Below are sample means and standard deviations from ten samples, each of size n = 4.
(a) Suppose process standards μ = 6.0 and σ = 1.5 are provided. Find the standards given center line and control limits for an x chart. If these limits had been applied to the values in the table as they were collected, would there have been out-of-control signals?
(b) Using the standards in (a), find the standards given center line and control limits for an s chart. If these limits had been applied to the values in the table as they were collected, would there have been out of-control signals?
(c) Suppose that the standards in (a) were not available. Make retrospective x and s charts, and assess whether there is evidence of process instability in the values in the table.
(d) What is an estimate of σ based on the average sample standard deviation? Use this estimate and estimate the mean of a range for an additional sample of size n = 6.