01 · Purpose
Why and when to use it
Use it alongside location and charts, and in models whose assumptions justify a standard-deviation-based interpretation.
Who takes part?
The measurement owner works with people who understand the process and the recorded data. Statistical or measurement-system decisions should involve someone able to check the assumptions and study design.
02 · Application
How to apply it
Start with an agreed measurement purpose, explicit units and trustworthy observations. Identify missing cases and assumptions before calculating.
- Check the population, units and variance convention.
- Calculate variance from squared deviations.
- Take its square root.
- State whether the estimate is overall or a within-subgroup process estimate.
- Inspect the distribution and time behaviour before using normal-model claims.
03 · Example
A worked measurement example
Original fictional teaching example. Small datasets illustrate the method; they are not proposed as sufficient study sizes. Supplied parameters are assumptions, not estimates from a real process.
| Sample 2, 4, 4, 6, 9 minutes | Result |
|---|---|
| Sample variance | 7 min² |
| Sample standard deviation | √7 = 2.646 minutes |
| Mean ± one sample SD | 5 ± 2.646 minutes; descriptive interval, not a confidence interval |
04 · Interpretation
What the result tells you
A standard deviation has the original unit. Roughly 68% within one standard deviation is a normal-distribution property, not a universal rule for any dataset.
Completion check: A labelled spread estimate with units and intended use made clear.
05 · Judgement
Mistakes and limitations
The ordinary sample SD is not automatically the within-process sigma required for Cp/Cpk. Outliers, dependence and mixtures can change what the estimate represents.
07 · Reading
Sources and further reading
The tool list follows the accepted LeanTrainingLab overview and its reference to Six Sigma+Lean Toolset, second edition (Lunau, editor; Springer, 2013). The book chapters were not available for direct review during this build. Explanations, examples and worksheets are original teaching material. Further reading supplies professional background; local conventions are stated explicitly.