Stat 567:Statistical Reliability
Fourth Class (September 10, 1997)

Empirical Survivor Function

Class Objectives:

• Learn about the empirical survivor function
• Learn the basis of graphical methods of life data analysis

Homework Assignments:

• For the ball bearing data of Example 2.1 on Page 37 of your textbook. obtain 95% confidence intervals for S(50) and H(50).
• For the ball bearing data of Example 2.1 on Page 37 of your textbook plot the empirical survivor function using the plotting points derived on Page 40. Then plot the empirical integrated hazard. Do you think that the underlying distribution of the data is IFR? Why?

Class Outline and Main Points:

• Empirical survivor function
  • Mean and variance at a time point
  • Pointwise approximately normal confidence intervals
• Empirical integrated hazard function
  • Approximate mean and variance at a time point
  • Pointwise approximately normal confidence intervals
• Plots of the empirical survivor function
  • Improved plotting points
  • Graphical life data analysis methods
  • Judging whether the hazard rate is increasing or decreasing

Study Questions:

• What is the relationship of the empirical survivor function and the empirical cumulative distribution function?
• Why can you use results about the Binomial distribution to obtain pointwise confidence intervals for the empirical survivor function?
• What is the difference between pointwise and simultaneous confidence intervals?
• What information about aging can you infer from the a plot of the empirical integrated hazard function?
• Why is it sometimes best to work with the log of Weibull and lognormal data?

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