|
|
| Line 1: |
Line 1: |
| ====Initialization Time====
| | #REDIRECT [[Reliability_Growth_Planning#Initialization_Time]] |
| <br>
| |
| 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.
| |
| <br>
| |
| <br>
| |