Binomial Sample Size Calculator
Calculate minimum sample sizes for reliability testing and determine demonstrated reliability from test results using non-parametric one-sided binomial distribution methods
Binomial Sample Size Calculator (Non-Parametric)
Calculate the minimum sample size required to demonstrate a reliability level with a given confidence using one-sided binomial distribution.
Formula:
n = ln(1 - C) / ln(R)Where: R = Reliability, C = Confidence, k = Allowed Failures
Target reliability level (e.g., 95 for 95%)
Statistical confidence (e.g., 90 for 90%)
Maximum number of failures allowed in test (max 20)
Minimum Sample Size:
N/A
Test N/A with 0 or fewer failures to demonstrate 95.00% reliability with 90.0% confidence
Sample Size vs. Desired Reliability
Required sample sizes across different reliability targets with multiple confidence levels.
Demonstrated Reliability Calculator (Non-Parametric)
Calculate the demonstrated reliability based on test results (reverse one-sided binomial calculation)
Use this calculator to:
- Determine reliability demonstrated by your test results
- Validate if your test meets reliability requirements
- Plan follow-up testing if needed
(%)
Demonstrated Reliability:
N/A
With 30 units tested, 0 failure(s) observed, and 90.0% confidence, the demonstrated reliability is at least N/A
Reliability vs. Sample Size
Lower and higher sample sizes with multiple confidence levels to visualize demonstrated reliability.
About Binomial Sample Size Calculation
The binomial sample size calculator is used in reliability engineering to determine the minimum number of units that must be tested to demonstrate a required reliability level with a specified confidence. This is a one-sided test, meaning it demonstrates that reliability is at least the target value.
- Zero-failure test: The simplest case where all units must pass. Formula: n = ln(1 - C) / ln(R)
- Allowing failures: When some failures are acceptable, the calculation uses the cumulative binomial distribution
- Common applications: Reliability demonstration tests, qualification testing, acceptance testing