Efficiency Contours for Estimators of Reliability in a 2-Parameter Exponential Failure Model

When several point estimators of some parametric function are available, it is desirable to compare the estimators based on some measure of closeness to the true value. Along these lines, the concept of Pitman-closeness (PC) efficiency is introduced. Essentially, when comparing two estimators, PC efficiency gives the odds in favor of one of the estimators being closer to the true value in a given situation than is the other. The traditional method of comparison, i.e., meansquared (MS) efficiency is also considered. This paper presents graphical results based on simulation techniques which depict PC & MS efficiencies of the following estimators of the reliability function R(τ) of a 2-parameter exponential failure model: i) the maximum likelihood estimator, R
_MLE
(τ); ii) the minimum variance unbiased estimator, R
_MVUE
(τ); and iii) a Bayesian/structural estimator, R
_SE
(τ). Based on the graphs, R
_SE
(τ) is, in general, preferred (in the sense of having the best chance of being closest to the true value of R(τ) except a) when R(τ) is very high, in which case R
_MLE
(τ) is preferred, and b) when R(τ) is moderate and the sample size is small to moderate, in which case R
_MVUE
(τ) is preferred.