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Using the General Log-Linear Model in ALTA PRO for Thermal Cycling



Having higher reliability than competitors is one of the key factors for success. This is especially true for the electronics industry. The reliability of electronic products can be predicted based on the design, the manufacturing process and the expected operating conditions. There are many different approaches for reliability estimation such as standards based reliability prediction, physics of failure and life testing. ReliaSoft's ALTA PRO employs a physics of failure approach and can be used to analyze test data for single or multiple stress conditions. In this article, we will analyze accelerated test data using the Norris-Landzberg model for lead-free solder joint low-cycle fatigue, by using the general log-linear (GLL) model in ALTA PRO.

Comparing the Norris-Landzberg Model and the GLL Model

In electronic devices, failures can occur due to fatigue caused by temperature cycling and thermal shock. These fatigue failures are often a result of cyclical stresses that are induced during the device’s normal power-up and power-down cycles. These stresses lead to weakened materials that may fail due to several different causes, including dielectric/thin-film cracking, lifted bonds and solder fatigue. The Coffin-Manson model and a modified version of it known as the Norris-Landzberg model have been used successfully to model crack growth in solder joints due to repeated temperature cycling as the device is switched on and off. The number of cycles to failure in the Norris-Landzberg model is represented as:

Norris-Landzberg model


Nf is the number of cycles to failure

C is a coefficient

f is the cycling frequency [cycles/day]

ΔT is the temperature range during a cycle [K]

Tmax is the maximum temperature during each cycle [K]

Ea is the activation energy [eV]

K is the Boltzmann's constant [8.617 × 10-5 eV/K]

p and m are the model parameters

The cycling frequency (f), the temperature range (ΔT) and the maximum temperature (Tmax) are the stresses considered for testing. The activation energy (Ea) can be determined by test data and it is usually related to certain failure mechanisms and failure modes. Typical parameters of the Norris-Landzberg model have been published for various solder types. For example, for tin-lead (SnPb) solder and tin-silver-copper (SnAgCu or SAC) solder, the parameters are: p = 0.33, m = 1.9, and Ea = 0.122.

Acceleration factor can also be calculated as:

Acceleration factor equation

Acceleration factor equation

The general log-linear (GLL) model in ALTA PRO assumes a log-linear relation for the life characteristic, tp, and is formulated as:

Log-linear equation


tp is the life characteristic

α0, α1, ... αn are the parameters of the life-stress relationship

χ1, χ2, ... χn are the covariates

This equation can be rewritten in a more compact form as:

Log-linear compact form

And we can express this in terms of the life characteristic as:

Life characteristic

The life characteristic, tp, can represent any percentile of the assumed underlying life distribution. It can be the scale parameter eta (Weibull distribution), mean (exponential distribution) or median (lognormal distribution).

The advantage of representing the life characteristic with the log-linear relationship is that life-stress relationship models can be assumed for the covariates by performing a simple transformation. Therefore, the Norris-Landzberg model, which is a combination of a power model for f, a power model for ΔT, and an exponential model for Tmax, can be formulated via the GLL model by applying a logarithmic transformation to f and ΔT, and a reciprocal transformation to Tmax. Hence, for three stresses the GLL model becomes:

GLL model with three stresses

Applying the transformations:

GLL model with three stresses - transformation

GLL model with three stresses - transformation

where the relationships between the parameters of the Norris-Landzberg and GLL models are described as:

p = −α1

m = −α2

EαK = α3


40 electronic components were tested to failure due to crack growth in solder joints as a result of repeated temperature cycling at three different elevated stress conditions. The associated data set is entered into an ALTA PRO standard folio, as shown below.

Test data for crack growth in solder joints of electronic components due to repeated temperature cycling

To represent the Norris-Landzberg model, choose the GLL-Lognormal model on the control panel, and then use the following stress transformations for the three stresses.

Stress transformation

You can then use the GLL results from ALTA PRO to calculate the parameters of the Norris-Landzberg model, as shown next:

Comparison of results


In this article, we introduced the Norris-Landzberg physics of failure model for crack growth in solder joints resulting from repeated temperature cycling in electronic devices. The relationship between the Norris-Landzberg model and the general log-linear model was presented, and ALTA PRO was used to estimate the Norris-Landzberg parameters for a given data set. A similar process can be used to analyze accelerated test data in ALTA for many physics of failure models with multiple stresses.


  1. Wayne Nelson, Accelerated Testing: Statistical Models, Test Plans and Data Analyses. New York: Wiley, 1990.
  2. "Reliability Prediction Methods for Electronic Products," Reliability Edge 9, no. 1: http://www.ReliaSoft.com/newsletter/v9i1/prediction_methods.htm?_ga=1.123553672.244422347.1440020929
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  9. Jinhua Mi, Yan-Feng Li, Yuan-Jian Yang, Weiwen Peng, and Hong-Zhong Huang, "Thermal Cycling Life Prediction of Sn-3.0Ag-0.5Cu Solder Joint Using Type-I Censored Data," The Scientific World Journal 2014 (2014).