The Psychology of Quality and More

Calculation detail for X-bar/R Control Charts

1. Calculate basic averages (X- bar) from measured values, averaging the values in each subgroup and also measuring the range, R (the maximum minus the minimum values in the subgroup). Then average these averages to give the grand average (X-double bar) and the average range (R-bar). The grand average and the average range give the central ‘average’ line in the X-bar and the R charts.

2. Calculate upper and lower control limits for each of the two charts. This requires the use of a ‘magic’ constants, A_2, D₃ and D₄, which are simply looked up in the table, based on the number of measures in each subgroup. The control limits are calculated then using the formulae as in Fig. 2.

 Calculating X-bar/R control limits

Next time: Calculation detail for X-bar/S Control Charts

This article first appeared in Quality World, the journal of the Institute for Quality Assurance