Fuzzy Reliability Research Articles

Design of High-Speed Thin Steel Plate Roller Based on the Fuzzy Reliability

Rupture often happens when high-speed thin steel plate roller endures exchanging stress. Based on fuzzy theory, the paper discusses the fuzzy reliability design of roller with random variables and fuzzy variables, puts forward a basic method of digital simulation, and furthermore takes actions to improve the reliability of the rollers.

A novel approach for solving fuzzy differential equations using Runge-Kutta and Biogeography-based optimization

The objective of this work is to present a methodology for solving the Kolmogorov's differential equations in fuzzy environment using Runga-Kutta and Biogeography-based optimization (RKBBO) algorithm. As most of the data are usually uncertain and hence the fuzzy set theory has been used for handling the uncertainties and therefore the corresponding differential equations becomes fuzzy Kolmogorov's differential equations. The obtained differential equations has been solved by Runga-Kutta method and improvement of their solution has been found by formulating a nonlinear optimization problem and solved by BBO for finding the global or near to global solutions. Performance index has been used for finding the most critical component of the system for increasing the performance of system by considering reliability, availability and maintainability index. Final results are compared with the existing results. To show the application of the proposed method, a case of the thermal power plant, a repairable industrial system, has been taken for evaluating the fuzzy reliability of the system.

Fuzzy analytic hierarchy process to a structure under 2-out-of-3:F modeling

The lack of consistency in reliability modeling under human failure can lead to inconsistent conclusions. However, fuzzy logic allows an address to the ambiguity in reliability modeling. The Analytic Hierarchy Process (AHP) is one of the comprehensively used multi-criteria decision making methods. This paper reveals the application of fuzzy AHP in a structure consisting of a 2-out-of-3:F substructure under human failure. In reliability engineering, failure is a major concern for system design, planning and operations and it is imperative to focus more on system failures. The novelty of this paper is that the major failure rates of the system are selected and the weight of each failure rate is calculated after constructing a pair wise comparison matrix. The fuzzy reliability index is then evaluated with the help of the linguistic variables considered by experts in the form of performance ratings of different reliability indexes, and then the reliability is measured using multi-criteria decision making technique. The contribution of the paper is the ranking of failure rates which shows the relative importance of each failure rate and how it affects the overall system reliability to decide on a desirable action plan.

Fuzzy reliability analysis using cellular automata for network systems

This paper concentrates on the performance evaluation of networks, whose arc failure rates are not deterministic numbers, but imprecise ones. Conventional literatures analyze the network reliability assuming that the failure rates of all components in networks following the same membership function. However, most real-world networks do not abide by this regulation, especial complex ones. Therefore, in this paper, a new method is developed based on cellular automata (CA) and fuzzy logic following different types of fuzzy failure rates. The proposed method has two separate processing procedures: the computing of fuzzy numbers (CFN) and the decomposing model based on cellular automata (DB-CA). The combination of these procedures can be used to topology decomposition and the fuzzy reliability evaluation of any real network. Finally, The proposed method is improved by numerical network examples with a variety of membership functions, and the benchmark water delivery network in Shelby county is provided to estimate the feasibility and effectiveness of the proposed model.

Combination of unreliable evidence sources in intuitionistic fuzzy MCDM framework

In this paper, we consider the combination of unreliable evidence sources in multiple criteria decision making (MCDM) framework in intuitionistic fuzzy environment. In the intuitionistic fuzzy MCDM framework, evidence sources can be combined based on intuitionistic fuzzy aggregation operators when reliability factors are known. Generalized intuitionistic fuzzy aggregation operators are applied to combine evidence sources with intuitionistic fuzzy reliability factors. Discounting operation on unreliable evidence bodies is also extended to deal with uncertain reliability factors. Then we define a combination operation on intuitionistic fuzzy values to combine evidence bodies in the intuitionistic fuzzy MCDM model. Finally the estimation of the reliability factors without prior knowledge is studied. Our proposed evaluation method is based on the principle of self-assessment. It is implemented by the probabilistic comparison between intuitionistic fuzzy values. Moreover, the proposed evaluation method is independent of the dissimilarity measure between basic probability assignments. Numerical examples demonstrate the performance of our combination rules and reliability estimation method.

Fuzzy FMECA-Based Reliability Analysis of Welding Robots

Fuzzy FMECA-Based Reliability Analysis of Welding Robots

Multi-objective Fuzzy Reliability Optimization Model: A Parametric Geometric Programming Approach

This paper presents a multi-objective reliability optimization model taking system reliability and cost of a series system as objective functions. Due to the vagueness of judgements of the decision maker, the objective as well as constraint goal can involve many uncertain factor and other imprecise parameters with vague in nature in a reliability optimization model. Thus the model is formulated in fuzzy environment by considering cost coefficients and the exponential factor as triangular fuzzy number. Here, the nearest interval approximation method is applied to make the fuzzy model in crisp in nature. There are two types of parametric geometric programming technique is used to solve the proposed model. The performance of these two types of solution approach is evaluated by numerical example at the end of this paper.

Z-valued T-norm and T-conorm Operators-based Aggregation of Partially Reliable Information

T-norm and T-conorm operators are successfully used for processing uncertainty in system analysis, decision analysis, control, modeling and forecasting applications. The complexity of real-world applications is that relevant information is partially reliable. In this regard, Prof. L.A. Zadeh suggested the concept of a Z-number as an ordered pair Z1+Z2 of fuzzy numbers used to describe a value of a random variable X, where A is a fuzzy constraint on values of X and B is a fuzzy reliability of A, and is considered as a value of probability measure of R2. However, processing of Z-number based information is at its initial stage of crystallization. In this paper we consider Z-number valued T-norm and T-conorm operators of Z-numbers. A real-world application is used to illustrate validity and efficiency of Z-number valued T-norm and T-conorm operators based processing of partially reliable information.

Компьютерное моделирование показателей нечеткой надежности

Компьютерное моделирование показателей нечеткой надежности

Reliability Analysis of Relay Protection Based on the Fuzzy-Markov Model

Relay protection and safety device are regarded as the sentry of safe and reliable operation of the power grid. It plays a very important role in the power grid, and can determine whether the normal operation of the power system. This article considers the influence of the fuzzy uncertainty of relay protection failure rate to power system on the basis of Markov model, and researches the dynamic fault tree analysis method in the case of fuzzy failure parameter. A dynamic fault model has been built. The triangular fuzzy numbers are used to express the failure rate of the components and system, after which the fuzzy Markov model has been established based on the dynamic fault tree model obtained before. The fuzzy reliability curve and fuzzy failure probability on given degree of membership could be obtained. Finally, the fuzzy Markov model based dynamic fault tree analysis method is used for reliability modeling and analysis of relay protection. The results show that this method can conduct reliability modeling and quantitative assessment effectively for systems which have dynamic failure characteristics and uncertainty of failure rate.

Reliability analysis of turbine blades based on fuzzy response surface method

To improve the precision of reliability analysis on turbine blades, the fuzzy response surface method of reliability analysis is proposed by considering the fuzziness of the input variables and the vagueness of the limit state variables. Initially, the fuzzy basic variables were converted into equivalent random variables according to the method of equivalent transformation. Additionally, the mathematic model of the fuzzy response surface for structural reliability analysis was established, based on the quadratic polynomial response surface function. The mean value and variance of the blade stress and radial deformation were obtained by using the Monte-Carlo method based on generous linkage sampling to the model. Finally, the probability of failure and fuzzy random reliability index were calculated based on the probability integral method. Results indicate that the reliability probability of the blade is 97.665%, when the allowable stress and deformation are 390 MPa and 0.195 mm, respectively. It is demonstrated that with an increase of the fuzzy coefficient, the blade reliability index decreases; thus, the random reliability of the blade is slightly higher than the fuzzy reliability.

Fuzzy Reliability Assessment of Systems With Multiple-Dependent Competing Degradation Processes

Components are often subject to multiple competing degradation processes. For multicomponent systems, the degradation dependence within one component or/and among components need to be considered. Physics-based models and multistate models are often used for component degradation processes, particularly when statistical data are limited. In this paper, we treat dependence between degradation processes within a piecewise-deterministic Markov process (PDMP) modeling framework. Epistemic (subjective) uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters, to take this into account, we describe the parameters of the PDMP model as fuzzy numbers. Then, we extend the finite-volume method to quantify the (fuzzy) reliability of the system. The proposed method is tested on one subsystem of the residual heat removal system of a nuclear power plant, and a comparison is offered with a Monte Carlo simulation solution the results show that our method can be most efficient.

A non-linear fuzzy degradation model for estimating reliability of a polymeric coating

Oftentimes, material components follow non-linear degradation because the material loss trough time is non-linear; the components present different levels of resistance during a degradation process. Constructing predictions of the component life span and performing reliability analyses regarding degradation is possible by non-linear regression. Generally, this method ignores the prediction error in the extrapolated time and it does not account measurement error in the observed sample paths. In this paper, it is proposed new means for predicting time to failure of the components, using a calibration regression method for measuring the error prediction in the extrapolation process. In order to consider the uncertainty, we proposed to perform the estimated times by a trapezoidal fuzzy numbers, providing a more reliable prediction without loss of information. Since the times to failure are shaped by fuzzy numbers, it was adapted the fuzzy probability theory to the classical reliability analysis for estimating the fuzzy reliability of a component. An accelerated test of a polymeric coating process was performed and also an application for a preventive maintenance frequency was proposed.

Fuzzy reliability analysis using a new alpha level set optimization approach based on particle swarm optimization

In real world application of structural reliability analysis some random variables contains two types of random and epistemic uncertainty, while in classic methods of structural reliability only the random uncertainty is considered completely. Therefore in order to have a reliable estimation of structural safety, random variables should cover both random and epistemic uncertainty. In this paper, modeling of epistemic uncertainty of random variables has been brought in to focus. Hybrid random variables are simulated using fuzzy numbers. A new alpha level set optimization approach applying particle swarm optimization technique was addressed in order to determine the minimum and the maximum members of reliability index interval. Importance sampling technique was used for reliability analysis to decrease the computational effort. Three numerical examples were given to illustrate the accuracy and efficiency of the proposed method. Results showed that the proposed method was more efficient compared to the alternative search approaches thorough low computational burden.

Time-variant structural fuzzy reliability analysis under stochastic loads applied several times

A new structural dynamic fuzzy reliability analysis under stochastic loads which are applied several times is proposed in this paper. The fuzzy reliability prediction models based on time responses with and without strength degeneration are established using the stress-strength interference theory. The random loads are applied several times and fuzzy structural strength is analyzed. The efficiency of the proposed method is demonstrated numerically through an example. The results have shown that the proposed method is practicable, feasible and gives a reasonably accurate prediction. The analysis shows that the probabilistic reliability is a special case of fuzzy reliability and fuzzy reliability of structural strength without degeneration is also a special case of fuzzy reliability with structural strength degeneration.

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.

Fuzzy reliability research on carbon fibre composites under random vibration based on fuzzy failure domain

Currently, the reliability calculation of carbon fibre composites is through by the stress strength interference, which may not fully reflect the fuzziness of stress, strength and the stress degradation under the depletion failure. To overcome this problem, this paper proposes a reliability calculation method based on fuzzy failure domain and establishes the fuzzy reliability model of carbon fibre composites. Borrowing the membership function in fuzzy mathematics represents the stress degradation processes of carbon fibre composites which would make the interference region boundary of stress strength interference model fuzzy. The feasibility of method is tested through a numerical example. Finally, by comparing the simulation results of the fuzzy reliability model with the simulation results of the static stress strength interference model and the simulation result of the dynamic stress strength interference model, the rationality of the method is verified. The fuzzy reliability model can calculate the reliability without the gradual degradation processes; thus, it is used more widely.

Modeling of Epistemic Uncertainty in Reliability Analysis of Structures Using a Robust Genetic Algorithm

In this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The First Order Reliability Method (FORM) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. The sensitivity level of fuzzy response due to the introduced epistemic uncertainty was also measured using the modified criterion of Shannon entropy. By introducing bounds of uncertainty, the fuzzy response obtained from the proposed method presented more realistic estimation of the structure reliability compared to classic methods. This uncertainty interval is of special importance in concrete structures since the quality of production and implementation of concrete varies in different cross sections in reality. The proposed method is implementable in reliability problems in which most of random variables are fuzzy sets and in problems containing non-linear limit state functions and provides a precise acceptable response. The capabilities of the proposed method were demonstrated using different examples. The results indicated the accuracy of the proposed method and showed that classical methods like FORM cover only special case of the proposed method.

A fuzzy reliability approach for structures based on the probability perspective

To investigate fuzzy reliability problem deeply, the traditional failure possibility of the structures with fuzzy variables is explained from the probability perspective. By treating the membership levels of all fuzzy variables as the same random variable following standard uniform distribution, it is verified in theory that the failure probability where the membership levels follow the same standard uniform distribution equals to the traditional failure possibility. Furthermore, by treating the membership levels of the different fuzzy variables as the independent standard uniform distributions, a novel fuzzy reliability model is proposed to measure the safety of the structures with fuzzy variables, which provides a new perspective to analyze the failure mechanism of the structures with fuzzy variables. Comparing the principles and results of the examples with the traditional failure possibility, the proposed model based on the probability perspective utilizes available information more adequately and the results are much closer to the engineering practices, while the traditional approach is too conservative. Moreover, according to the feature of the established fuzzy reliability model, a highly efficient solution based on the kriging surrogate model method is proposed to analyze the reliability of the structure with fuzzy variables.

An Approach for Analyzing the Reliability of Industrial System Using Fuzzy Kolmogorov’s Differential Equations

The main objective of this paper is to present a technique to permit the reliability analyst’s or system manager for increasing the performance of the system. As traditionally, it was assumed that probabilities in Markov chain models are deterministic in nature, but as the system are growing complex and more complex these days, so the reliability data are either insufficient or mixed with uncertainty. Thus to handle these kind of issues, the nth-order fuzzy Kolmogorov’s differential equations are developed by using a fuzzy Markov model of a repairable industrial system from its transition diagram and then evaluate the fuzzy reliability of the system both in transient as well as in steady state using Runge–Kutta method. Sensitivity analysis has been conducted for finding the most critical component of the system by varying the failure and repair rates of the system. Final results are compared with the existing results. To show the application of the proposed method, a case of the thermal power plant, a repairable industrial system, has been taken for evaluating the fuzzy reliability of the system.