Norris-Landzberg-Exponential Model: Difference between revisions
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{{Reference Example| | {{Reference Example|{{Banner ALTA Reference Examples}}}} | ||
This example validates the results for the Norris-Landzberg life-stress relationship in ALTA standard folios. This is accomplished in ALTA by using the general log-linear model (GLL) with proper stress transformations. | |||
{{Reference_Example_Heading1}} | {{Reference_Example_Heading1}} | ||
The data set is from Example 7.2 on page 257 in book ''Life Cycle Reliability Engineering'' by Dr. Guangbin Yang, John Wiley & Sons, 2007. | |||
{{Reference_Example_Heading2}} | {{Reference_Example_Heading2}} | ||
The following table shows the thermal cycling profiles and test results for chip-scale package solder joints. In this example, the thermal cycling profile is represented by three independent stresses. These are: maximum temperature (<math>\,\!T_{Max}</math>), temperature difference (<math>\,\!\Delta T</math>) and cycling frequency (<math>\,\!f</math>). | |||
{| {{table|50%}} | |||
!Failure Time | |||
!T<sub>MAX</sub> (°C) | |||
!Delta T (°C) | |||
!<math>\,\!f</math> | |||
|- | |||
| 208||80||120||1 | |||
|- | |||
| 225||80||120||2 | |||
|- | |||
| 308||80||120||3 | |||
|- | |||
| 142||100||140||2 | |||
|- | |||
| 108||120||160||2 | |||
|- | |||
| 169||100||120||2 | |||
|- | |||
| 131||120||120||2 | |||
|- | |||
| 1300||80||50||2 | |||
|- | |||
| 650||100||70||2 | |||
|- | |||
| 258||120||90||2 | |||
|- | |||
| 6231||30||50||2 | |||
|- | |||
| 1450||30||70||2 | |||
|} | |||
{{Reference_Example_Heading3}} | {{Reference_Example_Heading3}} | ||
The book uses a multiple linear regression model to analyze the data set. The model parameters are estimated using the least squares method. The regression model is shown next: | |||
::<math>\begin{align}\\ | |||
=&ln\left ( L \right )=\alpha _{0}+\alpha _{1}ln\left ( \Delta T \right )+\alpha _{3}ln\left ( \frac{1}{T_{MAX}} \right )\\ | |||
\\ | |||
=&9.517-2.0635\times ln\left ( \Delta T \right )+0.3452\times ln\left ( f \right )+2006.4\times \left ( \frac{1}{T_{MAX}} \right ) | |||
\end{align}\,\!</math> | |||
{{Reference_Example_Heading4|ALTA}} | {{Reference_Example_Heading4|ALTA}} | ||
In ALTA, we use the general log-linear life-stress relationship with the exponential distribution (GLL-exponential model). The following picture shows the proper transformation for each stress. | |||
[[image:Norris-Landzberg Exp_Stress Transform.png|center]] | |||
The following picture shows the results in ATLA. Note that ALTA uses maximum likelihood estimation to estimate the parameters; therefore, the results are close to, but not exactly the same, as the results given in the book, where the least squares method is used. | |||
[[image:Norris-Landzberg Exp_Analysis Summary.png|center]] |
Latest revision as of 18:21, 28 September 2015
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