Estimation in Compound Exponential Failure Models

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Abstract
When items on life-test are subject to two independent single parameter exponential causes of failure, the resulting failure times can be used to estimate these parameters. The maximum likelihood estimates of the parameters are derived for the case when exact failure times are recorded and when the data is censored at a fixed time T. Properties of the estimators are considered conditioned upon the event of obtaining a failure by either cause. The expressions for the means, variances, and covariance of the estimator are found to be functions of expected values of ratios and reciprocals of multinomial random variables. Two examples are included to show possible applications of estimation from this type of compound model.

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