The double sampling <i>S</i>² chart with estimated process variance

Abstract

This paper proposes useful exact bounds for the parameters of the double sampling S2 chart with known process variance and it also investigates the properties of the double sampling S2 chart with estimated process variance, in terms of the average run length, the standard deviation of the run length and the average sample size, providing a numerical comparison with the known process variance case. It also provides guidelines to systematically design the double sampling S2 chart both with known and estimated process variance and proposes two optimal design procedures with estimated process variance, for (a) minimizing the out-of-control average run length and (b) minimizing the out-of-control average sample size.