Zero-Failure Reliability Demonstration Sample Size

Calculate required sample sizes using the Binomial Success-Run Theorem

Test Parameters
Probability that the true reliability is at least R (e.g., 90%, 95%)
%
Minimum probability of success for a single trial (e.g., 90%, 95%, 99%)
%
Number of test failures accepted during the demonstration
Zero-failure Plan Formula:
n = ceil( ln(1 - C) / ln(R) )

Allowed-failures Plan:
Find min n where: ∑i=0f [C(n,i) × (1-R)i × Rn-i] ≤ 1 - C
Results
Required Sample Size (n)
-
Exact Achieved Confidence: -
Comparison Table (Fixed C and R)
Allowed Failures (f) Sample Size (n) Achieved Confidence

About the Zero-Failure Reliability Demonstration Sample Size

Calculate the exact test sample size needed to prove product reliability with specific confidence levels. Quality engineers and testing technicians can quickly determine how many units must survive a zero-failure test to demonstrate a target reliability. Skip complex statistical lookup tables and rapidly optimize your test plans for new hardware qualifications and compliance testing.

How it works

  1. Input your required product reliability percentage.
  2. Enter the target statistical confidence level for the demonstration.
  3. Specify the number of failures allowed during the test (typically zero).
  4. View the calculated required sample size and alternative binomial test plans.

Frequently asked questions

What mathematical formula governs a zero-failure reliability test?

The sample size is calculated using the Success-Run Theorem based on the binomial distribution. The specific formula is n = ln(1 - C) / ln(R), where C is the confidence level and R is the required reliability.

What happens to the required sample size if I allow test failures?

Allowing one or more failures significantly increases the total sample size required to mathematically prove the exact same reliability level. However, a multi-failure plan is often more practical when testing complex systems over long periods.

Does this calculation account for test duration and wear-out?

The fundamental success-run formula assumes the test duration matches the specific reliability life requirement. If testing for a different duration or aiming to compress test time, Weibull distributions or specific exponential acceleration factors must be incorporated.

What are typical confidence levels used in hardware engineering?

Standard confidence levels are usually 90% or 95% for consumer and industrial hardware. Life-critical medical devices or aerospace components often require 99% confidence based on strict risk management regulations.

References