Mathematical Analysis of Reliability and Availability of Soap manufacturing Industry

Abstract

In the present work, a mathematical analysis of reliability and availability of neat soap manufacturing plant has been carried out. The reliability and availability analysis of this industry has not been satisfactorily tackled so far. The Govind Soap Industry, situated in Patiala, India is chosen for the present study. This is a medium size complex industry consisting of two main units namely neat soap production system and soap mixing and milling system. The neat soap production system is further divided into three subsystems namely crutcher, spray dryer, plodder but soap mixing and milling system contain four subsystems: screw conveyor, roll mill, amalgamator, and refining plodder. Mathematical formulation of the Chapman - Kolmogorov differential difference equation has been developed for determining the reliability and availability of neat soap manufacturing plant assuming constant failure and repair rates of each constant failure and repair rates of each subsystem. The system of differential equations thus obtained has been solved numerically using Runge - Kutta fourth order method for various combination of failure and repair rates of the subsystem and computed reliability of the manufacturing plant. The availability of the system has also been obtained by solving the steady state linear equations recursively. The reliability and availability of the neat soap manufacturing plant have been analysed with the actual data of failure and repair rates of the subsystems taken from the concerned industry. Certain conclusions based on the present analysis have also been drawn.