Buying & quotation · Standard & custom equipment

Cpk, Ppk or a Short Machine Trial: What Evidence Are You Buying?

Define variation estimates, rational subgroups and trial coverage before putting a capability index into a drilling or tapping machine acceptance agreement.

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The short answer

A short trial can demonstrate the inspected samples under its recorded conditions, but a capability number needs a defined measurement system, population, sampling plan and statistical method. Cpk and Ppk use different variation estimates in normal capability analysis. Neither label makes a brief run representative of future production. Specify the evidence behind the number before agreeing an acceptance threshold.

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Review the published specifications and configuration options against your part drawing before requesting a quote.

Separate sample conformance from a process claim

A report saying every inspected hole passed answers a question about those observations. A proposal promising process capability makes a broader claim. Ask which characteristic, operating conditions and production interval the claim covers. A diameter result cannot stand in for thread acceptance or hole position, and a successful demonstration on one tool does not automatically cover its replacement.

NIST describes capability as a comparison between a stable process and specification limits, with distributional assumptions behind the familiar normal indices. Accordingly, ask for a time-ordered stability assessment and a justified analysis method before treating an index as predictive. An unstable series can be summarized, but its summary is not assurance that tomorrow's process will behave the same way.

Name the standard deviation, not just the index

Minitab distinguishes Cpk calculated with a within-subgroup standard deviation from Ppk calculated with the overall standard deviation. For a two-sided normal analysis, both take the smaller of the upper and lower distances from the mean, divided by three times the relevant standard deviation. Overall variation describes all observations collected; within variation depends on the subgroup design and estimation method.

In that framework, a rational subgroup collects observations made under comparable conditions close together in time. It is not a collection of whichever readings happen to be similar. Request the actual subgroup identifiers and estimation settings. Do not rearrange a completed series to improve its index, or call a Ppk result long-term merely because the software prints that label. The observation period still determines its coverage.

An invented example shows why the same mean is insufficient

This original arithmetic illustration uses no production measurements. Assume diameter limits of 9.950 and 10.050 mm, a mean of 10.010 mm, a supplied within standard deviation of 0.008 mm and a supplied overall standard deviation of 0.012 mm. The two deviations are hypothetical inputs, not estimates calculated from a hidden sample. No subgroup count, stability conclusion or confidence interval is implied.

The nearer limit is 0.040 mm from the mean. Using the normal-index formulas gives Cpk = min(0.040, 0.060) / (3 × 0.008) = 1.67 after rounding; Ppk = min(0.040, 0.060) / (3 × 0.012) = 1.11. These are arithmetic outputs, not passing or failing grades. Their difference invites questions about the supplied variation estimates; it does not diagnose tool wear or validate the assumptions.

Original hypothetical calculation: all dimensions and deviations in mm
Input or resultWithin calculationOverall calculation
Shared upper / lower distance0.040 / 0.0600.040 / 0.060
Assumed standard deviation0.0080.012
Three times standard deviation0.0240.036
Smaller distance divided by denominatorCpk = 1.67Ppk = 1.11
What remains unprovedSubgroup validity and stabilityRepresentation of future production

Put an analysis brief beside the drawing

Use the following original template when asking for an evidence-based trial proposal. Its fields describe the statistical deliverable rather than another machine commissioning checklist. The quality owner should determine the sample size from the decision, uncertainty and operating coverage required. A universal sample count or index threshold is not supplied here.

Capability evidence brief to complete before quotation acceptance
FieldDefinition to agree
PopulationOne characteristic, unit, drawing revision and stated production conditions
CoverageRun duration, sampling intervals, material lots and tool-life stages included or excluded
SubgroupsHow observations are grouped, why conditions are comparable and which estimator is used
MeasurementMethod suitability and retained unrounded readings with traceable identities
AnalysisStability review, distribution method, independence considerations and interval estimates
DecisionAgreed threshold, confidence basis, exclusions and action if evidence is insufficient

Do not let a larger spreadsheet hide a different process

For a multi-spindle proposal, state whether each hole stream is evaluated separately and what justifies any pooled result. Combining distinct nominal sizes or treating several correlated holes on one part as independent parts can change the question being answered. Preserve hole, part, time and tool identities so the analyst can evaluate the intended population instead of reverse-engineering it from an average.

NIST also discusses uncertainty in estimated indices and approaches for non-normal data. Request an appropriate confidence statement, not just extra decimal places. Do not translate an index into a reject-rate promise without checking the underlying model. If only pass/fail observations exist, do not manufacture numerical diameters to feed a normal capability calculation. Agree a suitable analysis for the actual data.

Prepare your part information

  • Define the characteristic and population
  • Record time and subgroup identity
  • Name the variation estimator and distribution method
  • Specify coverage and confidence requirements
  • Agree how insufficient evidence will be handled
Discuss capability evidence →

Common questions

Does a high Cpk guarantee that the machine will meet the drawing?

No. Review the measurement method, stability, data coverage and required characteristics. A statistic for one evaluated feature is not an equipment-wide performance guarantee.

Must every trial use the same sample count or acceptance index?

No. Agree the decision and statistical evidence with the quality owner before collecting data. Sample count alone does not establish representative coverage or adequate precision.

Sources and further reading

Define the evidence your machine trial must deliver

Send the marked drawing, measurement basis and proposed capability requirement. Include the production conditions and data coverage your quality team needs so the trial scope can be reviewed.

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