Question

The data for 30 samples of 5 measurments each were collected from a process at Hawkeye Plastics. They've asked you to create an x_bar chart and an s-chart for the process and to interpret the results for them.

a) What vallues will be used for the centerline, upper control limit, and lower control limit of each chart?

b) Creat the control charts.

c) Does the process appear to be in statistical control? Why or why not?

d) The specification for this process is 12.0 + or - 3.0. Does the process appear capable of meting specifications? Why or why not?

Sample		Data	(n = 5)
1	12.37	13.38	12.27	13.68	11.66
2	13.79	12.98	13.28	13.08	13.38
3	12.37	12.67	13.48	12.98	13.58
4	12.77	12.67	12.37	12.27	12.57
5	13.90	13.30	14.20	11.70	13.80
6	13.28	12.67	12.57	12.77	13.18
7	12.57	12.77	12.57	11.96	12.67
8	12.98	12.77	12.06	13.08	11.76
9	12.98	12.37	12.87	12.06	12.57
10	12.60	14.50	13.30	12.40	14.00
11	13.18	12.27	12.57	12.27	12.67
12	12.67	11.86	12.16	12.57	12.06
13	12.77	12.67	13.18	12.37	12.27
14	12.57	12.06	12.37	12.27	11.86
15	14.40	12.40	14.10	12.50	13.08
16	12.67	11.66	13.08	11.66	13.38
17	13.18	13.38	13.08	12.47	12.98
18	13.08	13.58	12.16	13.89	12.67
19	12.16	12.57	11.56	12.47	12.67
20	13.30	13.90	11.50	14.60	13.00
21	11.86	13.18	11.66	13.18	12.67
22	12.98	12.67	12.27	12.77	12.77
23	12.06	11.76	12.67	12.87	12.77
24	12.47	12.57	12.47	12.37	12.37
25	11.70	13.60	13.50	14.20	13.08
26	12.57	12.67	11.76	12.16	12.27
27	13.38	12.06	12.67	12.06	11.86
28	12.67	12.27	12.27	12.37	12.67
29	11.86	11.86	13.08	13.08	12.06
30	12.37	13.08	13.68	12.57	12.98

Answer 1

For n= 5,

B3	B4	A3
0	2.089	1.427

= Average of the entire sample = 12.723

Standard deviation, s is caluclated for all the 30 samples.

Average of the standard deviation, = 0.530

UCL = + A3   = 12.723 + (1.427*0.530) = 13.47860

LCL = - A3  = 12.723 - (1.427*0.530) = 11.96686

CL = = 12.723

X bar S Chart :

S chart

s	UCL = B4s	LCL = B3s	CL =
0.8358	1.1065	0	0.530
0.3153	1.1065	0	0.530
0.5176	1.1065	0	0.530
0.2074	1.1065	0	0.530
0.9935	1.1065	0	0.530
0.3167	1.1065	0	0.530
0.3174	1.1065	0	0.530
0.5866	1.1065	0	0.530
0.3736	1.1065	0	0.530
0.8961	1.1065	0	0.530
0.3741	1.1065	0	0.530
0.3443	1.1065	0	0.530
0.3600	1.1065	0	0.530
0.2750	1.1065	0	0.530
0.9149	1.1065	0	0.530
0.7985	1.1065	0	0.530
0.3402	1.1065	0	0.530
0.6929	1.1065	0	0.530
0.4486	1.1065	0	0.530
1.1589	1.1065	0	0.530
0.7191	1.1065	0	0.530
0.2616	1.1065	0	0.530
0.4880	1.1065	0	0.530
0.0837	1.1065	0	0.530
0.9372	1.1065	0	0.530
0.3609	1.1065	0	0.530
0.6237	1.1065	0	0.530
0.2049	1.1065	0	0.530
0.6370	1.1065	0	0.530
0.5076	1.1065	0	0.530

c)

According to the Xbar S chart the process is under control.

WIth reference to teh S bar chart, The sample 20 is out of control.

D)

The specification limit is higher than the control limit. The process is capable of meeting the specifications.