THE EFFICIENCY OF N MACHINES UNI-DIRECTIONALLY PATROLLED BY ONE OPERATIVE WHEN WALKING TIME AND REPAIR TIMES ARE CONSTANTS

SUMMARY THE solution is given to the problem of determining the efficiency of N machines looked after by an operative who walks round them in one direction, always taking the same time to walk to a given machine from the previous one and to inspect it and service it (we call this overall time the "walking time"), and then, if the machine has stopped, taking a fixed time to repair it. neglecting these points, Ashcroft (1950) gives the efficiency for variable repair times and extensive tables for constant repair times. Benson & Cox (1951) give further details for distributed repair times and groups of machines attended by teams of operatives, and they also discuss the problem of ancillary work, that is work other than the repair of stopped machines. They deal approximately with what they call "spread" ancillary work (which we call "servicing") by an adjustment of one of their parameters. These papers also assume that the operative attends to the machines in the order in which they stopped, and so any systematic patrolling is excluded. In the present paper we discuss a problem more realistic in some work study applications, though to do this we assume a regular patrolling system (somewhat different from that discussed by Brunnschweiler, 1954). The operative walks round the group of machines in a strictly defined order, and repairs and restarts any machines which are found stopped, passing after inspecting and/or servicing any machine which is running. We assume that the operative takes a fixed time to walk from a given machine to the next, (though this may be different for different pairs of machines) and that the repair or clearing times are constant for each stoppage and each machine. Further, we assume that the machines stop at random with the same mean frequency and indepen- dently of each other. The difficulty in dealing with these problems lies in calculating the effect of "interference" which is the term sometimes used for the incidence of simultaneous stoppages at several machines. In fact, if the optimum number of machines is being controlled by one operative, interference will often be a marked feature. No simple or approximate treatment of the problem appears possible if account of interference is to be accurately taken; but with the above assumptions we have obtained formulae which are comparatively simple, are straightforward to compute, and are exact solutions. We also provide tables of the running efficiency, i.e. the percentage of running time to total (stopped + running) time; hence decisions can be made (by interpolation if necessary) with