|
|
| (3 intermediate revisions by 2 users not shown) |
| Line 1: |
Line 1: |
| ===IPL-Exponential Reliability Function===
| | #REDIRECT [[Inverse_Power_Law_(IPL)_Relationship#IPL-Exponential]] |
| <br>
| |
| The IPL-exponential reliability function is given by:
| |
| | |
| <br>
| |
| ::<math>R(T,V)={{e}^{-TK{{V}^{n}}}}</math>
| |
| | |
| <br>
| |
| This function is the complement of the IPL-exponential cumulative distribution function:
| |
| | |
| | |
| <br>
| |
| ::<math>R(T,V)=1-Q(T,V)=1-\mathop{}_{0}^{T}f(T,V)dT</math>
| |
| | |
| <br>
| |
| :or:
| |
| | |
| <br>
| |
| ::<math>R(T,V)=1-\mathop{}_{0}^{T}K{{V}^{n}}{{e}^{-K{{V}^{n}}T}}dT={{e}^{-K{{V}^{n}}T}}</math>
| |
| | |
| <br>
| |
| {{ipl ex conditional rel}}
| |
| | |
| ====Reliable Life====
| |
| <br>
| |
| For the IPL-exponential model, the reliable life or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is given by:
| |
| | |
| <br>
| |
| ::<math>R({{t}_{R}},V)={{e}^{-K{{V}^{n}}{{t}_{R}}}}</math>
| |
| | |
| <br>
| |
| ::<math>\ln [R({{t}_{R}},V)]=-K{{V}^{n}}{{t}_{R}}</math>
| |
| | |
| <br>
| |
| :or:
| |
| | |
| <br>
| |
| ::<math>{{t}_{R}}=-\frac{1}{K{{V}^{n}}}\ln [R({{t}_{R}},V)]</math>
| |
| | |
| <br>
| |