Question

A fast-food chain is examining the time customers spend waiting in line waiting to place their orders at its restaurants in the Hampton Roads area. Waiting times (expressed in minutes) were collected on 9 random days at 8 restaurants. Compute appropriate control limits to study this. Round and report all calculations to three decimal places.

Observation	1	2	3	4	5	6	7	8	9
1	4.20	5.85	9.30	4.75	10.12	13.38	9.18	10.72	8.67
2	11.47	11.55	10.82	12.27	9.24	13.68	10.23	13.34	8.34
3	14.38	15.48	5.50	11.35	11.26	13.83	11.17	8.36	5.45
4	9.59	13.60	9.37	14.70	10.34	7.50	12.01	5.54	12.56
5	12.58	8.98	7.35	7.86	7.67	13.00	10.32	0.69	10.61
6	13.89	11.54	16.31	14.49	9.37	13.81	7.82	14.65	11.14
7	16.23	12.19	9.59	9.61	7.95	11.14	13.42	11.92	11.10
8	9.82	11.42	11.16	8.66	8.86	11.14	12.55	9.63	12.98

Overall Mean =
Average Range =
A2 =
D3 =
D4 =
UCLx-bar =
LCLx-bar =
UCLR =
LCLR =

Answer 1

Observation - >	1	2	3	4	5	6	7	8	Mean	Range
Days (Below)
1	4.2	11.47	14.38	9.59	12.58	13.89	16.23	9.82	11.52	12.03
2	5.85	11.55	15.48	13.6	8.98	11.54	12.19	11.42	11.32625	9.63
3	9.3	10.82	5.5	9.37	7.35	16.31	9.59	11.16	9.925	10.81
4	4.75	12.27	11.35	14.7	7.86	14.49	9.61	8.66	10.46125	9.95
5	10.12	9.24	11.26	10.34	7.67	9.37	7.95	8.86	9.35125	3.59
6	13.38	13.68	13.83	7.5	13	13.81	11.14	11.14	12.185	6.33
7	9.18	10.23	11.17	12.01	10.32	7.82	13.42	12.55	10.8375	5.6
8	10.72	13.34	8.36	5.54	0.69	14.65	11.92	9.63	9.35625	13.96
9	8.67	8.34	5.45	12.56	10.61	11.14	11.1	12.98	10.10625	7.53
									10.56319	8.825556
									X- double bar(Above)	R-bar(Above)

Note: The days are taken vertically and observations in any day is taken horizontally. The calculations are done in the same manner.

Overall mean = 10.56319

Average Range = 8.825556

Below three values are taken from the referance charts of x-bar and r chart for the observations in one sample = 8

A2 = 0.373

D3 = 0.136

D4 = 1.864

UCL x-bar = Overall mean + A2 * r-bar = 10.563 + 0.373 * 8.825 = 13.8547

LCL x-bar = Overall mean - A2 * r-bar = 10.563 - 0.373 * 8.825 = 7.2712

UCLR = D4 * R-bar = 1.864 * 8.825 = 16.4498

LCLR = D3 *R-bar = 0.136 * 8.825 = 1.2002