2. Measurement Process Characterization
2.3. Calibration

## What are calibration designs?

Calibration designs are redundant schemes for intercomparing reference standards and test items Calibration designs are redundant schemes for intercomparing reference standards and test items in such a way that the values can be assigned to the test items based on known values of reference standards. Artifacts that traditionally have been calibrated using calibration designs are:
• mass weights
• resistors
• voltage standards
• length standards
• angle blocks
• indexing tables
• liquid-in-glass thermometers, etc.
Outline of section The topics covered in this section are:

A catalog of calibration designs is provided in the next section.

Assumptions for calibration designs include demands on the quality of the artifacts The assumptions that are necessary for working with calibration designs are that:
• Random errors associated with the measurements are independent.
• All measurements come from a distribution with the same standard deviation.
• Reference standards and test items respond to the measuring environment in the same manner.
• Handling procedures are consistent from item to item.
• Reference standards and test items are stable during the time of measurement.
• Bias is canceled by taking the difference between measurements on the test item and the reference standard.
Important concept - Restraint The restraint is the known value of the reference standard or, for designs with two or more reference standards, the restraint is the summation of the values of the reference standards.
Requirements & properties of designs
• The differences must be nominally zero.
• The design must be solvable for individual items given the restraint.

It is possible to construct designs which do not have these properties. This will happen, for example, if reference standards are only compared among themselves and test items are only compared among themselves without any intercomparisons.

Practical considerations determine a 'good' design We do not apply 'optimality' criteria in constructing calibration designs because the construction of a 'good' design depends on many factors, such as convenience in manipulating the test items, time, expense, and the maximum load of the instrument.
• The number of measurements should be small.
• The degrees of freedom should be greater than three.
• The standard deviations of the estimates for the test items should be small enough for their intended purpose.
Check standard in a design Designs listed in this Handbook have provision for a check standard in each series of measurements. The check standard is usually an artifact, of the same nominal size, type, and quality as the items to be calibrated. Check standards are used for:
Estimates that can be computed from a design Calibration designs are solved by a restrained least-squares technique (Zelen) which gives the following estimates:
• Values for individual reference standards
• Values for individual test items
• Value for the check standard
• Repeatability standard deviation and degrees of freedom
• Standard deviations associated with values for reference standards and test items