The efficiency of bi-directionally patrolled machines when repairs are not always successful

This paper solves the problem of calculating the effective rate of production of a set of N machines, under the care of one operative, whose method of working is to patrol the machines, first in one direction until all the machines have been inspected and then in the opposite direction, and so on. The time taken to walk from one machine to the next, and inspect and service that machine is assumed to be a constant and is called the walking time. If a machine is stopped when the operative reaches it he spends an additional constant repair time putting it in order before proceeding to the next machine. The problem arises in the practical context of a textile winding process in which the operative is a robot which is not always successful in its attempt to carry out a repair. The numerical results are of value in monitoring this process.