Stat 567:Statistical Reliability
Fifth Class (September 15, 1997)

Simple Data Analytic Methods:
Quantile-Quantile Plots

Class Objectives:

• Learn simple but effective methods for analyzing life data when there is no censoring or covariate information
• Learn the basis of graphical methods of life data analysis
• Learn to use Weibull and lognormal plots

Homework Assignments:

• Take a look at the homepage of the course Graphical Data Analysis out of the University of Montana
• Use JMP to do Weibull and lognormal plots of the Aircraft component data of Example 2.2 on Page 43 of your textbook. You can see how this is done below. You can download a text file containing these data. (Instructions for importing a text file into JMP)
• Identify the standard survivor function G that leads to the Gumbel and normal QQ plot. Find G inverse for the Gumbel plot.

Class Outline and Main Points:

• Weibull and Lognormal plots
  • Interpretation
  • Graphical estimates of distribution parameters
• Quantile-Quantile (Q-Q) plots
  • Normal and Gumbel plots
  • Justification for the name
  • Cumulative hazard plot is the exponential distribution Q-Q plot
  • What about the Gamma distribution?
• Graphical analysis for Type I censored data
• Graphical analysis for Type II censored data

Screen shots of JMP analysis of the aircraft data of Example 2.2 on Page 43 of your textbook:

Data set in text format

(Instructions for importing a text file into JMP)

Study Questions:

• What is the main benefit of graphical plots?
• Why are the Weibull and Log-normal plots useful?
• What is one way to choose between a Weibull and a lognormal model for a particular data set?
• Why can the Weibull and lognormal plots be used to estimate model parameters when the data is right censored?
• Why can't the method-of-moments method be used to estimate model parameters when the data is right censored?
• Why isn't it possible to develop a Q-Q plot for the Gamma distribution?
• In what situation would a statistician want to use empirical cumulative distribution functions for both the G and F cumulative distribution functions in a Q-Q plot?
• How can you use Q-Q plots to chose among the Weibull, Gumbel, normal, and lognormal distributions for a set of data?

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