Three-parameter Weibull probability distribution function is used to represent the time-to-failure data. For parameter estimation, the errors-in-variables, maximum likelihood, and least squares methods are compared. The results obtained from five data sets show that maximum likelihood method gives the most reliable parameter estimates which are close to those obtained by errors-in-variables approach. The least squares method gave the poorest results in most cases. For parameter estimation, the Luus-Jaakola direct search optimization procedure yielded the optimal parameter values in negligible computation time, taking less than a second of computation time on a Pentium4/2.66MHz personal computer for 50 data points.
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Luus et al. (2005) studied this question.