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 47 1 150 230 120 2 3 4 5 88 110 115 85 150 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. b) After the control chart was established, a sample of five service personnel was observed, and the following customer service times in seconds were recorded: 289, 235, 105, 146, and 171. Is corrective action called for?

Answer 1

Answer a):

Service Person 1 2 3 4 5 Mean (X) 132.6 Range (R) 142 230 120 88 110 115 Observations Observation 1 Observation 2 Observation 3 Observation 4 150 85 150 90 65 108 85 199 105 145 75 115 127.8 124 90 75 175 105 125 114 100 112.75 120.6 i R

Based on the sample size, the Control chart constants are:

Sample size	5
A2	0.577
D3	0
D4	2.114

X-bar chart(X̅ chart) control limits:

UCL	X̿ + A2*R̅	185.66
LCL	X̿ - A2*R̅	55.54

Range Chart (R-chart) control limits:

UCL	D4*R̅	238.35
LCL	D3*R̅	0.00

Answer b):

The new observation is as under:

Observations	1	2	3	4	5	Mean (X̅)	Range (R )
Observation 5	289	235	105	146	171	189.2	184

Populate the data for X bar-chart:

Sample	1	2	3	4	5
Mean (X̅)	132.6	108	127.8	114	189.2
UCL	185.66	185.66	185.66	185.66	185.66
LCL	55.54	55.54	55.54	55.54	55.54
CL (X̿)	120.60	120.60	120.60	120.60	120.60

Plot the X bar-chart:

200 180 160 140 120 Mean (X) 100 UCL 80 LCL CL (X) 60 40 20 0 1 2. 3 4 5

Populate the data for Range chart (R-chart):

Sample	1	2	3	4	5
Range (R)	142	85	124	100	184
UCL	238.35	238.35	238.35	238.35	238.35
LCL	0.00	0.00	0.00	0.00	0.00
CL (R̅)	112.75	112.75	112.75	112.75	112.75

Plot the R-chart:

300 250 200 -Range (R) 150 UCL LCL 100 -CL (R) 50 0 1 2 3 4 5

Corrective action is required as the X-bar chart which was within range of control limit has breached the UCL for Observation 5. Thought the range chart is still in process control.