional stacked-vector methods.     

Summary from the epistemic uncertainty workshop: consensus amid diversity

The ‘Epistemic Uncertainty Workshop’ sponsored by Sandia National Laboratories was held in Albuquerque, New Mexico, on 6–7 August 2002. The workshop was organized around a set of Challenge Problems involving both epistemic and aleatory uncertainty that the workshop participants were invited to solve and discuss. This concluding article in a special issue of Reliability Engineering and System Safety based on the workshop discusses the intent of the Challenge Problems, summarizes some discussions from the workshop, and provides a technical comparison among the papers in this special issue. The Challenge Problems were computationally simple models that were intended as vehicles for the illustration and comparison of conceptual and numerical techniques for use in analyses that involve: (i) epistemic uncertainty, (ii) aggregation of multiple characterizations of epistemic uncertainty, (iii) combination of epistemic and aleatory uncertainty, and (iv) models with repeated parameters. There was considerable diversity of opinion at the workshop about both methods and fundamental issues, and yet substantial consensus about what the answers to the problems were, and even about how each of the four issues should be addressed. Among the technical approaches advanced were probability theory, Dempster–Shafer evidence theory, random sets, sets of probability measures, imprecise coherent probabilities, coherent lower previsions, probability boxes, possibility theory, fuzzy sets, joint distribution tableaux, polynomial chaos expansions, and info-gap models. Although some participants maintained that a purely probabilistic approach is fully capable of accounting for all forms of uncertainty, most agreed that the treatment of epistemic uncertainty introduces important considerations and that the issues underlying the Challenge Problems are legitimate and significant. Topics identified as meriting additional research include elicitation of uncertainty representations, aggregation of multiple uncertainty representations, dependence and independence, model uncertainty, solution of black-box problems, efficient sampling strategies for computation, and communication of analysis results.     

Fuzzy-logic-based network for complex systems risk assessment: Application to ship performance analysis

In this paper, a new interpretation of intuitionistic fuzzy sets in the advanced framework of the Dempster–Shafer theory of evidence is extended to monitor safety-critical systems’ performance. Not only is the proposed approach more effective, but it also takes into account the fuzzy rules that deal with imperfect knowledge/information and, therefore, is different from the classical Takagi–Sugeno fuzzy system, which assumes that the rule (the knowledge) is perfect. We provide an analytical solution to the practical and important problem of the conceptual probabilistic approach for formal ship safety assessment using the fuzzy set theory that involves uncertainties associated with the reliability input data. Thus, the overall safety of the ship engine is investigated as an object of risk analysis using the fuzzy mapping structure, which considers uncertainty and partial truth in the input–output mapping. The proposed method integrates direct evidence of the frame of discernment and is demonstrated through references to examples where fuzzy set models are informative. These simple applications illustrate how to assess the conflict of sensor information fusion for a sufficient cooling power system of vessels under extreme operation conditions. It was found that propulsion engine safety systems are not only a function of many environmental and operation profiles but are also dynamic and complex.     

Imprecise reliabilities: experiences and advances

Imprecise probability theories are considered useful in reliability and risk assessments, but some of them were found to be unsatisfactory. This paper summarizes the authors’ experience in dealing with the Dempster–Shafer theory of evidence and demonstrates the authors’ advances in the application of the theory of coherent imprecise probabilities for reliability assessments. The obtained lower and upper reliabilities of series, parallel and general systems have very specific useful properties that cannot be obtained in the framework of standard probability theory.     

A belief-based model for characterizing the spread of awareness and its impacts on individuals' vaccination decisions

During an epidemic, individuals'' decisions on whether or not to take vaccine may affect the dynamics of disease spread and, therefore, the effectiveness of disease control. Empirical studies have shown that such decisions can be subjected to individuals'' awareness about disease and vaccine, such as their perceived disease severity and vaccine safety. The aim of this paper is to gain a better understanding of individuals'' vaccination behaviour by modelling the spread of awareness in a group of socially connected individuals and examining the associated impacts on their vaccination decision-making. In our model, we examine whether or not individuals will get vaccinated as well as when they would. In doing so, we consider three possible decisions from an individual, i.e. to accept, to reject, and yet to decide, and further associate them with a set of belief values. Next, we extend the Dempster–Shafer theory to characterize individuals'' belief value updates and their decision-making, having incorporated the awareness obtained from their connected neighbours. Furthermore, we examine two factors that will affect individuals'' vaccination decisions: (i) reporting rates of disease- and vaccine-related events, and (ii) fading coefficient of awareness spread. By doing so, we can assess the impacts of awareness spread by evaluating the vaccination dynamics in terms of the number of vaccinated individuals. The results have demonstrated that the former influences the ratio of vaccinated individuals, whereas the latter affects the time when individuals decide to take vaccine.     

Pre-selection of suppliers through an integrated fuzzy analytic hierarchy process and max-min methodology

There are a variety of analytical models for supplier selection ranging from simple weighted techniques to complex mathematical programming approaches. However, these models are specifically aimed at supporting a decision maker in a single phase, especially in the final selection phase and they have failed to consider the supplier selection process from a holistic point of view. Although the methodology presented in this paper primarily focused on the prequalification of potential suppliers, the outputs of the previous phases, namely problem definition and formulation of criteria, are used as inputs in this methodology. The methodology utilises a fuzzy analytic hierarchy process (AHP) method to determine the weights of the pre-selected decision criteria, a max-min approach to maximise and minimise the supplier performances against these weighted criteria, and a non-parametric statistical test to identify an effective supplier set. This information supports decision makers in making the final selection with effective alternative choices. Potential application of the proposed methodology is demonstrated in Audio Electronics in Turkey's electronics industry.     

A supply chain transparency and sustainability technology appraisal model for blockchain technology

Blockchain technology is a technology that can effectively support supply chain transparency. An important initial managerial activity is for organisations in supply chains to evaluate and select the most suitable blockchain technology. However, uncertainty and emphasis on sustainable transparency has made this appraisal more complex. This paper: (1) introduces blockchain technology performance measures incorporating various sustainable supply chain transparency and technical attributes; and (2) introduces a new hybrid group decision method, integrated hesitant fuzzy set and regret theory, for blockchain technology evaluation and selection. This method emphasises decision maker psychological characteristics and variation in decision maker opinions. An illustrative application and sensitivity analysis is introduced to aid supply chain managers and researchers understand the blockchain technology selection decision. Methodological and managerial implications associated with the decision tool and application are introduced. This research sets the foundation for significant future research in blockchain technologies evaluation in a supply chain environment.     

Interpretations of alternative uncertainty representations in a reliability and risk analysis context

Probability is the predominant tool used to measure uncertainties in reliability and risk analyses. However, other representations also exist, including imprecise (interval) probability, fuzzy probability and representations based on the theories of evidence (belief functions) and possibility. Many researchers in the field are strong proponents of these alternative methods, but some are also sceptical. In this paper, we address one basic requirement set for quantitative measures of uncertainty: the interpretation needed to explain what an uncertainty number expresses. We question to what extent the various measures meet this requirement. Comparisons are made with probabilistic analysis, where uncertainty is represented by subjective probabilities, using either a betting interpretation or a reference to an uncertainty standard interpretation. By distinguishing between chances (expressing variation) and subjective probabilities, new insights are gained into the link between the alternative uncertainty representations and probability.     

The role of social cost–benefit analysis in societal decision-making under large uncertainties with application to robbery at a cash depot

Social cost–benefit analysis is a well-established method for guiding decisions about safety investments, particularly in situations in which it is possible to make accurate predictions of future performance. However, its direct applicability to situations involving large degrees of uncertainty is less obvious and this raises the question of the extent to which social cost–benefit analysis can provide a useful input to the decision framework that has been explicitly developed to deal with safety decisions in which uncertainty is a major factor, namely risk analysis. This is the main focus of the arguments developed in this paper. In particular, we provide new insights by examining the fundamentals of both approaches and our principal conclusion is that social cost–benefit analysis and risk analysis represent complementary input bases to the decision-making process, and even in the case of large uncertainties social cost–benefit analysis may provide very useful decision support. What is required is the establishment of a proper contextual framework which structures and gives adequate weight to the uncertainties. An application to the possibility of a robbery at a cash depot is examined as a practical example.     

Group-based product scheme-screening decision method based on fuzzy AHP and evidential reasoning theory

Selecting the favourable product scheme is the first step to successful new product development (NPD). There are usually large numbers of uncertainties in product scheme evaluation and screening process of NPD due to lack of or incomplete reliable information. Considering fully the uncertainties and then conducting correct reasoning could guarantee reliability and rationality of scheme-screening results. As an extension of analytic hierarchy process (AHP), fuzzy AHP inherits multi-merits of the AHP approach and is capable of dealing with fuzzy information effectively, but it still has two weaknesses. One is the well-known ranking reversal problem. Although several researchers have analysed the reasons, we think the root cause for ranking reversal problem is due to the fact that AHP treats weights of attribute criteria and performance scores of alternatives in the same way. Therefore, we intend to deal with attribute weights and performance scores of alternatives separately and introduce evidential reasoning (ER) theory, which is good at uncertain reasoning, into fuzzy AHP to calculate the performance scores of alternatives. On the other hand, in view of the difficulty in resolution for fuzzy weights from fuzzy comparison matrix, a linear goal-programming model is proposed to calculate fuzzy weights, whose objective is to minimise the inconsistency degree of comparison matrix. By combining fuzzy AHP with ER, a group-based hybrid decision model FAHP-ER is developed. The hybrid model not only gets a great improvement in the capability of dealing with uncertainty, but also reflects the most real decision scenario and thinking process of the decision maker. Finally, a case study for schemes screening of the rotor and bearing system in the turbine generator is presented to demonstrate the application of the hybrid decision method.     

Filter allocation and replacement strategies in fluid power system under uncertainty: a fuzzy robust nonlinear programming approach

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.     

Achieving robust design through statistical effect screening

This work proposes a method for statistical effect screening to identify design parameters of a numerical simulation that are influential to performance while simultaneously being robust to epistemic uncertainty introduced by calibration variables. Design parameters are controlled by the analyst, but the optimal design is often uncertain, while calibration variables are introduced by modeling choices. We argue that uncertainty introduced by design parameters and calibration variables should be treated differently, despite potential interactions between the two sets. Herein, a robustness criterion is embedded in our effect screening to guarantee the influence of design parameters, irrespective of values used for calibration variables. The Morris screening method is utilized to explore the design space, while robustness to uncertainty is quantified in the context of info‐gap decision theory. The proposed method is applied to the National Aeronautics and Space Administration Multidisciplinary Uncertainty Quantification Challenge Problem, which is a black‐box code for aeronautic flight guidance that requires 35 input parameters. The application demonstrates that a large number of variables can be handled without formulating simplifying assumptions about the potential coupling between calibration variables and design parameters. Because of the computational efficiency of the Morris screening method, we conclude that the analysis can be applied to even larger‐dimensional problems. (Approved for unlimited, public release on October 9, 2013, LA‐UR‐13‐27839, Unclassified.) Copyright © 2015 John Wiley & Sons, Ltd.     

Fuzzy linear programming approach for solving transportation problems with interval-valued trapezoidal fuzzy numbers

Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving interval-valued trapezoidal fuzzy numbers for the transportation costs and values of supplies and demands. We propose a fuzzy linear programming approach for solving interval-valued trapezoidal fuzzy numbers transportation problem based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To illustrate the proposed approach an application example is solved. It is demonstrated that study of interval-valued trapezoidal fuzzy numbers transportation problem gives rise to the same expected results as those obtained for TP with trapezoidal fuzzy numbers.     

Provident decision making by considering dynamic and fuzzy environment for FMS evaluation

When evaluating complexity, cost and risk increase, it is difficult to make a proper decision. In such situations it is necessary to develop a model which simulates a decision maker's mind and consider both a dynamic and a fuzzy environment. In this study future oriented indices are presented which enable us to consider the effect of future changes in the index value during the decision making process. These future oriented indices are named provident indices. Also in this study to effectively integrate these multiple criteria into the decision making process, based on the analysis of the decision situation in such assessments, a suitable concept is selected. This method is based on the preference ranking organisation method for enrichment evaluations (PROMETHEE) which brings together flexibility and simplicity for the user and is therefore chosen for the enhancement towards the evaluation of fuzzy data on preferences, scores and weights. The model developed to investigate these impacts cannot perfectly reproduce all the events of the real system, but it can consider a fair number of elements of variability, which should be identified and analysed by considering present conditions and prediction about criteria values in future periods. Such a model may provide solutions with a high degree of robustness and reliability, comparable with those obtained by direct experimentation, but with a low computational cost. The uniqueness of this paper lies in two important areas: first, the incorporation of variability fuzzy and provident measures in the performance of alternatives into the decision making process; and second, is in the application of fuzzy PROMETHEE that provides the decision maker with effective alternative choices by identifying significant differences among alternatives and appropriate choices through considered future periods, and presents graphic aids for better interpretation of results. A comprehensive numerical example of a flexible manufacturing system (FMS) is provided to illustrate the results of the analysis. In a real-world manufacturing environment, the dynamics of an FMS and its stochastic characteristics require a specific approach for evaluation. This paper specifically focuses on FMSs due to the complexities involved in their proper evaluation that include factors such as high operational and managerial expertise in system implementation phases, high costs and risks. Due to these, evaluation, justification, and implementation of an FMS have been areas of major concern and importance for practitioners and researchers. In this case, various strategic, economic and operational criteria that envelop quantitative, qualitative, tangible, and intangible factors are considered.     

A multi-criteria decision model to determine inspection intervals of condition monitoring based on delay time analysis

In periodic monitoring, the main problem is determining the inspection interval of condition monitoring. For this problem, the decision variable is represented by the time of next inspection of condition monitoring. There are several studies that deal with prescribing inspection intervals. But only a few of these allow the decision maker to observe simultaneously more than one aspect. This does not accord with the natural tendency of the decision maker who desires to see the decision problem from a broader perspective, by having different viewpoints or dimensions of choices. Therefore, the main objective of this paper is to propose a decision model, which can simultaneously determine inspection intervals for condition monitoring regarding the failure behavior of equipment to be inspected, features of maintainability and decision maker preferences about cost and downtime.     

Fuzzy multiobjective system reliability optimization by genetic algorithms and clustering analysis

System reliability optimization is a key element for a competitive and safe industrial plant. This paper addresses the multiobjective system reliability optimization in the presence of fuzzy data. A framework solution approach is proposed and based on four steps: defuzzify the data into crisp values by the ranking function procedure, the defuzzified problems are solved by the non-sorting genetic algorithms II and III (NSGA-II and NSGA-III), the Pareto fronts are compared by the spacing method for selecting the best one, and then the best Pareto front is reduced by the clustering analysis for helping the decision maker. A case study presented in the literature as a mono-objective redundancy allocation problem with fuzzy data is investigated in the present paper as multiobjective redundancy allocation and reliability-redundancy allocation problems show the applicability of the approach.     

A subjective and objective integrated multiple attribute decision making method for material selection

The selection of an optimal material for an engineering design from among two or more alternative materials on the basis of two or more attributes is a multiple attribute decision making (MADM) problem. The selection decisions are complex, as material selection is more challenging today. There is a need for simple, systematic, and logical methods or mathematical tools to guide decision makers in considering a number of selection attributes and their interrelations and in making right decisions. This paper proposes a novel MADM method for material selection for a considered design problem. The method considers the objective weights of importance of the attributes as well as the subjective preferences of the decision maker to decide the integrated weights of importance of the attributes. Furthermore, the method uses fuzzy logic to convert the qualitative attributes into the quantitative attributes. Three examples are presented to illustrate the potential of the proposed method.     

Integrating production-transportation planning decision with fuzzy multiple goals in supply chains

This work presents a novel fuzzy multi-objective linear programming (f-MOLP) model for solving integrated production-transportation planning decision (PTPD) problems in supply chains in a fuzzy environment. The proposed model attempts to simultaneously minimise total production and transportation costs, total number of rejected items, and total delivery time with reference to available capacities, labor level, quota flexibility, and budget constraints at each source, as well as forecast demand and warehouse space at each destination. An industrial case demonstrates that the proposed f-MOLP model achieves an efficient compromise solution and overall decision maker satisfaction with determined goal values. Additionally, the proposed model provides a systematic framework that facilitates decision makers to interactively modify the fuzzy data and parameters until a satisfactory solution is obtained. Overall, the f-MOLP model offers a practical method for solving PTPD problems with fuzzy multiple goals, and can effectively improve producer–distributor relationships within a supply chain.