In this class we analyze Wayne Nelson's data set (see reference below) as simplified in JMP's APPLIANCE data set (found in the Sample Data folder that comes with the software).
There are a total of 36 units and fifteen failure modes in the JMP data set . Wayne Nelson's original data set has 407 units and 18 failure modes. "Time" is number of cycles to failure or removal. Cause 0 is a removal time. Replacement of unfailed units with new ones allowed more testing of the early failures.
(This is a competing risk situation because each of the appliances could fail due to any of the 15 failure modes. Is is as if the fifteen failure modes were competing with each other to kill each the appliances in one group. Contrast this with the rat data situation. There, there are three groups but only one "failure mode", namely, the development of a tumor.)
We follow the analysis found in the JMP user's manual.
First, we do a simple analysis using box plots.
From the box plots we see that most of the early failure were due to Cause 6. And that most of the late failures are due to Cause 9. (In JMP the width of the box plots are proportional to the sample size.) Hence,
Also, note that there are only one Cause 1 failure and two Cause 15 failures, and that all three are early failures.
To aid in the interpretation of the box plots recall that the Weibull alpha parameter corresponds to the 63.2% quantile of the failure time.
Below we do a more sophisticated analysis using JMP's Survival platform.
The empirical survival and the fitted Weibull survival (dashed line) in the plot above are for all failure modes put together.
The table gives the alpha and beta parameters for fitted Weibulls of the separate failures modes. Notice that Cause 15 failures have a very large alpha parameter (63.2% quantile of failure time). This is strange since the two Cause 15 failures occurred very early, 35 and 49. However, this is a common phenomenon since failure modes that do not cause many early failures usually tend to not cause later failures.
How would the reliability be affected if we could remove the Cause 9 failures? (Recall that these failures were most of the late-life failures. )
We see (dashed line) that the survival probability does not change much until 2000 cycles, but then becomes much better at 10,000 cycles.
What do we expect if we omit all failure modes except for Cause 9 ?
In this case there is a big improvement in the very beginning, but almost no improvement at 10,000 cycles.
(Instructions for importing a text file into JMP)
