Question

Problem 1. (25 points) To get full credit, please show all your work. 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 4 230 199 150 85 90 75 2 120 105 3 88 150 145 75 4 90 110 115 175 105 125 5 65 115 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

Service person	O1	O2	O3	O4	Mean(Sum of all observations/4)	Range(Max-Min)
1	230	150	199	90	167.25	140
2	120	85	105	75	96.25	45
3	88	150	145	175	139.5	87
4	110	90	75	105	95	35
5	115	65	115	125	105	60
					603	367
Xbar = Sum of Means/5=		120.6
Rbar=Sum of Ranges/5 =		73.4

Given sample size =5

(a)

3- Sigma control charts

For X bar chart

A2 =0.577

UCL = Xbar +A2*Rbar = 120.6 + 0.577*73.4 =120.6 + 42.35 =162.95

LCL =Xbar - A2*Rbar = 120.6 - 0.577*73.4 = 120.6 - 42.35 = 78.25

For Rbar Chart

D3 = 0 , D4 = 2.114

UCL = D3*Rabr =0*73.4 =0

LCL = D4* Rbar = 2.114 * 73.4=155.17

(b)

Given five observations are 289 ,235,105,146 and 171 .

Out of 5 observations 3 ( 289,235,171) are out of Upper control limit . Therefore the process needs a corrective action.