Norris-Landzberg-Exponential Model: Difference between revisions

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Revision as of 21:43, 10 June 2014

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ALTA_Reference_Examples

This example validates the calculation of the Norris-Landzberg relationship (can be done using the GLL model in ALTA with proper transformation for each stress).


Reference Case

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.


Data

The thermal cycling profiles and test results for chip-scale package solder joints are given below. A thermal cycling profile can be represented by 3 independent stresses in Norris-Landzberg relationship. They are the maximum temperature ([math]\displaystyle{ \,\!T_{Max} }[/math]), the temperature difference ([math]\displaystyle{ \,\!\Delta T }[/math]) and cycling frequency ([math]\displaystyle{ \,\!f }[/math]).

Failure Time TMAX (°C) Delta T (°C) [math]\displaystyle{ \,\!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


Result

For this data set, a multiple linear regression model is used in the book. The model parameters are estimated using the least squared estimation. The regression model is shown next:

[math]\displaystyle{ \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]


Results in ALTA

In ALTA, the General Log-linear model is used with the proper transformation for each stress. The failure time distribution is Exponential.


Norris-Landzberg Exp Stress Transform.png


In ALTA, the maximum likelihood estimation is used. Therefore, the estimated model parameters are not exactly the same as the one given in the book where least squares method is used. The model result in ATLA is:

Norris-Landzberg Exp Analysis Summary.png


The above results are close to what the book has.

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