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Is It in Spec ... or Not?
A. A previous DataPoints article on how to account for test imprecision^{1} and ASTM D3244, Practice for Utilization of Test Data to Determine Conformance with Specifications, spawned the above question from a reader. While the question is simple, the answer is not.
I will begin by stating a most common error, that is, use of R as an acceptable tolerance for judgment of a test result against a specification.
The primary purpose of R is not to be used for judgment of a test result against a specification. R is intended to be used to judge whether the difference between two single results obtained from two different labs using the same test method can be reasonably attributable to common causes that are deemed to be part of the test method, under the assumption that both labs have executed the test method correctly, and both labs tested essentially the same material.
The key word is difference. If the difference as described above exceeds R, we reject the notion that this difference can be attributable to common causes associated with the test method, and we look for special causes. The most frequently encountered special causes are:
If the difference does not exceed R, we accept both results as valid single point estimates of the property in question. We can then calculate the average using both results to obtain a more precise estimate for the property. In D3244, this average is called the assigned test value (ATV) for the product in question. Now comes the part that is not simple: how to use this ATV to make the specification conformance decision.
In order to make the specification conformance decision, the receiver (consumer) and supplier (producer) will first need to agree on what value to compare this ATV against to make the decision. This value is referred to as the acceptance limit (AL) in practice D3244. The AL may or may not coincide with the specification limit because it is dependent on the required degree of confidence (assurance) that the product conforms to specification.
Setting the degree of confidence depends on the perspective used to make the product conformance decision. From a consumer's perspective, the decision will logically be based on minimizing consumers' risk, the risk of accepting a product based on the ATV meeting the AL, but the true value of the property is nonconforming. From a producer's perspective, the decision will logically be based on minimizing the producer's risk, the risk of rejecting a product based on the ATV not meeting the AL, but the true value of the property is conforming.
Practice D3244 advocates setting the AL based on the probability of product acceptance if the true value of the property is exactly at the specification limit, as described below:
For critical specifications, the AL will be on the conforming side of the specification limit, while for noncritical specifications, the AL will be on the nonconforming side, except for the special case of 50 percent, where the AL coincides with the specification limit. Since most consumers will hesitate to accept a product with the ATV in the nonconforming side, the AL is seldom set in the nonconforming region, regardless of the statistical implications.
The following numerical example, in table form (Table 1), tabulates the AL at different degrees of confidence for octane (antiknock index, or AKI) in gasoline to illustrate the aforementioned concepts.
Table 1 — Acceptance Limit at Different Degree of Confidence for Octane
Minimum Specification, Antiknock Index (AKI) 
Published Test Method Reproducibility (R) 
Probability of Acceptance (P) if True Value of Product is Exactly at 93.0 
Acceptance Limit (AL) 

93.0 
0.6 
5% 
93.25 
critical specification 
93.0 
0.6 
10% 
93.20 
limit  
93.0 
0.6 
50% 
93.00 
noncritical 
93.0 
0.6 
90% 
92.80 
specification 
93.0 
0.6 
95% 
92.75 
treatment 
Reference
1. Lau, A.T., "Test Method Imprecision  How to Account for It," ASTM Standardization News, July/Aug. 2012, pp. 1617.
Alex T. Lau, TCLConsulting, Whitby, Ontario, Canada, is chairman of Subcommittees D02.94 on Quality Assurance and Statistics and D02.01B on Precision, which are part of ASTM Committee D02 on Petroleum Products and Lubricants. An ASTM International fellow, Lau is also a member of Committees E11 on Quality and Statistics, E36 on Accreditation and Certification and F08 on Sports Equipment and Facilities.
Dean V. Neubauer, Corning Inc., Corning, N.Y., is an ASTM fellow; he serves as chairman of Committee E11 on Quality and Statistics, chairman of E11.90.03 on Publications and coordinator of the DataPoints column.
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