**3. Digital Calibration Certificates**

#### *3.1. Overview*

A DCC [13] provides all information relating to a calibration in machine-readable form. Its structure mirrors the information that is required by ISO/IEC 17025 [14] for reporting the results of calibration. Consequently, a DCC is divided into four main sections:


The focus of this paper is on uncertainty-related aspects of the measurement results section of a DCC.

#### *3.2. Measurement Results Section*

A number of internationally recognised documents provide the foundation for the representation of measurement data within the D-SI: the BIPM SI brochure [9], the GUM [6], the VIM [5] and ISO 80000-1 [15]. The D-SI allows several types of measurement data—real, complex, univariate, multivariate, etc.—to be represented.

#### 3.2.1. Univariate Real Quantity

Table 1 lists the components of the D-SI for a univariate real quantity. The information marked in bold shows the minimal information required and comprises the numerical value of the quantity and the unit of measurement. Additional information may optionally be provided: a label providing descriptive information for the quantity, e.g., to provide metadata related to the measurement, and the date and time of the measurement.

**Table 1.** Component structure for a univariate real quantity. Components in bold are mandatory. The notation '>' indicates that the component on the right is a subcomponent of the component on the left.


In practice, a measurement result is generally considered to be incomplete if it is not accompanied by information regarding its uncertainty. The D-SI allows for uncertainty information by extending the basic concept in Table 1 to allow the provision of an expanded uncertainty or a probabilistically symmetric coverage interval.

Tables 2 and 3 list the components of the D-SI that can be used to represent a univariate real quantity with uncertainty information provided in the form of an expanded uncertainty and a coverage interval, respectively. For each case, uncertainty information is provided using an additional, optional, component which itself comprises a number of mandatory and optional components. Therefore, for example, **uncertainty** is a subcomponent of **expandedUnc** which is itself a subcomponent of **real**. Note that the unit of measurement is not explicitly provided for the uncertainty information but is implicitly inherited from the unit component.


**Table 2.** Component structure for a univariate real quantity with expanded uncertainty.

For expanded uncertainty, in addition to the numerical value and the unit of measurement, the mandatory information comprises the coverage probability and the expanded uncertainty and coverage factor corresponding to that coverage probability. The expanded uncertainty and coverage factor allow the standard uncertainty to be determined if required. Information about the probability distribution, e.g., distribution type, parameter values, may optionally be provided.

For a coverage interval, the additional mandatory information comprises the standard uncertainty, the coverage probability and the lower and upper limits of the coverage interval corresponding to the coverage probability. Again, information about the probability distribution may optionally be provided.


**Table 3.** Component structure for a univariate real quantity with coverage interval.
