To illustrate what we mean we use the data of Watson, A. S. and Smith, R. L. (1985) on the failure stresses of single carbon fiber. (Table 4.1, Page 81 of your textbook). Notice that in this examplex failure stress plays the role of time.
After some rearrangement of columns we get this table:
For some reason that I don't know JMP adds an extra 250 rows to this table that we have to clean up. (Does anybody know how to keep JMP from adding these extra rows?)
Notice that log(-log(Surv)) is another way to write log(Integrated Hazard). Also notice that log(Time) is really log(Stress) in this problem because of the way we made the column assignments in this JMP platform.
Using the Fit Y by X JMP platform we obtain:
If the Proportional Hazards Model assumption holds these lines should be parallel. What do you think?
Notice that second plot above is really a group of Weibull plots - one for each load level (length). So if these plots are straight line this would mean that for each load level (length) the distribution is Weibull.
