Samples of 12-volt batteries are taken at 30-minute intervals during a production run. Each sample consists of three batteries, and a technician records how long each battery will produce 400 amperes during a standard test. Given the following data, also listed in file XR20042, construct- 3-sigma mean, range control charts, and evaluate whether the process is in control.
Sample Battery1 Battery2 Battery3
1 13.3 9.4 12.1
2 12.2 13.4 8.5
3 11.2 8.2 9.2
4 7.8 9.7 10.0
5 10.1 11.4 13.8
6 9.9 11.7 8.5
Minutes
13.3
9.4
12.1
12.2
13.4
8.5
11.2
8.2
9.2
7.8
9.7
10.0
10.1
11.4
13.8
9.9
11.7
8.5
Please I need help, can you give the step to do this exercises.
Thank you very much.
As you can see, cutting and pasting does not work so well on the jiskha site. Sorry.
To construct the 3-sigma mean and range control charts for the given data and evaluate whether the process is in control, follow these steps:
1. Calculate the mean (average) and range for each sample:
- For each sample, calculate the mean by summing the values of the three batteries and dividing by 3.
- Calculate the range by finding the difference between the maximum and minimum values in each sample.
2. Calculate the overall mean and range:
- Calculate the mean of the sample means obtained in step 1.
- Calculate the range of the sample ranges obtained in step 1.
3. Calculate the standard deviation of the sample means and the sample ranges:
- Calculate the standard deviation of the sample means using the formula: σ_x̄ = R / d2, where R is the average range and d2 is a constant from the control chart factors table (usually 2.574 for sample size of 3).
- Calculate the standard deviation of the sample ranges using the formula: σ_R = R / d3, where R is the average range and d3 is a constant from the control chart factors table (usually 1.693 for sample size of 3).
4. Calculate the control limits for the mean and range charts:
- For the mean chart, the control limits are ±3 times the standard deviation of the sample means calculated in step 3.
- For the range chart, the control limits are ±3 times the standard deviation of the sample ranges calculated in step 3.
5. Plot the data on the control charts:
- For the mean chart, plot the sample means with a centerline at the overall mean and the control limits calculated in step 4.
- For the range chart, plot the sample ranges with a centerline at the overall range and the control limits calculated in step 4.
6. Analyze the control charts:
- Look for any points that fall outside the control limits on either chart. These indicate special causes of variation.
- Look for any patterns or trends in the data, such as consecutive points above or below the centerline or within the control limits. These may indicate common causes of variation.
7. Determine if the process is in control:
- If there are no points outside the control limits and no patterns or trends are present, the process is considered to be in control.
- If there are points outside the control limits or patterns/trends are present, the process may be out of control, and further investigation is needed to identify and address the causes of variation.
By following these steps, you can construct the 3-sigma mean and range control charts and evaluate whether the process is in control for the given data.