What Can a Supplier's Cpk Actually Promise? Process Evidence Before Lot Acceptance

By Daoyu Guan

A supplier's Cpk can support an assessment of a defined production process relative to specified limits, when the study's stability, sampling and distribution assumptions are justified. It cannot establish monthly production capacity, the percentage of arriving lots that will pass an AQL plan, or acceptance of your shipment. The useful buying decision is whether the evidence supports a particular characteristic under the proposed production conditions, and what monitoring or requalification must accompany that assessment. Request the study behind the index, match it to your requirement, and keep delivery allocation and lot disposition as separate decisions.

Decide which promise you are evaluating

An overseas buyer receives three documents: a brochure advertising 10,000 parts per month, a slide showing Cpk 1.33, and an inspection report marked accepted. All three may be relevant. They answer different questions.

Capacity concerns how much relevant output can be supplied within a period and allocated to the order. Cpk concerns process location and variation relative to limits for a measured characteristic. A lot inspection applies its agreed decision rule to an identified lot. None of these documents supplies the missing contents of the others.

The earlier guide to comparing two 10,000-part capacity claims addresses scheduling and output assumptions. Here the narrower question is whether a capability study justifies including a particular process commitment in a supplier agreement.

These are decision categories, not an engineering approval procedure. The buyer and supplier must agree which requirements govern their actual order.

Stability comes before a capability conclusion

A spreadsheet can calculate an index from unstable data. The presence of a number does not demonstrate that the process has a repeatable statistical pattern. NIST's process-stability explanation places stability before capability and describes stable mean, variance and distribution over time. It discusses observations in time order and graphical assessment, including control charts.

Ask for the sequence behind the summary. Does the study cover the intended operating period, or only a short demonstration after adjustment? Were different machines, cavities, shifts or process settings combined? Were observations removed, and on what documented basis? A histogram alone loses the order in which the measurements occurred.

Suppose the first half of a study comes from one setting and the second half follows an adjustment. Pooling them may conceal the change. Conversely, splitting data until each selected group looks attractive can conceal what production actually does. The review needs the process history and a justified grouping method.

A stable process can still perform poorly against specifications. Stability concerns the behavior over time; suitability against the buyer's limits is another question. Likewise, a dimension that stayed inside tolerance during a short demonstration does not establish stability across the operating conditions that matter to the order.

This is why the requested evidence should name its period and conditions. A supplier should be able to explain which production state the index describes and what changes would require its interpretation to be revisited.

Read Cp and Cpk as different pieces of information

For the conventional two-sided case, let LSL and USL be the lower and upper specification limits, μ the process mean, and σ its standard deviation. The formulas are:

Cp = (USL − LSL) / (6σ)

Cpk = min[(USL − μ) / (3σ), (μ − LSL) / (3σ)]

Cp compares specification width with process spread. Cpk also reflects the mean's position relative to the nearer limit. Two processes can therefore have the same Cpk while presenting different combinations of spread and offset. NIST's capability assessment explains the distinction and gives the corresponding formulas using sample estimates.

For a real study, the mean and spread are estimated. Ask which spread estimator was used, how the observations were grouped, and how uncertainty was evaluated. NIST's capability-index chapter discusses independent observations, normal-distribution assumptions, sample-size conditions and confidence limits. A point estimate without its study design is incomplete evidence.

If the data are not adequately represented by the assumed distribution, request a justified analysis rather than a familiar label. A different statistical label does not fill a missing explanation of the data or demonstrate stability. This article does not prescribe a replacement index or a universal sample size.

A fictional calculation: identical Cpk, different next questions

The following is an invented teaching example, not a supplier study or a recommended process. Assume two separate, stable, normally distributed populations with known parameters. Both have specification limits of 24.90 mm and 25.10 mm. No observations were collected for this article.

For Process A, assume μ = 25.040 mm and σ = 0.015 mm. Its specification width is 0.200 mm, so:

Cp(A) = 0.200 / (6 × 0.015) = 2.222…

The upper-side ratio is 0.060 / 0.045 = 1.333…. The lower-side ratio is 0.140 / 0.045 = 3.111…. Therefore Cpk(A) = 1.333….

For Process B, assume μ = 25.000 mm and σ = 0.025 mm. Its mean is at the specification midpoint:

Cp(B) = 0.200 / (6 × 0.025) = 1.333…

Each side is 0.100 / 0.075 = 1.333…, so Cpk(B) = 1.333… too.

A buyer reading only Cpk would miss that A has narrower spread but less distance to the upper limit, while B is centered with wider spread. The useful follow-up differs: investigate A's centering and its control, or B's sources of variation. Those are questions for the responsible process specialists, not instructions to adjust a machine from a marketing article.

Re-centering A while preserving its assumed spread would produce a different hypothetical result. It does not prove that the real operation can be re-centered or will remain stable afterward. Nor does either calculation establish a monthly quantity, a lot-acceptance probability or an actual nonconforming rate.

Turn the index into a scoped evidence commitment

A defensible commitment begins with the characteristic and production state. Identify the drawing revision, material, process stage, facility and relevant equipment or route. A study of a diameter before coating cannot automatically support the same dimension after coating. A result for one product does not silently qualify a family with different geometry.

Next, identify what the supplier is actually undertaking to provide. It might be a dated study for a specified feature, periodic evidence under an agreed control plan, or a review after defined changes. Those are concrete, reviewable deliverables. An unconditional claim that all future parts will conform is much broader than a historical index can support.

Keep a chosen threshold within the agreement that created it. A buyer may have a customer requirement, internal criterion or industry-specific procedure. State the required index, calculation basis, evidence period and whether the decision uses an estimate or an agreed confidence bound. This guide does not designate 1.33, or any other value, as a universal approval threshold.

Document change triggers too. Moving a process, replacing tooling, changing material or revising a feature can alter the relevance of an earlier study. The parties should decide how those events are reviewed and who can authorize continued reliance on existing evidence.

The earlier tolerance-claim guide distinguishes drawing limits, measured results and process evidence. The additional decision here is what evidence the supplier must continue to furnish once a capability claim becomes part of the buying discussion.

Request the study in six practical steps

1. Freeze the requirement being reviewed. Name the characteristic, units, limits, drawing revision and process stage. Resolve whether the specification is two-sided before applying the formulas above.
2. Match the proposed production conditions. Identify the facility, route, equipment grouping, material and operating period represented. Record differences from the buyer's intended order instead of assuming transferability.
3. Inspect the data history. Obtain the authorized time-ordered measurements or an adequate controlled review, stability assessment and explanation of excluded observations. Respect confidentiality while preserving a reviewable basis.
4. Review the statistical method. Ask about independence, subgrouping, distribution assessment, the spread estimator, sample-size rationale and uncertainty. Check that the calculation can be reconstructed from the supplied information.
5. Define the ongoing obligation. Agree the evidence to be supplied, applicable criterion, review frequency, change triggers and escalation route. Have the responsible technical parties approve the actual commitment.
6. Keep release decisions separate. Preserve the order-specific capacity confirmation and the lot acceptance requirements. Record explicitly whether any inspection change has been authorized; do not infer one from Cpk.

A missing study need not imply a dishonest supplier. It means the proposed statistical claim has not yet supplied the basis for this decision. Ask for the missing evidence or narrow the commitment to what can be established.

An accepted lot does not validate every process claim

NIST describes acceptance sampling as using a sample to decide the disposition of a lot, rather than primarily estimating its quality. Its sampling-plan overview separately describes AQL and the operating characteristic relationship between lot quality and acceptance probability. Cpk is neither an AQL parameter nor the observed proportion of lots accepted.

A report saying that nine of ten inspected lots were accepted records a defined set of lot outcomes, if supported by the records. It does not establish Cpk. Conversely, a capability study does not override a shipment's failed inspection or authorize relaxing the agreed sampling plan. The AQL explainer covers that lot-decision boundary in detail.

Do not convert a Cpk value into a universal defects-per-million promise. Distribution, stability, the two specification sides and the population represented matter. This article intentionally calculates indices only; no universal defect-rate conversion or shipment guarantee follows from its fictional example.

Publish the promise with its boundary intact

A supplier page can state which capability evidence is available for technical review, its supported scope and how current relevance is confirmed. A bare badge reading Cpk 1.33 is less useful than an explanation that connects the statistic to a characteristic and a dated study. Keep the operational requirement in the quotation and controlled quality documents.

Xindar's manufacturing content work can help turn approved technical information into English buyer pages. The underlying study and production commitment still require the authorized parties' review.

For reviewing sampled AI summaries of a capability claim, Semvi by Xindar has product-team-confirmed consumer-web sampling for ChatGPT and Gemini. That monitoring does not validate manufacturing capability.

Frequently asked questions

Can a high Cpk compensate for insufficient production capacity?

1. It does not allocate machines, materials or production time to your order. Obtain a separate feasible capacity and delivery assessment.

Does an incoming lot passing inspection prove that the process is stable?

1. A lot decision and a time-based process assessment use evidence for different purposes. Review the production history and agreed statistical method.

Should a buyer always prefer the higher Cpk?

First check whether the studies describe comparable requirements and conditions. A higher number from a different feature or selected demonstration may not answer your question.

Can the same index be copied after a drawing revision?

Only after the responsible reviewers establish that the study remains relevant. A changed limit or process stage can change the meaning of the comparison.

Is a capability report an engineering approval?

It is evidence for the applicable review. Approval, production controls and shipment disposition require their own defined authority and records.

Sources and scope

The linked NIST handbook pages and Xindar pages were checked on November 2, 2026. NIST supplies statistical explanations; it does not approve the fictional processes or prescribe this article's purchasing workflow. All process values, supplier-document scenarios and example lot counts are invented for teaching. No factory was inspected, customer dataset tested, shipment accepted or engineering approval issued for this article.