32 333333333 766 774 779 781 773 777 773 777 786 774 34 789 783 771 775 782 35 782 778 766 769 767 36 773 782 767 773 770 37 783 769 777 777 761 38 782 782 780 770 772 39 782 770 770 774 775 40 777 769 780 768 779 Answer the following questions regarding this manufacturing process: 1. Construct and interpret X-bar and R controls. If the process is not stable, revised control limits need to be recalculate. Use the single criteria that points are supposed to be within the control limits. 2. Construct a histogram of the 200 individual measurements. Comment on the shape of the histogram to see if approximately a normal distribution assumption is valid. 3. What proportion of the observed measurements is above the upper specification limit? Below the lower specification limit? 4. Give values of the estimated process potential, C, and process performance, Cpk indices using the standard deviation estimated out of the overall 200 measurements. 5. What is the predicted (expected) proportion of future measurements that will be above the upper specification limit? Below the lower specification limit? Use the standard deviation estimated out of the overall 200 measurements. 6. Give values of the estimated process potential, C, and process performance, C indices using the standard deviation estimated out of the average subgroup R range, 7. What is the predicted (expected) proportion of future measurements that will be above the upper specification limit? Below the lower specification limit? use the standard deviation estimated out of the average subgroup range R 8. Is there much difference between your answer in parts (4) and (5) compared to those in (6) and (7). 9. Summarize your findings in an executive summary that would be read by a person in management. You may include any graphs that may help management understand what is happening with this process. (must be printed in a Word processor)