sum of the sample standard deviations for 25 subgroups of size 4

Question: A new process is started, and the sum of the sample…

A new process is started, and the sum of the sample standard deviations for 25 subgroups of size 4 is 750. If the specifications are 70080:

1. a) What is the process capability index?
2. b) What action would you recommend?
3. c) What is the Cpkvalue for this process when the process average is 700, 780, and 820? Explain and say in which case the process is centered.
4. d) Compute the rejection rates in each case of question c)
5. e) A four sigma program is introduces at the company. The lower specification limit (LSL) and the process σ remain the same. Describe the Cp and Cpk reject rates and show the X-bar and R chart limits, using the same sample size.
6. f) Repeat for a six sigma program with 1.5σ shift, with the process average and sigma remaining the same.