# What’s that Number on My Certificate?

Measurement Uncertainty, you know it’s there. It’s that plus/minus number on your calibration certificate. You just received your prized possession from your calibration lab and you’ve looked over the whole certificate. All of it except that one number, or maybe you look at that number and wonder why it is different this year from last. Maybe, its larger than it was last year. Does this mean they are less certain about my calibration than they were last year?

## No Measurement is Perfect

All measurements have an inherent graininess to them. Think of a classroom ruler. The one-inch mark has width to it. So which side of this line in one inch? Is it the middle of the line? This is one of the key contributions to measurement uncertainty. All measurements have some form of resolution associated with them. In some cases, they can be very small, but they never go away. There are a number of other factors that can impact a measurement as well. These factors are best divided into two categories: random and systemic.

## Random vs. Systemic Errors

Random errors exist in every measurement system. They are typically represented best by a Gaussian probability distribution (bell curve) because small random errors happen frequently and large errors happen rarely. Systemic errors come from poorly designed experiments or inherent shortcomings in a measurement system. Systemic errors will typically show a bias in a measurement system, and can be dramatically reduced in any measurement system, but it might be preferable not to remove them. The cost of removing systemic sources of error might not be justified. You may use a set of gage blocks that has been worn to the point of being de-classed to “shop grade” to calibrate calipers. Here other sources of inaccuracy of measurement more than compensate for a 50μin gage block tolerance.

## Measurement Uncertainty is Random Error

Measurement uncertainty is a way to quantify random error associated with a given measurement and is expressed as a Gaussian probability distribution with a certain “k” factor. The calculation of a measurement uncertainty involves identifying all potential sources of imprecision in a measurement, quantifying their potential impact on the measurement, and combining them in a meaningful way. Once all of this has been performed you have a meaningful measurement uncertainty on your calibration certificate. This number is intended to qualify the reported measurement.

## Why Would a Measurement Uncertainty Change?

When identifying sources of error, the measurement system and the unit under test(UUT) are both considered. A UUT can change over time. The repeatability of the UUT, how well it reports a repetition of the same measurement, can change dramatically. This would result in an increased measurement uncertainty.

Other factors are the more likely culprit here though. ISO 17025 accredited labs are constantly trying to improve their scopes of accreditation, and assessments required by the standard will require refinements in a lab’s scope of accreditation. A lab’s published scope of accreditation includes “Calibration and Measurement Capabilities” (CMC). CMCs are the best uncertainty values that a laboratory can report on a calibration certificate. Calibration standards from ISO, ASME, ASTM, and others are constantly changing as well. Sometimes these standards will identify additional sources of uncertainty that must be considered in a measurement.

## Σ it up

Calibration laboratories exist in a fluid environment. They are dedicated to continuous improvement. Measurement uncertainties are constantly changing because of the continuous improvement process. Process changes, standards changes, assessment results, and equipment improvements all result in changes in the reporting of uncertainty of measurement. Most times these changes are for the better and result in smaller measurement uncertainties, but sometimes they will reveal areas of uncertainty that might not have been considered before and result in larger quantities.

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