# Variability

Variability is the tendency of the measurement process to produce slightly different measurements on the same test item, where conditions of measurement are either stable or vary over time, temperature, operators, etc. In this chapter we consider two sources of time-dependent variability:

• Short-term variability ascribed to the precision of the instrument
• Long-term variability related to changes in environment and handling techniques

### Sources of time-dependent variability

Depiction of two measurement processes with the same short-term variability over six days where process 1 has large between-day variability and process 2 has negligible between-day variability

Process 1                Process 2
Large between-day variability  Small between-day variability

Distributions of short-term measurements over 6 days where distances from the centerlines illustrate between-day variability

### Short-term Variability

Short-term errors affect the precision of the instrument. Even very precise instruments exhibit small changes caused by random errors. It is useful to think in terms of measurements performed with a single instrument over minutes or hours; this is to be understood, normally, as the time that it takes to complete a measurement sequence.

### Terminology

Four terms are in common usage to describe short-term phenomena. They are interchangeable.

1. precision
2. repeatability
3. within-time variability
4. short-term variability

#### Precision is quantified by a standard deviation

The measure of precision is a standard deviation. Good precision implies a small standard deviation. This standard deviation is called the short-term standard deviation of the process or the repeatability standard deviation.

#### Caution -- long-term variability may be dominant

With very precise instrumentation, it is not unusual to find that the variability exhibited by the measurement process from day-to-day often exceeds the precision of the instrument because of small changes in environmental conditions and handling techniques which cannot be controlled or corrected in the measurement process. The measurement process is not completely characterized until this source of variability is quantified.

### Terminology

Three terms are in common usage to describe long-term phenomena. They are interchangeable.

1. day-to-day variability
2. long-term variability
3. reproducibility

#### Caution -- regarding term 'reproducibility'

The term 'reproducibility' is given very specific definitions in some national and international standards. However, the definitions are not always in agreement. Therefore, it is used here only in a generic sense to indicate variability across days.

We adopt precise definitions and provide data collection and analysis techniques in the sections on check standards and measurement control for estimating:

In the section on gauge studies, the concept of variability is extended to include very long-term measurement variability:

We refer to the standard deviations associated with these three kinds of uncertainty as "Level 1, 2, and 3 standard deviations", respectively.

### Long-term variability is quantified by a standard deviation

The measure of long-term variability is the standard deviation of measurements taken over several days, weeks or months. The simplest method for doing this assessment is by analysis of a check standard database. The measurements on the check standards are structured to cover a long time interval and to capture all sources of variation in the measurement process.