Reliability HotWire: eMagazine for the Reliability Professional
Reliability HotWire

Issue 1, March 2001

Hot Topics
Which Analysis Settings Should I Use?

When analyzing reliability data, the analyst is faced with a number of options on how to carry out the analysis. These choices can sometimes seem confusing: Regression or maximum likelihood analysis? Fisher matrix bounds or likelihood ratio bounds? Median ranks or Kaplan-Meier estimates? While there are no hard and fast rules regarding the use of these analysis options, some of these options work better for particular data types than others. In this section, we will attempt to outline which analysis options may be more appropriate for specific types of data. In Weibull++, users can select the desired analysis options from the Set Analysis tab, pictured in the following figure:

Weibull++ Control Panel

Additionally you may choose to experiment with these choices using ReliaSoft’s newest tool "SimuMatic®." This advanced tool is available free to all registered users of Weibull++ 6. Download SimuMatic from weibull.com.  

Parameter Estimation

There are basically two methods of parameter estimation in widespread use in reliability analysis: maximum likelihood estimation and regression. Of the latter, there are also two forms: regression on X and regression on Y. Regression generally works best with data sets with smaller sample sizes (as sample sizes get larger, 30 or more, these differences become less important) that contain only complete data (i.e., data in which all of the units under consideration have been run or tested to failure). This failure-only data is best analyzed with rank regression on X, as it is preferable to regress in the direction of uncertainty. If a reliability test is repeated with the same number of units operated to failure in each experiment, the failure times would change from test to test, but the rank values would remain the same, since they are based solely on sample size and order number. Hence, the uncertainty is on the failure time values, which is on the x-axis, thus regression in the X direction is the most appropriate. It has also been shown that for smaller sample sizes, rank regression on X tends to produce more accurate results than rank regression on Y. Analyzing the results of Monte Carlo simulation has shown that the rank regression on X results are closer to the actual distribution used to generate the data than the results of regression on Y.

Rank regression on Y is best used with data other than time-to-failure data, such as free-form data. An example of this would be warranty data that have unreliability estimates for each month of a warranty period. These would be plotted on a probability plot much as regular failure time data. Since we know the time values in question, and the unreliability values are estimates, the uncertainty is in the Y direction, and regression on Y would be more appropriate.

For data sets that contain a number of random suspensions, maximum likelihood estimation methods usually provide better results. This is because this method better incorporates the time-to-suspension points into the parameter estimates.

Confidence Bounds

The Fisher matrix method of calculating confidence bounds is a fairly standard way of performing these calculations, and is used by many statistical software applications. There has been some concern, however, that this method produces results that are not sufficiently conservative with data sets with very few data points. The likelihood ratio method produces results that are more conservative in such cases, but for data sets with larger numbers of data points, there is not much of a significant difference in the results of these two methods. The beta-binomial method of confidence bound calculation is generally regarded to be inferior to the Fisher matrix or likelihood ratio methods. In Weibull++, it can only be used with mixed-Weibull distributions.

Rank Method

Rank methods determine the way estimated unreliabilities are associated with the user-provided failure times. The median rank method assigns unreliability estimates based on the failure order number and the cumulative binomial distribution. The Kaplan-Meier estimator uses the product of the surviving fractions, producing a modified empirical distribution. In general, the median ranks method is preferable and more widely used for unreliability estimation.

The median rank method tends to work well with data sets consisting of exact failure times and suspensions. The Kaplan-Meier method works well with interval data, provided that none of the intervals are overlapping. However, for data sets that have interval data, we recommend the ReliaSoft Rank Method (RRM), which provides a more accurate estimate for the failure time within the interval. Overall, it is a good idea to use the median rank method or ReliaSoft rank method unless one has a specific reason to use the Kaplan-Meier methodology.
 
We appreciate the contribution of Dr. David Olwell (Director of ReliaSoft Professional Services) to the material included in this article.   

 

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