Samples of six items are taken from a service process at regular intervals. A quality characteristic is measured and x̅ and R values are calculated from each sample. After 50 groups of size 6 have been taken we have x̅ = 40 and R̅ = 4. The data is normally distributed.

a. Compute control limits for the x̅ and R control charts. Do all points fall within the control limits?

b. Estimate the mean and standard deviation of the process. What are the ± 2 standard deviation limits for the individual data?

c. If the specification limits are 41 ± 5, do you think the process is capable of producing within these specifications?