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Probability of Exceedance

The frequency of exceedance, sometimes called the annual rate of exceedance, is the number of times in a certain period that a random process exceeds some critical value.

The average annual occurrences equal the number of times exceeded divided by the observed time period. The probability of exceedance equals 1 minus the exponential of the negative of the average annual occurrences times the prediction time period. The mean recurrance interval equals the reciprocal of the average annual occurrences.

Formula

{QuantityVariable[Subscript["N", "a"], "Frequency"] == QuantityVariable["N", "Unitless"]/QuantityVariable[Subscript["T", "o"], "Time"], QuantityVariable["P", "Unitless"] == 1 - E^(-(QuantityVariable[Subscript["N", "a"], "Frequency"]*QuantityVariable[Subscript["T", "p"], "Time"])), QuantityVariable[Subscript["T", "x"], "Time"] == QuantityVariable[Subscript["N", "a"], "Frequency"]^(-1)}

symbol description physical quantity
Na average annual occurrences "Frequency"
N number of times exceeded "Unitless"
To observed time period "Time"
P probability of exceedance "Unitless"
Tp prediction time period "Time"
Tx mean recurrence interval "Time"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Probability of Exceedance"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Probability of Exceedance"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject["Probability of Exceedance"], {QuantityVariable[ \!\(\*SubscriptBox[\("N"\), \("a"\)]\),"Frequency"] -> Quantity[0.06`, 1/("Years")]}]
Out[3]=

Publisher Information