Statistical Reliability: Class No. 17

Accelerated Life Models

Definition of accelerated life models
- In terms of random variables
- In terms of survivor functions
- Base survivor function
- Acceleration constant as a function of stress
- The physical age of an item versus its lifetime.
Example of an accelerated life model
- Inverse power law with exponential base survivor function
- Accelerated Life Tests are one of the most important applications
Log-time formulation of accelerated life model
- Derivation
- Weibull base survivor function and Gumbel "errors"
Hazard rate relationships
Diagnostic plots
- Stress versus log-time plots
- Plots for grouped data
  - Plots at the different values of the stress of the survivor functions versus log time should be horizontally shifted copies of each other
  - Plots of Log quantiles at each load versus the log of the average of the quantiles should be parallel lines with slope one
We preview where we are going in reliability data regression by considering the following model:

Fitting the model above using SAS JMP to the data of Watson and Smith (1985). The JMP file is provided below.

Why do engineers frequently like the accelerated life model?
How can the age of an item be different from its life time?
Why is the Accelerated Life model frequently used to study the effect on life time of temperature and voltages stresses on electronic equipment?
Why do we need all the theory in today's class?
Don't you love where we are going with this regression stuff?

Data on the failure stresses of single carbon fiber. (Table 4.1, Page 81 of your textbook)

Find out how to download a JMP file