We illustrate how to use JMP with a subset of Nelson's data found in:
Applied Life Data Analysis. (1982). Wayne Nelson. Wiley & Sons. New York.
The data consist of the number of cycles to failure for 36 units, together with their causes of failure (failure code). Failure code 0 means that the unit was removed from test before failure occurred. Replacement of unfailed units with new ones allowed more testing of the early life.
Import into JMP file:
(Instructions for importing a text file into JMP)
The JMP data table should look as follows:
Note that the Cause-Code column is declared nominal (N),
We follow the analysis found in the excellent JMP user's manual.
We start with a simple analysis using box plots:
From the box plots we see that most of the early failures are 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 - all three early failures.
To aid in the interpretation of the box plots recall that the Weibull alpha parameter corresponds the 63.2% quantile of failure time.
Below we do a more sophisticated analysis using JMP"s Survival Platform.
The empirical survival and 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 failure modes. Notice that Cause 15 failures have a very large alpha parameter (63.2% quantile of failure time). This is strange sine the two Cause 15 failures occurred very early, at 35 and 49 cycles. 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 Cause 9 failures? (Recall that these failures were most the late-life failures.)
We see (dashed line) that the survival probability does not change much until 2000 cycles, but then becomes much better as far a 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 after10,000 cycles.
We repeat this analysis with Cause 6 failures. Recall that these failure were most of the early life failures.
In this case we see some improvement between 2000 and 6000 hours. What would happen if all causes of failure except for 6 were eliminated?
In this case great improvement is seen except for the early life.
Questions: