In a car manufacturing company, an automated painting process has been introduced, and the quality assurance team suspects there might be issues that require investigation. The team decides to conduct a root cause analysis to identify potential problems. Through the root cause analysis and further investigation, it appears that the drying time of the paint in minutes is affecting the overall quality of the finish. The aspect they need to examine is the variation in drying time across different colours of paint. Considering the ongoing concerns in the painting process, the team chooses to collect a sample of six drying time measurements every 20 minutes from various colours of paint. The recorded drying time values for a day's production are presented in Table 1. A total of 10 sets of measurements, each consisting of six drying time values in minutes, have been collected. Each time a set of measurements is taken, the individual drying time values are recorded. Table 1: Drying Time Measurements Subgroup 1 2 3 4 5 6 1 12.5 12.3 12.6 12.4 12.2 12.7 2 11.8 11.6 11.9 11.7 11.5 12.0 3 13.2 13.0 13.3 13.1 12.9 13.4 4 10.9 10.7 11.0 10.8 10.6 11.1 5 12.0 11.8 12.1 11.9 11.7 12.2 6 13.8 13.6 13.9 13.7 13.5 14.0 7 11.3 11.1 11.4 11.2 11.0 11.5 8 12.7 12.5 12.8 12.6 12.4 12.9 9 10.5 10.3 10.6 10.4 10.2 10.7 10 11.9 11.7 12.0 11.8 11.6 12.1 Calculate the mean drying time and range for each subgroup, then compute the grand average drying time and grand range from all 10 subgroups.. Calculate the control limits for both the X-bar and R charts using the appropriate constants. Construct the X-bar and R control charts by using all the calculated data obtained in a) and b). Explain how the X-bar and R control charts help in monitoring the process.
In a car manufacturing company, an automated painting process has been introduced, and the quality assurance team suspects there might be issues that require investigation. The team decides to conduct a root cause analysis to identify potential problems. Through the root cause analysis and further investigation, it appears that the drying time of the paint in minutes is affecting the overall quality of the finish. The aspect they need to examine is the variation in drying time across different colours of paint.
Considering the ongoing concerns in the painting process, the team chooses to collect a sample of six drying time measurements every 20 minutes from various colours of paint. The recorded drying time values for a day's production are presented in Table 1. A total of 10 sets of measurements, each consisting of six drying time values in minutes, have been collected. Each time a set of measurements is taken, the individual drying time values are recorded.
Table 1: Drying Time Measurements
|
Subgroup |
1 |
2 |
3 |
4 |
5 |
6 |
|
1 |
12.5 |
12.3 |
12.6 |
12.4 |
12.2 |
12.7 |
|
2 |
11.8 |
11.6 |
11.9 |
11.7 |
11.5 |
12.0 |
|
3 |
13.2 |
13.0 |
13.3 |
13.1 |
12.9 |
13.4 |
|
4 |
10.9 |
10.7 |
11.0 |
10.8 |
10.6 |
11.1 |
|
5 |
12.0 |
11.8 |
12.1 |
11.9 |
11.7 |
12.2 |
|
6 |
13.8 |
13.6 |
13.9 |
13.7 |
13.5 |
14.0 |
|
7 |
11.3 |
11.1 |
11.4 |
11.2 |
11.0 |
11.5 |
|
8 |
12.7 |
12.5 |
12.8 |
12.6 |
12.4 |
12.9 |
|
9 |
10.5 |
10.3 |
10.6 |
10.4 |
10.2 |
10.7 |
|
10 |
11.9 |
11.7 |
12.0 |
11.8 |
11.6 |
12.1 |
- Calculate the mean drying time and range for each subgroup, then compute the grand average drying time and grand range from all 10 subgroups..
- Calculate the control limits for both the X-bar and R charts using the appropriate constants.
- Construct the X-bar and R control charts by using all the calculated data obtained in a) and b).
Explain how the X-bar and R control charts help in monitoring the process.
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