01 · Purpose
Why and when to use it
Use these indices only after measurement, stability, specification and model suitability have been assessed. They help distinguish spread limitations from off-centre location.
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.
- Verify genuine specification limits and their units.
- Assess stability and distribution suitability.
- Estimate within-process sigma using a justified method and subgroup design.
- Calculate Cp and both one-sided distances for Cpk.
- Report estimates, uncertainty and the applicable acceptance requirement; compare overall Pp/Ppk separately if useful.
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 |
|---|---|
| LSL / USL / mean / within sigma | 8 / 12 / 10.5 / 0.5 |
| Cp | (12 − 8)/(6 × 0.5) = 1.333 |
| Upper / lower index | 1.5/1.5 = 1.000; 2.5/1.5 = 1.667 |
| Cpk | min(1.000, 1.667) = 1.000 |
04 · Interpretation
What the result tells you
Cp exceeds Cpk because the mean is off-centre. The supplied sigma is a hypothetical validated within-process estimate; the ordinary overall SD of an arbitrary dataset cannot simply be substituted. No universal pass threshold is assumed.
Completion check: A capability assessment with genuine specifications and documented assumptions.
05 · Judgement
Mistakes and limitations
With a single specification, use the appropriate one-sided index; Cp is not defined by inventing a second limit. If the mean is beyond a limit Cpk can be negative. Non-normal processes need justified alternative treatment.
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.