Using the 10:1 Ratio Rule and the 4:1 Ratio Rule

Q: Can you explain when I should be using  the 10:1 ratio rule and the 4:1 ratio rule within my calibration lab? We calibrate standards as well as manufacturing gages.

A: First, I will use the right nomenclature. What the user means is 10:1 and 4:1 Test Accuracy Ratio (TAR). That is, one uses standards 4 or 10 times as accurate as the Unit Under Test (UUT) to calibrate it with.

Unfortunately, the answer to the user’s question is NEVER if we were to use newer metrologically accepted practices.

The TAR is replaced by Test Uncertainty Ratio (TUR).  The ANSI/NCSLI Z540.3:2006 definition of TUR is:

“The ratio of the span of the tolerance of a measurement quantity subject to calibration, to twice the 95% expanded uncertainty of the measurement process used for calibration.”

*NOTE: This applies to two-sided tolerances.

The TUR is represented as a mathematical equation below:

Test Uncertainty Ratio (TUR) represented as an equation


Because of advances in technology, one can purchase highly precise and accurate instrumentation at the end user level, it gets challenging to find standards 4 or 10 times as precise with which to calibrate it and maintain metrological traceability at the same time (definition per ISO Guide 99:2007, Property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty).

Proper measurement uncertainty analysis of the UUT (including standards used with its uncertainty) identifies all the errors associated with the measurement process and ensures confidence that calibration is within the specification desired by the end user.

ISO/IEC 17025-2005: General requirements for the competence of testing and calibration laboratories, clause, third paragraph, also states that “When statements of compliance are made, the uncertainty of measurement shall be taken into account.”

This would also ensure confidence in the calibration employing the metrological and statistical practices recommended.

The other rule of thumb not to be confused in this discussion is to measure/calibrate with the right resolution. In the ASQ Quality Progress March 2011 Measure for Measure column, I wrote more on resolution with respect to specification and measurement uncertainty. The general rule of the thumb is if you want to measure/calibrate a 2-decimal place resolution device, you need at least 3-decimal place or higher resolution device.

This is a very good question posed and it is also unfortunately the most misunderstood practice among a lot of folks performing calibration.

Dilip A Shah
President, E = mc3 Solutions
Chair, ASQ Measurement Quality Division (2012-2013)
Secretary and Member of the A2LA Board of Directors (2006-2014)
Medina, Ohio

Related Content: 

Measure for Measure: Avoiding Calibration Overkill, Quality Progress

History and overview of calibration science. Read more.

Evolution of Measurement Acceptance Risk Decisions, World Conference on Quality and Improvement

TAR, TUR, and GUM are examined. Read more. 

Measure for Measure: Calculating Uncertainty, Quality Progress

Understanding test accuracy and uncertainty ratios. Read more. 

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