01 · Purpose
Why and when to use it
Use it before analyses that rely on a distribution assumption, such as normal-model capability calculations.
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.
- Choose a plausible distribution based on the characteristic and context.
- Sort observations and calculate plotting positions using a documented convention.
- Compare them with theoretical quantiles.
- Inspect curvature, tails, ties and outlying points.
- Combine the plot with process knowledge, sample size and appropriate model checks.
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.
| Ordered value (minutes) | Illustrative position (i − 0.5) / n |
|---|---|
| 2 | 0.10 |
| 4 | 0.30 |
| 4 | 0.50 |
| 6 | 0.70 |
| 9 | 0.90 |
04 · Interpretation
What the result tells you
These positions specify where to compare each value with the chosen distribution’s quantiles. The five-value example teaches construction; it is insufficient to confidently establish tail behaviour.
Completion check: A documented assessment of a candidate distribution’s plausibility.
05 · Judgement
Mistakes and limitations
A straight-looking plot does not prove independence or stability. Non-significant normality tests may simply reflect low power; large samples can reveal practically minor deviations.
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.