Stat 567:Statistical Reliability
Nineteenth Class (November 17, 1997)

Accelerated Life Models

Class Objectives:

• Learn the definition and properties of Accelerated Life models
• Learn how to use JMP to fit a simple accelerated life model

Homework Assignments:

• Reproduce the last JMP output of the links from this class summary

Class Outline and Main Points:

• 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).

Study Questions

• 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?

SAS JMP files (Mac) of classroom examples and homework

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

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