Calculator Input
Example Data Table
| Target Reliability | Confidence | Allowed Failures | Required Sample | Common Use |
|---|---|---|---|---|
| 90% | 95% | 0 | 29 | Zero failure demonstration |
| 95% | 95% | 0 | 59 | Higher reliability claim |
| 90% | 95% | 1 | 46 | One failure allowed |
| 99% | 90% | 0 | 230 | Strict product validation |
Formula Used
The calculator uses a one-sided binomial reliability demonstration model.
Producer risk:
alpha = 1 - confidence
Binomial pass probability at target reliability:
P(pass | R) = Σ C(n, i) × (1 - R)i × Rn - i, for i = 0 to c
Sample size rule:
Find the smallest n where P(pass | R) ≤ alpha.
Zero failure shortcut:
n = ceiling[ ln(1 - confidence) / ln(reliability) ]
Achieved confidence from observed failures:
Achieved confidence = 1 - Σ C(n, i) × (1 - R)i × Rn - i, for i = 0 to observed failures
Finite population correction:
n adjusted = ceiling[ N × n / (N + n - 1) ]
How to Use This Calculator
- Enter the target reliability as a percentage.
- Enter the desired confidence level.
- Choose the number of failures allowed during the test.
- Add a finite population size if sampling from a fixed lot.
- Enter observed units and failures after a test is complete.
- Add cost and time values if planning resources.
- Press calculate to view the result above the form.
- Download the result as CSV or PDF for records.
Confidence Reliability Sample Size Calculator Guide
A reliability demonstration test answers a direct question. How many units must pass to support a target reliability? This calculator plans that test before time, cost, and lab capacity are committed. It also evaluates completed tests. You can enter target reliability, confidence, allowed failures, observed failures, and optional finite population size. The tool then estimates the required sample size and the confidence achieved by the observed data.
Reliability means the probability that an item performs as intended. Confidence describes how strongly the test result supports that reliability claim. A higher confidence level needs a larger sample. A higher reliability target also needs more samples, especially when no failures are allowed. Allowing a small number of failures can make a plan more realistic, but it usually increases the required sample because the pass rule is less strict.
The main calculation uses the binomial distribution. Each tested unit is treated as a pass or fail outcome. The calculator finds the smallest sample size where the chance of passing, when the true reliability only equals the target, is no greater than the producer risk alpha. For zero failures, the formula becomes a simple logarithm. For one or more allowed failures, the page searches the binomial cumulative probability.
Finite population correction is included as an optional planning aid. It can be useful when sampling from a known lot. The correction reduces the initial binomial sample size. It should be used carefully, because many life tests represent future production, not only the current lot. For critical products, confirm the final plan with quality, safety, or regulatory guidance.
Use this calculator during design validation, acceptance sampling, supplier qualification, and field return planning. Enter conservative targets when the cost of failure is high. Review the pass rule before testing begins. After testing, enter the tested units and observed failures. The achieved confidence result then shows whether the evidence supports the target claim. Export the result for reports, audits, or test records. Keep inputs documented. Record the test environment, inspection method, and failure definition. A clear failure definition prevents disputes later. Small changes in reliability or confidence can change sample size sharply. Run several scenarios before choosing the final plan for management approval and scheduling with shared assumptions.
FAQs
What is a confidence reliability sample size?
It is the number of units needed to support a reliability claim at a chosen confidence level. The result depends on target reliability, allowed failures, and test assumptions.
What does target reliability mean?
Target reliability is the required probability that a unit performs successfully. A 90% target means the claim supports at least 90 successful units out of 100 under stated conditions.
Why does higher confidence need more samples?
Higher confidence requires stronger evidence. More tested units reduce uncertainty and make the reliability claim harder to satisfy by chance alone.
What does allowed failures mean?
Allowed failures are the maximum failures accepted during the test. Zero failures gives the simplest plan. Allowing failures may reflect realistic testing but often requires a larger sample.
When should finite population correction be used?
Use it when sampling from a fixed and limited lot. Avoid it when the test represents future production, repeated manufacturing, or long-term field reliability.
What is achieved confidence?
Achieved confidence measures support from actual test results. It uses tested units, observed failures, and target reliability to estimate how strong the evidence is.
Can this calculator handle one failure?
Yes. Enter one as the allowed failures value. The calculator uses the binomial cumulative probability to search for the required sample size.
Is this suitable for regulated products?
It is useful for planning and documentation. For regulated, safety-critical, or medical products, confirm the final test plan with applicable standards and qualified reviewers.