Reliability Estimation in the Mixed Distribution of Exponential and Geometric Distributions

The exponential and geometric distributions have been recognized as a useful model for survival model associated with reliability studies and life testing experiments. This paper deals with estimating reliability from a mixture of exponential and geometric distributions. First, the maximum likelihood estimation is used to estimate the reliability of mixed model when data are grouped and Type-1 censored. Second, the Bayesian estimation is used to estimate the reliability. Third, the plug-in estimation is used to estimate the reliability. Forth, the mean square error of maximum likelihood estimator (MLE) is obtained. Finally, Bayesian and plug-in estimators for MLE will be compared numerically in the terms of various mission times, parameter values in the sense of asymptotic relative efficiency through Monte Carlo simulation.