Mathematical modeling and performance evaluation of A-pan crystallization system in a sugar industry

Research Article Mathematical modeling and performance evaluation of A‑pan crystallization system in a sugar industry Ombir Dahiya1 · Ashish Kumar1 · Monika Saini1 © Springer Nature Switzerland AG 2019 Abstract In this paper, an effort has been made to formulate a mathematical model of A-pan crystallization system of a sugar plant using fuzzy reliability approach. The sugar plant comprises eight subsystems. A-pan crystallization system is one of the most important representative among sugar plant systems. The A-pan crystallization system has four subsystems arranged in a series. The configuration of first and second subsystems is 2-out-of-2: G with two cold standby while third and fourth subsystems are in single-unit configuration. A mathematical model has been proposed by considering exponential distribution for failure and repair rates. By considering fuzzy reliability approach and Markov birth–death model differential equations have been derived. These equations are then solved by Runge–Kutta method of fourth order using MATLAB (Ode 45 function) to obtain the fuzzy availability. The results of the proposed model are beneficial for system designers. Keywords A-pan crystallization system · Markov process · Fuzzy availability · Runge–Kutta method 1 Introduction Due to the population explosion in last century sugar consumption is rapidly increasing throughout the world. According to Meriot [1] sugar production by centrifugal/ structured sugar plants in India is more than 84% of the total production of sugar. One important ration of any sugar plant is the assurance of high availability for maximum production. To achieve higher availability of a system it is mandatory that all of its subsystem attain higher reliability. In this study, an effort has been made to analyze the availability of A-pan crystallization system of a sugar plant. The existing literature like Adamyan and David [2], Gupta et al. [3], Mehmood and Lu [4], Garg and Sharma [5], Kumar and Mudgil [6], Loganathan et al. [7], and Saini and Kumar [8] shows that a lot of techniques have been used to analyze the performance of the industrial systems in terms of reliability and availability such as Reliability block diagram, semi-Markov process, Markovian approach and fault tree analysis. However, in above techniques all operating states have been considered that system either work in full capacity or completely fail but in many industrial systems this condition does not seems realistic. Therefore, here an effort has been made to analyze the system in all reduced states between failed and operative states, i.e., in fuzzy states. In previous studies including Nailwal and Singh [9] and Neeraj and Barak [10], it is also observed lot of computational work has been carried out to obtain the availability. Here, Runge–Kutta method of fourth order has been opted to obtain the numerical solution of differential difference equations. A lot of successful applications of fuzzy reliability approach and Runge–Kutta method has been reported in literature. The concept of fuzzy set theory has been coined by Zadeh [11]. He described the importance of fuzzy sets in the development of scientific and industrial systems. The concept of component failure possibility rather than failure probability was introduced by Kaufmann [12]. He presented a lot of applications of * Ashish Kumar, | 1Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan 303007, India. SN Applied Sciences (2019) 1:339 | https://doi.org/10.1007/s42452-019-0348-0 Received: 30 November 2018 / Accepted: 7 March 2019 / Published online: 13 March 2019 Vol.:(0123456789) Research Article SN Applied Sciences (2019) 1:339 | https://doi.org/10.1007/s42452-019-0348-0 fuzzy sets in various fields like hardware/software reliability, risk analysis, etc. Srinath [13] used Markovian approach for availability analysis considering constant failure and repair rates. Arora and Kumar [14] performed availability analysis of power generation system. The recurrence relations for availability and MTBF have been derived by considering constant failure and repair rates. Barabady and Kumar [15] carried out performance evaluation of a repairable system in terms of system reliability and availability. Kiureghian and Ditlevson [16] examined the availability, reliability and downtime of system with repairable constituents. Garg et al. [17] proposed a mathematical model of a repairable block board manufacturing system using a birth–death Markov Process. The differential equations have been solved for the steady-state performance evaluation. Rahman et al. [18] studied root causes for failure of a division wall super heater tube of a coal-fired power station. Kumar et al. [19] developed a simulation model for performance evaluation of urea decomposition unit in fertilizer plant. Kumar and Tewari [20] suggested a mathematical model for performance evaluation of CO2 cooling system. Adhikary et al. [21] accomplished RAM investigation of coal-fired thermal power plants. Goyal and Grover [22] comprises a comprehensive bibliography on effectiveness measurement of manufacturing systems. Kumar [23] used Markov approach to analyze an availability simulation model for power generation system. Khanduja et al. [24] designated a performance improvement model of crystallization unit of a sugar plant using MA and GA. Hojjati-Emami et al. [25] performed reliability prediction for the vehicles equipped with advanced driver assistance systems and passive safety systems. Aggarwal et al. [26] discussed the performance analysis and optimization of a butter oil production system using MA and Runge–Kutta method to calculate the mean time between failure (MTBF). Kumar et al. [27] developed a stochastic model for casting process and performed sensitivity analysis for various reliability measures. Kadyan and Kumar [28] analyzed the availability and profit of feeding system in sugar manufacturing plant. Aggarwal et al. [29] formulated a mathematical model and obtained the results for reliability of the serial processes in feeding system. Kumar and Tewari [30] used PSO technique for performance analysis and optimization of CSDGB filling system of a beverage plant. Kadyan and Kumar [31] analyzed the availability based operational behavior of B-Pan crystallization system in the sugar industry. Kumar and Saini [32] developed a mathematical model of sugar plant as a whole system. Recently, Dahiya et al. [33] analyzed a feeding system of sugar plant subject to coverage factor. Dahiya et al. [33, 34] evaluated the fuzzy availability of a harvesting system using fuzzy reliability approach. Vol:.(1234567890) Keeping in view the above facts and figures in mind, in this paper, an effort has been made to formulate a mathematical model of A-pan crystallization system of a sugar plant using fuzzy reliability approach. The objective of this study is to help the sugar industry management persons to e (...truncated)