The three most important quality attributes at Mike€™s Super Service fast-food restaurant are considered to be good food, fast service, and a clean environment. The restaurant manager uses a combination of customer surveys and statistical measurement tools to monitor these quality attributes. A national marketing and research firm has developed data showing that when customers are in line up to five minutes their perception of that waiting time is only a few minutes; however, after five minutes customer perception of their waiting time increases exponentially. Furthermore, a five-minute average waiting time results in only 2% of customers leaving. The manager wants to monitor speed of service using a statistical process control chart. At different times during the day over a period of several days the manager had an employee time customers€™ waiting times (from the time they entered an order line to the time they received their order) at random, with the following results:

a. Develop an xˉ-chart to be used in conjunction with an Rchart to monitor speed of service and indicate if the process is in control using this chart.
b. Management at Mike€™s Super Service Drive-In restaurant wants customers to receive their orders within 5 minutes ±1 minute, and it has designed its ordering and food preparation process to meet that goal. Using the process mean and control limits developed in (a), compute the process capability ratio and index, and indicate if the process appears to be capable of meeting the restaurant€™s goal for speed ofservice.

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Walting Times (min) Sample1 2 3 5 6 6.3 27 5 3.9 57 5.9 3.8 6.2 55.1 7 5.3 5.6 6.2 505.3 4.9 3.9 7.2 64574.2 1 46 3.9 5 48 5.6 6.0 5.5 63 52 7 8. 59 6.1 73 65 59 5.7 84 2.2 36 5753 56 5.0 6.5 4.7 5 9.3 62 53 47 5.8 54 5 5.0 59 34 2.9 16 48 6.1 53 4.5 6.3 54 57 2.1 34 74 3.9 42 4.9 5.6 37 5.7 53 37 58 57 6.0 3.6 24 54 5.53.9 13