Comparison of MLE and Rank
Regression Analysis When the Data Set Contains
In previous issues of the HotWire, we have discussed the maximum likelihood estimation (MLE) and rank regression methods for parameter estimation. We have also mentioned that when your data set contains a large number of suspensions, it is suggested that you use MLE for parameter estimation. But why? In this month's Reliability Basics, we will take a closer look at this "rule of thumb" and illustrate how rank regression does not take into account the characteristics of the entered data when there are a large number of suspensions.
Even though the rank adjustment method is the most widely used method for performing suspended items analysis, there is a shortcoming to the method that must be understood. As you may have noticed when using this analysis method for suspended items, the position where the failure occurred is taken into account but not the exact time-to-suspension. For example, rank regression would yield the exact same results for the two cases described in Figure 1.
Figure 1: Two data sets to be analyzed with rank regression and MLE methods for comparison purposes
This shortfall is significant when the number of failures is small and the number of suspensions is large and not spread uniformly between failures, as with these data sets. In cases like this, it is highly recommended that you use maximum likelihood estimation (MLE) to solve for the parameters instead of least squares, since maximum likelihood does not look at ranks or plotting positions, but rather considers each unique time-to-failure or suspension. For the data sets given above the results are as follows:
The estimated parameters using the rank regression method are the same for both cases (1 and 2):
However, the MLE results for Case 1 are:
and the MLE results for Case 2 are:
As you can see, there is a sizable difference in the results of the two sets calculated using MLE and the results using regression. The results for both cases are identical when using the regression estimation technique, as regression considers only the positions of the suspensions. The MLE results are quite different for the two cases, with the second case having a much larger value of η, which is due to the higher values of the suspension times in Case 2. This is because the maximum likelihood technique, unlike rank regression, considers the values of the suspensions when estimating the parameters.
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