An Empirical Procedure for Estimating the Parameters of a Mixed Exponential Life Testing Model

A failure-time distribution made up of two exponential distributions having two distinct failure rates and a specific mixture proportion is considered. The associated experiment is terminated after a predetermined time has elapsed and the numbers of failures in each time interval are recorded. As soon as an item fails it can be attributed to the appropriate subpopulation. An empirical procedure is proposed to estimate the 3 parameters of the model. The maximum likelihood estimators and our estimators are compared using both real and simulated data. The procedure can be extended to a mixed model of three or more exponential distributions, and can be applied to ungrouped and/or uncensored samples.