Process Capability (Cpk, Ppk, Cp, Pp)

Calculate Cpk, Ppk, Cp, and Pp values instantly. Determine if your process meets specifications with professional capability studies.

Six Sigma Foundation: Capability indices evaluate how process performance compares to customer specifications, quantifying the ability to produce output within defined tolerance limits. Statistical process control must confirm stability before capability evaluation—analyzing unstable processes produces meaningless results.

Core methodology in the Six Sigma Measure and Control phases, supporting PPAP submissions, supplier qualification, and continuous improvement initiatives.

Calculate Process Capability →

Understanding Capability Indices

Process capability analysis determines whether your manufacturing process can consistently produce output within specification limits. It's essential for PPAP submissions, Six Sigma projects, and continuous improvement initiatives.

Simple terms: Cpk tells you if your process is centered within specifications and how much variation exists. A Cpk of 1.33 means your process is 4 standard deviations away from the nearest specification limit—generally considered the minimum for manufacturing.

Cp (Process Potential)

≥ 1.33

Measures potential spread relative to tolerance. (USL-LSL)/6σ

Statistical Interpretation: Cp evaluates process potential by comparing the specification width (tolerance) to the process spread (6σ). It assumes perfect centering and represents the best possible performance if the process mean aligns exactly with the target.

Cpk (Process Capability)

≥ 1.33

Evaluates centering AND spread simultaneously. min[(USL-μ)/3σ, (μ-LSL)/3σ]

Statistical Interpretation: Cpk accounts for both process variation and centering by measuring distance from the mean to the nearest specification limit. It represents the actual protection against specification violations, penalizing off-center processes.

Pp (Performance Index)

≥ 1.33

Long-term variation using overall standard deviation

Statistical Interpretation: Pp reflects long-term performance including process drift, shifts, and instability between subgroups. It uses overall standard deviation (all data combined) rather than within-subgroup variation, capturing total observed variation over time.

Ppk (Performance Index)

≥ 1.67

Long-term with centering for new processes

Statistical Interpretation: Ppk combines long-term variation assessment with centering evaluation. It represents the actual historical performance including all sources of variation—within-subgroup, between-subgroup, and temporal drift. Required for new process validation.

Short-Term vs. Long-Term Variation

Short-term (Cp/Cpk): Uses within-subgroup variation (R-bar/d2 or S-bar/c4), capturing inherent process capability under stable conditions. Reflects potential if process remained stable.

Long-term (Pp/Ppk): Uses overall standard deviation (sample standard deviation of all data), capturing total variation including drift, tool wear, material lot changes, and environmental shifts. The gap between Cpk and Ppk indicates process stability.

Analysis Output & Interpretation

Capability Histogram + Normal Curve

Visual distribution with specification limits (LSL, USL, Target) overlay and normal curve fit. See exactly where your process sits relative to requirements.

Interpretation: Distribution fit visualization reveals skewness, outliers, and alignment with specifications. If the normal curve poorly fits the histogram, capability indices may misrepresent actual defect risk. Bimodal or skewed distributions suggest special causes or mixed populations requiring investigation.

Cpk/Ppk with Confidence Intervals

Point estimates with 95% confidence intervals. Know the precision of your capability assessment based on sample size.

Interpretation: Sampling uncertainty means calculated Cpk is an estimate, not the true value. Confidence intervals show the range likely containing the true capability. Small samples (n<50) produce wide intervals—decisions based on point estimates alone risk false conclusions.

Normality Test (Anderson-Darling)

Validate the normality assumption required for standard capability indices. Includes probability plot for visual assessment.

Interpretation: Standard capability formulas assume normal distribution. Non-normal data (common in bounded processes, wear patterns, or natural limits) produces incorrect defect rate estimates. Anderson-Darling detects non-normality; if p-value < 0.05, use Box-Cox transformation or non-parametric methods.

Defect Rate Estimation (PPM)

PPM (parts per million) defective calculation based on fitted distribution. Translate Cpk into real-world defect rates.

Interpretation: Converts capability indices into expected defect rates assuming normal distribution. Cpk = 1.33 predicts ~66 PPM (0.0066% defect rate). Cpk = 1.67 predicts ~0.6 PPM. These estimates assume statistical control—unstable processes will produce higher actual defect rates.

Is Your Process Capable? Professional Context

Cpk < 1.0 Not capable. Significant defects expected. Immediate improvement required.
1.0 ≤ Cpk < 1.33 Marginally capable. May meet requirements but needs close monitoring.
1.33 ≤ Cpk < 1.67 Capable. Meets automotive and general manufacturing standards.
Cpk ≥ 1.67 Highly capable. Six Sigma level (3.4 DPMO) with margin for drift.

Industry Variation: Capability thresholds vary by industry and risk severity. Automotive (AIAG) requires Cpk ≥ 1.33 for initial production, ≥ 1.67 for critical safety characteristics. Aerospace may require Cpk ≥ 2.0 for flight-critical dimensions. Medical devices balance capability with functional validation—high Cpk does not guarantee clinical performance.

Risk Consideration: Target capability must consider consequence of failure. Safety-critical features require higher Cpk than cosmetic features. Regulatory standards (FDA, FAA, automotive) mandate specific minimums based on risk classification.

Process Capability Assumptions

Methodological Requirements for Valid Analysis

  • Statistical Stability: Process must be in statistical control (stable mean and variation) before capability evaluation. Control charts must show no special causes or trends. Analyzing unstable processes produces meaningless capability indices.
  • Measurement System Validation: Measurement systems must be validated through MSA (Gage R&R) before capability studies. If measurement error exceeds 30% of tolerance, capability indices reflect measurement variation rather than process performance.
  • Production Representativeness: Data must represent actual production conditions including all sources of variation (operators, material lots, environmental conditions). Excluding "outliers" that represent real production conditions biases results.
  • Observation Independence: Data points must be independent observations. Autocorrelation (sequential dependency) in processes like chemical batches or continuous flows violates independence assumptions and requires time-series analysis methods.
  • Distribution Verification: Standard indices assume normal distribution. Non-normal processes (bounded at zero, natural limits, wear patterns) require transformation (Box-Cox) or non-parametric capability methods to avoid misleading conclusions.

Model Limitations & Constraints

Critical Interpretation Constraints

  • Static Process Assumption: Capability indices assume static process behavior during the sampling period. Rapid process changes, tool wear, or material shifts during data collection invalidate the single-capability summary.
  • Specification Sensitivity: Capability indices are extremely sensitive to specification limit placement. Arbitrary or incorrect specifications produce misleading capability assessments—tightening specifications artificially reduces Cpk without process changes.
  • Non-Normal Misrepresentation: Normal capability indices may significantly misrepresent non-normal distributions. Skewed data bounded at zero (e.g., flatness, runout) often shows artificially high Cpk while producing actual defects.
  • Customer Satisfaction Gap: High Cpk does not guarantee customer satisfaction without functional validation. Capable processes may still produce functionally defective products if specifications do not map to functional requirements.
  • Subgroup Selection Bias: Rational subgrouping significantly affects Cp/Cpk calculations. Improper subgrouping (grouping by time instead of production order) can hide variation or overestimate capability.

When NOT to Use Capability Analysis

Capability analysis is inappropriate in these situations:

Unstable Processes

Never calculate capability on processes showing trends, shifts, or special causes on control charts. Control charts must confirm stability first.

Attribute/Defect Data

Capability indices require continuous variable data (measurements). Attribute data (pass/fail, counts) requires DPMO or yield analysis, not Cpk/Ppk calculations.

Small Sample Sizes

Samples below 30 observations produce unreliable capability estimates with wide confidence intervals. Minimum 100 observations recommended for confident decision-making.

Prototype/Pilot Production

Pre-production or prototype processes do not represent manufacturing variation. Use Pp/Ppk only after process qualification with production-intent conditions.

Changing Specifications

Processes with undefined or frequently changing customer specifications cannot be evaluated meaningfully. Specifications must be fixed and customer-approved.

One-Sided Specifications

While Cpk can be calculated for one-sided specs (only LSL or USL), interpretation requires different considerations than two-sided capabilities.

Industry Applications & Decision Framework

Automotive (AIAG PPAP)

AIAG PPAP requires capability studies for all critical characteristics. Level 3 submissions need Cpk/Ppk ≥ 1.33 with histograms. Our reports meet these requirements with proper documentation.

Decision Context: Supplier qualification gates require demonstrated capability before production approval. Low capability triggers containment actions and 100% inspection until improvement verified.

Medical Devices (FDA 21 CFR Part 820)

FDA 21 CFR Part 820 requires process validation. Capability indices demonstrate that manufacturing processes consistently produce devices meeting specifications—essential for design controls.

Decision Context: Validation protocols require statistical evidence of capability. Process validation reports must include capability studies linking specification compliance to clinical performance.

Aerospace (AS9100)

AS9100 quality systems emphasize statistical process control. Capability studies validate that critical dimensions remain within tight tolerances required for flight safety and reliability.

Decision Context: Safety-critical tolerances often require Cpk ≥ 2.0. First Article Inspection Reports (FAIR) include capability evidence for key characteristics.

General Manufacturing

Any process with measurable specifications benefits from capability analysis. Common applications include machining dimensions, injection molding weights, plating thicknesses, and assembly torques.

Decision Context: Yield and scrap reduction decisions rely on capability data. Processes with Cpk < 1.0 justify capital investment for improvement; capable processes justify reduced inspection frequency.

Additional Industry Examples

Semiconductor Wafer Thickness

Silicon wafer thickness control requires Cpk ≥ 1.67 to ensure uniformity across wafer surface. Thickness variation affects subsequent lithography and etch processes.

Pharmaceutical Tablet Weight

Drug dosage accuracy depends on tablet weight consistency. FDA requires demonstrated capability for content uniformity, with capability studies supporting batch release decisions.

Injection Molding Dimensional Consistency

Plastic part dimensions (wall thickness, hole positions) require Cpk ≥ 1.33 for automotive and consumer electronics assembly compatibility.

Precision Machining Tolerance Control

CNC machining of aerospace fittings and medical implants requires tight tolerance control (±0.001") with high capability to prevent assembly interference or functional failure.

Food Manufacturing Fill Weight

Net weight compliance requires capability analysis to minimize giveaway (overfilling) while ensuring regulatory minimum weight compliance. Legal requirements mandate capable filling processes.

Coating Thickness Uniformity

Protective coatings (painting, plating, PVD) require thickness capability to ensure corrosion protection without material waste or functional interference.

Beginner's Guide to Process Capability

What Capability Analysis Measures

Process capability quantifies how well your manufacturing process meets customer requirements. Unlike simple defect counts, capability indices compare your process variation to the allowed specification width. A capable process consistently produces parts within tolerance limits.

Why Meeting Specifications Matters

Specifications represent customer requirements for fit, function, and safety. Consistently meeting specifications ensures product performance, reduces warranty costs, enables assembly without rework, and maintains regulatory compliance. Poor capability leads to scrap, customer complaints, and potential safety recalls.

Real-World Example: Machining a Shaft

A machine shop produces shafts with diameter specification 25.00 ± 0.05 mm (LSL = 24.95, USL = 25.05). After measuring 100 shafts, they calculate Cpk = 1.45. This means:

  • The process is capable (Cpk > 1.33)
  • They expect approximately 10 defective parts per million (PPM)
  • No 100% inspection required—sample inspection sufficient
  • Process can tolerate some drift before producing defects

If Cpk were 0.80 instead, the shop would expect 16,000 PPM defective (1.6% defect rate), requiring sorting, rework, or process improvement.

Important Prerequisites & Methodology

Critical Prerequisites for Valid Analysis

1. Process Stability (Control Charts): Capability analysis assumes statistical control. Use our Control Chart Maker first to verify stability. Control charts detect variation sources (trends, shifts, cycles) that must be eliminated before capability evaluation. Calculating Cpk on an unstable process is statistically meaningless.

2. Measurement System Analysis (MSA): Validate measurement reliability using Gage R&R studies before capability analysis. If measurement error (GRR%) exceeds 30% of the tolerance, capability indices reflect measurement variation rather than true process performance. Never skip MSA—capable measurements are required to judge process capability.

3. Sample Representativeness: Data must represent actual production conditions across all expected variation sources—different operators, material lots, environmental conditions, and time periods. Convenience sampling or excluding "outliers" produces biased capability estimates that fail to predict future performance.

4. Normality: Standard indices assume normal distribution. Our tool includes Anderson-Darling tests and handles non-normal data with Box-Cox transformations when necessary. Non-normal processes without transformation produce incorrect defect rate estimates.

Frequently Asked Questions

What is the difference between Cp and Cpk?

Cp measures process potential using only the spread (variation) relative to specification width—(USL-LSL)/6σ. It assumes perfect centering. Cpk measures actual performance accounting for both spread and centering, calculating distance from the mean to the nearest specification limit. A process can have excellent Cp (low variation) but poor Cpk (off-center). Always use Cpk for final capability assessment.

What is the difference between Cpk and Ppk?

Cpk uses short-term variation (within-subgroup standard deviation) reflecting process potential under stable conditions. Ppk uses long-term variation (overall standard deviation) including between-subgroup drift and shifts. Cpk answers "How capable could this process be?" while Ppk answers "How capable is this process historically?" For new process validation, use Ppk; for ongoing monitoring, use Cpk with control charts.

What Cpk value indicates Six Sigma performance?

Six Sigma performance corresponds to Cpk = 2.0 (assuming the process is centered, which gives Cp = 2.0). This represents 6 standard deviations between the mean and nearest specification limit, predicting 3.4 defects per million opportunities (DPMO). However, many industries consider Cpk ≥ 1.67 (5 sigma) as "Six Sigma capability" accounting for 1.5 sigma process drift over time.

Can capability be calculated for non-normal data?

Yes, but standard Cpk formulas assume normality. For non-normal distributions (common with bounded data, wear patterns, or natural limits), use these methods: (1) Box-Cox transformation to normalize data, (2) Non-parametric capability indices using percentiles, or (3) Distribution fitting (Weibull, lognormal) with appropriate calculations.

Why does capability analysis require a stable process?

Capability indices assume the process mean and variation remain constant over time. Unstable processes (showing trends, shifts, or cycles on control charts) violate this assumption—calculated Cpk represents only the sampling period and cannot predict future performance. Always establish statistical control using control charts before capability studies. Unstable processes require investigation and elimination of special causes before capability evaluation.

What sample size is needed for reliable capability analysis?

Minimum 30 data points for rough estimates, but 100+ recommended for confident decision-making. Small samples produce wide confidence intervals—Cpk calculated from 30 points might have 95% confidence interval of ±0.30, meaning true capability could range from marginal to excellent. For critical characteristics or PPAP submissions, collect 125+ measurements (25 subgroups of 5) for reliable short-term capability estimates.

Analyze Your Process Capability

Get Cpk, Ppk, histograms, and professional reports instantly.

Start Capability Study →