Problem 1 Widgets are made in a two- shift operation. Management is wondering if there is any difference in the proportion of defectives produced by these two shifts. They suspect that the second shift has a higher rate of defectives, since the workforce is not as highly trained, and supervision may be lacking. Management wants to use p control chart to determine if there is any difference between the two shifts. a. On the first shift, 12 samples of 50 units have been used and the proportions of difference were found as: .01, .03, .01, .03, .01, .02, .02, .03, .03, .03, .00, and .02. Calculate CL, UCL, LCL for the first shift. b. On the second shift, 100 units were selected, and 9 mistakes were found. Discuss in detail if the process mean shifted upward or downward? Why or why not.

Problem 2 A soda manufacturing company wants to use control charts to maintain and test the accuracy of measurements at its filling station. Thirty random samples, each containing 6 cans, were taken in a control chart application and it was found that the grand average is = 12.14 oz and = 0.3. a. Determine the upper and lower control limits for the and R charts. (7) b. The following measurements are taken last week: 12.7, 12.4, 11.8, 12.6, 12.5 and 12.4. Is the process still in control? Provide complete logic for your answer. (3)