Specialized Control Charts

Multiple Components of Variation

See SHWMULTC in the SAS/QC Sample Library

In the preceding section, the excessive variation in the conventional Shewhart chart in Figure 49.1 is the result of positive autocorrelation in the data. The variation is "excessive" not because it is due to special causes of variation, but because the Shewhart model is inappropriate. This section considers another form of departure from the Shewhart model; here, measurements are independent from one subgroup sample to the next, but there are multiple components of variation for each measurement. This is illustrated with an example involving two components.^*

A company that manufactures polyethylene film monitors the statistical control of an extrusion process that produces a continuous sheet of film. At periodic intervals of time, samples are taken at four locations (referred to as lanes) along a cross section of the sheet, and a test measurement is made of each sample. The test values are saved in a SAS data set named FILM. A listing of FILM is shown in Figure 49.7.

sample	lane	testval
1	A	93
1	B	87
1	C	92
1	D	78
2	A	87
2	B	83
2	C	79
2	D	77
3	A	88
3	B	88
3	C	73
3	D	79
4	A	80
4	B	83
4	C	76
4	D	72
5	A	91
5	B	99
5	C	90
5	D	79
6	A	89
6	B	89
6	C	92
6	D	83
7	A	92
7	B	93
7	C	93
7	D	85
8	A	83
8	B	95
8	C	80
8	D	87
9	A	79
9	B	85
9	C	91
9	D	85
10	A	84
10	B	96
10	C	91
10	D	83
11	A	89
11	B	95
11	C	90
11	D	93
12	A	90
12	B	94
12	C	93
12	D	91
13	A	102
13	B	104
13	C	103
13	D	89
14	A	93
14	B	98
14	C	88
14	D	83
15	A	85
15	B	99
15	C	91
15	D	83
16	A	83
16	B	95
16	C	90
16	D	80
17	A	92
17	B	98
17	C	88
17	D	84
18	A	88
18	B	98
18	C	91
18	D	86
19	A	88
19	B	95
19	C	94
19	D	84
20	A	89
20	B	83
20	C	90
20	D	76
21	A	82
21	B	91
21	C	96
21	D	82
22	A	83
22	B	88
22	C	89
22	D	85
23	A	88
23	B	98
23	C	85
23	D	85
24	A	88
24	B	101
24	C	93
24	D	88
25	A	93
25	B	103
25	C	103
25	D	85
26	A	101
26	B	99
26	C	96
26	D	84
27	A	88
27	B	97
27	C	97
27	D	87
28	A	86
28	B	90
28	C	90
28	D	78
29	A	91
29	B	93
29	C	90
29	D	86
30	A	85
30	B	98
30	C	93
30	D	86
31	A	75
31	B	76
31	C	82
31	D	72
32	A	76
32	B	80
32	C	78
32	D	75
33	A	78
33	B	85
33	C	71
33	D	72
34	A	74
34	B	84
34	C	87
34	D	83
35	A	90
35	B	99
35	C	93
35	D	89
36	A	87
36	B	83
36	C	94
36	D	88
37	A	94
37	B	92
37	C	89
37	D	90
38	A	158
38	B	174
38	C	187
38	D	90
39	A	88
39	B	88
39	C	93
39	D	98
40	A	87
40	B	108
40	C	104
40	D	85
41	A	107
41	B	83
41	C	76
41	D	81
42	A	93
42	B	99
42	C	94
42	D	83
43	A	84
43	B	103
43	C	91
43	D	88
44	A	97
44	B	95
44	C	88
44	D	81
45	A	94
45	B	105
45	C	98
45	D	98
46	A	94
46	B	102
46	C	100
46	D	95
47	A	96
47	B	110
47	C	101
47	D	95
48	A	92
48	B	88
48	C	90
48	D	95
49	A	93
49	B	97
49	C	95
49	D	93
50	A	76
50	B	93
50	C	84
50	D	75
51	A	78
51	B	97
51	C	97
51	D	89
52	A	85
52	B	97
52	C	86
52	D	82
53	A	88
53	B	80
53	C	92
53	D	94
54	A	87
54	B	88
54	C	94
54	D	78
55	A	89
55	B	83
55	C	80
55	D	91
56	A	88
56	B	95
56	C	78
56	D	75

Figure 49.7: Polyethylene Sheet Measurements in the Data Set FILM

Preliminary Examination of Variation

Determining the Components of Variation

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