Fuzzy System Reliability Research Articles

Fuzzy system reliability analysis based on new aging indexes

The concept of aging plays an important role in reliability analysis. The aim of this paper is providing the novel method to definition aging indexes based on fuzzy random variables and using the concept of α-pessimistic in both parametric and non-parametric approaches. In parametric approach, the concepts of survival function, hazard rate function and mean residual function were extended for fuzzy random variables. After that, we obtain and analyse these indexes for fuzzy exponential and fuzzy two-parameter Weibull distributions as two frequently used lifetime distribution in reliability theory. Moreover, with the assumption that the distribution of fuzzy observations is unknown (non-parametric approach), first an estimate for the fuzzy distribution function is presented, and then an estimate for the aging indices of the system is investigated. To do this, the concept of fuzzy empirical distribution function is investigated as an estimator of cumulative distribution function. Moreover, some properties of investigated estimator have been established.

Multitype Optimal Component Allocation of Multicomponent Systems Considering Fuzzy State

A real system may go through several states ranging from full performance to complete failure, carrying out infinite partial performances during service time. This paper portrays such a non-binary state of systems via the fuzzy membership function. Then, the relation between the system reliability under the binary state and that under the fuzzy state is deduced, on which a multi-type component allocation problem (MCAP) is investigated to search for the optimal permutation of different types of components to maximize the fuzzy system reliability. After that, we inherit the exploration ability of genetic algorithm (GA) and the exploitation ability of Birnbaum importance (BI) to propose a fuzzy-BI-based two-stage approach combined with GA (FBITS-GA) in order to deal with the MCAP under fuzzy state assumption efficiently and accurately. The k-out-of-n systems in both low and high dimensions are presented to illustrate the effectiveness of the proposed algorithm and demonstrate the similarity and difference between the MCAP under binary state and that under fuzzy state. The experimental results showcase that the proposed approach outperforms the existing state-of-the-art approaches for MCAP.

Reliability Estimation of Parallel Repairable System under Uncertainty in Lifetime Data

Abstract Reliability is a popular concept that has been used in the manufacturing industry. In this paper, we consider a parallel system containing n non-identical and independent components in which each component is repairable except when all components are failed. As a special case, estimating the reliability of the system with identical components is considered. In real life, the data obtained for repair rate and failure rate could be subject to uncertainty. Here, to address this situation, failure and repair rates are considered as fuzzy numbers to estimate the reliability of the system. Fuzzy system reliability is estimated using fuzzy failure and repair rates, which are obtained by using confidence intervals and point estimators of failure rate and repair rate.

Fuzzy System Reliability Analysis for Kumaraswamy Distribution: Bayesian and Non-Bayesian Estimation with Simulation and an Application on Cancer Data Set

This paper proposes the fuzzy Bayesian (FB) estimation to get the best estimate of the unknown parameters of a two-parameter Kumaraswamy distribution from a frequentist point of view. These estimations of parameters are employed to estimate the fuzzy reliability function of the Kumaraswamy distribution and to select the best estimate of the parameters and fuzzy reliability function. To achieve this goal we investigate the efficiency of seven classical estimators and compare them with FB proposed estimation. Monte Carlo simulations and cancer data set applications are performed to compare the performances of the estimators for both small and large samples. Tierney and Kadane approximation is used to obtain FB estimates of traditional and fuzzy reliability for the Kumaraswamy distribution. The results showed that the fuzziness is better than the reality for all sample sizes and the fuzzy reliability at the estimates of the FB proposed estimated is better than other estimators, it gives the lowest Bias and root mean squared error.

직관 퍼지 와이블 분포에서 알파 컷 셋을 이용한 시스템 신뢰성 분석

Purpose This study is to analyze system reliability using fuzzy Weibull lifetime distribution in which scale parameters are assumed to be Intuitionistic Fuzzy Set (IFS) with α-cut set due to uncertainties and inaccuracy of data. Methods The IFS is utilized to present the information of membership function and non-membership function with the three intervals that include belief, disbelief and unbelief functions. The paper discusses the intuitionistic fuzzy Weibull system reliability models to assess the membership function and non-membership function by considering the different types of component intuitionistic fuzzy scale parameter. Due to the existence of different types of uncertainties, the three types of component TIFS (Triangular IFS) and TrIFS (Trapezoidal IFS) with α-cut set were presented for computing intuitionistic fuzzy system reliability in both series structure and parallel structure. Results The validity of proposed model is demonstrated by analyzing intuitionistic fuzzy Weibull system reliabilities with α-cut set using different types of intuitionistic fuzzy scale parameter. A numerical example is indicated to discuss the usefulness and practicality of the proposed model. Conclusions When conducting a group decision making for evaluating the intuitionistic fuzzy Weibull system reliability, α-cut set models proposed in this paper can be used to reflect various experts’ judgments on agreement, disagreement and undecidedness when evaluating system reliability.

Fuzzy Reliability of a Marine Power Plant Using Interval Valued Vague Sets

In conventional reliability analysis, the failure probabilities of the components of a system are treated as exact values. It is often difficult to obtain data for failure probabilities under changing environmental conditions. Hence fuzzy sets are used to analyze the fuzzy system reliability, where a fuzzy number represents the reliability of each component. Chen [14] analyzed the fuzzy system reliability using vague set theory. The values of the membership and non-membership of an element, in a vague set, are represented by a real number in [0, 1]. A specialist is always uncertain about the values of the membership and non-membership of an element in a set. Hence, it is better to represent the values of the membership and non-membership of an element in a set by intervals of possible real numbers instead of real numbers. In this paper a new method has been developed for analyzing the fuzzy system reliability of a series and parallel system using interval valued trapezoidal vague sets, where the reliability of each component of each system is represented by an interval valued trapezoidal vague set defined in the universe of discourse [0, 1].The developed method has been used to analyze the fuzzy reliability of a marine power plant. The major advantage of the proposed approach (the concept of interval valued vague sets) over the existing approaches [7, 8, 14] is that the proposed approach separates the positive and negative evidence for the membership of an element in a set. Also in the proposed approach the values of the membership and non- membership of an element in a set are intervals instead of a single real number.

The Fuzzy Arithmetic Operations of Transmission Average on Pseudo-Hexagonal Fuzzy Numbers and Its Application in Fuzzy System Reliability Analysis

In most natural science fields, triangular and trapezoidal fuzzy numbers are commonly used while in engineering and social science fields such as sociology and psychology while treating the uncertainties these numbers are not applicable and fuzzy numbers with more parameters and clear definitions of their arithmetic operations are needed. In order to fill this gap in the literature, we propose the new fuzzy arithmetic operations based on transmission average on pseudo-hexagonal fuzzy numbers, which was already implied in [1] in its rudimentary form and was finally presented in its fully fledged form in [2]. Several illustrative examples were given to show the accomplishment and ability of the proposed method. We present a new method for fuzzy system reliability analysis based on the fuzzy arithmetic operations of transmission average, where the reliabilities of the components of a system are represented by pseudo- hexagonal fuzzy numbers defined in the universe of discourse [0, 1]. The proposed method has the advantages of modeling and analyzing fuzzy system reliability in a more flexible and more intelligent manner. Finally, a marine power plant is considered in fuzzy environment. The reliability of components of the proposed model is considered as pseudo-hexagonal fuzzy numbers.

Fuzzy multiobjective system reliability optimization by genetic algorithms and clustering analysis

AbstractSystem 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.

Analysis The Barrier of E-learning in Mathematics Using Type-2 Fuzzy Data

E-Learning is learning utilizing electronic technologies to access educational curriculum outside of a traditional classroom. In most cases, it refers to a course, program or degree delivered completely online. E-learning is also a big platform to learn mathematics. But in the current public health crisis, we are all working quickly to move our classes out of the classroom. Fortunately, even if online teaching and learning are new to all of us, some uncertainties are there exists. According to modern view uncertainty is considered essential to science and technology, it is not only the unavoidable plague but also it has impact a great utility. Generally, fuzzy sets are used to analyse fuzzy system reliability. To analyse the fuzzy system reliability, the reliability of each component of the system is considered as a Triangular intuitionistic Type 2 fuzzy number (TIT2FN).

Fuzzy reliability‐redundancy allocation problem of the overspeed protection system

AbstractSystem reliability is defined as the probability of satisfactory performance of a system under stated conditions for a specified period of time. According to this definition, four parameters, including probability, satisfactory performance, specific conditions, and time should be exactly characterized to evaluate the system reliability accurately. However, due to the uncertainty involved in real situations, it is hardly possible to assess the aforementioned parameters precisely. In this article, two general and distinct approaches, including Zadeh's extension principle and modification of fuzzy parametric programming (FPP), are proposed to take into account such uncertainty in a famous reliability problem called the overspeed protection system. According to Zadeh's extension principle, a pair of nonlinear programming problems is formulated to compute α‐level cuts of fuzzy system reliability. The membership function of fuzzy system reliability can then be constructed analytically by numerating different values of α. This fuzzy system reliability presents flexibility for further system analysis. In the second approach, from a different point of view, a variant of FPP is improved that provides a crisp value as a system reliability measure. The rewarding point of the latter procedure is to handle the problem in a computationally easier way.

Time-dependent intuitionistic fuzzy system reliability analysis

The purpose of the present paper is to provide a method for constructing time-dependent reliability systems based on intuitionistic fuzzy random variables. A lifetime variable cannot be precisely recorded due to machine errors, experimentation pitfalls, personal judgments, estimation errors or other unexpected sources of error. In order to satisfy the purpose of this paper, an intuitionistic fuzzy random variable with exact parameters was introduced and adopted to evaluate the reliability functions of a k-out-of-n system, with some reliability evaluation criteria discussed and interpreted. Numerical evaluations were further presented to illustrate the calculation of the system reliability criteria in the form of intuitionistic fuzzy numbers. Finally, a number of potential engineering applications of the proposed method were presented.

TRAPEZOIDAL INTUITIONISTIC FUZZY NUMBER WITH SOME ARITHMETIC OPERATIONS AND ITS APPLICATION ON RELIABILITY EVALUATION

In fuzzy mathematics fuzzy system reliability can be analysed by fuzzy sets. We can use various types of fuzzy sets for that analyzing the fuzzy system reliability but here we specially used intuitionistic fuzzy set theory. At first, TrIFNs and their arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system, parallel system, series-parallel and parallel-series system following TrIFNs have been described. Here an imprecise failure to start of a truck is taken. To compute the imprecise failure of the above said system, failure of each component of the systems is represented by Trapezoidal Intuitionistic Fuzzy Number. This process can be utilise to measure the failure is various aspects like portfolio in stock market etc. The numerical expression also calculated and presented in this paper for the failure to start of a truck using TrIFN.

ANALYSIS OF SYSTEM RELIABILITY OF AN ILLUMINATED DARK ROOM BY TIT2FNS FUZZY DATA WITH SOME OF ITS ARITHMETIC OPERATIONS

According to modern view uncertainty is considered essential to science and technology, it is not only the unavoidable plague but also it has impact a great utility. Generally, fuzzy sets are used to analyse fuzzy system reliability. To analyse the fuzzy system reliability, the reliability of each component of the system is considered as a Triangular intuitionistic Type 2 fuzzy number (TIT2FN). At first, TIT2FN and their arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system and a parallel system following TIT2FN have been described. Here, an imprecise reliability model of an electric network model of a dark room is taken. To compute the imprecise reliability of the above said system, the reliability of each component of the systems is represented by TIT2FN. A corresponding numerical example is presented.

Location and scale fuzzy random variables

Several interpretations have been proposed so far for fuzzy random variables to describe imprecision and randomness. In this paper, a novel notion of fuzzy random variable was proposed to model fuzziness and randomness in a statistical procedure. For this purpose, a frequently used family of probability distributions called location and scale were first employed as the origin of randomness. Then, α-values of fuzzy numbers were combined with randomness to describe the fuzziness in the nature of the processes to produce a new concept of fuzzy random variable called location and scale fuzzy random variables. Then, some essential statistical features of the proposed fuzzy random variables including fuzzy cumulative distribution function, fuzzy expectation, exact variance and imprecise probability of an interval were discussed. The classical method of moment estimator was also developed to estimate the location and scale parameters. The developed technique was illustrated via several numerical evaluations. As an real-life application of the proposed fuzzy random variable, the reliability functions of k-out-of-n system and some reliability evaluation criteria were introduced and interpreted. Some numerical examples were also presented to illustrate the calculation of the proposed fuzzy system reliability criteria.

New operations on pseudo-octagonal fuzzy numbers and its application

In engineering and social science fields such as sociology and psychology while treating the uncertainties of triangular and trapezoidal fuzzy numbers are not applicable and fuzzy numbers with more parameters and clear definitions of their arithmetic operations are needed. In order to fill this gap in the literature, in this paper we propose the new fuzzy arithmetic operations based on transmission average on pseudo-octagonal fuzzy numbers, which was already implied in Abbsi et al. (J Intell Fuzzy Syst 29:851–861, 2015) in its rudimentary form and was finally presented in its fully fledged form in Abbsi et al. (J Fuzzy Set Valued Anal 2:1–18, 2016). The properties of these propose operations and their fundamental qualities are discussed. Several illustrative examples were given to show the accomplishment and ability of the proposed method. We present a new method for fuzzy system reliability analysis based on the fuzzy arithmetic operations of transmission average, where the reliabilities of the components of a system are represented by pseudo-octagonal fuzzy numbers defined in the universe of discourse [0, 1]. The proposed method has the advantages of modeling and analyzing fuzzy system reliability in a more flexible and more intelligent manner. Finally, dissatisfaction of a vice training and further education of arbitrary university with two faculties is considered in fuzzy environment.

Fuzzy reliability estimation using the new operations of transmission average on Rational-linear patchy fuzzy numbers

This paper presents a new practical method for fuzzy system reliability analysis based on the fuzzy arithmetic operations of transmission average (TA) (Abbasi et al. in J Intell Fuzzy Syst 29:851–861, 2015) on Rational-linear patchy fuzzy numbers. The concept of fuzzy numbers is extended by idea of Rational-linear patchy fuzzy numbers. Then, we have introduced fuzzy arithmetic operations of TA between two Rational-linear patchy fuzzy numbers. Finally, a new method has been developed for analyzing the fuzzy system reliability of series and parallel systems based on the fuzzy arithmetic operations of TA, where the reliability of each component is represented by a Rational-linear patchy fuzzy number. A technical example is given to illustrate applying the method and comparing the results of the new method with the previous methods. The proposed method can model and analyze the fuzzy system reliability in a more flexible and intelligent manner in comparison with the other methods.

Hybrid Fuzzy Estimation of System Reliability for Multi-State System

This article is purpose a hybrid estimation of the fuzzy system reliability for the Non-repairable multi-state series-parallel system (NMSS). Considering the fuzzy parameter of NMSS are prior fuzzy parameters. Then the posterior fuzzy parameters of NMSS are constructed by fuzzy Bayesian point estimate of fuzzy system reliability. Moreover, an approach to construct interval estimation of the fuzzy system reliability of NMSS will be used in estimation of the prior fuzzy confidence interval and posterior fuzzy confidence interval of fuzzy system reliability. Finally, the coverage probability and the expected length that it is used to interpret the efficiency of both fuzzy confidence intervals are presented.

Evaluation of Maximum Reliability Using Co-efficient of Variance for Parallel System Model

The reliability analysis of a component or a system is an important concept in almost all engineering disciplines. In general, fuzzy sets are used to analyze the system reliability. The system reliability may be formed as linear or nonlinear programming with cost function in fuzzy environment. To analyze the fuzzy system reliability, the reliability of each component of the system is represented as fuzzy number in nature. In this paper, we have presented the parallel system model with fuzzy cost function to evaluate the maximum reliability subject to minimum cost using trapezoidal fuzzy number and to find out the Co-efficient of Variance for each membership function. A numerical example is given to illustrate the model for nonlinear programming and to evaluate the system reliability.

A new concept for fuzzy variable based non-linear programming problem with application on system reliability via genetic algorithm approach

Fuzziness is the primary and foremost perception of science and technology. This paper, for the first time, introduces a new concept on solution technique for fuzzy variable based non-linear programming problem with both decision variables and restriction being fuzzy in nature. First the problem is transformed in to a multi-objective non-linear programming problem, and then solving it by multiobjective genetic algorithm (MOGA) approach. The proposed procedure is applied on complex system reliability model to evaluate the system reliability in fuzzy environment, using MOGA by implementing new feature as refining operation. Numerical example is presented to illustrate proposed fuzzy system reliability model.

A novel approach for analyzing the reliability of series-parallel system using credibility theory and different types of intuitionistic fuzzy numbers

The main objective of this paper is to present an alternative method for computing the membership function of the system under intuitionistic fuzzy set environment. Conventionally, it is not always easy to obtain the system reliability for components with different individual failure probability density function due to necessary but complicated combination and integration of various probability density functions. Also, in the literature, it is assumed that failure rates of all the components of a system follow the same type of fuzzy set which is rarely occurring in the practical situations. Thus, this paper addresses the fuzzy system reliability analysis to construct the membership and non-membership functions by considering the different types of intuitionistic fuzzy failure rates. Functions of intuitionistic fuzzy numbers are calculated using credibility theory. The effectiveness of the proposed approach is illustrated with analyze of the fuzzy reliability of series, parallel and series-parallel systems using different types of intuitionistic fuzzy failure rates. The computed results from the analysis have a less range of uncertainty as the comparability of existing results.