Abstract
This paper shows how to predict the availability of machines which are maintained by a repairman (or robot) who patrols them in a systematic fashion. The identical machines may be arranged in a circle or in a line. The repairman patrols them either uni-directionally (circular or two adjacent lines layout) or bi-directionally (linear layout). The time to travel from one machine to the next is taken into account. With random breakdowns and constant repair times it is shown that the system can be modelled as a Markov chain. From this model it is possible to calculate the availability of the individual machines and compare the relative efficiency of the different arrangements and patrolling disciplines. This type of situation arises in many automated industrial processes. In some contexts the repairman is a robot and repairs are not always satisfactorily executed. This complication can be catered for and its effect on the availability calculated. Finally these same problems with two or more robots have been solved. The relative positions of the robots in order to obtain the maximum availability have been studied.
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