Crack Growth Calculator

A reliability engineering calculator covers three interconnected disciplines: system reliability (MTBF, MTTR, availability), failure mode analysis (FMEA / Risk Priority Number), and structural fatigue assessment (S-N curve, Basquin's relation, endurance limit). These are core tools in mechanical, aerospace, and industrial engineering, underpinning maintenance scheduling, design validation, and safety certification.

Reliability engineering quantifies and improves the probability that a system performs its intended function for a specified time under stated conditions. MTBF (Mean Time Between Failures) and MTTR (Mean Time To Repair) determine system availability. FMEA (Failure Mode and Effects Analysis) systematically identifies failure modes and prioritises them using RPN = Severity × Occurrence × Detection. Fatigue analysis uses S-N (stress vs cycles) curves to predict fatigue life under cyclic loading.

1. MTBF and Availability tab: enter total operating time, number of failures, and total downtime to compute MTBF, MTTR, and availability.
2. FMEA / RPN tab: rate each failure mode on Severity, Occurrence, and Detection (each 1–10). RPN = S × O × D; higher values indicate higher risk and priority for corrective action.
3. Fatigue and S-N tab: enter stress amplitude at a known failure point and a reference stress–cycle pair to estimate the S-N slope, endurance limit, and fatigue life under different loading conditions.

Reliability engineering formulas

MTBF = total operating time / number of failures. MTTR = total downtime / number of failures. Availability A = MTBF / (MTBF + MTTR). Reliability at t = MTBF: R(MTBF) = e⁻¹ ≈ 36.8% (exponential failure distribution).

RPN = Severity × Occurrence × Detection. Each factor rated 1–10 (10 = worst). RPN range: 1–1000. Industry thresholds vary; RPN ≥ 100–200 typically triggers mandatory corrective action.

Basquin's relation (S-N curve): σ_a = σ_f′ × (2N_f)^b, where σ_f′ is the fatigue strength coefficient and b is the fatigue strength exponent (typically −0.05 to −0.12 for metals). Endurance limit ≈ 0.5 × ultimate tensile strength for steels (below ~200 ksi).

Interpreting reliability results

Availability targets by industry

High-availability systems target: data centres 99.999% ("five nines", ≈ 5 min downtime/year); medical devices 99.99%; manufacturing 99.9% (8.76 h/year); general commercial 99%. FMEA RPNs ≥ 200 are critical and require immediate corrective action in aerospace (AS9100) and automotive (IATF 16949) quality systems. Fatigue failures cause 80–90% of all mechanical engineering failures — understanding fatigue life is essential for rotating machinery, bridges, aircraft structures, and pressure vessels.

Engineering tips and best practices

• Availability from MTBF/MTTR assumes exponential failure distribution (constant hazard rate). For systems with wear-out (e.g. bearings), use Weibull analysis with β > 1.
• RPN should not be used as the sole prioritisation criterion — a severity-10 failure with RPN 100 (S=10, O=1, D=10) is more critical than severity-4 with RPN 200 (S=4, O=5, D=10). Always address severity-10 failure modes first regardless of RPN.
• The endurance limit approximation (0.5 × UTS) applies only to wrought steels below ~200 ksi UTS. Aluminium alloys, titanium, and composites do not have a true endurance limit.
• FMEA is most effective when done before design is finalised — corrective actions cost 10× more to implement after production begins.

MTBF and availability formulas assume an exponential failure distribution. FMEA severity and occurrence rating scales are based on AIAG/VDA FMEA Handbook (2019). Fatigue formulas use Basquin's relation from ASTM E739 standard practice. S-N curve estimates are approximations — actual fatigue life testing per ASTM E466 or ISO 1099 is required for engineering certification. This calculator is for educational and estimation purposes; it does not substitute for professional engineering analysis or regulatory safety certification.

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