Temperature-Nonthermal (TNT)-Weibull Model
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This example validates the calculation of Temperature-nonthermal relationship for Weibull distribution.
Reference Case
Data is from Table 7.10 on page 300 in book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.
Data
Temperature and switching rate are the two stresses used in the accelerated life test for a type of 18-V compact electromagnetic relays. The cycles to failure are provided next.
| Number in Group | State F/S | Time to State | Temperature (F) | Switching Rate | Subset ID | Number in Group | State F/S | Time to State | Temperature (F) | Switching Rate | Subset ID |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | F | 47154 | 337.15 | 10 | 1 | 1 | F | 29672 | 398.15 | 10 | 3 |
| 1 | F | 51307 | 337.15 | 10 | 1 | 1 | F | 38586 | 398.15 | 10 | 3 |
| 1 | F | 86149 | 337.15 | 10 | 1 | 1 | F | 47570 | 398.15 | 10 | 3 |
| 1 | F | 89702 | 337.15 | 10 | 1 | 1 | F | 56979 | 398.15 | 10 | 3 |
| 1 | F | 90044 | 337.15 | 10 | 1 | 6 | S | 57600 | 398.15 | 10 | 3 |
| 1 | F | 129795 | 337.15 | 10 | 1 | 1 | F | 7151 | 398.15 | 30 | 4 |
| 1 | F | 218384 | 337.15 | 10 | 1 | 1 | F | 11966 | 398.15 | 30 | 4 |
| 1 | F | 223994 | 337.15 | 10 | 1 | 1 | F | 16772 | 398.15 | 30 | 4 |
| 1 | F | 227383 | 337.15 | 10 | 1 | 1 | F | 17691 | 398.15 | 30 | 4 |
| 1 | F | 229354 | 337.15 | 10 | 1 | 1 | F | 18088 | 398.15 | 30 | 4 |
| 1 | F | 244685 | 337.15 | 10 | 1 | 1 | F | 18446 | 398.15 | 30 | 4 |
| 1 | F | 253690 | 337.15 | 10 | 1 | 1 | F | 19442 | 398.15 | 30 | 4 |
| 1 | F | 270150 | 337.15 | 10 | 1 | 1 | F | 25952 | 398.15 | 30 | 4 |
| 1 | F | 281499 | 337.15 | 10 | 1 | 1 | F | 29154 | 398.15 | 30 | 4 |
| 59 | S | 288000 | 337.15 | 10 | 1 | 1 | F | 30236 | 398.15 | 30 | 4 |
| 1 | F | 45663 | 337.15 | 30 | 2 | 1 | F | 33433 | 398.15 | 30 | 4 |
| 1 | F | 123237 | 337.15 | 30 | 2 | 1 | F | 33492 | 398.15 | 30 | 4 |
| 1 | F | 192073 | 337.15 | 30 | 2 | 1 | F | 39094 | 398.15 | 30 | 4 |
| 1 | F | 212696 | 337.15 | 30 | 2 | 1 | F | 51761 | 398.15 | 30 | 4 |
| 1 | F | 304669 | 337.15 | 30 | 2 | 1 | F | 53926 | 398.15 | 30 | 4 |
| 1 | F | 323332 | 337.15 | 30 | 2 | 1 | F | 57124 | 398.15 | 30 | 4 |
| 1 | F | 346814 | 337.15 | 30 | 2 | 1 | F | 61833 | 398.15 | 30 | 4 |
| 1 | F | 452855 | 337.15 | 30 | 2 | 1 | F | 67618 | 398.15 | 30 | 4 |
| 1 | F | 480915 | 337.15 | 30 | 2 | 1 | F | 70177 | 398.15 | 30 | 4 |
| 1 | F | 496672 | 337.15 | 30 | 2 | 1 | F | 71534 | 398.15 | 30 | 4 |
| 1 | F | 557136 | 337.15 | 30 | 2 | 1 | F | 79047 | 398.15 | 30 | 4 |
| 1 | F | 570003 | 337.15 | 30 | 2 | 1 | F | 91295 | 398.15 | 30 | 4 |
| 1 | F | 12019 | 398.15 | 10 | 3 | 1 | F | 92005 | 398.15 | 30 | 4 |
| 1 | F | 18590 | 398.15 | 10 | 3 |
Result
The following temperature non-thermal life stress relationship is used.
- [math]\displaystyle{ \,\!L\left ( f,T \right )=Af^{B}e^{\left ( \frac{E_{a}}{kT} \right )} }[/math]
where [math]\displaystyle{ \,\!f }[/math] is the switching rate, [math]\displaystyle{ \,\!T }[/math] is temperature. [math]\displaystyle{ \,\!L\left ( f,T \right ) }[/math] is the life characteristic affected by the two stresses. This relationship is called temperature non-thermal model in ALTA.
This relationship also can be expressed as the following:
Results in ALTA