Stress-Strength Interference Calculator
Stress-strength interference computes reliability as the probability that strength exceeds stress, treating both as distributions rather than single numbers. It replaces the deterministic safety factor with an actual probability — and frequently shows that a comfortable-looking safety factor hides an uncomfortable failure probability, because it is the tails that interfere, not the means.
Formula
Worked example
Component strength is normal with mean 1200 MPa and σ = 90 MPa. Applied stress is normal with mean 900 MPa and σ = 70 MPa.
- Safety factor = 1200 / 900 = 1.33
- z = (1200 − 900) / √(90² + 70²) = 300 / √(8100 + 4900)
- = 300 / √13000 = 300 / 114.02 = 2.631
- R = Φ(2.631) = 0.99574, so Pf = 4.26 × 10⁻³
A safety factor of 1.33 delivers 99.57% reliability — about 4 failures per 1000. If strength variability were halved to σ = 45, z rises to 3.58 and Pf drops to 1.7 × 10⁻⁴, a 25-fold improvement with no change to the mean strength at all. Controlling variation beats adding margin.
Common mistakes
- Assuming normality for strength data that is skewed. Material strength is often better modelled as Weibull or lognormal, and the difference shows up precisely in the lower tail that governs the answer.
- Using a nominal stress instead of the peak or extreme-value stress the component actually experiences.
- Ignoring strength degradation over time. Corrosion, fatigue and creep shift the strength distribution left, so a design that passes at time zero can interfere badly by end of life.
- Reporting only the safety factor to reviewers when the variances are known.
Related tools
About Reliability Pro
Stress-Strength is part of a suite of 126 reliability, maintenance and quality engineering tools covering life data analysis, accelerated testing, system reliability, FMEA and root cause, SPC, and design for reliability. It runs in the browser and as native iOS and Android apps, so the same calculation is available at a desk or in front of the asset.