When we repeat analysis of a sample several times, we get a spread of results surrounding its average value. This phenomenon gives rise to data precision, but provides no clue as to how close the results are to the true concentration of the analyte in the sample.
However, it is possible for a test method to produce precise results which are in very close agreement with one another but are consistently lower or higher than they should be. How do we know that? Well, this observation can be made when we carry out replicate analysis of a sample with a certified analyte value. In this situation, we know we have encountered a systematic error in the analysis.
The term “trueness” is generally referred to the closeness of agreement between the expectation of a test result or a measurement result and a true value or an accepted reference value. And, trueness is normally expressed in terms of bias. Hence, bias can be evaluated by comparing the mean of measurement results and an accepted reference value, as shown in the figure below.
Therefore, bias can be evaluated by carrying out repeat analysis of a suitable material containing a known amount of the analyte (i.e. reference value) mu, and is calculated as the difference between the average of the test results and the reference value:
We often express bias in a relative form, such as a percentage:
or as a ratio when we assess ‘recovery’ in an experiment:
The revised ILAC G8 document with reference to general guidelines on decision rules to issuance of a statement of conformance to a specification or compliance to regulatory limits has been recently published in September 2019. Being a guideline document, we can expect to be provided with various decision options for consideration but the final mode of application is entirely governed by our own decision with calculated risk in mind.
The Section 4.2 of the document gives a series of decision rules for consideration. In sub-section 4.2.1 which considers a binary statement (either pass or fail) for simple acceptance rule, it suggests a clear cut of test results to be given a pass or a fail without taking any risk of making a wrong decision into account, as long as the mean measured value falls inside the acceptance zone, as graphically shown in their Figure 3, whilst the reverse is also true:
In this manner, my view is that the maximum risk that the laboratory is assuming when declaring conformity to a specification limit is 50% when the test result is on the dot of the specification limit. Would this be too high a risk for the test laboratory to take?
When guard bands (w) are used to reduce the probability of making an incorrect conformance decision by placing them between the upper and lower tolerance specification limit (TL) values so that the range between the upper and lower acceptance limits (AL) are narrower, we can simply let w = TL – AL = U where U is the expanded uncertainty of the measurement.
By doing so, we can have one of the two situations, namely for a binary statement, see Figure 4 of the ILAC G8 reproduced below and for a non-binary statement where multiple terms may be expressed, see Figure 5 of the ILAC document.
In my opinion, the decision to give a pass for the measurement found within the acceptance zone in Figure 4 is to the full advantage of the laboratory (zero risk as long as the laboratory is confident of its measurement uncertainty, U), but to state a clear “fail” in the case where the measurement is within the w-zone of the acceptance zone may not be received well by the customer who would expect a “pass” based on the numerical value alone, which has been done all this while. Shouldn’t the laboratory determine and bear a certain percentage of risk by working out with the customer on its acceptable critical measurement value where a certain portion of U lies outside the upper and lower specification limits?
Similarly, the “Conditional Pass / Fail” in Figure 5 also needs further clarification and explanations with the customer after considering a certain percentage of risk to be borne for the critical measurement values to be reported by the test laboratory. A statement to the effect that “a conditional pass / fail with 95% confidence” might be necessary to clarify the situation.
But from a commercial point of view, the local banker clearing a shipment’s letter of credit for payment with the requirement of a certificate of analysis to certify conformance to a quality specification laid down by the overseas buyer might not appreciate such statement format and might want to hold back the payment to the local exporter until his overseas principal agrees with this. Hence, it is advisable for the contracted laboratory service provider to explain and get written agreement with the local exporter on the decision rule in reporting conformity, so that the exporter in return can discuss such mode of reporting with the overseas buyers during the negotiation of a sales contract.