The management of the Diners Delight franchised restaurant chain is in the process of establishing quality-control charts for the time that its service people give to each customer. Management thinks the length of time that each customer is given should remain within certain limits to enhance service quality. A sample of six service people was selected, and the customer service they provided was observed four times. The activities that the service people were performing were identified, and the time to service one customer was recorded as noted below:
Service Person Sample 1 Sample 2 Sample 3 Sample 4
1 200 150 175 90
2 120 85 105 75
3 83 93 130 150
4 68 150 145 175
5 110 90 75 105
6 115 65 115 125
a. After the control chart was established, a sample of six service personnel was observed, and the following customer service times in seconds were recorded: 180, 125, 110, 98, 156, and 190. Is corrective action called for?
b. Determine the upper and lower control limits for an X-chart and an R -chart with a sample size of 6.