1. 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:
30 i=1 Xi = 712.5
30 i=1 Ri = 143.7
30 i=1 si = 62.5

a. Compute the 3σ control limits for the R chart.

b. Compute the 3σ control limits for the S chart.

c. Using the sample ranges, compute the 3σ control limits for the X chart.

d. Using the sample standard deviations, compute the 3σ control limits for the X chart.