repairable systems

performance measures

preventive maintenance

queue length

ruin probability

ruin probabilities

geometric process

repair times

optimal replacement

renewal processes

Journal of The Royal Statistical Society Series B-statistical Methodology

SUMMARY It is established in this note that the stationary probabilities of Palm's model for a large number of machines and repairmen (and the relation between them) can be approximated by a probability density, which is the “pasting together” of two normal densities with different variances. Further, this result is used to find o ( n ½ )‐optimal number of repairmen in the problem of minimization of the expected costs of production. In the last part of the paper, in connection with the investigation of the asymptotics of the operative efficiency, some results by Naor (1957) are discussed.

On Palm's Model with a Large Number of Machines and Repairmen