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Detecting under-reported emissions. The Environmental
Chapter 13, Problem 19E(choose chapter or problem)
Detecting under-reported emissions. The Environmental Protection Agency (EPA) regulates the level of carbon dioxide (\(CO_2\)) emissions. Periodically these emissions measurements are under-reported due to leakage or faulty equipment. Such problems are often detected only by an expensive test (RATA) that is typically conducted only once per year. Just recently, the EPA began applying an automated control chart methodology to detect under-measurement of emissions data (EPRI CEM Users Group Conference, Nashville, TN, May 13, 2008). Each day, the EPA collects emissions data by measuring \(CO_2\) concentration for each of 6 randomly selected hours. The daily average \(CO_2\) levels for each of 30 days are shown in the table above. The EPA considers these values to truly represent emissions levels because the RATA test was recently performed and showed no problems with under-reporting. The lower and upper control limits for the averages were established as LCL = 12.26 and UCL = 13.76.
a. Construct a control chart for the daily average \(CO_2\) levels.
b. Based on the control chart, describe the behavior of the measurement process.
c. The following average \(CO_2\) levels were determined for a later 10-day period: 12.7, 12.1, 12.0, 12.0, 11.8, 11.7, 11.6, 11.7, 11.8, 11.7. Make an inference about the potential under-reporting of the emissions data for this 10-day period.
Daily Average CO2 Measurements for 30 Consecutive Days |
|||||||||||||
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
12.9 |
13.2 |
13.4 |
13.3 |
13.1 |
13.2 |
13.1 |
13 |
12.5 |
12.5 |
12.7 |
12.8 |
12.7 |
12.9 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
12.9 |
12.8 |
12.7 |
13.2 |
13.2 |
13.3 |
13 |
13 |
13.2 |
13.2 |
13.4 |
13.1 |
13.3 |
13.4 |
Questions & Answers
QUESTION:
Detecting under-reported emissions. The Environmental Protection Agency (EPA) regulates the level of carbon dioxide (\(CO_2\)) emissions. Periodically these emissions measurements are under-reported due to leakage or faulty equipment. Such problems are often detected only by an expensive test (RATA) that is typically conducted only once per year. Just recently, the EPA began applying an automated control chart methodology to detect under-measurement of emissions data (EPRI CEM Users Group Conference, Nashville, TN, May 13, 2008). Each day, the EPA collects emissions data by measuring \(CO_2\) concentration for each of 6 randomly selected hours. The daily average \(CO_2\) levels for each of 30 days are shown in the table above. The EPA considers these values to truly represent emissions levels because the RATA test was recently performed and showed no problems with under-reporting. The lower and upper control limits for the averages were established as LCL = 12.26 and UCL = 13.76.
a. Construct a control chart for the daily average \(CO_2\) levels.
b. Based on the control chart, describe the behavior of the measurement process.
c. The following average \(CO_2\) levels were determined for a later 10-day period: 12.7, 12.1, 12.0, 12.0, 11.8, 11.7, 11.6, 11.7, 11.8, 11.7. Make an inference about the potential under-reporting of the emissions data for this 10-day period.
Daily Average CO2 Measurements for 30 Consecutive Days |
|||||||||||||
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
12.9 |
13.2 |
13.4 |
13.3 |
13.1 |
13.2 |
13.1 |
13 |
12.5 |
12.5 |
12.7 |
12.8 |
12.7 |
12.9 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
12.9 |
12.8 |
12.7 |
13.2 |
13.2 |
13.3 |
13 |
13 |
13.2 |
13.2 |
13.4 |
13.1 |
13.3 |
13.4 |
ANSWER:
Step 1 of 4
Here we have the data on the daily average 
and upper control limits are given as LCL = 12.26 and UCL = 13.76 .
a) Using software, we construct a control chart for the given daily average
levels as follows:
