01 · Purpose
Why and when to use it
Use it for a unit-level nonconformance rate, particularly when a percentage is small.
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.
- Define the unit and what makes it nonconforming.
- Count each nonconforming unit once even if it has several defects.
- Count all eligible inspected units.
- Calculate the unit-level rate and scale it by one million.
- Report coverage and uncertainty, especially with few failures.
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.
| Illustrative input / result | Value |
|---|---|
| Inspected / nonconforming units | 2,000 / 6 |
| Rate | 6 / 2,000 = 0.003 = 0.3% |
| ppm | 0.003 × 1,000,000 = 3,000 |
04 · Interpretation
What the result tells you
Three thousand ppm means three nonconforming units per thousand in the observed sample. It is an estimate from 2,000 units, not a census of one million.
Completion check: A unit-level nonconformance rate with an explicit denominator.
05 · Judgement
Mistakes and limitations
Zero observed failures does not prove a zero population rate. Do not use a count of individual defects in a formula labelled nonconforming-unit ppm.
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.