17.4 Process Capability Metrics & Outliers
Key Takeaways
Cp measures potential capability from process spread vs. tolerance and ignores centering; Cpk measures actual capability including location relative to the nearest specification.
Valid capability analysis requires a stable process, correct specifications, adequate data, and a distribution (often approximate normality) that matches the index assumptions—or an appropriate alternative method.
Cpk < 1 generally indicates the process is not meeting specs consistently; higher values (e.g., ≥1.33) are common industry targets but customer/regulatory requirements govern.
Outliers are observations unusually far from the bulk of the data; they can be special causes, data errors, or extreme common-cause tails—and they strongly affect mean, SD, and capability.
Auditors should verify how outliers were identified (charts, residual rules, domain review), whether they were investigated, and whether exclusion from analysis was justified and documented.
17.4 Process Capability Metrics & Outliers
Quick Answer: Cp = (USL − LSL) / (6σ) measures spread only (potential capability). Cpk = min[(USL − μ)/(3σ), (μ − LSL)/(3σ)] measures spread and centering (actual capability vs. nearest spec). Use capability only on stable processes with correct specs and suitable distribution assumptions. Outliers are extreme points that need investigation—not automatic deletion. BoK V.D.2–3. Practice at /practice/cqa.
What “capability” means
Process capability describes how well a stable process’s natural variation and location fit within specification limits for a characteristic. It is not the same as:
- Control (stability vs. control limits—voice of the process)
- Performance sometimes labeled Pp/Ppk (often using overall long-term σ including all sources)
- Customer satisfaction (broader than one CTQ index)
Auditors meet capability claims in validation reports, supplier scorecards, PPAP/FAI packages, and management reviews. Your job is to understand the metrics and apply skepticism: correct formula, correct inputs, correct assumptions.
Specifications and process parameters
| Symbol | Meaning |
|---|---|
| LSL / USL | Lower / upper specification limits (customer or design) |
| Tolerance width | USL − LSL (two-sided) |
| μ or | Process mean (population or sample estimate) |
| σ or s | Process standard deviation (definition depends on method) |
| Target T | Preferred value (may equal midpoint; not always) |
Critical audit check: Are LSL/USL the current approved limits for this product/revision? Many “incapable” or “capable” stories use obsolete drawings.
Cp — potential capability (spread only)
For a two-sided specification and a process spread taken as 6σ (common normal-based model spanning roughly ±3σ):
- Cp asks: If the process were perfectly centered, would the spread fit the tolerance?
- Cp does not detect off-center processes. A process can have high Cp and still produce massive defects if mean sits near one limit.
Worked mini-calculation — Cp
USL = 20.0, LSL = 10.0, σ = 1.0
- Tolerance = 10.0
- 6σ = 6.0
- Cp = 10 / 6 ≈ 1.67
That looks strong—but only if the mean is near the center. If mean = 18 with the same σ, defects explode near the USL even though Cp is unchanged.
Cpk — actual capability (spread + centering)
- Uses the nearest specification
- Falls when the process is off-center or when σ is large
- For a centered process, Cpk ≈ Cp; when off-center, Cpk < Cp
Worked mini-calculation — Cpk
USL = 20, LSL = 10, μ = 16, σ = 1.0
- (USL − μ)/(3σ) = (20 − 16)/3 = 4/3 ≈ 1.33
- (μ − LSL)/(3σ) = (16 − 10)/3 = 6/3 = 2.00
- Cpk = min(1.33, 2.00) = 1.33
- Cp was 10/(6) ≈ 1.67 → Cpk < Cp shows centering loss
Second worked example — incapable centering
USL = 10.50, LSL = 9.50, μ = 10.40, σ = 0.10
- Cp = (1.00)/(0.60) ≈ 1.67
- (USL − μ)/(3σ) = 0.10 / 0.30 ≈ 0.33
- (μ − LSL)/(3σ) = 0.90 / 0.30 = 3.00
- Cpk ≈ 0.33 → process looks “capable” by Cp but is badly off-center; audit must challenge any claim based on Cp alone.
Interpreting magnitude (rules of thumb)
Targets vary by industry and customer. Common teaching benchmarks (not universal law):
| Cpk (approx.) | Rough interpretation |
|---|---|
| < 1.0 | Process spread/location not fitting specs; nonconformances expected |
| ≈ 1.0 | Marginal; about ±3σ at the nearer limit if normal and stable |
| ≥ 1.33 | Common many-industry minimum for ongoing production |
| ≥ 1.67 | Stronger target in some automotive/high-reliability contexts |
| ≥ 2.0 | Associated with “6σ” style short-term thinking in some curricula |
Auditor stance: Compare claims to contractual/customer requirements and to stability evidence, not only to a memorized number.
Prerequisites for valid capability (Understand/Apply)
- Statistical stability — process in control; special causes addressed
- Correct specs — current, applicable, same units
- Representative data — right product, period, sampling plan
- Measurement system adequacy — high measurement error inflates apparent σ and tanks Cpk
- Distribution fit — normal-based Cp/Cpk mislead for strongly skewed data; may need transform, non-normal indices, or percent nonconforming methods
- σ definition clarity — within-subgroup vs. overall (Cp/Cpk vs. Pp/Ppk distinctions in many Six Sigma contexts)
If any prerequisite fails, treat published indices as claims needing validation, not as facts.
Centering vs. spread — improvement strategy
| Diagnosis | Evidence | Typical improvement direction |
|---|---|---|
| Wide spread, well centered | Cp and Cpk both low, similar | Reduce variation (method, equipment, materials) |
| Tight spread, off-center | Cp high, Cpk much lower | Center the mean (setup, target, bias) |
| Both problems | Cp low, Cpk even lower | Reduce variation and center |
| Unstable | Chart out of control | Restore control before capability projects |
This table is pure audit gold: it connects metrics to correct CAPA/system projects.
Outliers — definition and impact
An outlier is an observation unusually distant from the bulk of the data—far in the tail relative to the rest of the sample or to a fitted model.
Impacts:
- Pulls the mean toward the extreme
- Inflates range, variance, and SD
- Can crash Cpk (or, if wrongly deleted, inflate Cpk unrealistically)
- May be the most important signal (special cause, safety event) or a clerical error (extra zero typed)
Identification methods (common)
| Method | Idea | Caveat |
|---|---|---|
| Visual | Histogram, box plot, time-series plot | Subjective alone |
| Control chart | Point beyond limits / pattern rules | Needs proper limits |
| z-score / residual | e.g., |z| > 3 under a normal model | Model-dependent |
| IQR rule | < Q1 − 1.5·IQR or > Q3 + 1.5·IQR | Sensitive to distribution; screening only |
| Domain review | Impossible physically? Wrong unit? | Always required before deletion |
Never delete outliers solely to improve a customer scorecard. Document investigation: root cause, data error correction, or retained extreme with analysis that includes it (or uses robust methods).
Worked outlier impact sketch
Data: 10.0, 10.1, 9.9, 10.0, 10.2, and 14.0 (possible bad reading).
- With 14.0: mean jumps, s inflates, Cpk collapses
- Investigation finds a decimal error; true value 10.4 → correct the record
- Investigation finds a real process excursion → treat as special cause, contain product, fix cause; do not silently drop the point and claim high Cpk for the period without disclosure
Auditor checklist for capability & outliers
- Request control chart evidence for the capability period
- Verify LSL/USL/revision and characteristic definition
- Confirm σ method and software settings
- Compare Cp vs. Cpk to diagnose centering vs. spread
- Ask how outliers were detected, investigated, and treated
- Cross-check with actual nonconformance rates—huge mismatch suggests bad assumptions or sorting
- Align findings with system improvement (common cause / low Cpk) vs. event CAPA (outlier special cause)
Common exam traps
- Using Cp when the process is off-center (Cp looks fine; Cpk does not)
- Computing capability on unstable data
- Confusing control limits with specification limits
- Treating outlier deletion as routine “data cleaning” without cause
- Assuming Cpk ≥ 1.33 is a universal legal requirement
- Ignoring measurement system error as a driver of poor Cpk
Chapter close
Chapter 17 built the auditor’s statistical core: center (mean/median/mode), spread and qualitative/quantitative patterns, common vs. special cause, and capability/outliers. Domain V continues with sampling, change control, V&V, and risk tools. Keep drilling application scenarios at /practice/cqa and the full study path at /study-guides/cqa.
For USL = 50, LSL = 20, and σ = 5, what is Cp, and what does it not tell you?
Cp = 6.0; it proves zero defects regardless of mean
Cp = 0.5; it equals Cpk by definition always
Cp cannot be calculated without the mode
Cp = 1.0; it does not tell you whether the process mean is centered between the specs
A supplier reports Cp = 1.8 and Cpk = 0.6 for the same dataset. What is the best auditor interpretation?
The process is perfectly centered; only random software error can separate Cp and Cpk
Spread may be relatively tight vs. tolerance (high Cp), but the process is off-center toward a specification (much lower Cpk)
Cpk is always higher than Cp for two-sided specs
Outliers are impossible when Cp exceeds 1.5
Which prerequisite most directly undermines a published Cpk of 1.5 for last month’s production?
The median was reported alongside the mean
Qualitative interview notes were coded in parallel
The control chart for the same characteristic and period shows repeated out-of-control signals that were never investigated
The sample size was greater than 30
An analyst removes the three highest values from a capability study solely because they make Cpk look bad, with no investigation. What should the auditor conclude?
Unacceptable: outliers require investigation; silent deletion to improve indices can hide special causes or data integrity issues
Acceptable standard practice because outliers never contain process information
Required whenever Cp exceeds Cpk
Necessary to convert qualitative data into quantitative data
Sections you finish are checked off in the contents.