Problem Set 2: Statistical Process Control 1 . Whole Grains LLC uses statistical process control to ensure that their health-conscious, low-fat, multi-grain sandwich loaves have the proper weight of 6 oz. Over the past few days, they have taken five observations of four samples and have found the following. Construct the upper and control limits. Do the results suggest that the process is in control? Observations Loaf #1 Loaf #2 Loaf #3 Loaf #4 6.3 6.0 5.9 5.9 2 6.0 6.1 6.3 5.8 3 6.3 4.8 5.6 5.3 4 6.2 6.0 6.2 5.9 5 6.5 6.4 6.5 6.8 Totals 31.3 29.3 30 5 29.7 a. Determine the mean and range of each sample. b. Compute for the average mean and average range. c. From the table (Factors of three-sigma control limit for x and R charts), obtain A2, DA, and D3. d. Compute for the upper and lower limits. e. Determine if the results suggest that the process is in control. 2. A woodworker is concerned about the quality of the finished appearance of her work. She has finished a total of 50 unit split-willow hand-woven baskets. However, she has found the following number of finish defects in ten units sampled: 4, 0, 3, 1, 2, 0, 1, 2, 0, 2. a. Calculate the average number of defects per basket b. If 3-sigma control limits are used, calculate the lower control limit and upper control limit. 3. Suppose a process has been monitored daily for the last ten days and the number of machine failures each day was noted. The results follow: Day Number: 2 3 4 5 6 7 8 9 10 Number of Failures: 8 6 10 12 4 9 11 9 1 Compute control limits for a c-chart that monitors the average number of machine failures per day. Is the process in a state of control