Interpretation of test results

When several laboratories test an identical sample, they never find exactly the same test results. The measure of the variations in the results is called the reproducibility R (of the test method). R is 2.85 times the standard deviation of the series of test results. This uncertainty in a test result must be considered when you check compliance with a product specification limit.

Reproducibility

The reproducibility R is determined by interlaboratory studies on the specific test method. R is a quality characteristic laid down in the test method. Alternative test methods usually have a different reproducibility. Test results can therefore only be interpreted if the test method is mentioned. If the test method is not known results can best be interpreted using the R value of the least reproducible method.

Probability of compliance

In product acceptance, seller is interested in a low risk of false rejection, whereas buyer wants a low risk of false acceptance. Unless otherwise agreed, common industry practice is to reject a product with a 5% chance of false rejection. Parties can agree in advance about other limits for rejection or acceptance, especially on product aspects that are critical.

Compliance check

Quality testing against specification is done according to EN ISO 4259, ASTM D3244 or IP 367. On a single test result (X), compliance with the specification limit (A) at 95% chance of true rejection is checked by the formula:

X < A(max) – 0.59R

X > A(min) + 0.59R

Other probabilities give different values for 0.59: 90% -> 0.46; 99% -> 0.84; 99.5% -> 0.93

Ex. 1 (95% probability, true rejection):

The maximum specification limit for a parameter is A= 2.00; the reproducibility of the test method is R= 0.20 and the measured test result is X= 2.13; the 95% chance of true rejection gives 2.118 < 2.13, thus the product does not meet the specification.

Ex. 2 (99% probability, true rejection):

A (max) = 2.00; the R of the test method = 0.20 and X= 2.13; the 99% chance of true rejection gives 2.168 > 2.13, thus the product does meet the specification.

Ex. 3 (critical specification; 95%, true acceptance):

A(max) = 2.00; R = 0.20; X = 1.90; buyer wants only a 5% chance of false acceptance. The compliance test gives: 2.02 > 2.00, hence the product should be rejected.

Ex. 4 (critical specification; 90%, true acceptance):

A(max) = 2.00; R = 0.20; X = 1.90; buyer and seller agree on a 10% chance of false acceptance. The compliance test gives: 1.99 < 2.00, hence the product is accepted.

Regulatory authorities

Some regulatory authorities do not provide allowances for variability in tests. EPA for example does not allow tolerances for refiners on test results for ASTM D86-01 on RFG. Please check with local authorities or ask Saybolt to make sure that you are up-to-date informed about zero tolerance policies.