Chapter 10.2, Problem 1E

The quality-control plan for a certain production process involves taking samples of size 4. The results from the last 30 samples can be summarized as follows:

$\begin{array}{lll}{\displaystyle \underset{i=1}{\overset{30}{\sum }}{\bar{X}}_i=712.5}\hfill & {\displaystyle \underset{i=1}{\overset{30}{\sum }}{R}_i=143.7}\hfill & {\displaystyle \underset{i=1}{\overset{30}{\sum }}{S}_i=62.5}\hfill \end{array}$

1. a. Compute the 3σ control limits for the R chart.
2. b. Compute the 3σ control limits for the S chart.
3. c. Using the sample ranges, compute the 3σ control limits for the $\bar{X}$ chart.
4. d. Using the sample standard deviations, compute the 3σ control limits for the $\bar{X}$ chart.