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

Abstract

**Please note that the full text is embargoed** ABSTRACT: When there are available several point estimators of some parametric function, it would seem desirable to make a comparison among 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., mean squared (MS) efficiency is also considered. This paper presents graphical results based on simulation techniques which depict PC efficiencies as well as MS efficiencies of the following estimators of the reliability function R(t) of a 2-parameter exponential failure model: (i) the maximum likelihood estimator(R ^_MLE (t)), (ii) the minimum variance unbiased estimator (R ^_MVUE (t)) and (iii) a Bayesian/structural estimator (R ^_SE (t)). Based on the graphs, R ^_SE (t) is, in general, preferred (in the sense of having the best chance of being closest to the true value of R(t)) except (a) when R(t) is very high, in which case (R ^_MLE (t)) is preferred, and (b) when R(t) is moderate and the sample size is small to moderate, in which case R ^_MVUE (t) is preferred.