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?
Do
you have something to tell me?