Controlling the Standard Deviation by Cusums and Warning Lines

Abstract

The usual process inspection scheme for controlling the standard deviation (S.D.) of a normal distribution is to plot a Shewhart chart on which are recorded the ranges of small samples; a common size is 5 items. Action is taken if any sample range exceeds a previously determined amount. The rapidity with which the scheme detects a departure from the accepted value of σ can be increased by considering the results of several of the latest samples together. A fixed number of samples can be taken into account by Warning Lines on the Shewhart-type chart (4); a more sensitive scheme uses cumulative sums (cusums) of the sample ranges together with a rule for deciding what change of direction of the cusum path should require action. Both these approaches can be applied to gauged observations. In this paper we compare these four schemes and provide a short table of cusum schemes using the range.