Set an individuals-chart baseline from ordered measurements

Define one observation

Use one measurement per comparable occasion. Record its unit, acquisition order and the conditions that make occasions comparable. A suitable research example is the elapsed time for a fixed synthetic benchmark to run on the same machine. A software upgrade or an overnight gap may break comparability. Mark that boundary before calculating adjacent differences.

Estimate a reference range

For a stable historical segment, calculate each absolute difference between consecutive observations and average the differences. With ranges of length two, divide that mean by 1.128 to estimate within-process standard deviation. Center the individuals chart on the historical mean and put limits three estimated standard deviations on either side. This construction assumes approximately normal, independent measurements from a stable process. Strong serial correlation can make adjacent differences misleadingly small.

Hypothetical calculation

Four benchmark times of 10, 12, 11 and 13 seconds have mean 11.5. The adjacent absolute differences are 2, 1 and 2 seconds. Their mean is 5/3, giving a dispersion estimate of about 1.478 seconds and reference limits near 7.07 and 15.93 seconds. Four occasions illustrate the arithmetic. A study needs a longer representative baseline before relying on the limits.

Freeze the chosen baseline and record its dates. For an observation outside the reference limits, confirm the original timestamp, unit and measurement conditions before interpreting a change. Process limits describe historical variation. Set operational acceptance thresholds independently.

Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 6.3.2.2. Individuals Control Charts.

Individuals-chart reference limits · Download the monitoring baseline selection record