Question

El toro grande restaurant advertises that customers will have their orders taken with three minutes of being seated. Management wants to monitor average times, as it is such an important guarantee for business. Construct x? - and s-charts for the data given in the worksheet pro07-05 in the ch07data.xlsx file for this chapter.

a. compute the sample means and the average standard deviation, calculate the control limits, and plot them on control charts.

b. does the process appear to be in statistical control? Why or why not?

c. calculate the process capability statistics, using three minutes as the upper tolerance limit and zero as the lower tolerance limit. What recommendation would you make to management concerning the process, based on your findings?

El Toro Grande Restaurante
1	1.22	1.54	1.53	1.86	1.49
2	1.48	1.18	1.41	1.29	1.61
3	2.12	1.76	1.29	1.78	1.74
4	1.34	1.22	1.29	1.69	1.42
5	1.11	1.21	1.34	1.95	1.22
6	0.73	1.97	1.51	1.67	1.77
7	1.20	1.46	1.05	1.14	1.80
8	1.72	1.58	1.79	1.95	0.83
9	1.23	1.39	1.57	1.49	1.58
10	0.70	0.94	1.14	1.54	1.81
11	1.50	1.83	1.60	1.15	1.79
12	1.72	1.61	1.63	1.84	1.95
13	1.64	1.13	1.60	1.87	1.36
14	0.73	1.39	1.39	1.85	1.86
15	1.72	1.42	1.59	0.70	1.55
16	1.91	2.08	1.64	1.77	1.60
17	1.63	1.57	0.95	2.02	1.69
18	1.53	1.47	2.05	1.19	1.52
19	1.18	1.78	1.37	1.53	1.30
20	1.74	2.14	1.24	0.92	1.34
21	1.47	1.89	1.53	2.28	1.84
22	1.68	1.35	1.26	1.58	1.63
23	0.99	1.57	1.45	1.50	1.98
24	1.92	1.01	0.93	1.68	1.96
25	2.15	1.57	1.75	1.72	1.63
26	1.13	0.99	1.27	1.35	1.37
27	1.87	1.74	0.89	1.61	1.77
28	0.99	1.36	0.89	1.54	2.01
29	1.75	1.96	1.57	1.67	2.31
30	1.59	2.15	1.68	1.42	1.50
31	0.93	1.65	1.29	1.02	1.48
32	1.40	1.98	1.54	0.97	1.62
33	1.69	1.62	1.47	1.81	0.97
34	1.98	1.26	1.32	1.17	1.39
35	1.73	1.42	2.06	1.27	1.34
36	1.45	1.57	1.70	1.32	1.26
37	1.98	1.61	1.45	1.46	2.19
38	1.46	1.46	1.70	1.56	1.93
39	1.80	1.34	1.46	1.91	1.10
40	1.04	1.29	1.30	1.77	1.13

Answer 1

(a) Step 1: Calculate X? and s (std deviation) for each subgroup. Excel formula AVERAGE() can be used for calculation of mean and STDEV() for standard deviation calculation

Sample	obs 1	obs 2	obs 3	obs 4	obs 5	Xbar	s
1	1.22	1.54	1.53	1.86	1.49	1.528	0.227
2	1.48	1.18	1.41	1.29	1.61	1.394	0.167
3	2.12	1.76	1.29	1.78	1.74	1.738	0.295
4	1.34	1.22	1.29	1.69	1.42	1.392	0.182
5	1.11	1.21	1.34	1.95	1.22	1.366	0.336
6	0.73	1.97	1.51	1.67	1.77	1.530	0.477
7	1.20	1.46	1.05	1.14	1.80	1.330	0.304
8	1.72	1.58	1.79	1.95	0.83	1.574	0.437
9	1.23	1.39	1.57	1.49	1.58	1.452	0.146
10	0.70	0.94	1.14	1.54	1.81	1.226	0.449
11	1.50	1.83	1.60	1.15	1.79	1.574	0.273
12	1.72	1.61	1.63	1.84	1.95	1.750	0.144
13	1.64	1.13	1.60	1.87	1.36	1.520	0.283
14	0.73	1.39	1.39	1.85	1.86	1.444	0.462
15	1.72	1.42	1.59	0.70	1.55	1.396	0.404
16	1.91	2.08	1.64	1.77	1.60	1.800	0.198
17	1.63	1.57	0.95	2.02	1.69	1.572	0.389
18	1.53	1.47	2.05	1.19	1.52	1.552	0.311
19	1.18	1.78	1.37	1.53	1.30	1.432	0.232
20	1.74	2.14	1.24	0.92	1.34	1.476	0.473
21	1.47	1.89	1.53	2.28	1.84	1.802	0.325
22	1.68	1.35	1.26	1.58	1.63	1.500	0.184
23	0.99	1.57	1.45	1.50	1.98	1.498	0.353
24	1.92	1.01	0.93	1.68	1.96	1.500	0.496
25	2.15	1.57	1.75	1.72	1.63	1.764	0.227
26	1.13	0.99	1.27	1.35	1.37	1.222	0.160
27	1.87	1.74	0.89	1.61	1.77	1.576	0.395
28	0.99	1.36	0.89	1.54	2.01	1.358	0.451
29	1.75	1.96	1.57	1.67	2.31	1.852	0.293
30	1.59	2.15	1.68	1.42	1.50	1.668	0.286
31	0.93	1.65	1.29	1.02	1.48	1.274	0.303
32	1.40	1.98	1.54	0.97	1.62	1.502	0.366
33	1.69	1.62	1.47	1.81	0.97	1.512	0.327
34	1.98	1.26	1.32	1.17	1.39	1.424	0.321
35	1.73	1.42	2.06	1.27	1.34	1.564	0.328
36	1.45	1.57	1.70	1.32	1.26	1.460	0.180
37	1.98	1.61	1.45	1.46	2.19	1.738	0.331
38	1.46	1.46	1.70	1.56	1.93	1.622	0.198
39	1.80	1.34	1.46	1.91	1.10	1.522	0.333
40	1.04	1.29	1.30	1.77	1.13	1.306	0.282

Step 2: Calculate and s?

(b) The process seem to be in statistical control (as explained above)

(c)

USL = 3 minutes

LSL = 0 minutes

Process mean, µ =1.5178

Process Standard Deviation, ? = sbar = 0.3082  

Process capability index, Cpk = MIN( (USL-µ)/3?, (µ-LSL)/3?)

= MIN( (3-1.5178)/(3*0.3082), (1.5178-0)/(3*0.3082) )

= MIN(

= MIN( 1.6031, 1.6416)

= 1.6031

Process capability ratio, Cp = (USL-LSL)/6? = (3-0)/(6*0.3082) = 1.6223