Cpk and Ppk in a Supplier Report: Check the Data Before the Number
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A capability index can look precise while its underlying process is unclear. If a supplier pools two machines, changes a tool during the study, uses the wrong drawing limits or removes inconvenient values without explanation, the reported Cpk or Ppk may not describe the production process that will make the order.
The review must therefore start with the characteristic, specification and ordered data. This guide does not set a universal capability threshold, accept a shipment or change a drawing tolerance. For the product context around hardened rollers, keep the existing track-roller process and wear context separate from the statistical evidence review.
Start with one characteristic and its specification
Identify the part number, drawing revision, feature and measurement location. Write the characteristic in operational terms: which diameter, thickness, hardness location, profile or other output was measured. Record the units and whether the data are individual readings, averages or another summary. A report heading that says “critical dimension” is not enough.
Copy the lower and upper specification limits from the controlled source. If the characteristic has only one legitimate specification limit, record that fact and verify that the analysis uses an appropriate one-sided method. Keep the engineering target separate from the specification limits; a target is not automatically an acceptance boundary.
Check that the report uses the same limits and units. A drawing change can leave an old capability worksheet with obsolete tolerances. Unit conversion and rounding can also change an index. Preserve the original values at suitable precision and record any conversion method rather than entering rounded display values into a new calculation.
Define the process population. Record machine, cavity, spindle, tool, material heat, supplier site, shift, operator or other sources that can create distinct streams. Pooling streams may be justified for a stated purpose, but the report must explain why they represent one process. Otherwise request separate analyses.
Capture the data period, sample selection, sample size and production conditions. Were values collected consecutively, periodically or from finished inspection records? Did the study include start-up, tool changes or multiple material lots? A large spreadsheet is not representative merely because it contains many rows.
Record the software, analysis type and options used. The label “Cpk” can hide choices about subgroup estimation, transformed data, non-normal models, omitted observations and confidence levels. Preserve the raw ordered data and analysis file where possible so another qualified reviewer can reproduce the result.
The NIST/SEMATECH process-capability handbook defines capability as a comparison between process variation and specification and discusses Cpk in relation to the nearest specification limit. It also places conditions on interpretation, including stability, distribution and sample adequacy. A supplier number should be read within those conditions, not as a standalone score.
Check stability and the data structure
Plot the observations in production order before relying on a histogram. A time-order plot or suitable control chart can reveal a drift, step change, cycle, start-up effect or special cause that a distribution plot hides. Ask the supplier to explain the chronology and the reaction to signals rather than calculating one index across a known change.
NIST’s process-stability guidance describes a stable process as having constant mean, variance and distribution over time and says stability should be demonstrated before capability is discussed. This does not dictate one control chart for every characteristic; it establishes why predictable behaviour matters.
Review subgroup construction. A rational subgroup is intended to capture short-interval common variation while differences between subgroups show changes over time. If a report groups unrelated machines or days simply to create a convenient subgroup size, its within-subgroup estimate may lose operational meaning. Record subgroup size, frequency and selection rule.
Check independence. Measurements taken rapidly from one continuous strip, repeated readings on the same part or values generated by an autocorrelated process may contain less independent information than the row count suggests. The analyst should address the real data structure rather than assuming every entry is an independent production unit.
Look for mixed populations. Multiple cavities, tools, materials or shifts can create a multi-modal distribution. NIST’s discussion of capability assumptions notes that mixed sources and instability can create non-normal data and undermine credibility. Separate the sources and investigate the mechanism before choosing a distribution model.
If the process is stable but fundamentally non-normal, record the model, transformation or non-parametric method and its validation. Do not force a normal curve because the software produces a familiar Cpk. Review goodness-of-fit evidence, tail behaviour and whether the model represents the physical process near the specification limit.
Confirm the measurement system is suitable. NIST’s general modelling assumptions say data should represent the process and the measurement system should be capable of the needed precision and accuracy. Link the applicable calibration and measurement-system evidence, but keep that review distinct from the capability calculation.
Account for missing and excluded data. Ask why a value is absent and whether exclusions were defined before analysis. Scrapped pieces, remeasurements and operator corrections can bias the sample if only preferred readings remain. Preserve the original series and the reason for every change.
Separate within-subgroup and overall variation
Cpk commonly compares the distance from the process mean to the nearest specification limit with an estimate of within-process variation. Ppk commonly uses overall variation calculated across the observed data. The exact estimator and terminology depend on the software and method, so read the report definitions before comparing the indices.
Within-subgroup variation attempts to describe short-term variation under the chosen subgroup plan. Its meaning depends on rational subgroups and a stable process. Overall variation includes the spread across the complete study period, including between-subgroup shifts. A difference between the two estimates can therefore be informative, but it is not a universal diagnosis of one named problem.
Ask for subgroup size, subgroup count, sampling frequency and the sigma estimation method. Moving ranges, pooled subgroup standard deviations and other estimators can yield different Cpk values from the same observations. Do not compare a supplier’s index with a customer threshold until the required method is confirmed.
Confirm that Cpk and Ppk were calculated from the same data, mean and limits. Reports sometimes display a current Cpk beside a historical Ppk or use different exclusions. Put the inputs side by side. If the populations differ, treat the numbers as separate studies.
Review centring. Cpk is affected by the distance from the mean to the nearer limit; a process can have modest spread but a poor Cpk when shifted toward one boundary. Cp or Pp, when reported, focuses on spread between two limits and does not account for the same centring effect. This is why the full set of statistics and plots matters more than one preferred index.
Avoid the loose labels “short term” and “long term” unless the report defines the actual time, subgrouping and estimator. A study conducted during one shift can still produce both within and overall estimates, but neither automatically predicts performance over months. State the observed study period and production conditions.
Check calculation precision. Reproducing an index from displayed mean and standard deviation may not match the software because the display is rounded. Use raw data or full-precision exports. If the report applies a bias correction, transformation or distribution fit, record it rather than forcing the normal Cpk formula.
Review uncertainty and follow-up evidence
A capability index is an estimate from a sample. Request a confidence bound or interval when the customer’s requirement depends on statistical assurance, and verify the method. The NIST handbook discusses confidence limits and warns that sample adequacy matters. A point estimate slightly above a threshold can have substantial uncertainty.
Do not translate a Cpk or Ppk into an expected defect rate unless the stability, distribution and model assumptions support that calculation. Tail predictions are sensitive to model error. Report the observed nonconforming count separately from a model-based estimate and keep inspection findings linked to the actual lot.
A high index does not prove every delivered part conforms. Capability describes a process model, while lot acceptance concerns identified product and the applicable inspection plan. Conversely, one nonconforming observation requires investigation even if the reported index is high; it should not be deleted solely to preserve the score.
Request a complete evidence package: ordered raw data, characteristic and specification source, sampling plan, subgroup rationale, time plot or control chart, distribution diagnostics, calculation settings, measurement-system reference, excluded-point log and process-change history. Link the study to the production lots it represents.
Record the threshold and authority separately. Customers may specify different minimum indices, confidence requirements, sample sizes or study methods. This article does not choose them. If the contract is silent, the buyer and supplier should agree on the decision purpose and method before treating the index as a release condition.
| Case | Characteristic and data | Stability and model | Cpk/Ppk method | Disposition |
|---|---|---|---|---|
| Normal | One controlled feature, revision, unit and specification are linked to ordered, representative data | Time sequence, subgroup plan, control state, measurement evidence and distribution method are documented | Within and overall estimators, software settings, intervals and threshold source are clear | Ready for authorised capability review within the stated process and period |
| Missing | Index appears without raw data, dates, machine, subgroup or current drawing limits | No time-order plot, stability assessment, model check or measurement-system reference is supplied | Report does not define sigma estimator, exclusions or confidence | Keep interpretation open and request the data and method package |
| Conflict | Report narrative names one machine or revision while data combine several | Control chart shows a shift, but one normal distribution is fitted across it | Cpk and Ppk use different limits or filtered populations without disclosure | Do not compare the indices; separate the populations and rerun the authorised analysis |
The review is complete when the index can be traced to one characteristic, specification, production population, ordered data set and stated method. Keep limitations with the result and name the owner of every follow-up. The number becomes meaningful only after the process and data structure support it; it never replaces inspection, engineering judgement or a controlled lot decision.