Summary (A systematic comparison of the statistical properties of present‐day sampling schemes).A survey of various sampling schemes, carried out with the aid of the, random walk diagram, ‘leads to the conception that it must be possible to effect the same degree of inspection by the application of different schemes. The degree of inspection of a scheme is contained in its, operating characteristic’, which is specified by two constants viz:its centre q0, for which P = 1/2, and its slope s in this point, defined bys= ‐(dP/dq)q=q0.It is shown that, if the operating characteristics of two different sampling schemes possess the same values of q0and s, the two characteristics are almost completely coincident. Thus two sampling schemes having the same q0and s will give identical inspection performances, and are consequently defined as, equivalent. ‘And by comparing the average sample sizes of equivalent schemes we may compute their relative efficiency’. For each set of values q0and s it is possible to construct a single sampling scheme possessing these characteristics. Hence to any scheme whatever there will correspond an, equivalent single sampling scheme, and, by adopting the single sampling scheme as a standard of reference, we may arrive at a general definition of efficiency.By the introduction of q0and s the formulae relating to the sequential sampling scheme are greatly simplified, and for each set of values q0and s there is one corresponding sequential scheme.By discussing a particular example of the double sampling scheme it is shown that the methods developed in this paper can successfully be applied to a systematic treatment of the variety of schemes now