Steady State availability analysis of a Physical System: Sole lasting system of Shoe Industry

Vikas Modgil, Pardeep Singh, S.K. Sharma


This paper deals with the performance analysis of sole lasting system of a shoe industry using Markovian approach. The plant is divided into many sections like shoe upper manufacturing system, sole lasting system and sole pasting system. In the present work sole lasting system has been taken for performance analysis. The system consists of six subsystems namely, Toe Humidifier Machine, Toe Lasting Machine, Heel Humidifier Machine, Heel Lasting Machine, Heating Chamber Machine and Rubbing & Buffing machine. Failure and repair rates of these subsystems are assumed to be constant and exponentially distributed. A mathematical model pertaining to the real environment of shoe industry has been developed using Markov birth-death process.  The differential equations have been derived on the basis of probabilistic approach using transition diagram. These equations are solved using normalizing conditions and recursive method to derive out the steady state availability expression of the system i.e. system’s performance criterion. The results give system availability for different combinations of failures and repair rates for various subsystems.


Steady State Availability; Shoe industry; Sole Lasting System; Markov approach

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