Fatigue Reliability Factor Calculator

Convert a target survival reliability and fatigue-strength scatter into a normal-distribution reliability correction factor.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Reliability inputs

Use a coefficient of variation from representative fatigue-strength data. Both inputs are dimensionless.

Screening result

Reliability correction factor Cᵣ0.814

Multiply the mean fatigue strength by 0.814 for the selected reliability.

Standard-normal quantile z2.328

The quantile z locates the selected cumulative reliability on a standard normal distribution; the curve is schematic.

How to use

Enter the fatigue-strength coefficient of variation Cᵥ = σ/μ. It is dimensionless and must be finite and non-negative.
Enter target survival reliability R as a probability strictly between 0 and 1; for example, use 0.99 for 99%.
Select Calculate, or edit either input for an immediate update. Reset restores Cᵥ = 0.08 and R = 0.99.
Read z as the standard-normal quantile and Cᵣ as the multiplier applied to mean fatigue strength.
Correct any warning before interpretation. A nonpositive Cᵣ indicates that the input/model combination is unsuitable.
Do not use this screening model for non-normal fatigue-strength populations, poorly characterized scatter, mean-stress corrections, load-spectrum damage, or safety-critical design without independent statistical and fatigue validation.

Worked example

1. Enter Cᵥ = 0.08 and R = 0.99. 2. Calculate. The approximation gives z = 2.328 and Cᵣ = 0.814. 3. If mean fatigue strength is 300 MPa, the reliability-adjusted screening strength is 0.814 × 300 = 244.2 MPa, before other size, surface, notch, temperature, and loading corrections.

Equations used

q = 0.5 − |R − 0.5|

w = √[−2 ln(q)]

z₀ = w − (a₁ + a₂w) / [1 + w(a₃ + a₄w)]

z = −z₀ for R < 0.5; otherwise z = z₀

Cᵣ = 1 − zCᵥ

Constants: a₁ = 2.30753, a₂ = 0.27061, a₃ = 0.99229, and a₄ = 0.04481. R is dimensionless survival reliability; q is the symmetric lower-tail probability; w and z are dimensionless intermediates; Cᵥ = σ/μ is the non-negative fatigue-strength coefficient of variation; Cᵣ is dimensionless. z and Cᵣ are rounded to three decimals for display.

Theory and method

The model treats fatigue strength as normally distributed about a positive mean μ with standard deviation σ. For target cumulative survival reliability R, the standard-normal quantile z reduces the mean by z standard deviations. Dividing by μ gives the multiplier Cᵣ = (μ − zσ)/μ = 1 − z(σ/μ).

Assumptions and limits: a representative, stationary, approximately normal fatigue-strength population; a defensible non-negative coefficient of variation; and consistent definitions of survival probability and fatigue strength. The approximation becomes increasingly sensitive near R = 0 or 1. It does not estimate σ or μ, fit a distribution, model censored fatigue data, or combine other fatigue correction factors. Validate tails with appropriate statistical software and material data.

References: M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, standard-normal probability approximations; A. van Beek, Advanced Engineering Design: Lifetime Performance and Reliability, fatigue reliability-factor calculation.

Continue in TriboSolver to combine the reliability factor with fatigue loading, geometry, materials, and other correction factors.

Weibull Reliability and Life Distribution supports life-distribution screening when a Weibull model is more appropriate.