What is Reliability Demonstration Testing?
Reliability Demonstration Testing is a pass/fail verification process used to validate that a product meets its reliability specifications under expected operating conditions. Unlike life-testing, which aims to find out when a product will break, RDT aims to prove it will not break during its intended service life.
The most common approach is the zero-failure test, also known as the Success-Run Theorem. In this test, a specific number of units are run for a set duration. If zero units fail, the product passes, and the required reliability is statistically proven. If even one unit fails, the test is a failure.
How to Calculate Zero-Failure Sample Size
To determine how many units you need to test without any failures, you must define two parameters: the desired Reliability (R) and the required Confidence Level (C). Reliability is the probability the product will survive, and the Confidence Level is the statistical certainty of your test results.
The Success-Run Theorem uses the following formula: n = ln(1 - C) / ln(R). Here, 'n' is the required sample size, and 'ln' represents the natural logarithm.
For example, suppose you want to demonstrate 95% Reliability (R = 0.95) with 90% Confidence (C = 0.90). The calculation is: n = ln(1 - 0.90) / ln(0.95). This translates to ln(0.10) / ln(0.95), which equals -2.302 / -0.0512 = 44.89. Since you cannot test a fraction of a unit, you round up. You must test 45 units with zero failures to prove this reliability.
- Formula: n = ln(1 - C) / ln(R)
- C = Confidence Level (e.g., 0.90 for 90%)
- R = Reliability Goal (e.g., 0.95 for 95%)
Testing with Allowed Failures
While zero-failure testing requires the smallest sample size, it carries a high risk. If a single random anomaly causes a failure, the entire test fails. To mitigate this, engineers sometimes design tests that allow for one or more failures.
When allowing failures, the sample size must be increased significantly to maintain the same confidence and reliability levels. This is calculated using the cumulative binomial distribution.
For example, proving 95% reliability with 90% confidence requires 45 units for zero failures. If you want to allow 1 failure during the test, the sample size jumps to 77 units. If you want to allow 2 failures, it increases to 105 units. You trade test volume for a higher chance of passing a test despite isolated defects.
Common Challenges in Reliability Testing
The biggest challenge in RDT is balancing the statistical requirements with the physical reality of testing. High reliability goals (e.g., 99.9%) require hundreds or thousands of units to be tested, which is often physically or financially impossible for complex hardware.
To reduce the sample size, engineers often use accelerated life testing—increasing stress (like temperature or vibration) to compress time. However, this introduces new variables and requires complex acceleration models (like the Arrhenius equation) to translate the accelerated time back to normal use conditions.
Frequently asked questions
Why must I round up the sample size?
You must round up to the next whole number because testing a fraction of a product is impossible. Rounding down would result in a sample size that mathematically falls short of your required confidence level.
What happens if a unit fails during a zero-failure test?
The test instantly fails to demonstrate the target reliability. You must investigate the root cause, implement a design or manufacturing fix, and completely restart the reliability demonstration test.
Can I use this formula for software reliability?
The Success-Run Theorem assumes independent, identical items failing randomly. Software failures are systematic (bugs), not random wear-out, so this formula is generally reserved for hardware.
How does confidence level impact the sample size?
Higher confidence levels require larger sample sizes. Increasing your confidence requirement from 90% to 95% or 99% will drastically increase the number of units you need to test.