Fuzzy System Reliability Analysis 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.

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.

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.

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.

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.

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.

Fuzzy system reliability analysis based on level (λ, 1) interval-valued fuzzy numbers

This study uses Level (λ,1) interval-valued fuzzy numbers to examine the fuzzy reliability of a serial system and a parallel system and obtain the estimated reliability of both systems in the fuzzy sense.

Fuzzy System Reliability Analysis Based on Confidence Interval

This paper proposes a new method for analyzing the fuzzy system reliability of a parallel-series and series-parallel systems using fuzzy confidence interval, where the reliability of each component of each system is unknown. To compute system reliability, we are estimated reliability of each component of the systems using fuzzy statistical data with both tools appropriate for modeling fuzzy data and suitable statistical methodology to handle these data. Numerical examples are given to compute fuzzy reliability and its cut set and the calculating was performed by using programming in software R.

A novel approach for analyzing fuzzy system reliability using different types of intuitionistic fuzzy failure rates of components

This paper addresses the fuzzy system reliability analysis using different types of intuitionistic fuzzy numbers. Till now, in the literature, to analyze the fuzzy system reliability, it is assumed that the failure rates of all components of a system follow the same type of fuzzy set or intuitionistic fuzzy set. However, in practical problems, such type of situation rarely occurs. Therefore, in the present paper, a new algorithm has been introduced to construct the membership function and non-membership function of fuzzy reliability of a system having components following different types of intuitionistic fuzzy failure rates. Functions of intuitionistic fuzzy numbers are calculated to construct the membership function and non-membership function of fuzzy reliability via non-linear programming techniques. Using the proposed algorithm, membership functions and non-membership functions of fuzzy reliability of a series system and a parallel systems are constructed. Our study generalizes the various works of the literature. Numerical examples are given to illustrate the proposed algorithm.

Fuzzy system reliability analysis usingTω (the weakestt‐norm) based arithmetic operations onL‐Rtype interval valued vague sets

Purpose – The purpose of this research is to develop a new approach for analyzing the fuzzy reliability of a series and parallel system. Also to introduce definition of L‐R type interval valued triangular vague set and certain Tω‐based arithmetic operations between two L‐R type interval valued triangular vague sets.Design/methodology/approach – In the proposed approach using a fault tree an interval valued vague fault tree is developed for the system in which the fuzzy reliability of each component of the system is represented by a L‐R type interval valued triangular vague set. Then with the help of a developed interval valued vague fault tree an algorithm is developed to analyze the fuzzy system reliability.Findings – For numerical verification of the proposed approach the fuzzy reliability of the basement flooding has been analyzed using the existing approaches and the proposed approach. Comparing the results of existing approaches and the proposed approach, it has been shown that the uncertainty about ...

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T ω -based addition preserves the shape of L- R type fuzzy numbers. In this paper, we show T ω -based multiplication also preserves the shape of L- R type fuzzy numbers. We then apply T ω -based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L- R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.

NEW METHOD FOR FUZZY SYSTEM RELIABILITY ANALYSIS

This paper presents a new method for fuzzy system reliability analysis based on fuzzy time series and the alpha-cuts arithmetic operations of fuzzy numbers, where we allow the reliabilities of the components of a system at different times t (t= ...,0,1,2,...) to be represented by different membership functions. Because the proposed method allows the reliabilities of the components of a system at different times t to have different membership functions, it is more flexible than the ones presented in Chen 1994 , Cheng and Mon 1993 , and Singer 1990 . Furthermore, because the proposed method uses the simple alpha -cuts arithmetic operations of fuzzy numbers rather than the complicated nonlinear programming techniques mentioned in Mon and Cheng 1994 , it is simpler in calculating fuzzy system reliability than the one presented in that paper.

Fuzzy system reliability analysis for components with different membership functions

This paper addresses the fuzzy system reliability analysis for components with different membership functions. Conventionally, it is not always easy to obtain a system reliability for components with different individual failure probability density functions (p.d.f.), due to the necessary but complicated combination and integration of various p.d.f.'s. For such a problem, and considering fuzzy environment and data imprecision in the real life, we now apply fuzzy set theory to solve the inadequacy of the conventional probability in accounting and processing of built-in uncertainties in the probabilistic data. Therefore, we will use fuzzy distributions instead of the classical probability distribution for the components, and calculate the functions of fuzzy numbers to solve for the fuzzy system reliability via non-linear programming techniques where the commercial packages are available to use. This solution procedure will be described in conjunction with an example used to illustrate the analysis, algorithm and computation of this proposed method.

Fuzzy system reliability analysis using fuzzy number arithmetic operations

This paper presents a new method to analyze fuzzy system reliability using fuzzy number arithmetic operations, where the reliability of each system component is represented by a triangular fuzzy number. Because the proposed method uses simplified fuzzy arithmetic operations of fuzzy numbers rather than the complicated interval arithmetic operations of fuzzy numbers mentioned by Cheng and Mon in Fuzzy Sets and Systems 56 (1993) 29–35 or the complicated extended algebraic operations of fuzzy numbers mentioned by Singer in Fuzzy Sets and Systems 34 (1990) 145–155, its execution is faster than the ones presented by Cheng and Mon, and Singer.

Fuzzy system reliability analysis by interval of confidence

The use of fuzzy number over interval of confidence instead of probability, and possibilitic considerations for evaluating the range value and interval of the fuzzy reliability is proposed. This approach of evaluating fuzzy system reliability by interval arithmetic and α-cuts has a considerable advantage. We can calculate reliability problems easily by the use of ‘DERIVE’ and ‘MATHCAD’ packages. Through theoretical analysis, an illustrative example and computational results, we show that the proposed approach is more general and simplified.