The Dynamics of Machine Servicing System

Abstract

Many of the daily events occur at random, and can be considered as time dependent discrete stochastic processes.
In this paper, as an example of discrete stochastic process, a machine service process, especially a machine being serviced by a single repairman is considered. By making use of the flow chart, the probability of the machine being in the working state or in the breakdown state is analyzed in the transient as well as in the stationary states.
As a result, it is proved that the probability of the working state when there is a man watching for the machine becomes 10∼15% higher than the probability when there is no man. The manner in which the repairman services the machine may greatly affect the total productivity and conseguently the profit. For example, it is proved that, in some relations between the pay of repairman per unit time and the yield of the machine per unit time, the total profits can be increased when the repairman is periodically hired much more than when he is hired at all times, although the breakdown probability in the former case becomes a little higher than that in the latter case.