The National Bank of Warwick 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 often cars in front and back of a customer, they cannot leave if the service is taking a long time. To correct this problem the bank installed an intercom system so the drive-through window teller can call for assistance if the line backs up or a customer has an unusually long transaction. The bank€™s objective is an average customer€™s waiting and service time of approximately 3 minutes. The bank€™s operations manager wants to monitor the new drive-through window system with SPC. The manager has timed five customers€™ waiting and service times at random for 12 days as follows:

Develop an -chart to be used in conjunction with an R-chart to monitor this drive-through window process and indicate if the process is in control using thesecharts.

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Observation Times (min) Sample1 3.05 671.35 7.21 2.56 1.05 3.78 1 1.50 2.66 345 3 3.12 5.11 37 5.20 2.65 2.96 3.81 15 5.01 2.15 3.25 3.11 63 1.29 3.7 247 2.98 2.15 188 4.95 6.05 2.03 3.17 3.18 2.34 1.87 2.65 98 274 3.63 3.33 415 8.06 2.98 3.05 261 2.15 3.80 3.05 3.16 3.52 5.66 1.18 3.45 2.07 3.18 7.73 2.06 .15 3.11 12