Suppose a company has decided that both X-bar and R-charts s…

Suppose a company has decided that both X-bar and R-charts should be maintained on a certain quality aspect. At 12 different points in time, a sample of six units was taken.  The total of all 12 sample averages was 96, and the total of all 12 sample ranges was 30.  The initial (trial) upper control limit for the X-bar chart would be

Suppose you had an X-bar chart and an R-chart for some quali…

Suppose you had an X-bar chart and an R-chart for some quality aspect, as follows. The center line for the X-bar chart was 20, the upper control limit was 21.8, and the lower control limit was 18.2. The center line for the R-chart was 2.  The sample size is 7.  A quick and dirty estimate of the natural tolerances would be