Dilemmas in making decision rules for conformance testing
In carrying out routine testing on samples of commodities and products, we normally encounter requests by clients to issue a statement on the conformity of the test results against their stated specification limits or regulatory limits, in addition to standard reporting.
Conformance testing, as the term suggests, is testing to determine whether a product or just a medium complies with the requirements of a product specification, contract, standard or safety regulation limit. It refers to the issuance of a compliance statement to customers by the test / calibration laboratory after testing. Examples of statement can be: Pass/Fail; Positive/Negative; On specification/Off specification.
Generally, such statements of conformance are issued after testing, against a target value with a certain degree of confidence. This is because there is always an element of measurement uncertainty associated with the test result obtained, normally expressed as X +/- U with 95% confidence.
It has been our usual practice in all these years to make direct comparison of measurement value with the specification or regulatory limits, without realizing the risk involved in making such conformance statement.
For example, if the specification minimum limit of the fat content in a product is 10%m/m, we would without hesitation issue a statement of conformity to the client when the sample test result is reported exactly as 10.0%m/m, little realizing that there is a 50% chance that the true value of the analyte in the sample analyzed lies outside the limit! See Figure 1 below.
In here, we might have made an assumption that the specification limit has taken measurement uncertainty in account (which is not normally true), or, our measurement value has zero uncertainty which is also untrue. Hence, by knowing the fact that there is a presence of uncertainty in all measurements, we are actually taking some 50% risk to allow the actual true value of the test parameter to be found outside the specification while making such conformity statement.
Various guides published by learned professional organizations like ILAC, EuroLab and Eurachem have suggested various manners to make decision rules for such situation. Some have proposed to add a certain estimated amount of error to the measurement uncertainty of a test result and then state the result as passed only when such error added with uncertainty is more than the minimum acceptance limit. Similarly, a ‘fail’ statement is to be made for a test result when its uncertainty with added estimated error is less than the minimum acceptance limit.
The aim of adding an additional estimated error is to make sure “safe” conclusions concerning whether measurement errors are within acceptable limits. See Figure 2 below.
Others have suggested to make decision consideration only based on the measurement uncertainty found associated with the test result without adding an estimated error. See Figure 3 below:
This is to ensure that if another lab is tasked with taking the same measurements and using the same decision rule, they will come to the similar conclusion about a “pass” or “fail”, in order to avoid any undesirable implication.
However, by doing so, we are faced with a dilemma on how to explain to the client who is a layman on the rationale to make such pass/fail statement.
For discussion sake, let say we have got a mean result of the fat content as 10.30 +/- 0.45%m/m, indicating that the true value of the fat lies between the range of 9.85 – 10.75%m/m with 95% confidence. A simple calculation tells us that there is a 15% chance that the true value is to lie below the 10%m/m minimum mark. Do we want to take this risk by stating the result has conformed with the specification? In the past, we used to do so.
In fact, if we were to carry out a hypothesis (or significance) testing, we would have found that the mean value of 10.30%m/m found with a standard uncertainty of 0.225% (obtained by dividing 0.45% with a coverage factor of 2) was not significantly different from the target value of 10.0%m/m, given a set type I error (alpha-) of 0.05. So, statistically speaking, this is a pass situation. In this sense, are we safe to make this conformity statement? The decision is yours!
Now, the opposite is also very true.
Still on the same example, a hypothesis testing would show that an average result of 9.7%m/m with a standard uncertainty of 0.225%m/m would not be significantly different from the target value of 10.0%m/m specification with 95% confidence. But, do you want to declare that this test result conforms with the specification limit of 10.0%m/m minimum? Traditionally we don’t. This will be a very safe statement on your side. But, if you claim it to be off-specification, your client may not be happy with you if he understands hypothesis testing. He may even challenge you for failing his shipment.
In fact, the critical value of 9.63%m/m can be calculated by the hypothesis testing for the sample analyzed to be significantly different from 10.0%. That means any figure lower than 9.63%m/m can then be confidently claimed to be off specification!
Indeed, these are the challenges faced by third party testing providers today with the implementation of new ISO/IEC 17025:2017 standard.
To ‘inch’ the mean measured result nearer to the specification limit from either direction, you may want to review your measurement uncertainty evaluation associated with the measurement. If you can ‘improve’ the uncertainty by narrowing the uncertainty range, your mean value will come closer to the target value. Of course, there is always a limit for doing so.
Therefore you have to make decision rules to address the risk you can afford to take in making such statement of conformance or compliance as requested. Also, before starting your sample analysis and implementing these rules, you must communicate and get a written agreement with your client, as required by the revised ISO/IEC 17025 accreditation standard.