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Weibull++ Standard Folio Control Panel

Weibull++ Standard Folio Analysis Settings

The Analysis page of the Weibull++ standard folio control panel includes the settings that are also displayed on the Main page, along with any additional settings that may be applicable for the current data sheet. This topic provides a brief description of all the settings. For the background theory of each analysis method, the ReliaWiki resource portal provides more information at: http://www.ReliaWiki.org/index.php/Parameter Estimation.

The Analysis page of the Weibull++ standard folio control panel contains the following settings:

As a rule of thumb, data sets with small sample sizes and mostly complete data may be best analyzed with rank regression, while MLE may be more appropriate for data sets with a high proportion of suspensions, interval data or many observed failures. This is because the MLE method is based on the likelihood function, which considers each time-to-suspension in the estimate of the parameters, unlike in rank regression where the solution is based on the plotting positions of the times-to-failure data. However, the MLE solution tends to be badly biased (statistically distorted) when performed on small sample sizes. As the sample size gets larger, the difference between the two methods become less important. To determine whether your sample size is large enough for MLE, you will need to take into account factors such as the amount of variability in your data set and the acceptable level of risk or margin of error in your calculations. For more information on rank regression vs. the MLE parameter estimation method, please read "Comparison of MLE and Rank Regression Analysis When the Analysis Contains Suspensions" at: http://www.Weibull.com/hotwire/issue16/relbasics16.htm

When choosing between rank regression on X (RRX) and rank regression on Y (RRY), note that data are best analyzed when regressed in the direction of uncertainty. For example, in reliability tests, the times-to-failure (x-axis) vary from test to test but the probabilities of failure (y-axis) remain consistent. Therefore, if the uncertainty is on the times-to-failure data, RRX may be the preferred analysis method.

On the other hand, in situations where the time value (x-axis) is known but the probability of failure (y-axis) varies for each time value, the RRY method may be the appropriate choice because the uncertainty is on the unreliability estimates.

The median ranks method assigns unreliability estimates based on the failure order number and the cumulative binomial distribution. Alternatively, 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. Thus, it is a good idea to use the median ranks method unless one has a specific reason to use the Kaplan-Meier methodology.

When using rank regression with grouped data, the software will plot only the data points that correspond to the highest median rank position in each group. For example, for two groups of data with 10 units each, the software will plot only two data points: the 10th rank position out of 20 and the 20th rank position out of 20. The regression line is then fitted to these two points. When you select the Ungroup on regression check box, the software will plot each individual data point in the group. The regression line is then fitted to all the data points. In general, grouped data analysis provides parameter estimates that have wider confidence bounds, while ungrouped data analysis provides parameter estimates with much narrower confidence bounds. The ReliaWiki resource portal provides more information about using rank regression with grouped data at: http://www.ReliaWiki.org/index.php/Grouped Data Parameter Estimation.

When using MLE analysis, the Ungroup on MLE check box ungroups the data during calculations and then plots all the data points in each group on the probability plot; however, the solution of the line is obtained from the likelihood function and not by the plotting positions of the data points. Therefore, the line is not expected to track the points on the plot. This option is useful for adjusting the way the grouped data points are displayed on the MLE probability plot.

Note: When working with grouped interval censored data, you have to be cautious about ungrouping the data. In interval censored data, it is assumed that the failures occur at some time in the interval between the previous and the current time-to-failure. For example, a group of 10 units may be interval censored between zero and 100 hours. If you select the Ungroup on Regression check box, the software will treat the 10 units as failures that occur at exactly 100 hours.

The MLE method is known to obtain biased (statistically distorted) estimates when performed on small sample sizes. The Unbias parameters check box corrects the biased estimate of the Weibull beta parameter due to the MLE sampling error. Weibull++ uses the correction factor proposed by Ross and Hirose to unbias both censored and non-censored data. The ReliaWiki resource portal provides more information about the correction factors at: http://www.ReliaWiki.org/index.php/The_Weibull_Distribution#Unbiased_MLE.

For more information about how you might correct biased estimates, please read "Unbiasing Parameters in Weibull++" at: http://www.Weibull.com/hotwire/issue109/relbasics109.htm. (Note that this article uses Weibull++ 7, but the theory remains the same.)

 

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