Models Per Distribution
In the Weibull Parameters pane for a parametric life data set, the selection you make for Distribution determines the choices available for Model. This is also the case in the Weibull Parameters pane for a warranty data set. Additionally, if a warranty data set is in the usage values data format, the Usage Parameters pane displays these two fields when Distribution is selected for Usage type. For more information, see Weibull Panes for Warranty Analysis.
In all cases where Distribution and Model are shown, the selections you make for these two fields determine the parameters that are shown under Calculation results in all panes in which parameters are entered. As indicated in Fixed Parameter Values, parameters with Fixed? checkboxes can either be calculated or have values specified. The estimation method selected in the Weibull Advanced pane also affects the display-only parameters shown.
• When Ranked Regression is selected, display-only ρ (Rho) and ρ2 (Rho2) values are shown. ρ is the correlation coefficient, which is a statistical measure of how closely the data points “fit” the probability plot. The closer ρ is to 1, the better the fit. ρ2 is the 10th percentile of the correlation coefficient. If an observed correlation coefficient is less than the critical value, it implies that the distribution is significantly different from the distribution considered at the 90% level.
• When MLE is selected, a display-only Log Likelihood (Λ) value is shown. Like the ρ value, this value can be used to compare the fit of different distributions.
In the case of a reliability growth data set, you do not select a distribution. However, you do select an estimation method in the Weibull Advanced pane, which affects the display-only parameters that are shown under Calculation results. As parameter values for a reliability growth data set can only be calculated, no Fixed? checkboxes are present. When Duane is the data type selected in the Weibull Parameters pane, the ranked regression method is used for parameter estimations. In this case, the display-only ρ2 value provides the correlation coefficient.
The following table lists the models available for each distribution and the parameters required by each model. For parametric life and warranty data sets, you use Fixed? checkboxes to specify parameter values as described in Fixed Parameter Values. The distributions with a γ value make use of the threshold parameter. You only want to use these distributions if you know there is some failure-free period. For more information, see Threshold Parameter. For the Weibull, lognormal, normal, exponential, and Rayleigh distributions, Competing Failure Modes is an additional model choice. When you select it, other parameters are shown in which to provide the values it requires. For more information, see Competing Failure Modes.
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Distribution
|
Model
|
Parameter
|
||
|---|---|---|---|---|
|
Weibull
|
2 Parameters
|
β (Beta)
|
||
|
η (Eta)
|
||||
|
3 Parameters
|
β (Beta)
|
|||
|
η (Eta)
|
||||
|
γ (Gamma)
|
||||
|
Lognormal
|
2 Parameters
|
μ (Mu)
|
||
|
σ (Sigma)
|
||||
|
Normal
|
2 Parameters
|
μ (Mu)
|
||
|
σ (Sigma)
|
||||
|
Gumbel- (Lower)
|
2 Parameters
|
δ (Delta)
|
||
|
ξ (Xi)
|
||||
|
Gumbel+ (Upper)
|
2 Parameters
|
δ (Delta)
|
||
|
ξ (Xi)
|
||||
|
Exponential
|
1 Parameter
|
λ (Lambda)
|
||
|
η (Eta)
|
||||
|
2 Parameters
|
λ (Lambda)
|
|||
|
η (Eta)
|
||||
|
γ (Gamma)
|
||||
|
Rayleigh
|
1 Parameter
|
ß (Beta)
|
||
|
η (Eta)
|
||||
|
2 Parameters
|
β (Beta)
|
|||
|
η (Eta)
|
||||
|
γ (Gamma)
|
||||
|
||||
|
Gamma
|
2 Parameters
|
θ (Theta)
|
||
|
α (Alpha)
|
||||
|
Logistic
|
2 Parameters
|
μ (Mu)
|
||
|
σ (Sigma)
|
||||
|
Log-logistic
|
2 Parameters
|
μ (Mu)
|
||
|
σ (Sigma)
|
||||
In the Weibull Plot pane, the parameter values used to calculate the data set and generate the plot are shown in the legend. For more information, see Weibull Plot Legend