# The fundamental concept of metrology

The fundamental concepts of metrology are revolved around these three aspects: traceability-calibration-uncertainty.

Two fundamental documents (the main reference documents) in metrology are guide to the expression of uncertainty in measurement (GUM) and international vocabulary of metrology (VIM). These documents are created and maintained by Joint Committee for Guides in Metrology (JCGM). The GUM and VIM documents can be freely downloaded from JCGM 100:2008(E) – in English Evaluation of measurement data and JCGM 200:2012 International vocabulary of metrology-Basic and general concept and associated terms, respectively. All type of measurements should refer to these reference documents, especially for both measurement uncertainty determination (in GUM) and definitions of metrology-related terms (in VIM).

VIM defines metrology as “the science of measurement and its application”. Metrology includes all aspects of measurement, including both theoretical and practical, in all types of measurement field applications (including manufacturing, chemistry, physics, astronomy, medicine, pharmacy and others). There are seven basic measurement units: time (s), length (m), mass (kg), electric current (A), thermodynamic temperature (K), amount of substance (mol) and luminous intensity (cd). We are focusing on manufacturing metrology that refer to length measurement (m or metre)as the basic measurement unit.

### The fundamental concept

The fundamental concepts of metrology are revolved around these three aspects: traceability-calibration-uncertainty. VIM defines these three aspects as:

• Traceability (metrological traceability)

“Property of a measurement results whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty

• Calibration

“Operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication”

• Uncertainty (measurement uncertainty)

“Non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used.” Measurand is a quantity intended to be measured.

In simple re-wordings, we can think the above definitions as:

• Traceability: each measurement should link to another instrument that has substantially higher (typically one magnitude) accuracy and so on until the link reaches the definition of metre.
• Calibration: an activity to compare the result of a measurement with another measurement result obtained from another instrument with higher accuracy. This step produces the uncertainty of the measurement result.
• Uncertainty: the range of the measurement results in which we believe the true values lie in between the range. From calibration, we will get this uncertainty estimation.

In manufacturing metrology, length measurements should be traceable to the definition of metre. The definition of metre (according to Bureu International des Poids et Measures (BIPM) in 1983) is:

“The length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second”

That is, metre is the length travelled by light in one second, where the speed of light is defined as 299792458 m/s.

The traceability chain for length measurement should be traceable to the definition of metre. This chain is shown in the figure 1 below:

In Figure 1 above, the calibration is the one who creates the link between two lower and upper levels. The farther the level of a measurement from the definition of metre, the higher its uncertainty (the lower its precision). The definition of metre does not have a stated uncertainty because it is a definition and its value is nominal.

All research and activities in measurements focus on these the three aspects (traceability, calibration and uncertainty). For example, many research try to propose procedure and reference artefacts to conduct calibration to realise the measurement traceability and new instrument developments (both tactile and optical) focus on improving accuracy and precision to obtain small measurement uncertainties.

### Presentation of measurement results

One of the most obvious importance of traceable length measurements is that the measurements can be compared to each other when each of the measurement is carried out, for example, with different instrument manufacturers or in different areas/countries. This comparable measurement is called a reliable measurement in which we know its true value lies in the specified uncertainty.

Reliable measurements should be presented in this format:

$$y=x\pm U$$

Where $y$ is the final measurement result presentation, $x$ is the measured value and $U$ is expanded measurement uncertainty (commonly using 95% confidence interval with coverage factor = 2 for normal distribution assumption). For example, $y=(10\pm 0.1) mm$.

To conclude, if our measurement is traceable to the definition of metre, our measurement is said to be reliable (trustable).