# Zero-Failure Reliability Demonstration Sample Size Calculator

> Source: https://netray.co/tools/zero-failure-reliability-demonstration-sample-size-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Find the number of units that must survive a test with no failures to claim a reliability level at a chosen confidence, and the total test effort.

## Category

quality

## Audience

- Reliability engineer
- Validation engineer
- Quality engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Reliability to demonstrate

**Key:** rel

**Type:** number

**Default:** 95

**Min:** 50

**Max:** 99.99

**Step:** 0.1

**Unit:** %

**Help:** Minimum probability that a unit meets the requirement.

#### Confidence level

**Key:** conf

**Type:** select

**Default:** 95

**Options:**

##### 80%

**Value:** 80

##### 90%

**Value:** 90

##### 95%

**Value:** 95

##### 99%

**Value:** 99

#### Test duration per unit

**Key:** hours

**Type:** number

**Default:** 500

**Min:** 0

**Step:** 10

**Unit:** hours

#### Cost per test unit

**Key:** cost_unit

**Type:** number

**Default:** 1200

**Min:** 0

**Step:** 50

**Unit:** $

**Currency:** $

**Outputs:**

#### Units required (zero failures allowed)

**Key:** n

**Expr:** ceil(ln(1 - conf / 100) / ln(rel / 100))

**Format:** integer

**Primary:** true

**Description:** Success run theorem: n = ln(1 - C) / ln(R).

#### Total unit test hours

**Key:** unit_hours

**Expr:** n * hours

**Format:** number

#### Test unit cost

**Key:** test_cost

**Expr:** n * cost_unit

**Format:** currency

**Primary:** true

#### Confidence actually achieved with this n

**Key:** actual_conf

**Expr:** (1 - pow(rel / 100, n)) * 100

**Format:** percent

**Chart:**

#### Required sample size vs reliability target

**Type:** line

**X:** rel

**From:** 80

**To:** 99.5

**Steps:** 40

**Series:**

- n

**Disclaimer:** Valid for pass/fail (binomial) data with zero failures. One failure requires a larger sample from the full binomial relationship.

## Content

**Intro:** Validation protocols often say test enough units to show 95 percent reliability at 95 percent confidence. This calculator gives the number, and shows what it costs.

**Sections:**

#### How to use the calculator

**Body:** Enter the reliability you must demonstrate and the confidence level your protocol or customer requires. Add test duration and unit cost to see the total effort. The result is the number of units that must all pass; a single failure invalidates the demonstration and you would need to test more or fix the design. The chart shows how steeply the sample size climbs as the target approaches 100 percent.

#### The success run theorem

**Body:** If a unit has reliability R, the probability that n independent units all pass is R to the power n. To claim at least R with confidence C, that probability must be no more than 1 minus C. Solving gives n = ln(1 - C) / ln(R). For 95 percent reliability at 95 percent confidence the answer is 59 units; for 90 at 90 it is 22. Round up, never down.

**Bullets:**

- Common pairs: 90/90 needs 22, 95/95 needs 59, 99/95 needs 299.
- The test must represent worst case conditions to support the claim.

#### Using it in risk-based validation

**Body:** Many quality systems tie sample size to risk: higher severity failure modes get higher reliability and confidence targets. Link the choice to the severity in the FMEA and record the rationale in the validation plan. Where destructive testing is costly, consider stress testing or a model-based approach and justify the departure.

#### Common mistakes

**Body:** Using this for variable data wastes samples, since a variable-data tolerance interval needs fewer units. Another error is drawing all units from one lot, which shows only lot-level reliability. Finally, do not pad the sample after seeing a failure; define the plan before testing.

**Cta:** Netray can help assemble lot and test traceability from your ERP so validation samples are properly representative and documented.

**Faq:**

#### Why 59 units for 95/95?

**Answer:** ln(0.05) divided by ln(0.95) is about 58.4, so you must test 59 units with zero failures to claim 95 percent reliability at 95 percent confidence.

#### What if one unit fails?

**Answer:** The zero-failure plan fails. You need a larger plan that allows one failure, computed from the binomial distribution, or you must fix the cause and retest.

#### Is this the same as AQL sampling?

**Answer:** No. AQL plans control lot acceptance risk. This demonstrates a reliability claim with a confidence level, typically for validation.

#### Can I use this for software or services?

**Answer:** Yes for any independent pass/fail trials, such as transactions or cycles, provided each trial is representative and independent.

## Search terms

success run theorem calculator, zero failure test sample size, reliability demonstration test, sample size for reliability and confidence, process validation sample size reliability, binomial zero failure calculator, 95 90 reliability confidence sample size, validation sample size 95/95

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