Whenever you run a standard sample with an analytical procedure, how do you know if it came out “good enough?” For instance, take the BOD standard of glucose-glutamic acid. Every analyst who has run a BOD test knows how variable that result can be. What if you make a BOD standard to give a 198 mg/L value, but the actual result is 175. Does this result indicate the rest of the BOD analyses are valid? Or is the result too far off the expected value thus invalidating the rest of the analyses? Control charts are designed to help answer that question.
Developing a Control Chart
In general, you’ll need fifteen to twenty data points of a standard to make a control chart (BOD is an exception, it requires a minimum of twenty-five glucose-glutamic acid data points). Then find the average and the standard deviation of this data set. Both of these calculations are easy to perform on a calculator. Use the average and the standard deviation to find the warning limits (WL) and the control limits (CL). The upper WL is the average + 2 times the standard deviation. The lower WL is the average – 2 times the standard deviation. Similarly, the CL is the average +/- 3 times the standard deviation.
In a real-life example, the analyses of a 5.00 mg/L phosphorus standard produced these fifteen values: 5.09, 5.12, 4.98, 5.05, 5.00, 4.93, 4.98, 4.89, 5.07, 5.00, 5.10, 5.03, 4.99, 4.92, and 5.01 mg/L. The average is 5.01 mg/L and the standard deviation is 0.0673. Therefore the upper WL is 5.01 + (2)(0.0673) = 5.14 mg/L. The lower WL is 5.01 – (2)(0.0673) = 4.88 mg/L. Calculating the upper and lower CL produces 5.21 and 4.81 mg/L respectively.
On graph paper plot the average, warning limits, and the control limits on the y-axis so that the average is in the middle of the page. Make your scale on the y-axis so that the CLs are about a quarter way from the top and bottom edges from the chart. The x-axis is for the date of future standard analyses.
Using the Chart
Once the control chart has been made, plot the standard values, such as the BOD glucose-glutamic acid values, each time you perform the analysis. If a standard tests outside the control limits, repeat the analyses immediately if possible. If it again falls outside the CLs, stop the analyses and determine the problem with the procedure. If the repeated analysis of the standard falls within the CLs, then proceed with the rest of the analyses.
If two out of three successive standard values exceed the warning limits, immediately test another standard sample. If the analysis again falls outside the WLs, stop the analysis and determine the problem. If it tests okay, then continue the analyses.
In general, random limit exceedences represent random problems in the analyses. Excedences clustered together (for instance, four data points that are outside the upper warning limit) indicates one specific cause. Similarly, if seven consecutive results fall above or below the average, even if the results are within the limits, determine the reason for the trend and correct the problem.
Control charts are a useful tool to validate your data incase your results are ever questioned. For more information on evaluating these charts, refer to the latest edition of Standard Methods for the Examination of Water and Wastewater or Wastewater Sampling for Process and Quality Control MOP #OM-1.
The information in this article is very general. As usual, check your federal, state, and local regulations. You may have additional regulations or requirements that you must meet.
If you have any questions, suggestions, or comments, please contact NEWEA Lab Practices Committee Chair Tim Loftus at (508) 949-3865 (firstname.lastname@example.org).