Mathematical modeling and performance evaluation of Apan crystallization system in a sugar industry
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Abstract
In this paper, an effort has been made to formulate a mathematical model of Apan crystallization system of a sugar plant using fuzzy reliability approach. The sugar plant comprises eight subsystems. Apan crystallization system is one of the most important representative among sugar plant systems. The Apan crystallization system has four subsystems arranged in a series. The configuration of first and second subsystems is 2outof2: G with two cold standby while third and fourth subsystems are in singleunit 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
Apan crystallization system Markov process Fuzzy availability Runge–Kutta method1 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 Apan 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, semiMarkov 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 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 steadystate performance evaluation. Rahman et al. [18] studied root causes for failure of a division wall super heater tube of a coalfired 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 coalfired 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. HojjatiEmami 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 BPan 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.
Keeping in view the above facts and figures in mind, in this paper, an effort has been made to formulate a mathematical model of Apan crystallization system of a sugar plant using fuzzy reliability approach. The objective of this study is to help the sugar industry management persons to evaluate the performance of the sugar plant by developing reliability model for Apan crystallization system. Apan crystallization system is one of the most important representative among sugar plant systems. The Apan crystallization system has four subsystems arranged in a series. The configuration of first and second subsystems is 2outof2: G with two cold standby while third and fourth subsystems are in singleunit 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 difference 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. Numerical and graphical results are also found to elucidate the effect of subsystems.
The whole manuscript has been organized in six sections. The first section in introductory in nature. A detailed literature review and gap of research is discussed here. In Sect. 2, system description, assumptions, notations, possible states and state transition diagram are appended. In Sect. 3, mathematical model has been developed for Apan crystallization system and differential difference equation are derived. Expressions for fuzzy availability, fuzzy busy period and fuzzy profit analysis are also carried out in this section. In Sect. 4, the effect of various failure rates and repair rates on availability and profit is deliberated through tables and graphs. Conclusion drawn from analysis is discussed in Sect. 5.
2 System description
The Apan crystallization system has four subsystems arranged in a series. In first subsystem crystallizer (subsystem A) semisolid form of the liquid is frenzied to evaporate remaining water. The frenzied process is performed in a long duration of time on slow heating. After conversion of semisolid form of the liquid into magma it is sent to centrifugal machine (subsystem B) to separates out sugar crystals. The subsystem C cooled and graded the sugar crystals. Finally, sugar is weighted and bagging in subsystem D. If there is some amount of sugar in power form, than it is again processed through crystallization. The detailed description of subsystems are as follows (for detailed description see Kumar [35].
2.1 Crystallizer (subsystem A)
Sahu [36] described crystallization as a process in which masecuites are slowly stirred while they cool from pan dropping temperature to surrounding temperature. Progressive cooling reduces the solubility of sugar and forced to crystallization. This whole procedure is carried out in special equipment called crystallizer. Crystallizers are U shaped or circular in diameter, open and horizontal containers. The massecuite is cooled by air and cooling action is very slow. In present study, subsystemA consist of four identical crystallizer unit working in the 2outof2: G with two cold standby configuration. In this subsystem, semisolid form of the liquid is frenzied to evaporate remaining water. The frenzied process is performed in a long duration of time on slow heating. In the unavailability of two operative units the subsystem fails and resulted as the complete failure of the Apan crystallization system. It is connected in series configuration with other subsystems B, C, and D.
2.2 Centrifugal machine (subsystem B)
Sahu [36] explained that masticates produced from crystallizer send to rotating type equipment know to be a centrifuge. In present study, present system also consists of four identical units working in the 2outof2: G with two cold standby configuration. This subsystem, after conversion of semisolid form of the liquid into magma, separates out sugar crystals. In the unavailability of two operative units the subsystem fails and resulted as the complete failure of the Apan crystallization system. It is connected in series configuration with other subsystems A, C, and D.
2.3 Grader (subsystem C)
Kumar [35] describes this subsystem as a series system which consists of hopper cooler and sugar grader. In this subsystem, the crystals are cooled and cut in small/medium pieces. It is connected in series configuration with other subsystems. It is a single unit system. Its failure causes the complete system failure.
2.4 Weighment and bagging (subsystem D)
Kumar [35] defined it as a system where sugar weighted and packed in bags. It is also connected in series configuration with other subsystems. It is also single unit system. Its failure causes the complete system failure.
 1.
All failure time and repair time random variables are exponentially distributed.
 2.
The failed unit after repair becomes as good as new.
 3.
The system may be any of the states between fully operative to complete failed. The value of coverage factor lies between 0 and 1.
 4.
Sufficient repair facility always remains available to perform various repair activities.
 5.
No simultaneous failures occurs.
2.5 Fuzzy availability
System states
The system may be any one of the following states:
\(S_{1} (A_{2,2,0} ,B_{2,2,0} ,C,D)\); \(S_{2} (A_{2,1,1} ,B_{2,2,0} ,C,D);\)\(S_{3} (A_{2,2,0} ,B_{2,1,1} ,C,D)\); \(S_{4} (A_{2,2,0} ,B_{2,0,2} ,C,D)\); \(S_{5} (A_{2,0,2} ,B_{2,2,0} ,C,D)\); \(S_{6} (A_{2,0,2} ,B_{2,1,1} ,C,D)\); \(S_{7} (A_{2,1,1} ,B_{2,1,1} ,C,D)\); \(S_{8} (A_{2,1,1} ,B_{2,0,2} ,C,D)\); \(S_{9} (A_{2,0,2} ,B_{2,0,2} ,C,D)\); \(S_{10} (A_{2,2,0} ,B_{2,2,0} ,c,D)\); \(S_{11} (A_{2,2,0} ,B_{2,2,0} ,C,d)\); \(S_{12} (A_{2,1,1} ,B_{2,2,0} ,C,d)\); \(S_{13} (A_{2,1,1} ,B_{2,2,0} ,c,D)\); \(S_{14} (A_{2,0,2} ,B_{2,2,0} ,c,D)\); \(S_{15} (a,B_{2,2,0} ,C,D)\); \(S_{16} (A_{2,0,2} ,B_{2,2,0} ,C,d)\); \(S_{17} (A_{2,0,2} ,B_{2,1,1} ,c,D)\); \(S_{18} (a,B_{2,1,1} ,C,D)\); \(S_{19} (A_{2,0,2} ,B_{2,1,1} ,C,d)\); \(S_{20} (A_{2,1,1} ,B_{2,1,1} ,C,d)\); \(S_{21} (A_{2,1,1} ,B_{2,1,1} ,c,D)\); \(S_{22} (A_{2,1,1} ,b,C,D)\); \(S_{23} (A_{2,1,1} ,B_{2,0,2} ,c,D)\); \(S_{24} (A_{2,1,1} ,B_{2,2,0} ,C,d)\); \(S_{25} (A_{2,1,1} ,b,C,D)\); \(S_{26} (A_{2,2,0} ,B_{2,0,2} ,C,d)\); \(S_{27} (A_{2,2,0} ,B_{2,0,2} ,c,D)\); \(S_{28} (A_{2,2,0} ,B_{2,1,1} ,C,d)\); \(S_{29} (A_{2,2,0} ,B_{2,1,1} ,c,D)\); \(S_{30} (a,B_{2,0,2} ,C,D)\); \(S_{31} (A_{2,0,2} ,B_{2,0,2} ,C,d)\); \(S_{32} (A_{2,0,2} ,B_{2,0,2} ,c,D)\); \(S_{33} (A_{2,0,2} ,b,C,D).\)

\(X_{(OU,\,SU\,,FUR)}\): States of the subsystem A and B.

A, B, C, D: working states of all the four subsystems with full capacity

a, b, c, d: failed states of subsystems A, B, C, and D respectively

OU: No. of operative units

SU: no. of standby unit

FUR: no. of failed units under repair

\(\lambda_{i} \,(1 \le i \le 4){:}\,\) failure rates of subsystem A, B, C, and D respectively

\(\beta_{i} \,(1 \le i \le 4){:}\,\) repair rates of subsystem A, B, C, and D respectively

\(S_{i} {:}\,\) ith state of the system

\(\alpha \,:\) coverage factor having values \(0 \le \alpha \, \le 1\). A fully restored state achieve coverage factor value \(\alpha .\)

\(P_{i} (t):\) it denotes the probability that the system is in ith state at time t.
3 Mathematical modeling
4 Numerical and graphical results
In this section, for a fixed set of values of failure and repair rates given as follows:
Effect of failure rate of various subsystems on the profit function of plant with respect to time at \(\alpha\) = 0.9
Time in days  Set1: initial observations  \(\lambda_{1} = 0.02\;{\text{to}}\;\lambda_{1} = 0.07\)  \(\lambda_{2} = 0.05\;{\text{to}}\;\lambda_{2} = 0.2\)  \(\lambda_{3} = 0.03\;{\text{to}}\;\lambda_{3} = 0.10\)  \(\lambda_{4} = 0.023\;{\text{to}}\;\lambda_{4} = 0.063\) 

20  9905.92  9898.251  9846.437  9810.858  9818.942 
40  9905.914  9898.237  9846.427  9810.852  9818.926 
60  9905.914  9898.237  9846.427  9810.852  9818.926 
80  9905.914  9898.237  9846.427  9810.852  9818.926 
100  9905.914  9898.237  9846.427  9810.852  9818.926 
120  9905.914  9898.237  9846.427  9810.852  9818.926 
140  9905.914  9898.237  9846.427  9810.852  9818.926 
160  9905.914  9898.237  9846.427  9810.852  9818.926 
Effect of failure rate of various subsystems on the profit function of plant with respect to time at \(\alpha\) = 0.7
Time in days  Set1: initial observations  \(\lambda_{1} = 0.02\;{\text{to}}\;\lambda_{1} = 0.07\)  \(\lambda_{2} = 0.05\;{\text{to}}\;\lambda_{2} = 0.2\)  \(\lambda_{3} = 0.03\;{\text{to}}\;\lambda_{3} = 0.10\)  \(\lambda_{4} = 0.023\;{\text{to}}\;\lambda_{4} = 0.063\) 

20  9724.772  9710.617  9608.394  9454.929  9477.488 
40  9724.756  9710.579  9608.35  9454.915  9477.455 
60  9724.756  9710.579  9608.35  9454.915  9477.455 
80  9724.756  9710.579  9608.35  9454.915  9477.455 
100  9724.756  9710.579  9608.35  9454.915  9477.455 
120  9724.756  9710.579  9608.35  9454.915  9477.455 
140  9724.756  9710.579  9608.35  9454.915  9477.455 
160  9724.756  9710.579  9608.35  9454.915  9477.455 
Effect of failure rate of various subsystems on the profit function of plant with respect to time at \(\alpha\) = 0.5
Time in days  Set1: initial observations  \(\lambda_{1} = 0.02\;{\text{to}}\;\lambda_{1} = 0.07\)  \(\lambda_{2} = 0.05\;{\text{to}}\;\lambda_{2} = 0.2\)  \(\lambda_{3} = 0.03\;{\text{to}}\;\lambda_{3} = 0.10\)  \(\lambda_{4} = 0.023\;{\text{to}}\;\lambda_{4} = 0.063\) 

20  9551.82  9160.514  9444.344  9125.438  9160.514 
40  9551.797  9160.473  9444.258  9125.419  9160.473 
60  9551.797  9160.473  9444.258  9125.419  9160.473 
80  9551.797  9160.473  9444.258  9125.419  9160.473 
100  9551.797  9160.473  9444.258  9125.419  9160.473 
120  9551.797  9160.473  9444.258  9125.419  9160.473 
140  9551.797  9160.473  9444.258  9125.419  9160.473 
160  9551.797  9160.473  9444.258  9125.419  9160.473 
Effect of failure rate of various subsystems on the profit function of plant with respect to time at \(\alpha\) = 0.3
Time in days  Set1: initial observations  \(\lambda_{1} = 0.02\;{\text{to}}\;\lambda_{1} = 0.07\)  \(\lambda_{2} = 0.05\;{\text{to}}\;\lambda_{2} = 0.2\)  \(\lambda_{3} = 0.03\;{\text{to}}\;\lambda_{3} = 0.10\)  \(\lambda_{4} = 0.023\;{\text{to}}\;\lambda_{4} = 0.063\) 

20  9385.743  8864.783  9326.7  8818.855  8864.783 
40  9385.715  8864.74  9326.611  8818.834  8864.74 
60  9385.715  8864.74  9326.611  8818.834  8864.74 
80  9385.715  8864.74  9326.611  8818.834  8864.74 
100  9385.715  8864.74  9326.611  8818.834  8864.74 
120  9385.715  8864.74  9326.611  8818.834  8864.74 
140  9385.715  8864.74  9326.611  8818.834  8864.74 
160  9385.715  8864.74  9326.611  8818.834  8864.74 
5 Conclusion
Effect of failure rate of various subsystems on the profit function of plant with respect to time at \(\alpha\) = 0.1
Time in days  Set1: initial observations  \(\lambda_{1} = 0.02\;{\text{to}}\;\lambda_{1} = 0.07\)  \(\lambda_{2} = 0.05\;{\text{to}}\;\lambda_{2} = 0.2\)  \(\lambda_{3} = 0.03\;{\text{to}}\;\lambda_{3} = 0.10\)  \(\lambda_{4} = 0.023\;{\text{to}}\;\lambda_{4} = 0.063\) 

20  9225.281  8587.487  9216.05  8532.143  8587.487 
40  9225.25  8587.446  9216.007  8532.12  8587.446 
60  9225.25  8587.446  9216.007  8532.12  8587.446 
80  9225.25  8587.446  9216.007  8532.12  8587.446 
100  9225.25  8587.446  9216.007  8532.12  8587.446 
120  9225.25  8587.446  9216.007  8532.12  8587.446 
140  9225.25  8587.446  9216.007  8532.12  8587.446 
160  9225.25  8587.446  9216.007  8532.12  8587.446 
Notes
Acknowledgements
The authors are grateful to the reviewers for giving valuable suggestions to enhance the quality of the paper. We are all thankful to Mr. Ashok Kumar for proof reading the manuscript to enhance the quality.
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
References
 1.Meriot A (2016) Indian sugar policy: Government role in production, expansion and transition from importer to exporter. Sugar Expertise LLC for the American Sugar Alliance, ArlingtonGoogle Scholar
 2.Adamyan A, David H (2002) Analysis of sequential failure for assessment of reliability and safety of manufacturing systems. Reliab Eng Syst Saf 76(3):227–236CrossRefGoogle Scholar
 3.Gupta P, Lal AK, Sharma RK, Singh J (2007) Analysis of reliability and availability of serial processes of plasticpipe manufacturing plant: a case study. Int J Qual Reliab Manag 24(4):404–419CrossRefGoogle Scholar
 4.Mehmood R, Lu JA (2011) Computational markovian analysis of large systems. J Manuf Technol Manag 22(6):804–817CrossRefGoogle Scholar
 5.Garg H, Sharma SP (2012) A twophase approach for reliability and maintainability analysis of an industrial system. Int J Reliab Qual Saf Eng 19(3):1250013CrossRefGoogle Scholar
 6.Kumar V, Mudgil V (2014) Availability optimization of ice cream making unit of milk plant using genetic algorithm. Int J Res Manag Bus Stud 4(3):17–19Google Scholar
 7.Loganathan MK, Kumar G, Gandhi OP (2015) Availability evaluation of manufacturing systems using semiMarkov model. Int J Comput Integr Manuf 29(7):720–735. https://doi.org/10.1080/0951192x.2015.1068454 CrossRefGoogle Scholar
 8.Saini M, Kumar A (2018) Stochastic modeling of a singleunit system operating under different environmental conditions subject to inspection and degradation. Proc Natl Acad Sci India Sect A Phys Sci. https://doi.org/10.1007/s4001001805587 CrossRefGoogle Scholar
 9.Nailwal B, Singh SB (2012) Reliability and sensitivity analysis of an operating system with inspection in different weather conditions. Int J Reliab Qual Saf Eng 19(02):1250009CrossRefGoogle Scholar
 10.Neeraj A, Barak MS (2016) Profit analysis of a two unit cold standby system with preventive maintenance and repair subjected to weather conditions. Int J Stat Reliab Eng. https://doi.org/10.1007/s4187201800486 CrossRefGoogle Scholar
 11.Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar
 12.Kaufmann A (1975) Introduction to the theory of fuzzy subsets, vol 2. Academic Press, CambridgezbMATHGoogle Scholar
 13.Srinath LS (1994) Reliability engineering, 3rd edn. EastWest Press Pvt. Ltd, New DelhiGoogle Scholar
 14.Arora N, Kumar D (1997) Availability analysis of steam and power generation systems in the thermal power plant. Microelectron Reliab 37(5):795–799CrossRefGoogle Scholar
 15.Barabady J, Kumar U (2007) Availability allocation through importance measures. Int J Qual Reliab Manag 24(6):643–657CrossRefGoogle Scholar
 16.Kiureghian AD, Ditlevson OD (2007) Availability, Reliability & downtime of system with repairable components. Reliab Eng Syst Saf 92(2):66–72Google Scholar
 17.Garg S, Singh J, Singh DV (2009) Availability and maintenance scheduling of a repairable block board manufacturing system. Int J Reliab Saf 4(1):104–118CrossRefGoogle Scholar
 18.Rahman MM, Purbolaksono J, Ahmad J (2010) Root cause failure analysis of a division wall superheater tube of a coalfired power station. Eng Fail Anal 17(6):1490–1494CrossRefGoogle Scholar
 19.Kumar S, Tewari PC, Kuma S, Gupta M (2010) Availability optimization of CO_{2} Shift conversion system of a fertilizer plant using genetic algorithm technique. Bangladesh J Sci Ind Res (BJSIR) 45(2):133–140CrossRefGoogle Scholar
 20.Kumar S, Tewari PC (2011) Mathematical modelling and performance optimization of CO_{2} cooling system of a fertilizer plant. Int J Ind Eng Comput 2:689–698Google Scholar
 21.Adhikary DD, Bose GK, Chattopadhyay S, Bose D, Mitra S (2012) RAM investigation of coalfired thermal power plants: a case study. Int J Ind Eng Comput 3:423–434Google Scholar
 22.Goyal S, Grover S (2012) A comprehensive bibliography on effectiveness measurement of manufacturing systems. Int J Ind Eng Comput 3(2012):587–606Google Scholar
 23.Kumar R (2014) Availability analysis of thermal power plant boiler air circulation system using Markov approach. Decis Sci Lett 3(1):65–72CrossRefGoogle Scholar
 24.Khanduja R, Tewari PC, Gupta M (2012) Performance enhancement for crystallization unit of sugar plant using genetic algorithm technique. J Ind Eng Int 28(6):688–703Google Scholar
 25.HojjatiEmami K, Dhillon B, Jenab K (2012) Reliability prediction for the vehicles equipped with advanced driver assistance systems (ADAS) and passive safety systems (PSS). Int J Ind Eng Comput 3(5):731–742Google Scholar
 26.Aggarwal AK, Singh V, Kumar S (2014) Availability analysis and performance optimization of a butter oil production system: a case study. Int J Syst Assur Eng Manag 8(1):538–554Google Scholar
 27.Kumar A, Varshney AK, Ram M (2015) Sensitivity analysis for casting process under stochastic modelling. Int J Ind Eng Comput 6(2015):419–432Google Scholar
 28.Kadyan MS, Kumar R (2015) Availability and profit analysis of a feeding system in sugar industry. Int J Syst Assur Eng Manag 8(1):301–316Google Scholar
 29.Aggarwal AK, Kumar S, Singh V (2017) Mathematical modeling and fuzzy availability analysis for serial processes in the crystallization system of a sugar plant. J Ind Eng Int 13(1):47–58CrossRefGoogle Scholar
 30.Kumar P, Tewari PC (2017) Performance analysis and optimization for CSDGB filling system of a beverage plant using particle swarm optimization. Int J Ind Eng Comput 8(2017):303–314Google Scholar
 31.Kadyan MS, Kumar R (2017) Availability based operational behavior of BPan crystallization system in the sugar industry. Int J Syst Assur Eng Manag 8(2):1450–1460CrossRefGoogle Scholar
 32.Kumar A, Saini M (2017) Mathematical modeling of sugar plant: a fuzzy approach. Life Cycle Reliab Saf Eng. https://doi.org/10.1007/s4187201700380 CrossRefGoogle Scholar
 33.Dahiya O, Kumar A, Saini M (2019) An analysis of feeding system of sugar plant subject to coverage factor. Int J Mech Prod Eng Res Dev (IJMPERD) 9(1):495–508Google Scholar
 34.Dahiya O, Kumar A, Saini M (2019) Performance evaluation and availability analysis of a harvesting system using fuzzy reliability approach. Int J Recent Technol Eng 7(5):248–254Google Scholar
 35.Kumar R (2018) Availability and profit analysis of sugar industrial systems. Ph.D. thesis, Kurkushetra University Kurkushetra, IndiaGoogle Scholar
 36.Sahu O (2018) Assessment of sugarcane industry: suitability for production, consumption, and utilization. Ann Agrar Sci 16:389–395CrossRefGoogle Scholar
 37.Kumar A, Saini M (2018) Fuzzy availability analysis of a marine power plant. Mater Today Proc 5:25195–25202CrossRefGoogle Scholar