Efficiency of Estimates for Reliability Function of Exponential Distribution in Life Testing

Z.X. Xiong, S.K. Sinha, and C.-L. Huynh (1996). Efficiency of Estimates for Reliability Function of Exponential Distribution in Life Testing. Journal of Statistical Research, Vol. 30, No. 2, pp. 47-55.

Abstract

Consider the life length $X$ of an object under the exponential distribution with parameter $\theta,$ the reliability function at time $t$ of $X$ is defined by $R(t)=P(X>t).$ For each sample size $n,$ there exist two real numbers $L(n)$ and $U(n)$ such that the uniformly minimum variance unbiased estimate (UMVUE) of the reliability function is more efficient than the maximum likelihood estimate (MLE) of the reliability function if the ration $t/\theta\notin[L(n),U(n)].$ In this paper, a table are derived as $n$ tends to infinity. It is recommended than the UMVUE of reliability function for life length should be chosen for inference instead of commonly used MLE.