Template:Initialization time rga: Difference between revisions

Latest revision as of 01:46, 27 August 2012

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-====Initialization Time====
+#REDIRECT [[Reliability_Growth_Planning#Initialization_Time]]
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-Reliability growth can only begin after a Type B failure mode occurs, which cannot be at a time equal to zero. Therefore, there is a need for an initialization time, different than zero, to be defined. The nominal idealized growth curve failure intensity is initially set equal to the initial failure intensity,  <math>{{\lambda }_{I}},</math>  until the initialization time,  <math>{{t}_{0}}</math> :
-::<math>{{r}_{NI}}({{t}_{0}})={{\lambda }_{A}}+(1-d){{\lambda }_{B}}+d\lambda \beta t_{0}^{(\beta -1)}</math>
-:Therefore:
-::<math>{{\lambda }_{I}}={{\lambda }_{A}}+(1-d){{\lambda }_{B}}+d\lambda \beta t_{0}^{(\beta -1)}</math>
-:Then:
-::<math>{{t}_{0}}={{\left[ \frac{{{\lambda }_{I}}-{{\lambda }_{A}}-(1-d){{\lambda }_{B}}}{d\lambda \beta } \right]}^{\tfrac{1}{\beta -1}}}</math>
-Using Eqn. (lambda initial) to substitute  <math>{{\lambda }_{I}}</math>  we have:
-::<math>{{t}_{0}}={{\left[ \frac{{{\lambda }_{A}}+{{\lambda }_{B}}-{{\lambda }_{A}}-(1-d){{\lambda }_{B}}}{d\cdot \lambda \cdot \beta } \right]}^{\tfrac{1}{\beta -1}}}</math>
-:Then:
-::<math>{{t}_{0}}={{\left( \frac{{{\lambda }_{B}}}{\lambda \cdot \beta } \right)}^{\tfrac{1}{\beta -1}}}</math>
-The initialization time,  <math>{{t}_{0}},</math>  allows for growth to start after a Type B failure mode has occurred.
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