# Success Run Sample Size Calculator for Medical Device Validation

> Source: https://netray.co/tools/medical-device-success-run-validation-sample-size-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Calculates the zero-failure sample size needed to claim a reliability at a confidence level, and splits it across your PQ lots.

## Category

quality

## Industry

Medical Devices

## Audience

- Quality engineer
- Validation engineer
- Regulatory affairs

## Tool

**Kind:** calculator

**Inputs:**

#### Required reliability

**Key:** reliability

**Type:** number

**Default:** 95

**Min:** 50

**Max:** 99.99

**Step:** 0.1

**Unit:** %

**Help:** Minimum proportion of units that must conform, for example 95, 99 or 99.9.

#### Confidence level

**Key:** confidence

**Type:** select

**Default:** 95

**Options:**

##### 90%

**Value:** 90

##### 95%

**Value:** 95

##### 99%

**Value:** 99

#### Number of PQ lots

**Key:** lots

**Type:** slider

**Default:** 3

**Min:** 1

**Max:** 10

**Step:** 1

**Unit:** lots

**Help:** Samples are split evenly across lots in this simple view.

**Outputs:**

#### Zero-failure sample size

**Key:** n

**Expr:** ceil(ln(1 - confidence / 100) / ln(reliability / 100))

**Format:** integer

**Primary:** true

**Description:** n = ln(1 - C) / ln(R). All n units must pass.

#### Samples per lot

**Key:** per_lot

**Expr:** ceil(n / lots)

**Format:** integer

**Description:** Rounded up so the total is at least n.

#### Total samples across lots

**Key:** total

**Expr:** per_lot * lots

**Format:** integer

#### Defect rate upper bound if all pass

**Key:** defect_bound

**Expr:** 100 - reliability

**Format:** percent

**Description:** The maximum nonconforming percent you can claim at the chosen confidence.

**Chart:**

#### Sample size vs required reliability

**Type:** line

**X:** reliability

**From:** 90

**To:** 99.5

**Steps:** 40

**Series:**

- n

**Disclaimer:** Zero-failure plans only. If a failure is possible or allowed, use a plan that permits an acceptance number. Confirm your rationale against your own validation procedure.

## Content

**Intro:** Process validation and design verification protocols for medical devices need a statistical rationale for sample size. The success run theorem gives the smallest zero-failure sample for a stated reliability and confidence. Enter your targets and get a number you can paste into the protocol.

**Sections:**

#### How to use the calculator

**Body:** Set the reliability the characteristic must demonstrate and the confidence level your procedure requires. Many companies tie these to the risk class of the failure mode, with higher severity getting higher reliability and confidence. The result is the number of consecutive conforming units needed. If you run PQ across several lots, the tool divides the total across lots and rounds up so you never end up short of the statistical minimum.

#### The method behind it

**Body:** If the true conforming proportion is R, the chance that n units all conform is R to the power n. To claim reliability R with confidence C, that chance must be at most 1 minus C when all n pass. Solving gives n = ln(1 - C) / ln(R). For 95% reliability at 95% confidence this gives 59 units, and for 99% at 95% it gives 299.

**Bullets:**

- 95/95 requires 59 units with zero failures
- 99/95 requires 299 units with zero failures
- 99/99 requires 459 units with zero failures
- A single failure invalidates the plan and requires a larger sample

#### Reading the result and common mistakes

**Body:** The sample size applies to attribute or pass/fail results, not to measured variables where a tolerance interval or capability index is more efficient. Sampling should be representative across the lot, shifts and operators, not the first units off the line. Teams often forget that a single failure in a zero-failure plan means retesting with a bigger sample, so plan test capacity and unit cost accordingly. Document the reliability and confidence choice with a link to the risk file.

**Cta:** If your validation protocols pull part counts and lot data from the ERP by hand, we can help automate the sample plan and evidence collection inside your own environment.

**Faq:**

#### Where does the 59 in 95/95 come from?

**Answer:** From ln(0.05) divided by ln(0.95), which is about 58.4, rounded up to 59. All 59 units must conform. Rounding down would give less than the claimed confidence, so the result is always rounded up.

#### What if one unit fails?

**Answer:** The zero-failure plan no longer supports the claim. You need either a larger zero-failure sample after investigation and correction, or a plan designed with an acceptance number of one or more, which needs a larger starting sample.

#### Can I use this for variable data?

**Answer:** You can, but it is conservative. For measurable characteristics with a normal distribution, a one-sided tolerance interval or capability analysis typically needs far fewer units. Use attribute plans when data is pass/fail.

#### How do I choose reliability and confidence?

**Answer:** Link them to risk. Many procedures set higher values for failure modes with higher severity or probability in the risk analysis. Your own quality procedure should state the table, and the protocol should cite it.

## Search terms

success run theorem calculator, medical device validation sample size, process validation sample size calculator, reliability confidence sample size, 95/95 sample size, zero failure sample size, design verification sample size, binomial sample size medical device

---
Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json