The present note is contributed, not because the numerical results obtained will be of use to actuaries, but in the belief that the methods adopted may be of interest to students as illustrating the application of the concepts of theoretical statistics to a problem which arose in practice.

The theory and technique of statistical Quality Control have been described by H. C. H. Carpenter in J.S.S. Vol. v, 1946, p. 207, and it is shown there how the control lines inserted on the charts are based on the assumption of a normal distribution.