Why is Cpk low when Cp looks good?

Cp can look good while Cpk is low because the process has enough room for its spread but is positioned too close to one specification limit. Cp compares widths. Cpk also considers where the average sits. Before acting on the gap, confirm that both figures use the same data, specification limits and variation estimate.

For a quality engineer, the useful question is what to investigate next: the process setting, its variation, or the evidence behind the calculation. This worked explainer is for manufacturing teams, with US search demand informing the topic. It is not a product-release rule or an industry-specific acceptance standard.

For the normal capability method used here, Cp is the specification width divided by six times the within-process standard deviation. Cpk takes the smaller of the distances from the mean to each specification limit, divided by three times that same standard deviation. The indices have no units. NIST capability definitions

Use the agreed product or process specifications, not the control limits calculated from a control chart. They answer different questions. In this article, “centered” means centered between the two specification limits. A separately specified engineering target need not be their midpoint.

In Minitab's normal analysis, Cp and Cpk use a within-subgroup variation estimate. Pp and Ppk use overall variation. A spreadsheet's standard deviation of every measurement is therefore not automatically the appropriate denominator for a reported Cpk. Record the estimation method rather than relying on a column heading. Minitab explanation of within and overall variation

All inputs below are fictional teaching assumptions, not measurements from a factory. Assume a stable, approximately normal process measuring one dimension in millimetres. The lower specification limit (LSL) is 9.75 mm and the upper specification limit (USL) is 10.25 mm. The assumed mean is 10.15 mm and the assumed within-process standard deviation is 0.05 mm. No raw observations or control chart are supplied, so these assumptions do not establish the capability of a real process.

The specification width is 10.25 − 9.75 = 0.50 mm. Six standard deviations span 6 × 0.05 = 0.30 mm. Thus Cp = 0.50 ÷ 0.30 = 1.67, rounded.

Now calculate each side separately. Three standard deviations equal 0.15 mm.

Calculations use unrounded values; results are displayed to two decimal places. The upper specification is the limiting side. The mean is only 0.10 mm below it, although the full specification window is 0.50 mm wide. That explains the gap between Cp and Cpk. It does not identify the physical cause of the offset.

A useful arithmetic cross-check is Cp = (CPU + CPL) ÷ 2 when both sides use the same inputs. Here, the exact values are 2/3 and 8/3; their average is 5/3, matching Cp. Cpk cannot exceed Cp under these definitions. If your report shows otherwise, reconcile the data, limits, units, methods and rounding before interpreting the process. NIST one-sided indices and relationships

Consider two separate hypothetical changes, each starting from the original inputs. These are calculations of possible outcomes, not forecasts or instructions to adjust a machine.

Move the mean to 10.00 mm while keeping the standard deviation at 0.05 mm. Each limit is then 0.25 mm away. CPU and CPL both become 0.25 ÷ 0.15 = 1.67. Cpk rises to 1.67, while Cp stays at 1.67. The spread has not improved; its position has changed.

Keep the mean at 10.15 mm but halve the standard deviation to 0.025 mm. Cp becomes 0.50 ÷ 0.15 = 3.33. CPU becomes 0.10 ÷ 0.075 = 1.33 and CPL becomes 0.40 ÷ 0.075 = 5.33. Cpk is 1.33, rounded. This route improves the limiting-side result but leaves the original offset in place.

Neither scenario establishes what is feasible, economical or safe. A setting change can also alter variation or another product characteristic. Have the responsible engineer define and authorise a trial, its restrictions and its evaluation criteria before changing the process. Re-estimate the results from the trial data instead of treating an assumed constant standard deviation as a verified outcome.

If the original Cp itself is below your required capability level, centering alone cannot raise Cpk above that Cp while the variation and limits remain unchanged. Conversely, widening a specification would change the arithmetic without improving the process. Any specification change needs its own technical authority and justification.

Normal capability analysis needs continuous measurement data, a suitable distribution model and evidence that the process is stable. Collect observations over conditions representative of the intended claim, using rational subgroups where appropriate. A few convenient measurements cannot establish ongoing capability. Minitab recommends trying to collect at least 100 observations; that is guidance, not a guarantee that the sampling design is adequate. Minitab data considerations

Start the review with the time-ordered data and appropriate control charts. Do not infer stability merely because Cp and Cpk are close. If shifts or special causes remain unresolved, do not use the capability estimate to promise future performance. If the normal model is unsuitable, select and justify an appropriate alternative analysis rather than forcing these formulas onto the data.

Check the measurement method as well. Record the instrument, resolution, calibration status and evidence of suitability for the dimension and tolerance. Mixing measurements from different methods or silently deleting inconvenient observations can change the apparent spread. Our guide to measurement suitability explains the use decision behind a calibration record; its Singapore accreditation context is not a US legal requirement.

Keep the sample size, subgroup design, study period and estimation method with the result. Use a suitable confidence interval or bound when assessing a real estimated capability index. A point estimate just above a chosen threshold is not certainty about the underlying process. Minitab's interpretation guidance discusses confidence bounds and comparison with the benchmark appropriate to the process. Capability interpretation and confidence intervals

There is no universal pass mark established here. Confirm the applicable customer, engineering or sector requirement and whether it governs a point estimate, a confidence bound or another measure. Neither 1.33 nor 1.67 in this example authorises shipment or proves product safety.

The following record is fictional and deliberately separates the arithmetic finding from an operational decision. Its evidence gaps must remain visible.

• Record: CAP-019-v1; one dimensional characteristic; units mm
• Input basis: LSL 9.75; USL 10.25; mean 10.15; within-process standard deviation 0.05; all assumed
• Result: Cp 1.67; CPU 0.67; CPL 2.67; Cpk 0.67; upper side limits the result
• Interpretation: The assumed mean is 0.15 mm above the specification midpoint; the calculation supports investigating centering
• Missing evidence: Raw measurements, study period, subgroup design, stability, distribution fit, measurement suitability and approved acceptance criterion
• Decision: No capability acceptance or product-release decision from this example; request the missing study evidence
• Owner and next step: Quality engineer reconciles the inputs; process engineer assesses whether a controlled centering trial is justified
• Closure evidence: Trial observations and updated charts/indices, evaluated against the agreed criteria; an improved spreadsheet scenario alone does not close the action

For a real record, replace each assumption with a traceable source and preserve the calculation version. Keep observed nonconforming counts and first-pass yield alongside the capability study when relevant. Those counts describe what happened; an index and its distribution model address a different question. This example does not convert Cpk into an observed defect percentage.

With only one genuine specification limit, use the appropriate one-sided measure; do not invent a second limit just to obtain Cp. If the mean falls beyond a limit, the corresponding index can be negative. A zero estimated standard deviation makes these divisions undefined and calls for checking the data and measurement resolution, not reporting infinite capability. Counts of defects or defective units need an analysis suitable for attribute data. NIST one-sided guidance · Minitab data considerations

The next useful action is to identify which side limits the result and whether the underlying study supports a decision. A high Cp is useful information about spread. It cannot compensate for an unexamined offset or an unreliable study.

NIST/SEMATECH e-Handbook section 6.1.6, definitions, one-sided indices and capability assumptions; current text checked 19 October 2026. No current page revision date is stated.

Minitab potential within capability and data considerations, current support guidance checked 19 October 2026; no publication or revision dates stated. Minitab Cp and Cpk explanation, published 29 June 2017, checked 19 October 2026.

The scenarios and CAP-019-v1 are QSE Advisory's original illustrative analysis. All operational inputs are fictional. Preparation included AI-assisted research, drafting and calculation checks. Reviewer and Assessor: Laraib Naveed Ahmad. Questions or corrections: office@qseadvisory.com.

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