This is an online calculator which can be used as part of the QC: The Levey-Jennings Control Chart lesson in the Basic QC Practices series.

Calculation of control limits

Let us take an example where two sets of control limits are needed to implement QC rules. The first set uses 2s control limits (for implementation of the 12s rule) calculated as the mean plus or minus 2 times the standard deviation. The second set uses 3s control limits (for implementation of the 13s rule) calculated as the mean plus or minus 3 times the standard deviation.

For this example, Control 1 has a mean of 200 and a standard deviation of 4 mg/dL.
The upper control limit would be:
200 + 2*4, which is 208 mg/dL.
The lower control limit would be:
200 - 2*4, or 192 mg/dL.

• What are the 3s control limits for Control 1?
• What are the 2s control limits for Control 2?
• What are the 3s control limits for Control 2?

NOTE: This Javascript Control Limit Calculator only works on browsers that support Javascript!

 Enter the control mean: Enter the control standard deviation: Enter the control limit you wish to evaluate (number only i.e. 2, 3, 3.5, etc.): Once you've entered these three values, click this button to calculate your limits Your Upper Limit will appear here: Your Lower Limit will appear here:

Results for the Cholesterol Example Control Limits

Control Material mean +/- 2s limits mean +/- 3s limits
Control 1   -    -
Control 2   -    -

You should end up with 3s control limits of 188 and 212 for Control 1. For Control 2, you should have 2s control limits of 240 and 260 and 3s control limits of 235 and 265.

Use of Control Charts

Once the control charts have been set up, you start plotting the new control values that are being collected as part of your routine work. The idea is that, for a stable testing process, the new control measurements should show the same distribution as the past control measurements. That means it will be somewhat unusual to see a control value that exceeds a 2s control limit and very rare to see a control value that exceeds a 3s control limit. If the method is unstable and has some kind of problem, then there should be a higher chance of seeing control values that exceed the control limits. Therefore, when the control values fall within the expected distribution, you classify the run to be "in-control," accept the results, and report patient test results. When the control values fall outside the expected distribution, you classify the run as "out-of-control," reject the test values, and do not report patient test results.

• Plot control results. For practice, the accompanying table provides some control results for our example cholesterol method. Plot these results, one from Control 1 and one from Control 2, for each day. You can print the Levey-Jennings QC Practice Exercise (below) to obtain a worksheet that shows all these control results. For day 1, the value for Control 1 is 200 and Control 2 is 247. On the chart for Control 1, find the value of 1 on the x-axis and the value of 200 on the y-axis, follow the gridlines to where they intersect, and place a mark; it should fall on the mean line. On the chart for Control 2, find the value of 1 on the x-axis and the value of 247 on the y-axis, then mark that point; it should fall a little below the mean line. In plotting control values, it is common practice to draw lines connecting the data points on the control chart to provide a stronger visual impression and make it easier to see patterns and shifts.

• Interpret control results. Apply the 12s and 13s control rules and make a decision whether you should accept or reject the run for each day. The control values for the first day are in-control and the patient results can be reported. Continue plotting the 2 control values per day and interpreting those results. Circle those points that correspond to runs that should be rejected. Keep track of the control rules that are violated on the worksheet for the Levey-Jennings QC Practice Exercise. Patient results obtained in runs where the 13s rule is violated are most likely incorrect. Results obtained in runs where the 12s rule is violated may or may not be incorrect because there is about a 10% chance of this occurring even when the method is working perfectly. This is a "false alarm" problem that is inherent with the use of 2s control limits with an N of 2. In spite of this serious limitation, many laboratories continue to use 2s control limits and just routinely repeat the run and the controls, or sometimes repeat only the controls by themselves. Note that if a control is out a second time, the actual control rule that is being used to reject a run is a 22s rule rather than the stated 12s rule. Unfortunately, the 22s rule by itself is not very sensitive, therefore, it is better to use the 13s and 22s rules together in a multirule procedure to improve error detection while, at the same time, maintaining a low false rejection rate. We'll provide more discussion of multirule QC procedures in a later lesson.

Return to the lesson on QC: The Levey-Jennings Control Chart in the Basic QC Practices series.