Setting up a Control Chart Using Subgroups of Varying Sizes

Abstract

Sometimes a control chart for X̄ and R is to be set up based on a number k = 20 to 30 subgroups that, it may turn out, are not all the same size. This causes no difficulties with respect to the calculation of the centerline for the X̄ chart. The centerline is found as the weighted average of the means of the subgroups, using the sample sizes as the weights. The same result can be obtained by summing all the observations and dividing by their number.

Estimation of the population standard deviation σ, however, poses a more difficult problem for which there are several solutions. One solution is to randomly discard observations so as to make all subgroup sizes equal to the smallest one. However, this is not recommended if more than about ten percent of the total number of observations have to be discarded. In what follows we shall discuss approaches that use all of the data at hand.

• Approximation
• Estimation
• Range
• Standard Deviation
• Variables Control Chart
• Variance