ALTA ALTA Standard Folio Data Eyring-Exponential

Reliability Web Notes
Standard Folio Data Eyring-Exponential
ALTA
The [math]\displaystyle{ pdf }[/math] of the 1-parameter exponential distribution is given by: [math]\displaystyle{ f(t)=\lambda \cdot {{e}^{-\lambda \cdot t}} }[/math] It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail in Chapter 5) is given by: [math]\displaystyle{ \lambda =\frac{1}{m} }[/math] thus: [math]\displaystyle{ f(t)=\frac{1}{m}\cdot {{e}^{-\tfrac{t}{m}}} }[/math] The Eyring-exponential model [math]\displaystyle{ pdf }[/math] can then be obtained by setting [math]\displaystyle{ m=L(V) }[/math] in Eqn. (eyring): [math]\displaystyle{ m=L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math] and substituting for [math]\displaystyle{ m }[/math] in Eqn. (pdfexpm2): [math]\displaystyle{ f(t,V)=V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}{{e}^{-V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}\cdot t}} }[/math]
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