Product Safety: Failure Risk & Redundancy Lab

Loading & Material

Applied stress σ 0 MPa

Material

Redundancy (design fix)

Backup fasteners per joint N 1 (none)

FMEA Risk Priority

Severity of failure S 5

Detection difficulty D 5

Risk Priority Number RPN = P × S × D

—

LowCritical

Live Readouts

Safety factor SF = σy/σ

∞

Single-unit P(fail)

0.0%

System P(fail) w/ redundancy

0.0%

Joints failed

0 / 24

How it works

Every fastener obeys linear elasticity up to yield: σ = Eε (Hooke's law). As applied stress σ approaches the material's yield strength σy, the safety factor SF = σy / σ collapses toward 1. Failure probability for one unit is modelled as a smooth reliability curve, not a hard cutoff — real components fail probabilistically because of manufacturing scatter:

P(fail) = 1 / (1 + e^(-k·(σ/σy − 1)))   (logistic model, k = 8)
SF = σy / σ

A single point of failure fails whenever its own draw fails. Redundancy changes the topology: N identical backups wired in parallel only bring the joint down if every one of them fails simultaneously — the same "N = 2k+1" logic used for fail-safe voting systems:

P(system fails) = P(fail)^N

The risk matrix follows the classic FMEA formula from failure-mode-and-effects analysis: Risk Priority Number combines how likely a failure is, how severe its consequence would be, and how hard it is to detect before it reaches the user:

RPN = Probability-rank(1–10) × Severity(1–10) × Detection(1–10)

Drag the stress slider (or hit auto-ramp) to load the 24 joints on the chassis past yield — spheres tint from green through amber to red as their own P(fail) rises, and flash white the instant they roll a failure. Raise redundancy N to see the same stress level become survivable: the system-level probability drops geometrically because every backup would have to fail on the same draw.

Low failure risk Elevated risk High risk / failed

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