2 2 5 1 4 5

You're staring at a string of numbers on a drawing, a spec sheet, or a quality report: 2 2 5 1 4 5. Maybe it's written as ISO 22514-5. Maybe someone just said "we need to follow 22514-5" in a meeting and you nodded while making a mental note to look it up later.

Here's the short version: it's the part of the ISO 22514 series that tells you how to calculate process performance statistics when your data is attributes — pass/fail, go/no-go, defect counts — instead of continuous measurements like length, weight, or temperature.

Most people know about Cp and Cpk. Far fewer know what to do when the only data you have is "37 defects out of 1,200 units." That's where this standard earns its keep.

What Is ISO 22514-5

ISO 22514-5:2014 is titled Statistical methods in process management — Capability and performance — Part 5: Process performance statistics for measurements by attributes*. It's one piece of a broader family (ISO 22514-1 through -7) that standardizes how organizations calculate and report process capability and performance indices.

The "attributes" part is the key. On the flip side, parts 2, 3, and 4 of the series deal with continuous data — variables you can measure on a scale. Which means part 5 addresses the reality that a huge chunk of industrial inspection doesn't produce measurements. It produces counts.

Number of nonconforming units in a lot
Number of defects per unit
Defects per million opportunities (DPMO)
First-pass yield

The standard defines the statistics you can calculate from that kind of data, the formulas, the assumptions, and — crucially — how to interpret them without overclaiming what they tell you.

Where It Fits in the 22514 Family

Part	Focus
22514-1	General principles and terminology
22514-2	Short-term capability for continuous data
22514-3	Long-term performance for continuous data
22514-4	Capability/proformance for multiple characteristics
22514-5	Performance statistics for attribute data
22514-6	Acceptance criteria for capability/performance
22514-7	Capability of measurement processes

If you're already using Parts 2 and 3 for your dimensional data, Part 5 is the parallel track for your go/no-go gauges, visual inspections, and functional test results.

Why It Matters

Here's the situation most quality engineers face: the Cpk on your shaft diameter is 1.45. Great. But the same shaft line also has a visual inspection for surface defects, and 2.Still, 3% of parts get rejected. What's the "Cpk equivalent" of that 2.3%?

You can't calculate Cpk. Worth adding: there's no distribution mean and standard deviation. You have a proportion nonconforming.

ISO 22514-5 gives you Pp_attr and Ppk_attr — performance indices for attribute data that are conceptually aligned with the variable-data indices your management already understands. It lets you put attribute performance on the same dashboard as variable

Attribute‑based performance indices

ISO 22514‑5 introduces two indices that mirror the familiar (P_p) and (P_{pk}) used for continuous data, but they are calculated from the proportion of nonconforming items (or defects per unit) rather than from a measured mean and standard deviation.

Symbol	Meaning	Formula (when the lower specification limit is 0 % defective)
(P_{p;attr})	Process performance – overall spread	(\displaystyle P_{p;attr}= \frac{USL}{6,\sqrt{\hat p,(1-\hat p)}})
(P_{pk;attr})	Process performance – centering	(\displaystyle P_{pk;attr}= \min!\left(\frac{USL-\hat p}{3,\sqrt{\hat p,(1-\hat p)}},;\frac{\hat p-0}{3,\sqrt{\hat p,(1-\hat p)}}\right))

(\hat p) = observed proportion nonconforming (e.g., 37/1200 = 0.0308).
(USL) = upper specification limit expressed as a proportion (the maximum allowable defect rate).
The term (\sqrt{\hat p,(1-\hat p)}) is the standard deviation of a binomial proportion; it replaces the (\sigma) that appears in the variable‑data formulas.

When a non‑zero lower specification limit (LSL

When a non‑zero lower specification limit (LSL) is present—for example, when a minimum number of defects per unit is required or when a process is expected to produce at least a certain level of a desirable attribute—the formulas are adjusted to reflect the two‑sided nature of the specification. In that case the observed proportion nonconforming (\hat p) is still the central quantity, but the “spread” term now measures the distance from (\hat p) to both limits:

[ P_{p;attr}= \frac{USL-LSL}{6,\sqrt{\hat p,(1-\hat p)}} ]

[ P_{pk;attr}= \min!\left( \frac{USL-\hat p}{3,\sqrt{\hat p,(1-\hat p)}}, ; \frac{\hat p-LSL}{3,\sqrt{\hat p,(1-\hat p)}} \right) ]

Interpretation – As with the variable‑data counterparts, a value of 1.0 indicates that the process spread (six times the binomial standard deviation) just fits inside the specification window. Values > 1.0 show margin; values < 1.0 signal that the observed defect rate is too close to—or beyond—one of the limits.
Special case LSL = 0 – The formulas reduce to the expressions shown earlier, because the distance to the lower limit becomes simply (\hat p) and the denominator remains unchanged.

Practical computation steps

Collect a representative sample (n ≥ 30 is a common rule‑of‑thumb for the binomial approximation to be reasonable).
Calculate (\hat p = \frac{x}{n}), where x is the number of nonconforming items (or total defects if you are working with defects‑per‑unit and then convert to a proportion by dividing by the maximum possible defects per unit).
Specify the limits – USL is the maximum allowable proportion nonconforming (often derived from a customer‑required defect rate, e.g., 0.02 = 2 %). LSL is set when a minimum performance is required (e.g., a process must achieve at least 0.5 % defect‑free yield, which translates to LSL = 0.005).
Plug into the formulas above to obtain (P_{p;attr}) and (P_{pk;attr}).
Report the indices alongside any variable‑data indices on the same quality dashboard; use the same traffic‑light rules (e.g., > 1.33 = excellent, 1.00–1.33 = acceptable, < 1.00 = needs improvement).

Example

A medical‑device line produces catheters. Think about it: the visual inspection for surface blemishes has a USL of 0. 015 (1.5 % maximum blemish rate) and an LSL of 0.Consider this: 004 (0. 4 % minimum acceptable blemish rate, reflecting a desire to keep the process sufficiently “tight” to avoid over‑inspection). In a daily lot of 500 units, 6 blemishes are found.

[ \hat p = \frac{6}{500}=0.In real terms, 012\times0. 012 ] [ \sqrt{\hat p(1-\hat p)} = \sqrt{0.988}=0.

[ P_{p;attr}= \frac{0.015-0.004}{6\times0.1089}= \frac{0.011}{0.6534}=0.0168;;(\text{≈ 0.02}) ]

[ P_{pk;attr}= \min!In practice, \left( \frac{0. Day to day, 015-0. Also, 012}{3\times0. 1089}, \frac{0.012-0.Think about it: 004}{3\times0. Here's the thing — 1089} \right)=\min! Plus, \left( \frac{0. 003}{0.Which means 3267}, \frac{0. 008}{0.Think about it: 3267} \right)=\min(0. 0092,0.0245)=0.

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Both indices are far below 1.0, indicating that the observed blemish rate is too close to

the USL and that the process is operating with virtually no margin to the upper specification. On top of that, the immediate interpretation is that the visual‑inspection step is not capable of meeting the 1. 5 % blemish cap with the current settings, and a root‑cause investigation (e.g., lighting, inspector fatigue, upstream surface‑finish variability) is warranted.

Extending the logic to defects‑per‑unit (DPU) and defects‑per‑opportunity (DPO)

When the quality characteristic is a count of defects per item rather than a binary pass/fail, the binomial is replaced by the Poisson distribution. In that case, the natural parameter is the mean number of defects per unit, (\hat\lambda), and its standard deviation is (\sqrt{\hat\lambda}). Substituting into the same template yields:

[ P_{p;count}= \frac{USL-LSL}{6,\sqrt{\hat\lambda}} \qquad P_{pk;count}= \min!\left( \frac{USL-\hat\lambda}{3,\sqrt{\hat\lambda}}, \frac{\hat\lambda-LSL}{3,\sqrt{\hat\lambda}} \right) ]

If LSL = 0, the lower‑side term simplifies to (\hat\lambda / (3\sqrt{\hat\lambda}) = \sqrt{\hat\lambda}/3), which is the classic “c‑index” (or Cp‑equivalent for Poisson data) used in semiconductor and automotive paint‑shop monitoring. But the interpretation rules remain identical: 1. But 0 indicates margin, < 1. 0 is the borderline, > 1.0 signals an incapable process.

When to use attribute indices versus variable indices

Situation	Recommended approach	Rationale
Measurement is naturally dichotomous (good/bad, conforming/nonconforming)	Attribute Pp / Ppk	Direct use of the binomial proportion; no need to invent a continuous scale.
Data are collected as pass/fail but engineering also tracks a continuous “severity” metric	Hybrid – report both	The variable index shows how well* good units are made; the attribute index shows how many* units are bad. g., diameter, hardness) and the spec is in the same units
A continuous measurement is available (e.Which means
Multiple defect types can occur on one unit and each is recorded as a count	Count‑based Pp / Ppk (Poisson)	Preserves the discrete nature of the data and avoids artificial “defect‑to‑proportion” conversions.
Sample sizes are very small (n < 30) and no distributional assumption can be defended	Attribute (binomial) with exact confidence limits	Exact binomial confidence intervals are straightforward and do not rely on the normal approximation.

Common pitfalls and how to avoid them

Mixing USL/LSL that are expressed in different units (e.g., USL in % nonconforming, LSL in ppm). Convert both to the same proportion before applying the formulas.
Using the wrong denominator. For attribute data, the standard deviation is (\sqrt{p(1-p)/n}); for capability we use (\sqrt{p(1-p)}) (the process‑level spread), not the sampling error.
Forgetting the LSL term when LSL = 0. Many software packages still display a “lower” Ppk value; if LSL = 0, the lower term is zero and should be omitted or reported as “not applicable.”
Over‑interpreting small samples. With n = 30 and (\hat p = 0.01), the 95 % confidence interval on p runs roughly from 0.001 to 0.055. A Ppk computed from the point estimate can be wildly optimistic or pessimistic depending on which end of that interval the true proportion lies. Always report the confidence interval alongside the index.
Ignoring autocorrelation. In many manufacturing lines, consecutive units are not independent. If the data are autocorrelated, the effective sample size is smaller, and the capability estimate may be artificially tight. Run a runs‑up‑and‑down or autocorrelation check before publishing the index.

Integrating attribute capability into a Six‑Sigma DMAIC project

Define – Capture customer‑critical‑to‑quality (CTQ) requirements as maximum allowable proportion nonconforming (e.g., ≤ 0.5 % defective).
Measure – Set up a data‑collection plan that yields a stable estimate of (\hat p) (subgroup size ≥ 30, rational subgroups). Record both the numerator (defectives) and denominator (units inspected).
Analyze – Plot a p‑chart* to verify statistical control. Only after the process is in control should the capability index be calculated; otherwise the index mixes common‑cause variation with special‑cause spikes.
Improve – Use Pareto and Ishikawa analyses on the defect types to target the largest contributors. After implementing countermeasures, re‑sample and re‑calculate Pp and Ppk to demonstrate improvement.
Control – Embed the attribute capability calculation in the control‑plan software so that each shift or lot automatically updates the index. Set up a capability dashboard* with traffic‑light alerts: green if Ppk > 1.33, yellow if 1.00 ≤ Ppk ≤ 1.33, red if Ppk < 1.00.

Quick‑reference checklist for reporting

[ ] Sample size n and number of defectives x are clearly stated.
[ ]
[ ] Specification limits (USL/LSL) are expressed in consistent units (proportion, %, or ppm) and explicitly defined.
[ ] The point estimate (\hat p = x/n) is reported alongside the exact Clopper–Pearson (or Wilson) confidence interval for p.
[ ] Both Pp and Ppk formulas are shown, with the LSL term omitted or marked “N/A” when LSL = 0.
[ ] A p‑chart* (or np‑chart*) demonstrating statistical control is included; capability indices are not reported for an out-of-control process.
[ ] Effective sample size is noted if autocorrelation or clustering was detected and adjusted for. Simple, but easy to overlook.
[ ] The capability dashboard thresholds (green/yellow/red) and the business rationale for those cut‑offs are documented.
[ ] All calculations are reproducible: raw data, code (R, Python, Minitab macros, or Excel formulas), and software version are archived.

Closing perspective

Attribute capability indices bridge the gap between shop‑floor defect counts and board‑room quality strategy. When calculated rigorously—using consistent units, correct denominators, confidence intervals, and a verified state of statistical control—Pp and Ppk become more than compliance artifacts; they turn into leading indicators that guide resource allocation, supplier negotiations, and design-for-manufacturability decisions. Embed the checklist above into your standard work, automate the calculations where possible, and treat every capability review as a cycle of the DMAIC loop rather than a one‑time audit. The result is a transparent, defensible, and actionable measure of how reliably your process meets the customer’s definition of quality.