Template:Arrhenius-Weibull: Difference between revisions

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{| border="1" cellpadding="4" cellspacing="0" align="center" style="border-bottom: rgb(255,229,184) 1px solid; border-left: rgb(255,229,184) 1px solid; background-color: rgb(255,229,184); color: rgb(0,0,0); border-top: rgb(255,229,184) 1px solid; border-right: rgb(255,229,184) 1px solid"
#REDIRECT [[Arrhenius_Relationship#Arrhenius-Weibull]]
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| colspan="2"  align="center" valign="middle" bgcolor="rgb(255,229,184)" | {{font|Arrhenius-Weibull|12|Tahoma|bold}}
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| colspan="2" bgcolor="rgb(255,229,184)" |
{| width="0" border="1" cellpadding="2" cellspacing="0"
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| align="center" valign="middle" bgcolor="rgb(240,240,237)" | Model 
| align="center" valign="middle" bgcolor="rgb(240,240,237)" |  Life Distribution
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| rowspan="3" | <math>f(t,V)=\frac{\beta }{C\cdot {{e}^{\frac{B}{V}}}}{{\left( \frac{t}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta -1}}{{e}^{-{{\left( \tfrac{t}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta }}}}</math>
| {{weibull2pdf}}
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| align="center" valign="middle" bgcolor="rgb(240,240,237)" | Life Stress Relationship
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|{{{Arrhenius}}}
|}
 
|-
| align="center" valign="middle"  | Type
| bgcolor="white" |Exponential LSR
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| align="center" valign="middle" | Reliability
| bgcolor="white" | {{ArrhWeibullrel}}
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| align="center" valign="middle"  | Reliable Life
| bgcolor="white" |<math>{T(R)}=C\cdot {{e}^{\tfrac{B}{V}}}{{\left\{ -\ln \left[R\right] \right\}}^{\tfrac{1}{\beta }}}</math>
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| align="center" valign="middle"  | BX Life
| bgcolor="white" |<math>{BX}=C\cdot {{e}^{\tfrac{B}{V}}}{{\left\{ -\ln \left[1-{\frac{X}{100}}\right] \right\}}^{\tfrac{1}{\beta }}}</math>
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| align="center" valign="middle"  | Failure Rate
| bgcolor="white" |<math>\lambda \left( T,V \right)=\frac{f\left( T,V \right)}{R\left( T,V \right)}=\frac{\beta }{C\cdot {{e}^{\tfrac{B}{V}}}}{{\left( \frac{T}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta -1}}</math>
|-
| align="center" valign="middle"  | Mean or MTTF
| bgcolor="white" |<math>\overline{T}=C\cdot {{e}^{\tfrac{B}{V}}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math>
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| align="center" valign="middle"  | Median
| bgcolor="white" |<math>\breve{T}=C\cdot {{e}^{\tfrac{B}{V}}}{{\left( \ln 2 \right)}^{\tfrac{1}{\beta }}}</math>
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| align="center" valign="middle"  | Mode
| bgcolor="white" |<math>\tilde{T}=C\cdot {{e}^{\tfrac{B}{V}}}{{\left( 1-\frac{1}{\beta } \right)}^{\tfrac{1}{\beta }}}</math>
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| align="center" valign="middle"  | Standard deviation
| bgcolor="white)" |<math>{{\sigma }_{T}}=C\cdot {{e}^{\tfrac{B}{V}}}\cdot \sqrt{\Gamma \left( \frac{2}{\beta }+1 \right)-{{\left( \Gamma \left( \frac{1}{\beta }+1 \right) \right)}^{2}}}</math>
|}

Latest revision as of 04:24, 16 August 2012

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