Question

The management of the Super Star Coffee 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 five 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 Time, Sec. Service Person Observation 1 Observation 2 Observation 3 Observation 4 150 2 85 3 4 5 230 120 88 110 115 150 90 65 199 105 145 75 115 90 75 175 105 125 a) Determine the upper and lower control limits for an X-bar chart and an R-chart with a sample size of 5.

Answer 1

# SAMPLE	1	2	3	4	5	AVERAGE	RANGE
1	230	120	88	110	115	132.6	142
2	150	85	150	90	65	108	85
3	199	105	145	75	115	127.8	124
4	90	75	175	105	125	114	100
AVERAGE						120.6	112.75

RANGE = LARGEST OBSERVATION - SMALLEST OBSERVATION

AVERAGE X = 120.6

AVERAGE R = 112.75

A2 FOR N = 5 = 0.577

D3 FOR N = 5 = 0, D4 = 2.115

FOR X

UCL X = X + (A2 * R) = 120.6 + (0.577 * 112.75) = 185.66

LCL X = X - (A2 * R) = 120.6 - (0.577 * 112.75) = 55.54

YES, SINCE ALL THE POINTS ARE WITHIN THE CONTROL LIMITS

FOR R

UCL R = R * D4 = 112.75 * 2.115 = 238.47

LCL R = R * D3 = 112.75 * 0 = 0

YES, SINCE ALL THE POINTS ARE WITHIN THE CONTROL LIMITS

2. YES, WE NEED CORRECTIVE ACTION BECAUSE FEW POINTS ARE OUTSIDE THE CONTROL LIMIT.

2.