Testing control chart subgroups for rationality

Abstract

AbstractOne of the key issues in statistical process control (SPC) is the forming ‘rational subgroups’. Rational subgroups are defined as Subgroups displaying only random within‐variation. Subgroups having small within‐variation to compare with variation between subgroups. In a previous paper1 we developed an approach of choosing the proper subgroup size for control charts for statistical process control. The approach is particularly appropriate for batch industries where some batch‐to‐batch variation is to be expected and should be accommodated. In this paper we will deal with the question of whether or not subgroups are rational. A randomness test can be used to verify rationality. The measure selected is the ratio of several different variance estimators. An example is provided to demonstrate the application of the measure.