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For Students · Reliability Analysis

Reliability Analysis for a hypothesis test

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a hypothesis test live below — adjust the inputs and watch it respond, right in your browser.

Distributions

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Probability DistributionsLive

PDF / PMF explorer

Controls

Presets

Mean μ

Std dev σ

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Data Inspector

Distributionnormal

Mean0.000

Variance1.000

Std dev1.000

Governing equation

f (x) = \frac{1}{2 π 1.00} e^{- \frac{( x - 0 ) ^{2}}{2 \cdot 1.00}}

Reading this result: The mean μ only slides the bell sideways while σ sets its width — variance is σ² = 1.00, so doubling σ quadruples the spread.

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Fatigue

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Fatigue (S-N Curve)Live

failure under cyclic load

Controls

Presets

Ultimate strength (MPa)

Stress amplitude (MPa)

Ferrous (has endurance limit)

Repeated loading well below the ultimate strength can still break a part — metal fatigue. The S-N curve plots stress amplitude against cycles to failure. Steels have an endurance limit: below it they last essentially forever, but aluminum has none and eventually fails at any stress. Cause of many catastrophic aircraft and bridge failures.

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Data Inspector

Endurance limit250 MPa

Cycles to failure1.17e+5

Verdictfinite life

Governing equation

N = (\frac{σ _{a}}{σ _{f}^{'}})^{1/ b}, σ_{a} = 300 MPa \Rightarrow N = 1.17 e + 5 cycles

Reading this result: At 300 MPa the part fails after about 1.2e+5 cycles. Drop below the 250 MPa endurance limit to reach infinite life.

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Frequently asked questions

Is this good for students?: Yes — this version of "Reliability Analysis for a hypothesis test" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.