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| ==Lognormal Statistical Properties==
| | #REDIRECT [[Lognormal Distribution Functions]] |
| {{ld mean}}
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| {{ld median}}
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| {{ld mode}}
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| {{ld standard deviation}}
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| {{ld lognormal reliability function}}
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| {{ld lognormal conditional reliability}}
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| ===The Lognormal Reliable Life===
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| As there is no closed-form solution for the lognormal reliability equation, no closed-form solution exists for the lognormal reliable life either. In order to determine this value, one must solve the equation:
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| ::<math>{{R}_{T}}=\int_{\text{ln}(T)}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{s-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}ds</math>
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| for <math>T</math> .
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| ===The Lognormal Failure Rate Function===
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| The lognormal failure rate is given by:
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| ::<math>\lambda (T)=\frac{f(T)}{R(T)}=\frac{\tfrac{1}{T\cdot {{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{(\tfrac{{T}'-{\mu }'}{{{\sigma }_{{{T}'}}}})}^{2}}}}}{\int_{{{T}'}}^{\infty }\tfrac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{(\tfrac{t-{\mu }'}{{{\sigma }_{{{T}'}}}})}^{2}}}}dt}</math>
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| As with the reliability equations, standard normal tables will be required to solve for this function.
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