A recent email question came in, asking about when it's best to use a single control rule and when it's better to use multirules:
"Our accreditation guidelines.... state the following:
Internal QC rules shall be designed to detect random and systematic
error.
rejection....
"We have been "dinged" ... on a recent
accreditation. The main reason being that when a result goes outside the [single rule] limit, we
can't tell whether it is a random or systemic error without looking at the
QC graphs. I am not sure how any rule like the 1-3.5s for CK mentioned
in the
Feb 2009 article (Sigma metrics of Four Glucose Methods) on your website would be able to do this?"
Let's start by identifying two issues and addressing them separately. In the first place, from a compliance point of view, if the accreditation guidelines have specific written instructions to use multirules, you probably need to use multirules. (Obviously, these are not the rules affecting US laboratories, where single rules are the norm.) Arguing the scientific merits of a procedure with an inspector can have unexpected results.
Next, we need to address how the QC procedures are chosen for a laboratory. If a laboratory chooses a single or multirule approach for QC procedures based on tradition, or because they simply apply one set of rules for all tests, regardless of performance, that is one thing. On the other hand, if a laboratory assesses the performance and quality requirements of its methods, choosing QC procedures via a
QC Design process, that's another thing entirely.
In the first scenario, where performance of test methods is unknown, multirules might be a better approach. The laboratory isn't adapting its QC procedures to fit the needs of the testing methods, so the additional information supplied by multirules may be valuable. It may also be overkill.
In the second scenario, QC Design has been used to determine the optimal QC procedure based on test performance and the quality required by the test. Thus, if QC Design has determined that the laboratory need only a single rule to QC a particular test, the additional information and detection power of a multirule is not necessary.
The email is correct that when a single-rule QC procedure is violated, for example, the 1
3s control rule, it is difficult to determine immediately whether or not that violation was a random or systematic error. A multirule would be able to help.
But in this example, where QC Design has determined a 1
3s rule is sufficient, that does not preclude you from applying multirules once an out-of-control rule has occurred. That is, you can use a 1
3s rule as your rejection rule, then apply multirules during trouble-shooting to determine the type of error. In some ways this is like the old 2s "warning rule" of the classic
"Westgard Rules." The difference here is that the violation is not a
warning rule, it's a
rejection rule, and the additional rules are being used to determine what kind of error has occurred. (In the classic rules, the additional rules were used to determine
if the run should be rejected, not
why.)
Take a look at an example with a 5.0 Sigma method (10% TE
a, 1.8% imprecision, 1.0% inaccuracy). The first graph will show you the operating point of the method in comparison with the 1
3s rule:
Now, let's highlight a multirule approach:
Can you spot the difference? It doesn't look like a big difference. The operating point is below both operating lines of the QC procedures. There's a bit more room under the multirule highlighted in the second chart.
Here's where a Sigma-metric / Critical-Error graph is more informative:
In this case, the multirule has approximately 3% false rejection and 100% error detection (it will detect the error within the first run that the error occurs), while the 1
3s has 1% false rejection and 99% error detection. Given that the rejection and detection numbers are determined experimentally and have a margin of +/- a percent or two, these procedures are almost the same. But the use of the multirule will generate some additional false rejections.
Bringing all of this discussion back to the concrete scenario of the question, I would show these graphs to the inspector (obviously, the graphs would have to illustrate the real tests), which should demonstrate the equivalence of a single rule and multirule QC procedure. I would further explain that a a multirule approach is used in trouble-shooting. That combination agrees with the spirit of the law, if perhaps not the letter.