A note on moving ranges

Corresponding to moving ranges we may speak of moving maxima and minima which analogously to charts of ordinary maxima and minima (Howell, 1949) are capable of application to quality control. This note deals with some properties of moving ranges, maxima and minima. In particular, an expression is obtained for the correlation between two ranges in overlapping samples in terms of means, variances and covariances of order statistics. For a normal parent population this result is applied to the determination of the efficiency of w1(n). The distribution of runs of equal ranges, which tend to occur in moving range charts, is also briefly discussed. It is realized that these devices have not been used widely and this study is offered in the hope that a clearer understanding of the methods and properties may