QUESTION 1: (a) Explain the differences between X-bar and R-charts. When should they be used and why is it important to use them together? [7 marks) (b) A manager at a Restaurant is concerned with complaints from customers about its drive-through window operation. Customers complain that it sometimes takes too long to be served and since there are cars in front and back of a customer, they cannot leave the service is taking a long time. To correct this problem the Restaurant installed an intercom system so the drive-through window cashier can call for assistance if the line backs up or a customer has unusually long transaction. The Restaurant's objective is an average customer's waiting time and service time of approximately three minutes. The Restaurant's operations manager wants to monitor the new drive-through window system with Statistical Process Control (SPC). The manager has timed five customers' waiting and service times at random for twelve days as follows: # of sompes S, Scomple E12 Table 1 Sizin Sample 1 2 3 4 5 6 7 8 9 10 11 12 Observation times (min) 1 2 3 4 3.05 6.27 1.35 2.56 7.21 1.50 2.66 3.45 3.12 5.11 1.37 5.20 2.96 3.81 4.15 5.01 3.25 3.11 1.63 1.29 2.47 2.98 2.15 1.88 6.05 2.03 3.17 3.18 1.87 2.65 1.98 2.74 3.33 4.15 8.06 2.98 2.61 215 3.80 3.05 3.52 5.66 1.18 3.45 3.18 7.73 2.06 1.15 5 1.05 3.78 2.65 2:15 3.74 495 2.34 3.63 3.05 3.16 2.07 3.11 (1) Develop X-bar and R-charts for the process [11 marks] (ii) What is your comment on the process based on your developed charts? [7 marks] 00