The α, β-Cut Intervals and Weakest t-Norm Based Importance Measure for Criticality Analysis in Intuitionisitic Fuzzy Fault Tree Analysis of LNG-ESD System

Abstract

Different importance measures have been developed and widely utilized in system reliability analysis to measure the importance of system components. During operation period of a complex system, it becomes more difficult to collect exact failure data of system components i.e. the collected failure data may have some sort of uncertainties due to various reasons. Generally, triangular shaped fuzzy numbers or intuitionistic fuzzy numbers (IFNs) are used to quantify the various types of uncertainty in failure data of the system’s components and fuzzy arithmetic operations are utilized which computes each reliability index with wide range of prediction due to accumulating phenomenon of fuzziness. In this paper, different types of intuitionistic fuzzy number (IFN) are used to quantify the failure data uncertainty of the system’s components while α, β-cut intervals and weakest t-norm (Tw)-based arithmetic operations are employed to reduce the range of prediction for each reliability index. The objective of the present study is to develop Tw-based importance measure for criticality analysis in intuitionistic fuzzy fault tree analysis (IF-FTA) of a system, when different types of uncertainties in crisp failure data of basic events are quantified by different types of membership and non-membership functions. The developed importance measure applies system fault tree, α-cut and β-cut intervals, different types of intuitionistic fuzzy number (IFN) and weakest t-norm (Tw) based intuitionistic fuzzy arithmetic operations. To demonstrate the applicability of the proposed measure, a case study of liquefied natural gas terminal emergency shutdown system (LNG-ESD system) is performed. The IF-FTA of LNG-ESD system is presented to evaluate the fault intervals of the system at different levels using Tw-based arithmetic operations on different types of IFNs. The developed importance measure is applied to identify and rank the critical basic events in IF-FTA of LNG-ESD system. The proposed measure is also compared with some existing importance measures.