Norris-Landzberg-Exponential Model: Difference between revisions

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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).
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.




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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>\,\!T_{Max}</math>), the temperature difference (<math>\,\!\Delta T</math>) and cycling frequency (<math>\,\!f</math>).
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>).
   
   
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!T<sub>MAX</sub> (°C)
!T<sub>MAX</sub> (°C)
!Delta T (°C)
!Delta T (°C)
!f
!<math>\,\!f</math>
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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:
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}\\
::<math>\begin{align}\\
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In ALTA, the General Log-linear model is used with the proper transformation for each stress.  The failure time distribution is Exponential.  
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]]
[[image:Norris-Landzberg Exp_Stress Transform.png|center]]




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:
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]]
[[image:Norris-Landzberg Exp_Analysis Summary.png|center]]
The above results are close to what the book has.

Latest revision as of 18:21, 28 September 2015

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Norris-Landzberg-Exponential Model

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 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 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]\displaystyle{ \,\!T_{Max} }[/math]), 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

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]\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, 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.

Norris-Landzberg Exp Stress Transform.png


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.

Norris-Landzberg Exp Analysis Summary.png
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