In order to complete the test faster, experiments are conducted at higher stress levels. Used-level PDF (Probability Density Function) is obtained by extrapolating from the high stress level PDFs along a Life-Stress-Relationship (LSR) model.
In this example, the Arrhenius life-stress model together with the Weibull distribution are used to model failure data under different stress levels. Arrhenius life-stress model is a single-stress model typically used when temperature is the accelerated stress.
An accelerated life test was conducted with temperature as the stress. Nine and six units were tested at 350- and 450-degree Kelvin respectively. The test was suspended after 1200 hours.
We want to derive the Weibull PDF at 300K.
For a single stress test (in this case, Temperature is the only stress), it requires at least 2 stress levels. In general, for N stresses experiment, the minimum number of stress levels is N+1.
Detailed discussion on Life-Stress-Relationship is beyond the scope of this presentation. You can find more information from the book, Accelerated Testing: Statistical Models Test Plans and Data Analyses, by Wayne Nelson.
Accelerated Life Test Analysis assumes that the distribution shape parameters are the same across each experiment. Since the assumed underlying distribution is Weibull, we need to verify if the beta (shape parameter) remains constant from the experiments at 350K and 450K.
To check if both experiments have common beta (shape parameter) values, create a contour overlay plot. Create LDA worksheets for respective 350K and 450K datasets.
Add an Overlay Plot and set Plot Type to Contour plot.
From the contour plot there is no evidence that the beta values are different. Hence, the assumption that “shape parameters are the same across each experiment” is not violated.
So, now we can proceed to perform accelerated life test analysis.
The dataset is entered into Weibull Toolbox ALTA module.
Given the models and data, Maximum likelihood estimation (MLE) solutions for the parameters are derived.
The Weibull PDF at 300K is:
We can derive the reliability matrices at 300K.
You can also obtain other reliability matrices from ALTA Calculator
Most ALT experiments are performed by manufacturers. In order to complete the test faster, experiments are conducted at higher stress levels. Used-level PDF (Probability Density Function) is obtained by extrapolating from the high stress level PDFs along a Life-Stress-Relationship (LSR) model.
To conduct an Accelerated Life Test (ALT) analysis, user need to:
- Identify the stress that can cause the units to failure faster.
- Determine the Life-Stress-Relationship model associated to the stress.
- Determine the underlaying distribution.
- Conduct the experiments at different stress levels (Designing the experiment is not discussion here) to obtain Time-To-Failure dataset.
- Compute the ALT model.