Please can you give me the step to do this exercise? Thank you
Samples of 12-volt batteries are taken at 30-minute intervals during a production run. Each sample consists of 3 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 and range control charts and evaluate whether the process is in control.
Minutes Sample Battery1 Battery2 Battery3
13.3 1 13.3 9.4 12.1
9.4 2 12.2 13.4 8.5
12.1 3 11.2 8.2 9.2
12.2 4 7.8 9.7 10.0
13.4 5 10.1 11.4 13.8
8.5 6 9.9 11.7 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
The "following data" does not show up with your question.
Minutes Sample Battery Battery Battery
$ e 1 2 3
13.3 1 13.3 9.4 12.1
9.4 2 12.2 13.4 8.5 12.1 3 11.2 8.2 9.2
12.2 4 7.8 9.7 10.0
13.4 5 10.1 11.4 13.8
8.5 6 9.9 11.7 8.5
11.2
8.2
Thank you drwls (this is the second part of the exercise)
To construct a 3-sigma mean and range control chart and evaluate whether the process is in control, you need to follow these steps:
Step 1: Calculate the mean and range for each sample
- Take each group of three batteries and calculate the mean of their values.
- Calculate the range for each group by subtracting the smallest value from the largest value.
Step 2: Calculate the overall mean and overall average range
- Find the mean of all the sample means calculated in Step 1.
- Calculate the average range by finding the mean of all the ranges calculated in Step 1.
Step 3: Calculate the control limits for the mean chart
- Determine the standard deviation of the sample means.
- Multiply the standard deviation by 3, and add/subtract this value to/from the overall mean calculated in Step 2 to get the upper and lower control limits.
Step 4: Calculate the control limits for the range chart
- Determine the standard deviation of the sample ranges.
- Multiply the standard deviation by 3, and add/subtract this value to/from the overall average range calculated in Step 2 to get the upper and lower control limits.
Step 5: Plot the control charts
- Create a graph with the sample number on the x-axis and the mean value on the y-axis for the mean chart.
- Plot the mean values calculated in Step 1 on the graph.
- Draw horizontal lines at the upper and lower control limits determined in Step 3.
- Repeat the same process for the range chart, plotting the range values calculated in Step 1.
Step 6: Evaluate whether the process is in control
- Look for any points that fall outside the control limits on either chart.
- If any points fall outside the control limits, it indicates that the process is out of control and further investigation is needed.
- If all points fall within the control limits, the process is considered to be in control.
Following these steps will help you construct the 3-sigma mean and range control charts and evaluate whether the process is in control for the given data.