What is the best practice for reporting results above the LOQ but beyond the signifcant figures of the test specification. Example: LOQ=0.005%, specification limit is 0.1% max and actual result measured is 0.034%. It doesn't seem right to reported not detected but reporting 0.0% seems equally flawed. What is a poor analyst to do. This point has come up in the testing of pharmaceuticals and our SOP's don't seem to cover this issue.

Everything below your spec requires more digits right of the decimal point than are in the spec expression. Your result is above the LOQ, so you have some confidence in its measurement resolution. It's not uncommon to express these with more decimal places than the spec expression, e.g., 0.03%.

Steve

In the original question I forgot to add that there is an SOP in place that requires rounding results to the significant figures of specification. It has been suggested that <0.1% be reported. I really believe it is a problem with our rounding SOP but was hoping to get feedback from anyone else that had experienced this issue. I tend to agree with your response since the LOQ is so much lower? Thanks for your help.

For what it's worth, I would suggest reporting the final result as 0.03%. In regards to sig figs, the zeros to the immediate right of the decimal don't count. So 0.03 only contains one sig fig, 0.030 has two. If you avg multiple inj's of the same sample, use as many decimal places as indicated by the quality of the data to calculate the final number.

Hi:
This has been a problem for some time. There is a subtle difference between testing to a specification requirement and testing to a method requirement. We are independent cargo testers where each sample ordinarily represents about $1M worth of the commodity being traded. Without specific case by case guidelines, we default to the same number of decimal places as the specification, since that would be required if there was a dispute that could go to arbitration or end up in a courtroom.

In this role we have no contribution to the quality control of the product, since we only test after it has been produced and can not influence its properties, we don't own it. We merely contribute to quality assurance with our referee analysis. You probably are expected to provide data for QC as well as certification to specs. The same raw data definitely needs to be rounded differently for these two purposes.

For product QC it would be best to track the impurities with unrounded 0.034% type data, but when issuing a certificate for the same batch (you can never say zero), with a spec of 0.1% max you could only choose from: < 0.1, 0.1, 0.2, etc. whichever the unrounded result is closer to. Therefore official reports should show < 0.1%.

If the spec was 0.10% max, then your choices would be < 0.01, 0.01, 0.02, etc., so you would report 0.03%.

I'm sure you can imagine that a spec writer might not understand the difference between 0.1 max & 0.10 max. It might just fall on your shoulders to educate them. For instance, if the measured result was 0.123%, in the former case you would report 0.1 & it would pass. In the latter, you would say 0.12 & it would fail. Even with the same results for the same product with the same intended spec.

It gets even more fun when one party has the 0.1 and their trading partner has 0.10 and they think their specs allow the same acceptable range of product impurity. The difference between the 0.144 and 0.104 maximum passing results is even greater than what you are typically even detecting right now. With complacency common when you are so well within range, it is even more of a ticking time bomb if there should be a process upset and levels rise for the first time in memory. Nobody might know what to do. What if a batch should come out 0.200%? What level would you have to blend it down to with good material?

So when testing to a specification, you report the same number of decimal places as the specification, unless the spec REQUIRES a test method which ordinarily reports the result differently. Significant figures have nothing to do with it, your SOP is likely flawed on this point.

Whoever is responsible for the specs may need your input, their scientific background may not have prepared them for speccing products in today's market. On the other hand they may be far more advanced at this than you or I, and considering things they are better at anticipating than we. You never know, but it may be worthwhile to check. Depending on the scale of operations, it could be possible for an administrator to thoughtlessly risk more losses on one product order than you might be able to compensate during an entire career.

Hope this helps

Best Regards,
Mike Setzer
Quality Analytical Services, Inc.

This has been a pet subject of mine for some time, Mike, and I pretty much agree with every thing you say. I've always been a little unhappy with the (admittedly accepted) practice of having a spec of 0.1%, and then treating 0.14% as a pass - mainly because I know that people setting the specs have never really considered the implications of decimal places / significant figures. As an example, one of the raw materials I've worked with in the past had a water spec of 0.1%. A batch with 0.10% was just about OK as far as the subsequent chemistry was concerned, but 0.14% was definitely too high, and caused problems, but because the spec was set at 0.1%...

For what it's worth, when setting a specification I think the following points should be considered:

1. What is the analytical method capable of? Can you genuinely differentiate between 0.10 and 0.11? If not, there's no point having the second sig fig in there.
2. What does the product actually need? Is the difference between 0.06 and 0.14 significant as far as the quality or performance of the product is concerned (even though there's a factor of nearly 3 in the results)? If yes, then have the second sig fig, otherwise don't bother.

Whatever the decision, the SOP should cover the general practice, and the change control documentation for the individual spec should justify the decision that's made about decimal places and significant figures.

It really comes down to trying to get some kind of consistency and understanding of the issue, but that could take some time...