Fuzzy Reliability Theory

This chapter analyzes fuzzy reliability theory using bibliometric analysis. Different aspects of fuzzy have already been analyzed using bibliometric analysis, and a series of bibliometric tools have also been used. VOSviewer software was used to identify maps showing the most relevant trends. The analysis includes scientific articles, citations, journals, authors, universities, keywords, and countries. Results show that countries belonging mainly to Asia are at the avant-garde in terms of research in the field, China and India being the most productive countries in terms of the number of articles published, citations, and universities invested in the topic. Other countries in North America, such as Canada and the United States, and in Europe, the UK, Poland, Italy, and France, also show a great interest in this area of science. Research on the topic is relatively recent. The first articles were published in 1991; therefore, it presents excellent opportunities that will quite possibly attract researchers and universities from different regions of the world.

Fuzzy Hybrid FMEA for Risk Assessment in Service Industry

Service products are mostly produced and consumed simultaneously through interaction between customer and service providers. To prevent external failures in service operations, it is important to identify potential risks and take relevant actions to eliminate or reduce the occurrence. Therefore, risk assessment is vital to customer satisfaction in any service organization. Failure mode and effects analysis (FMEA) is an effective and useful tool for risk assessment. Although FMEA has been extensively studied in the manufacturing literature, there are a limited number of studies considering the application of FMEA in the hospitality industry. In traditional FMEA, the risk priority of failure modes is determined by generating a crisp risk priority number (RPN). However, it has been claimed in the literature that crisp RPN doesn't have a good performance in reflecting real-life situations. To overcome this shortcoming, a fuzzy hybrid FMEA method is developed. The proposed method has been tested on a case study in a five-star hotel to assess its applicability and benefits.

Solving Interval Type-2 Fuzzy Reliability-Redundancy Allocation Systems With Efficient PSO Algorithm

A new type-2 fuzzy reliability-redundancy allocation problem (IT2FRRAP) is introduced in this study, which maximizes system reliability underneath the type-2 fuzzy uncertainty. Throughout the design process, estimation of system parameters with type-2 fuzzy sets is very rational, as many experts may have varying views on the numerous risks involved with the multi-state framework. The authors consider fuzzy membership functions of interval type-2 to fuzzy set to reflect the reliability of the sub-system. By using the extension theory, they evaluate the total system reliability as per respective configurations (i.e., series, parallel, non-parallel, and bridge). They developed a novel solution method focused on particle swarm optimization to address the IT2FRRAP. They carried out the computational simulations on various numerical databases to show the gravity of the proposed formulations. To compare its productiveness, a detailed analysis of the proposed solution was made with the genetic algorithm (GA).

A Novel Entropy Measure for Interval-Valued Intuitionistic Fuzzy Set and Its Application to Failure Mode and Effect Analysis

The failure mode and effect analysis (FMEA) is widely used an effective pre-accident risk assessment tool to identify, eliminate, and assess potential failure modes in different industries for enhancing the safety and reliability of systems, process, services, and products. Therefore, this chapter presents a new approach to rank the failure modes under the interval-valued intuitionistic fuzzy set (IVIFS). For this, a novel measure to measure the fuzziness known as entropy measure is proposed. Some properties and axiom definition of the proposed entropy measure have been presented to show the validity of it. Afterwards, the proposed entropy measure is utilized to obtain the weight of risk factor and developed an approach under the IVIFS environment to determine the risk priority order of failure modes. Finally, a real-life case of FMEA has been discussed to manifest the developed approach, and obtained results are compared with the results obtained by the existing methods for showing the feasibility and validity of the proposed approach.

Fuzzy System Reliability Using Hesitant Fuzzy Element and Score Function

The present work introduces a new technique for analyzing the fuzzy reliability of a system stem under hesitant fuzzy environment where the reliability of a component/unit of a system is represented by hesitant fuzzy element (HFE). In this study, the authors evaluate the fuzzy reliability for some complex systems (series configuration, parallel configuration, and bridge configuration) using score function which is very useful in reliability modelling (especially in decision making, risk analysis, and optimization problems). Reliability modelling under hesitant situations plays a key role in the reliability engineering field. The score function used in this study is helpful for a simple comparison between reliabilities of any two components as form of HFEs. Hesitancy is the most common problem in human behaviour, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Additionally, a numerical example is taken for demonstration of the present technique.

Fuzzy Cognitive Maps in Reliability Modeling

The fuzzy cognitive map is considered as a tool for the ranking of factors affecting reliability. The rank of a factor is defined as an equivalent of the Birnbaum importance index in the classical reliability theory. Models and algorithms are proposed for calculation of the importance indexes of single factors and their joint effects on the reliability. The method is exemplified by the reliability and safety of an automobile in the “driver-automobile-road” system subject to the driver's qualification, traffic situation, unit costs of operation, operating conditions, maintenance scheduling, quality of maintenance and repair, quality of automobile design, quality of operational materials and spare parts, as well as storage conditions. The advantages of the method include 1) use of available expert information with no collection and processing statistical data and 2) capability to take into account any quantitative and qualitative factors associated with people, technology, software, quality of service, operating conditions, etc.

Risk Evaluation of a Construction Building Using a Hybrid Approach

This chapter aims basically to ensure two benefits, which focus on method and application. Firstly, this chapter proposes a new approach, which is TOPSIS (technique for order preference by similarity to ideal solution) based on interval type-2 trapezoidal fuzzy (IT2TrF) numbers. Secondly, the proposed method is applied to failure mode and effects analysis (FMEA) problem to overcome the drawbacks of traditional FMEA, which determines possible failure modes. In traditional FMEA, the risk priority number method, which is obtained as the product of occurrence, severity, and detection risk factors, has been debated to have several drawbacks. The implementation of risk assessment is realized to indicate the validity of the suggested approach in a construction building. The results of the proposed approach and some other methods are compared. The aim and resources are optimized by using linear programming.

Fuzzy Reliability Theory in the Decision-Making Process

In the process of dealing with various problems that are related to the control and management of complex systems, uncertainty is always the issue. Most of the decisions to be made by engineers and governors are subject to a lack of data that causes uncertainty. Some information is not always accessible and insufficient at the time of decision-making (DM). It is important to use the concept of a human being's expert knowledge, so developing models to estimate and imitate human decision-making systems has been becoming necessary. This chapter will critically assess the fuzzy reliability theory and systems to demonstrate how fuzzy logic represents human behavior and non-linearity. The authors created a fuzzy inference system to model two different complex systems. Fuzzy approaches to real problems in DM are effective alternatives to traditional approaches. Fuzzy integrations improve DM models in five principal features: (1) expert knowledge, (2) uncertainty handling, (3) human and government behavior modeling, (4) flexible modeling, and (5) simpler representations.

Fuzzy Reliability of Weighted-((f / (r, s)), k)/ (m, n) G System

In this chapter, the authors study a weighted-((f / (r, s)), k)/ (m, n): G system. The system consists of mn components arranged in a matrix form and the system works if all the sub matrices of order (r, s), the total weight of the working components is greater than f and the total weight of the working components in the system is at least k. This chapter deals with the evaluation of fuzzy reliability and fuzzy mean time to failure of the considered system with the application of fuzzy universal generating function and fuzzy Rayleigh distribution. In this study, the authors formed some prepositions to understand the behaviour of the considered system with respect to different varying parameters and also present an illustrative example to understand them.

Fuzzy Reliability Evaluation of Complex Systems Using Intuitionistic Fuzzy Sets

In a system where it cannot be reduced to a pure series and parallel form (i.e., complex), reliability is obtained by universal generating function (UGF) technique. The intuitionistic fuzzy sets (IFS) concept with triangular fuzzy number (TFN) and Weibull lifetime distribution is introduced to find the fuzzy reliability of the same system. Also, averaging operator with given equal weights is used with the set of three triangular intuitionistic fuzzy number. A numerical example is solved for demonstration.