Question

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	Service Time (sec)
	Sample 1	Sample 2	Sample 3	Sample 4
1	200	150	175	113
2	120	85	105	75
3	83	93	130	150
4	68	117	145	175
5	110	90	75	105
6	102	65	115	125

Determine the upper control limit for an R-chart.

Answer 1

Range of sample 1 = 200-68 = 132
Range of sample 2 = 150-65 = 85
Range of sample 3 = 175-75 = 100
Range of sample 4 = 175-75 = 100

Average range of samples = R-bar = (132+85+100+100)/4 = 104.25

Upper control limit of the R-chart = D4*R-bar = 2.004*104.25 [for sample size 6, D4 = 2.004] = 208.917