Least squares estimates (LSXY) versus maximum likelihood estimates (MLE)

Least squares estimates are calculated by fitting a regression line to the points in a probability plot. The line is formed by regressing time to failure or log(time to failure) on the transformed percent.

Maximum likelihood estimates are calculated by maximizing the likelihood function. The likelihood function describes for each set of distribution parameters the chance that the true distribution has these parameters based on the sample.

Here are the major advantages of each method:

Least squares

·    The probability plot has a better graphical display because the line is fitted to the points.

·    For small or heavily censored samples, LSXY is more accurate than MLE. MLE tends to overestimate the shape parameter for a Weibull distribution and underestimate the scale parameter in other distributions. Therefore, MLE will tend to overestimate the low percentiles.

Maximum likelihood

·    Distribution parameter estimates are more precise than LSXY.

·    When there are few failures, MLE enables you to perform analyses. When there is only one failure and some right censored observations, maximum likelihood parameter estimates may exist.

·    MLE has attractive mathematical qualities.

When possible, both methods should be tried. If the results are consistent, then there is more support for your conclusions. Otherwise, you may want to use the more conservative estimates or consider the advantages of both approaches and choose one based on your problem.