On Consistent Estimation of Age Replacement Intervals

Abstract

A method of constructing consistent estimators of optimum age replacement intervals from a random sample of lifetimes is given. The method depends on the availability of a uniformly strongly consistent estimator of the underlying distribution function. Such estimators considered are the MLE and MVUE of the Weibull and Gamma distribution functions with unknown scale parameters, the empirical distribution function, and the MLE under the restriction of increasing failure rate. Monte Carlo studies suggest that, in the parametric cases, the MLE is nearly as good as the MVUE unless the ssmple size is quite small and the population variance large. The estimates of the optimum age replacement interval in the nonparametric cases rarely differ, indicating that one may use the empirical distribution frmction with no serious loss of information.

KEY WORDS:

• Age replacement
• Estimation
• Increasing failure rate
• Maximum likelihood
• Minimum variance unbiased
• Weibull