# Mathematical modeling and reliability analysis of the serial processes in feeding system of a sugar plant

• Anil Kr. Aggarwal
• Sanjeev Kumar
• Vikram Singh
Original Article

## Abstract

In this paper, a numerical method is proposed for the reliability analysis of serial processes in the feeding system of a sugar plant. The feeding system is a complex system and comprises of four repairable sub-systems viz. cutting system, crushing system, bagasse carrying system and heat generating system arranged in series or parallel configurations. Three sub-systems namely cutting system, bagasse carrying system and heat generating system are supported by standby units with perfect switch over devices. Mathematical modeling of the system based on Markov birth–death process is carried out to derive Chapman–Kolmogorov differential equations. These equations are solved by using the proposed method i.e. an adaptive step-size control Runge–Kutta method. The long-run availability, reliability and mean time between failures (MTBF) for the system are computed for performance analysis of the system. These results are presented and discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the performance of the feeding system of sugar plant.

## Keywords

Markov birth–death process Chapman–Kolmogorov differential equations Reliability Long-run availability MTBF

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© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2015

## Authors and Affiliations

• Anil Kr. Aggarwal
• 1
Email author
• Sanjeev Kumar
• 2
• Vikram Singh
• 2
1. 1.Mechanical Engineering departmentRattan Institute of Technology & ManagementPalwalIndia
2. 2.Mechanical Engineering departmentYMCA University of Science & Technology (YMCAUST)FaridabadIndia