Maximum likelihood estimates, from censored data, for mixed-Weibull distributions

Abstract

An algorithm for estimating the parameters of mixed-Weibull distributions from censored data is presented. The algorithm follows the principle of the MLE (maximum likelihood estimate) through the EM (expectation and maximization) algorithm, and it is derived for both postmortem and non-postmortem time-to-failure data. The MLEs of the nonpostmortem data are obtained for mixed-Weibull distributions with up to 14 parameters in a five-subpopulation mixed-Weibull distribution. Numerical examples indicate that some of the log-likelihood functions of the mixed-Weibull distributions have multiple local maxima; therefore the algorithm should start at several initial guesses of the parameters set. It is shown that the EM algorithm is very efficient. On the average for two-Weibull mixtures with a sample size of 200, the CPU time (on a VAX 8650) is 0.13 s/iteration. The number of iterations depends on the characteristics of the mixture. The number of iterations is small if the subpopulations in the mixture are well separated. Generally, the algorithm is not sensitive to the initial guesses of the parameters. >