The effluent stream from a wastewater treatment process is monitored to make sure that two process variables, the biological oxidation demand (BOD) and the solids content, meet specifications. Representative data are shown in Table 21.4. Shewhart charts for the sample means

Question

Table 21.4 Wastewater Treatment Data

Sample Number	BOD (mg/L)	Solids (mg/L)
1	17.7	1380
2	23.6	1458
3	13.2	1322
4	25.2	1448
5	13.1	1334
6	27.8	1485
7	29.8	1503
8	9	1540
9	14.3	1341
10	26	1448
11	23.2	1426
12	22.8	1417
13	20.4	1384
14	17.5	1380
15	18.4	1396
16	16.8	1345
17	13.8	1349
18	19.4	1398
19	24.7	1426
20	16.8	1361
21	14.9	1347
22	27.6	1476
23	26.1	1454
24	20	1393
25	22.9	1427
26	22.4	1431
27	19.6	1405
28	31.5	1521
29	19.9	1409
30	20.3	1392

Accepted Answer

are shown in parts (a) and (b) of Fig. 21.8. These univariate control charts indicate that the process appears to be incontrol because no chart violations occur for either variable. However, the bivariate control chart in Fig. 21.8c indicates that the two variables are highly correlated, because the solids content tends to be large when the BOD is large, and vice versa.When the two variables are considered together, their joint confidence limit (e.g., at the 99% confidence level) is an ellipse, as shown in Fig. 21.8.1 Sample #8 lies well beyond the 99% limit, indicating an out-of-control condition. By contrast, this sample lies within the Shewhart control chart limits for both individual variables.
This example has demonstrated that univariate SPC techniques such as Shewhart charts can fail to detect abnormal process behavior when the process variables are highly correlated. By contrast, the abnormal situation was readily apparent from the multivariate analysis.

Question 21.5: The effluent stream from a wastewater treatment process is m...

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