Specify the distribution fitting for Parametric Distribution Analysis

Specify how to estimate the parameters of the distribution.

Estimation Method

Maximum Likelihood

Estimate the distribution parameters by maximizing the likelihood function.

Least Squares (failure time(X) on rank(Y))

Estimate the distribution parameters by fitting a regression line to the points on a probability plot.

For more information on these two methods, go to Least squares estimation method and maximum likelihood estimation method.

Distribution parameters

Estimate from the data

Select to estimate the parameters of the distribution from the data.

Use historical estimates

Select this option to specify historical estimates for the distribution parameters. Use this method to specify all the parameters of a distribution. Put the estimates of the historical parameters in columns of the worksheet. Enter a column of parameters for every combination of sample and failure mode. Use the following rules to order the parameters in a column.

• For the Weibull distribution, enter the shape parameter in row 1 and the scale parameter in row 2.
• For the exponential distribution, enter the scale parameter in row 1.
• For any location-scale distribution, enter the location parameter in row 1 and the scale parameter in row 2.
• For a distribution with a threshold parameter, enter the parameters in the same order, then enter the threshold parameter in the last row.

For example, to enter the parameters for a Weibull distribution with a shape of 2 and a scale of 900, enter a column with the following values.

C1
Weibull (2, 900)
2
900

Estimate from the data assuming equal scale parameters or Estimate from the data assuming equal shape parameters

When you have multiple samples, select to estimate the parameters using a common shape or scale parameter for the distribution. For information on how this assumption affects the estimation method, go to Least squares estimation method and maximum likelihood estimation method and click "Assume common shape or scale parameters for parametric distribution analysis".

Set a parameter

When the distribution has 2 or 3 parameters and the analysis estimates all the parameters from the data, then you can set some of the distribution parameters instead of estimating all parameters from the data. You can set the parameters that most directly affect the location of the distribution. For the Weibull distribution, you can set the shape parameter. For other distributions, you can set the location parameter. You can also set the threshold parameter.

If you set the parameter for one distribution in the analysis, you must set that parameter for every distribution in the analysis.

If the analysis includes failure modes, then you can use different distributions for different failure modes. With multiple failure modes, you can set the threshold parameter only when all the distributions have a threshold parameter. If you use both a Weibull distribution and a location-scale distribution, then follow these rules:

• If you set the shape parameter for the Weibull distribution, also specify the scale parameter for the other distributions.
• If you specify the location parameter for a location-scale distribution, then specify the shape parameter for a Weibull distribution.