Fuzzy System Reliability Using Fuzzy Lifetime Distribution Emphasizing Octagonal Intuitionistic Fuzzy Numbers

2021 ◽  
pp. 192-208
Author(s):  
Pawan Kumar
Keyword(s):  
System Reliability ◽  
Fuzzy System ◽  
Fuzzy Numbers ◽  
Time To Failure ◽  
Fuzzy Reliability ◽  
Mean Time To Failure ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Mean ◽  
Mean Time

The present study proposes to determine the fuzzy reliability of different systems in which the lifetime of components are following fuzzy exponential distribution where fuzzy reliability function and its α-cut set are presented. The fuzzy reliability of different systems is defined on the basis of octagonal intuitionistic fuzzy numbers. The fuzzy reliability functions of k-out-of-m system, series system, parallel systems, and their fuzzy mean time to failure are discussed respectively using the concept of α-cut of octagonal intuitionistic fuzzy numbers. Finally, some numerical examples are discussed to illustrate how to calculate the fuzzy system reliability and α-cut of fuzzy mean time to failure (FMTTF).

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

2021 ◽  
pp. 20-42
Author(s):  
Seema Negi ◽  
S. B. Singh ◽  
Kamlesh Bisht
Keyword(s):  
Generating Function ◽  
Rayleigh Distribution ◽  
Matrix Form ◽  
Total Weight ◽  
Time To Failure ◽  
Fuzzy Reliability ◽  
Mean Time To Failure ◽  
Varying Parameters ◽  
Fuzzy Mean ◽  
Mean Time

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.

On classes of life distributions based on the mean time to failure function

2021 ◽  
Vol 58 (2) ◽  
pp. 289-313
Author(s):  
Ruhul Ali Khan ◽  
Dhrubasish Bhattacharyya ◽  
Murari Mitra
Keyword(s):  
Damage Model ◽  
Replacement Policy ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Moment Convergence ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
The Mean ◽  
Age Replacement ◽  
Mean Time

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

Interval-valued intuitionistic fuzzy multiple attribute decision making and their applications

2021 ◽  
Vol 25 (2) ◽  
pp. 251-277
Author(s):  
Hong-Jun Wang
Keyword(s):  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Green Supply Chain Management ◽  
Green Supply Chain ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Interval Valued

In this paper, we expand the Muirhead mean (MM) operator and dual Muirhead mean (DMM) operator with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval -valued intuitionistic fuzzy Muirhead mean (IVIFMM) operator, interval-valued intuitionistic fuzzy weighted Muirhead mean (IVIFWMM) operator, interval-valued intuitionistic fuzzy dual Muirhead mean (IVIFDMM) operator and interval-valued intuitionistic fuzzy weighted dual Muirhead mean (IVIFWDMM) operator. Then the MADM methods are proposed with these operators. In the end, we utilize an applicable example for green supplier selection in green supply chain management to prove the proposed methods.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

Contribution to Rolling Bearing Reliability Modeling

2011 ◽  
Vol 110-116 ◽  
pp. 2497-2503 ◽  
Author(s):  
Zdenek Vintr ◽  
Michal Vintr
Keyword(s):  
Operating Time ◽  
Rolling Bearing ◽  
Time To Failure ◽  
Rolling Bearings ◽  
Mean Time To Failure ◽  
Reliability Modeling ◽  
Time Between Failures ◽  
Large Groups ◽  
Mean Time

Rolling bearings are usually considered to be non-repaired items the reliability of which is characterized by mean time to failure, or so called basic rating life. Reliability describes these parameters well in case the bearings are used in operation up to the very time the failure occurs, or during the time corresponding with basic rating life. In case of railway applications the bearings are often used in large groups and are preventively replaced after much shorter operating time as compared with their basic rating life. In the article there is a model which enables us to describe the bearings reliability in this specific case and to specify a number of failures which might be expected from a group of bearings during operating time, or to determine mean operating time between failures of bearings.

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