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) Mean and Standard Deviation is calculated by Excel formula AVERAGE() and STDEV() as below

(b) Control limits are computed below. and Control charts are shown

(c) Process average, = 1.5178

Process standard deviation, s = 0.3082

Upper Specification Limit, USL = 3 minutes

Lower Specification Limit, LSL = 0

Process capability index, Cpk = MIN((USL-)/3s, ( - LSL)/3s) = MIN((3-1.5178)/(3*0.3082), (1.5178-0)/(3*0.3082))

= MIN( 1.603072, 1.641575)

= 1.606072

Process capability ratio, Cp = (USL-LSL)/3s = (3-0)/(6*0.3082) = 1.622143