The requirements is in the appendix.

To answer the question, is this a good process in questions one and two below, you have to think about (calculate) how many units/proportion of units produced, would be produced out of tolerance. It would be the summation of the two tails which are equal when the mean of the process is centered over the required mean.

1. If the specifications for a shaft were 30 mm +/- .003 mm and the standard deviation (SD) of the process is .0008, what sigma process do you have and what is the Cp index? Is this a good process?

1. If the specifications for a shaft were 30 mm +/- .003 mm and it is 4 sigma process, what is the SD and Cp index of the process? Is this a good process?

1. If a process has a 1.3 Cp index with a standard deviation of .0001 and the diameter of a shaft is 2 inches, what are UTL, LTL, UCL, and LCL?

1. If a process was a 5 sigma process and the specifications for the product are .5” +/-.00001”, and the mean of the process has shifted 1.25 SD above the desired mean, what is the current Cpk? Is the process producing any out of tolerance products at this point, if so, what proportion?
   

2. If both type one and two errors are expensive, what would you do from a control perspective to minimize both types of errors?