Weibull Advanced Pane for a Parametric Life Data Set
When a parametric life data set is selected in the LDA Navigator, you supply the parameters required for a distribution-based analysis in the Weibull Advanced pane. These same advanced parameters also apply to warranty data sets. For more information, see Warranty Analysis. The following table describes all of the parameters that appear in the Weibull Advanced pane.
|
Parameter
|
Description
|
||
|---|---|---|---|
|
Estimation method
|
The procedure for estimating the parameters for the failure distribution. The estimation method can help to determine how well the regression line fits the data points plotted on the probability graph. The estimation methods that can be used depend on the data type and number of data points in the data set. Computational time and fit quality are used to determine the best estimation method available. Choices are:
• MLE. When selected, MLE (maximum likelihood estimation) is used to calculate the best fit line. An iterative solution procedure, MLE maximizes the likelihood and log likelihood of the distribution. Although computations are intensive, MLE is the best method for a data set with 500 or more failures. If the Weibull, Lognormal, Normal, or Gumbel- (Lower) distribution is selected in the Weibull Parameters pane when this method is selected, Use MMLE and MMLE type are shown. These MLE parameters are described later in this table.
• Ranked Regression. When selected (default), linear regression is used to calculated the best fit line. In this case, Dependent variable is shown. This rank regression parameter is described later in this table.
|
||
|
Median ranking method
|
The type of ranking to use with the selected estimation method. Choices are:
• Median. When selected (default), the rank regression method is based on median values. This method is also known as the binomial rank method because it uses the binomial equation to solve for the probability of obtaining the observed value.
• Benard. When selected, the rank regression method is based on an approximation method of the median (binomial rank) method. This method requires less computational time than the median method.
• Mean. When selected, the rank regression method is based on mean (rather than median) values.
• Hazen. When selected, the rank regression method uses the midpoint to calculate rank regression. This method is a modified version of the mean method.
• Kaplan-Meier. When selected, the rank regression method is based on the interval function. This method is generally the best method for a data set with suspensions, although the other methods can be used.
|
||
|
When Rank Regression is selected as the estimation method, the parameter below is shown.
|
|||
|
Dependent variable
|
The method for finding the best fit line. This consists of determining the distance from each plotted data point to the best fit line, which gives the resulting parameter values for the data set. Choices are.
• Time. When selected (default), X on Y regression is used. In this case, the distance from the actual point to the theoretical point on the best fit line is considered in the X direction (left or right of the line). This method minimizes variation in the X direction. This method is preferred because the X value (time) tends to be more scattered and erroneous.
• Probability. When selected, Y on X regression is used. In this case, the distance from the actual point to the theoretical point on the best fit line is considered in the Y direction (above or below the line). This method minimizes variation in the Y direction.
|
||
|
When MLE is selected as the estimation method, the parameters below are shown if one of four distributions is chosen in the Weibull Parameters pane: Weibull, Lognormal, Normal, or Gumbel- (Lower). When using MLE, a bias problem for small samples arises only for certain parameters used by these distributions.
|
|||
|
Use MMLE
|
Indicates whether to use MMLE (modified maximum likelihood estimation) to reduce the bias that sometimes occurs in the MLE method. This checkbox is available only when Weibull, Lognormal, Normal, or Gumbel- (Lower) is the chosen distribution.
• When it is cleared (default), a bias corrective factor is not used to adjust the MLE.
• When it is selected, a bias corrective factor is used to adjust the MLE. In this case, MMLE type becomes available so that you can select the type of bias corrective factor to use.
|
||
|
MMLE type
|
This parameter is available only if Use MMLE is selected. For this parameter, you select the type of corrective factor to use to reduce the bias that sometimes occurs in the MLE method. Choices are:
• (N / (N − 1)). This factor is available if Normal or Lognormal is the distribution chosen in the Weibull Parameters pane.
• RBA Median (Standard). This factor is available if Weibull, Lognormal, Normal, or Gumbel - (Lower) is the distribution selected in the Weibull Parameters pane.
• RBA Mean. This factor is available if Normal or Lognormal is the distribution selected in the Weibull Parameters pane.
|
||
|
Regardless of whether Rank Regression or MLE is selected as the estimation method, one or more Confidence parameters are shown. These parameters are used to calculate and display confidence bounds for plots. Because MLE does not have a correlation coefficient associated with it, calculating confidence for this method is highly recommended. When you select a confidence type and level, in the Weibull Plot pane, the probability plot displays one or more lines above and/or below the best-fit line. These lines indicate the selected confidence bounds within which the estimated values of X and Y are most likely to fall.
|
|||
|
Confidence type
|
The type of bounds to use for the analysis and to display on the Weibull plot. This option is available only when supported by the selected plot type. Choices, are None, Lower Confidence, Double Confidence, Upper Confidence, and Upper and Lower. For a probability plot, an additional choice is available: Confidence = Reliability. For more information, see Confidence Types. When None is selected, no confidence bound is used. Consequently, no other confidence parameters are shown. When any other choice is selected, one or more additional confidence parameters are shown. For example, when a percentage value for a bound is entered, % is shown so that you can enter a percentage value.
|
||
|
%
|
The percentage value to use to calculate the confidence bounds. This parameter is not shown when either None or Confidence = Reliability is selected as the confidence type. When you select any other choice, this field is shown. Its default is 90.
|
||
|
Confidence method
|
The method to use to calculate confidence bounds for parameter estimations. This parameter is available when a choice other than None is selected as the confidence type. Choices are Fisher Matrix, Likelihood Ratio, and Binomial. The default is Fisher Matrix. For more information, see Confidence Methods.
|
||
|
Calculation results
The parameters that can be calculated or specified for each distribution/model combination differ. Calculated results appear in this area only after the data set has been calculated. To use a specific value for a parameter, you select Fixed? and then enter the value. For more information, see Models Per Distribution.
|
|||
