2. Measurement Process Characterization
2.5. Uncertainty analysis
2.5.3. Type A evaluations
2.5.3.1. Type A evaluations of random components

2.5.3.1.1.

Type A evaluations of time-dependent effects

Time-dependent changes are a primary source of random errors

One of the most important indicators of random error is time. Effects not specifically studied, such as environmental changes, exhibit themselves over time. Three levels of time-dependent errors are discussed in this section. These can be usefully characterized as:

1. Level-1 or short-term errors (repeatability, imprecision)
2. Level-2 or day-to-day errors (reproducibility)
3. Level-3 or long-term errors (stability - which may not be a concern for all processes)

Day-to-day errors can be the dominant source of uncertainty

With instrumentation that is exceedingly precise in the short run, changes over time, often caused by small environmental effects, are frequently the dominant source of uncertainty in the measurement process. The uncertainty statement is not 'true' to its purpose if it describes a situation that cannot be reproduced over time. The customer for the uncertainty is entitled to know the range of possible results for the measurement result, independent of the day or time of year when the measurement was made.

Two levels may be sufficient

Two levels of time-dependent errors are probably sufficient for describing the majority of measurement processes. Three levels may be needed for new measurement processes or processes whose characteristics are not well understood.

Measurements on test item are used to assess uncertainty only when no other data are available

Repeated measurements on the test item generally do not cover a sufficient time period to capture day-to-day changes in the measurement process. The standard deviation of these measurements is quoted as the estimate of uncertainty only if no other data are available for the assessment. For J short-term measurements, this standard deviation has v = J - 1 degrees of freedom.

A check standard is the best device for capturing all sources of random error

The best approach for capturing information on time-dependent sources of uncertainties is to intersperse the workload with measurements on a check standard taken at set intervals over the life of the process. The standard deviation of the check standard measurements estimates the overall temporal component of uncertainty directly -- thereby obviating the estimation of individual components.

Nested design for estimating type A uncertainties

Case study: Temporal uncertainty from a 3-level nested design

A less-efficient method for estimating time-dependent sources of uncertainty is a designed experiment. Measurements can be made specifically for estimating two or three levels of errors. There are many ways to do this, but the easiest method is a nested design where J short-term measurements are replicated on K days and the entire operation is then replicated over L runs (months, etc.). The analysis of these data leads to:

• s₁ = standard deviation with (J -1) degrees of freedom for short-term errors
• s₂ = standard deviation with (K -1) degrees of freedom for day-to-day errors
• s₃ = standard deviation with (L -1) degrees of freedom for very long-term errors

Approaches given in this chapter

The computation of the uncertainty of the reported value for a test item is outlined for situations where temporal sources of uncertainty are estimated from:

1. measurements on the test item itself
2. measurements on a check standard
3. measurements from a 2-level nested design (gauge study)
4. measurements from a 3-level nested design (gauge study)