A Statistical Process Control Method for Evaluating Subcontract Laboratory Reliability

Authors: R. Cary Tuckfield, Bob C. Henderson, and Moheb M. Khalil

Savannah River Site

A statistical method has been developed to assess the reproducibility of duplicate radiological sample results and is based on the statistical process control method known as the c-chart. The c-chart is a quality control method which tracks the number of non-conformities counted for a sample item obtained from the manufacturing process, and is not unlike the count of the number of radioactive disintegrations recorded for a given sample in a laboratory sample analysis process. Among analytical labs under subcontract to the US Department of Energy Savannah River Site (SRS), a quality control procedure has been implemented to measure analytical process reliability using duplicate sample results. An environmental monitoring sample is collected and homogenized. Two duplicate sub-samples are prepared from the homogeneous mixture, are separately labeled and identified, and shipped to the subcontract lab. The identity of each is known only to the Environmental Monitoring laboratory QA/QC coordinator at SRS. Because the duplicates are not made from an analytical standard, the magnitude and scale of measurement on the sample constituents can be very different. We introduce a unitless measurement of the relative difference between duplicate sample results based on the normal approximation to the Poisson probability distribution. A radioactivity count (e.g. dpm) is obtained for each of the two samples. Since the mean and variance of a Poisson random variable are estimated by the same quantity, then the difference between these measurements divided by the square root of their sum follows approximately, the standard normal probability distribution also known as a z-score. In the context of a Shewhart process control chart any z-score greater than 3 or less than –3 will occur about 1 in 370 sets of duplicate sample analyses if the analytical process is stable, i.e. reliable. The simple difference, or numerator of the z-score, could be used as a quality control measure also, but the scale of measure would be different for each environmental sample used in this reliability testing process. In fact, the c-chart method should be used instead if the sample duplicate process is based instead on a NIST or EPA standard. The use of the z-score simply allows us to use less costly environmental samples for the duplicate sample reliability testing process.