BIZOMAT MAKEOS · Quality
Process Capability from Summary Data
What Cp and Cpk follow from this mean and within-process spread?
Calculate two-sided Cp and Cpk from supplied specifications, process mean and within-process standard deviation.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Lower specification | unit | Engineering specification in the same unit as all other dimensional inputs. |
| Upper specification | unit | Upper engineering specification; not a control limit. |
| Process mean | unit | Mean from a representative stable process dataset. |
| Within-process standard deviation | unit | Appropriate within-subgroup estimate; not tolerance divided by six. |
| Stable process and suitable distribution confirmed? | choice | Review control charts, sampling and the distribution before interpreting capability. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Lower specification
- What it is
- The lowest value of the characteristic allowed by the engineering specification or drawing.
- Units and format
- Enter a number in unit: unit. The form accepts -1000000 unit to 1000000 unit. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9.9 unit as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raising it narrows the tolerance band and lowers Cp and the lower-side index.
- Get it right
- Use the specification limit, not a control chart limit; all four values must share one unit.
What this means: Upper specification
- What it is
- The highest value of the characteristic allowed by the engineering specification or drawing.
- Units and format
- Enter a number in unit: unit. The form accepts -1000000 unit to 1000000 unit. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.1 unit as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raising it widens the band, raising Cp and the upper-side index.
- Get it right
- This is a specification limit, not an upper control limit.
What this means: Process mean
- What it is
- The average value of the characteristic from a representative dataset of a stable process.
- Units and format
- Enter a number in unit: unit. The form accepts -1000000 unit to 1000000 unit. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.02 unit as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change Cp, but moving it off centre lowers Cpk.
- Get it right
- Use enough data from normal running; a short special run can mislead.
What this means: Within-process standard deviation
- What it is
- The short-term (within-subgroup) standard deviation of the process, estimated from control chart subgroups or a capability study.
- Units and format
- Enter a number in unit: unit. The form accepts 1e-9 unit to 1000000 unit. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.02 unit as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cp and Cpk are inversely proportional to sigma.
- Get it right
- Do not use the tolerance divided by six, or the overall standard deviation if you want within-process capability.
What this means: Stable process and suitable distribution confir…
- What it is
- Whether a separate study has confirmed the process is in statistical control and its data distribution suits these indices. It changes how the result is labelled, not the numbers.
- Units and format
- Choose one of 2 options from the list: Not yet confirmed; Confirmed by a separate study.
- Example
- The form opens with “Not yet confirmed” selected as a worked example. Choose the option that matches your case.
- Get it right
- Choose Confirmed only after reviewing control charts and the distribution; the tool does not test this.
Method and formulas
- Cp = (upper specification − lower specification) / (6 × within-process standard deviation).
- Cpk = minimum of [(upper − mean)/(3σ), (mean − lower)/(3σ)].
- Example: 9.9–10.1 limits, mean 10.02 and σ = 0.02 gives Cp = 1.666667 and Cpk = 1.333333.
Limitations
- No stability test, sigma estimation, confidence interval or defect-rate forecast is performed.
- If the spread is an overall sample standard deviation, the corresponding indices are Pp/Ppk, not Cp/Cpk.
- No universal capability acceptance threshold is assumed.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Cp Cpk
- process capability
- quality statistics
Who it is for
- Quality engineers
- Manufacturing engineers
What you get
- Cp
- Cpk
- Upper-side index
- Lower-side index
Interpreting the result
- Negative Cpk means the mean lies outside a specification limit. Compare with an agreed customer criterion only after validating the study.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
- NIST/SEMATECH e-Handbook: What is Process Capability? — https://itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Controlling the process
In Induction Hardening by the Numbers
What it covers: Keeping induction hardening the same part after part: monitoring each heat, charting case depth, control limits against specification limits, capability, and a chart that hid its signal.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.