[Chapter S6: 30 points ] Hospitals and health service centres across the Nation of Narnia have complaints about the " Oz delivery rate of masks for COVID-19 patients with mild symptoms that are manufactured by a local company. Every hospital allows some varian variation in the oxygen delivery rate, but theoretically, there should be none as the patients' health or life is at a stake. The quality control department at the manufacturing company feels that there is no problem with the %Oz delivery rate, which has been averaging just over 50% in terms of %02 delivered. The production department estimates that a considerable investment would be required to increase the %Oz delivery rate. These two operations management departments, after consulting with the marketing department and hospitals, suggest that a control chart be set up to monitor the %Oz delivery rate. Five observations (n=5) will be tested per day over nine days. Table 1 %O, delivery rate (day 1-9) Day #1 #2 #3 #4 #5 R 1 48.2 48.0 48.2 48.2 50.3 50.2 50.0 50.2 50.2 52.4 50.2 50.0 49.8 50.0 50.0 9.0 49.4 56.0 49.2 46.0 50.0 47.0 49.6 47.8 49.4 51.0 54.0 55.0 49.0 50.2 49.8 50.0 52.8 49.6 49.4 51.8 52.4 48.0 50.8 52.8 59.8 60.0 53.4 59.5 59.3 X = R = a) Use the data in Table 1 to calculate the averages, x, and the ranges, R, of these measurements for each sample (each day). Next, calculate the overall average, X , and the average range, R. b) Set up three-sigma control limits for average. Plot the data on the control charts and determine whether or not the averages for days 1-9 appear to be in control? c) Set up three-sigma control limits for range. Plot the data on the control charts and determine whether or not the ranges for days 1-9 appear to be in control? d) Based on your answers in (b) and (c) determine whether or not the process distribution is in control for days 1-9. Use Table 2 and the three-sigma control limits you developed for days 1-9 in (b) and (c) to determine whether or not the average, range and process distribution are in control for days 10-14. Table 2 %O, delivery rate (day 10-14) Day #1 #2 #3 #4 #5 X R 10 50.0 47.3 47.5 46.6 48.1 11 48.8 51.3 46.6 47.9 49.6 12 46.6 45.2 46.7 48.3 17.9 13 47.1 49.4 50.4 51.1 50.0 14 46.6 51.3 49.0 50.4 51.5 f) Suppose that the standard deviation of the process distribution is 2.0 for N95 masks. If the specifications for the %Oz delivery rate are 90 16 %Oz delivery rate, what are the upper and lower specification limits? The process is known to operate at a mean of 90 %Oz delivery rate. What are the Cp and Cpk for this process? Is the process capable of producing a three-sigma qualify? Why? Is the process capable of producing a six-sigma qualify? Why? If each nonconforming unit costs $0.02, and the daily volume is 600,000 units, what is the daily total cost of nonconforming units