Reliability Analysis of an Industrial System Using an Improved Arithmetic Operations

Abstract

Today's with the growing complexities of the system, it is difficult for the system analyst to maintain the performance of the system for a longer period of time in order to increase the sustainability of the system. This is mainly due to the failure phenomenon which are occurring during the analysis as the complete information of the system is not always available. To handle this, the problems need to be set up with the approximately available data. However, fuzzy set theory is one of the successful theory to deal with such types of data. In recent times, the use of fuzzy sets has been gaining popularity and is playing an important role in the areas of engineering and management disciplines. As compared to other research domains, the fuzzy arithmetic gained great interest in scientific areas such as decision problems, reliability analysis, optimization etc. In order to perform operations on fuzzy observations, fuzzy numbers came into existence. The difference between the arithmetic operations on generalized fuzzy numbers and the traditional fuzzy numbers is that the former can deal with both non-normalized and normalized fuzzy numbers, but the later with normalized fuzzy numbers.

The research work presented in this dissertation is devoted to present an improved arithmetic operations under the fuzzy environment. As the existing work on the arithmetic operations consider the same degree of confidence level for different fuzzy numbers and hence it observed that it loss the information which cause the inexact results. So in order to avoid this and to preserve the flatness of the fuzzy numbers we derived an improved arithmetic operators such as addition, scalar multiplication, subtraction, multiplication for generalized trapezoidal (triangular) fuzzy numbers. The advantage of the proposed operations is that it preserves the flatness of the data and hence give its significance.

The present thesis is organized into four chapters including the present one that contains mainly the literature review. The rest of chapters are described below: In Chapter 2, the basic and preliminaries related to the reliability theory and fuzzy set theory to be used in the subsequent chapters are given. In Chapter 3, an improved arithmetic operations on generalized fuzzy numbers have been presented by overcoming the some shortcoming of the existing operations. As it has been observed that arithmetic operations of generalized trapezoidal (triangular) fuzzy numbers with function principle cause the loss of information and do not give exact results. This motivates us to correct the results of arithmetic operations of generalized trapezoidal (triangular) fuzzy numbers. Various arithmetic operations, such as addition, subtraction, multiplication, division etc are studied and illustrated with a numerical examples. In Chapter 4, reliability analysis of repairable industrial systems has been analyzed by using the improved arithmetic operations for a generalized fuzzy numbers as described in Chapter 3 by considering the different degree of confidence levels. A case study from the washing unit of a paper mill, a complex repairable industrial system, has been taken for demonstrating the approach. Finally, the computed results are compared with the existing methodologies results. The presented technique utilizes uncertain data of the system and analyze its behavior with reduced level of uncertainty which makes the decision more realistic and generic for further application.