Continue in the context of problem 1, except now assume that no target values for the critical dimension or process standard deviation have previously been established. The average of the r = 40 subgroup averages was 3.9 cm, the average of the subgroup ranges was .56 cm, and the average of the 40 subgroup standard deviations was .48 cm.
(a) Find control limits and center line to assess the consistency of "hourly variation" quantified as subgroup ranges.
(b) Find control limits and center line to assess the consistency of process aim hour to hour based on subgroup averages. (Estimate the "withinhour" standard deviation based on subgroup ranges.)
(c) Repeat (a), except now use the subgroup standard deviations instead of ranges.
(d) Repeat (b), except now use the subgroup standard deviations to estimate the "within-hour" standard deviation.
(e) Suppose that none of the charts in (a) to (d) suggest lack of process stability (so that it makes sense to talk about a single process mean and single process standard deviation). Give a valid estimate of the process average distance from the container bottom to the handle. Give two valid estimates of the standard deviation of the distance from the container bottom to the handle. (Provide both the formulas you use and numerical answers.)