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# 59 or 8 Units? Attribute vs Variable Sampling for Design Verification
- URL: https://npitoproductguy.com/sample-size-design-verification-59-or-8/
- Published: 2026-11-14T06:15:20.000Z
- Updated: 2026-11-14T06:15:20.000Z
- Description: Why 95/95 means 59 units for pass/fail tests but only 8 with variable data.
- Author: NPItoProductGuy
- Tags: Design Verification, Sample Size, V&V

The auditor turns a page in your verification report and asks one question: "Why 59?" You know the answer. Everybody uses 59\. It's 95/95\. But "everybody uses it" is not a rationale, and the auditor knows that too.

Now flip it. A test engineer on your team comes back with a plan for 8 units on the same requirement. Same confidence, same reliability. Is he cutting corners, or does he know something you don't? He might be right.

The difference between 59 and 8 is not the risk level. It's the type of data you collect. Once you see that, you stop picking sample sizes and start deriving them.

Quick check before you read on: what's your default sample size for design verification? Keep the number in your head. We'll come back to it.

## Where 59 comes from

59 is what you get when the result of each test is pass or fail. That's attribute data. The math behind it is the success-run theorem:

![n = ln(1 - C) / ln(R)](https://storage.ghost.io/c/0b/fa/0bfa1672-9175-44fd-a62e-286961eaedb3/content/images/2026/11/formula1.png)

C is confidence, R is reliability. Plug in 95/95 and you get 58.4\. Round up: 59 units, zero failures allowed.

Read that last part again. Zero failures. One failed unit and the plan is dead. You either start over with a bigger sample or you go explain to the review board why it doesn't count.

The number also climbs fast as the risk goes up:

| Confidence / Reliability | Units (zero failures) |
| ------------------------ | --------------------- |
| 90 / 90                  | 22                    |
| 95 / 90                  | 29                    |
| 95 / 95                  | 59                    |
| 95 / 99                  | 299                   |

That's the price of pass/fail. Each unit tells you one bit of information: it worked or it didn't. You need a lot of bits to say anything strong.

## Where 8 comes from

Now say you don't record pass/fail. You record the actual number: burst pressure in kPa, pull force in N, flow rate in ml/min. That's variable data, and every unit now tells you much more than one bit. It tells you where the result sits and how far it is from the limit.

With variable data you use a tolerance interval. For a one-sided lower limit the test looks like this:

![x-bar - k.s >= LSL](https://storage.ghost.io/c/0b/fa/0bfa1672-9175-44fd-a62e-286961eaedb3/content/images/2026/11/formula2.png)

x̄ is the sample mean, s is the standard deviation, and k is a factor from a table (ISO 16269-6 has them). k depends on confidence, reliability and n.

An example. Seal burst pressure, spec minimum 30 kPa. You test 8 units and get a mean of 45 kPa with s = 3 kPa. For 95/95 with n = 8, k = 3.188\. 45 − 3.188 × 3 = 35.4 kPa. That's above 30\. Pass, with 8 units.

Here's the catch nobody puts on the slide: fewer units means a bigger k, and a bigger k means you need more margin.

| Units (n) | k (95/95, one-sided) |
| --------- | -------------------- |
| 8         | 3.19                 |
| 10        | 2.91                 |
| 15        | 2.57                 |
| 20        | 2.40                 |
| 30        | 2.22                 |

If your design sits close to the spec, 8 units won't save you. The math will fail you even when every single unit passed.

So the real choice is not 59 vs 8\. It's units vs margin. A robust design buys you a small sample. A marginal design pays in units.

## When 8 units will burn you

Variable sampling is not a free lunch. It rests on assumptions, and auditors know where to push:

- **The data isn't normal.** The k-factors assume a normal distribution. With 8 points, a normality test has almost no power to reject anything. "It passed Anderson-Darling" with n = 8 means very little. Know your process, or use a transformation or a non-parametric method and accept more units.
- **The requirement is truly pass/fail.** Leak or no leak. Label readable or not. Alarm triggers or doesn't. You can't invent a variable where there isn't one. Sometimes you can find a measurable proxy (leak rate instead of leak yes/no), and that's often the smartest move in the whole plan.
- **The 8 units all came from one build.** Small samples hide between-lot variation. If your units came from one mold cavity, one operator and one shift, your s is too optimistic. Spread them across the sources of variation you expect in production.
- **The units aren't production-representative.** Hand-built prototypes with tuned parts tell you about the prototype, not the product. FDA will ask what changed between your test units and the released design.

None of these kill the method. They just have to be written into the rationale before someone else points them out.

## The mistake I keep seeing

A verification plan cites ANSI/ASQ Z1.4 (or Z1.9 for variables) as the sample size basis. Those standards are for lot acceptance. They answer "should I accept this incoming batch from my supplier?" They're built around an AQL and a lot size. They say nothing about whether your design meets its requirement with a stated confidence and reliability.

Using them for design verification is like checking a bridge design by inspecting a truckload of bolts. Right tool, wrong question.

If your rationale references Z1.4 for a design requirement, fix it before an auditor finds it. Use success-run for attribute data and tolerance intervals (ISO 16269-6) for variable data.

## Five questions your rationale must answer

Remember the default number you had in your head at the start? Here's how to turn it into a rationale that holds up:

1. **Why this confidence and reliability?** Tie it to the severity of the hazard in your ISO 14971 risk file. Not "company standard." A severity-to-C/R table in a procedure is the cleanest way.
2. **Attribute or variable, and why?** If it's attribute, did you look for a measurable proxy?
3. **Which method and which reference?** Success-run, tolerance interval, ISO 16269-6\. Not Z1.4.
4. **What assumptions did you make?** Normality, independence, how you'll handle a failure.
5. **Are the units representative?** Which lots, cavities, operators, and how close to the released design.

If you can answer all five in one page, nobody will ask "why 59?" again. They'll read the page and move on.

Your turn: what's the hardest requirement you've had to justify a sample size for? Pass/fail, variable, something in between? Tell me in the comments. I'll pick the most interesting one for a future video.

Watch the 2-minute version: [59 or 8 Units? on YouTube](https://www.youtube.com/watch?v=FW%5FAUzfDf4E&ref=npitoproductguy.com)

Want the templates? The Sample Size Rationale Toolkit has an editable rationale template (DOCX), a calculator with the success-run and k-factor tables (XLSX), a method guide, and a fictional worked example, ready for your DHF. [Get it on Gumroad](https://npitoproducer.gumroad.com/l/sample-size-rationale?ref=npitoproductguy.com)