# Mathematical modeling of sugar plant: a fuzzy approach

Original Research

## Abstract

Conventional reliability of a system is defined as the probability that it can perform a pre-specific function without failure in a pre-fixed time interval under a predefined environment. It is based on the assumption that system’s failure behavior is characterized in probabilistic context and binary-state assumption for the demonstration of the states. At any time, the system is either in failed or operative state. But, this assumption seems unrealistic for large complex industrial systems. The uncertainty of each component enhances the uncertainty of the whole system. In this paper, the concept of fuzzy reliability has been used for the analysis of fuzzy availability of a sugar plant. The effect of coverage factor, failure and repair rates of subsystems on systems fuzzy availability had been analyzed. Chapman–Kolmogorov differential equations have been derived with the help of Markov birth–death process. The governing differential equations are solved by Runge–Kutta method of order four using MATLAB (Ode 45 function).

## Keywords

Sugar plant Markov process Fuzzy availability Runge–Kutta method Fault-tolerant system

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© Society for Reliability and Safety (SRESA) 2017

## Authors and Affiliations

1. 1.Department of Mathematics and StatisticsManipal University JaipurJaipurIndia