Create a Control Chart
Control charts are an efficient way of analyzing performance data to evaluate a process. Control charts have many uses; they can be used in manufacturing to test if machinery are producing products within specifications. Also, they have many simple applications such as professors using them to evaluate tests scores. To create a control chart, it is helpful to have Excel; it will simplify your life.
Contents
Steps
- Check to see that your data meets the following criteria:
- Data should usually be normally distributed revolving around a mean (average).
- In the example below, a bottle company fills their bottles to 16 oz. (mean); they are evaluating if their process is “in-control”. The amount in ounces over 16 oz. is normally distributed around the mean.
- Measurements need to be independent of one another.
- In the example, the measurements are in subgroups. The data in the subgroups should be independent of the measurement number; each data point will have a subgroup and a measurement number.
- Data should usually be normally distributed revolving around a mean (average).
- Find the mean of each subgroup.
- To find the mean, add all measurements in the subgroup and divide by the number of measurements in the subgroup.
- In the example, there are 20 subgroups and in each subgroup there are 4 measurements.
- To find the mean, add all measurements in the subgroup and divide by the number of measurements in the subgroup.
- Find the mean of all of the means from the previous step (X).
- This will give you the overall mean of all the data points.
- The overall mean will be the centerline in the graph (CL), which is 13.75 for our example.
- Calculate the standard deviation (S) of the data points (see tips).
- Calculate the upper and lower control limits (UCL, LCL) using the following formula:
- UCL = CL + 3*S
- LCL = CL – 3*S
- The formula represents 3 standard deviations above and 3 standard deviations below the mean respectively.
- Refer to the below chart with steps 7 through 10.
- Draw a line at each deviation.
- In the above example, there is a line drawn at one, two, and three standard deviations (sigma’s) away from the mean.
- Zone C is 1 sigma away from the mean (green).
- Zone B is 2 sigma away from the mean (yellow).
- Zone A is 3 sigma away from the mean (red).
- In the above example, there is a line drawn at one, two, and three standard deviations (sigma’s) away from the mean.
- Graph the X-bar Control Chart, by graphing the subgroup means (x-axis) verses measurements (y-axis). Your graph should look like something like this:
- Evaluate the graph to see if the process is out-of-control. The graph is out-of-control if any of the following are true:
- Any point falls beyond the red zone (above or below the 3-sigma line).
- 8 consecutive points fall on one side of the centerline.
- 2 of 3 consecutive points fall within zone A.
- 4 of 5 consecutive points fall within zone A and/or zone B.
- 15 consecutive points are within Zone C.
- 8 consecutive points not in zone C.
- State whether the system is in-control or out-of-control.
Sample Control Charts
Doc:Control Chart,Control Chart for Subgroups,Control Chart for Multiple Groups
Tips
- Excel commands that will make your data analyze easier are:
- Use Excel when creating your charts, because it has built in functions (shown below) that will speed up your calculations.
Warnings
- Control charts are (generally) based on data being normally distributed. In practice, however, they are reasonably robust to non-normal data.
- Moving Range charts (often used with the Individuals Chart (also known as the X or I chart) use different interpretation rules to cater for the very strong non-normality of Moving Range data.
- For some charts, e.g. the c chart, data probably will be non-normally distributed.
- X-bar charts, such as the one explained above, chart means rather than individual values. As explained by the Central Limit Theorem, Means tend to be normally distributed even if the underlying data are not.
Things You'll Need
- Basic understanding of graphical analysis.
- Access to Excel.
