UNIFORMLY MINIMUM VARIANCE UNBIASED ESTIMATOR OF STRESS STRENGTH RELIABILITY UNDER TWO PARAMETER EXPONENTIAL DISTRIBUTIONS WHEN THE SCALE PARAMETERS ARE EQUAL

Abstract

In this paper, we consider a stress-strength model where both the stress and strength are distributed independently as two-parameter exponential distributions, with all the parameters unknown. It is assumed that the scale parameters of the distributions are equal, though the threshold parameters may be unequal. Based on random samples of stress and strength, uniformly minimum variance unbiased estimator of the stress-strength reliability is proposed. The UMVUE of the variance of the above estimator is also indicated. Illustrative examples are given using simulated data and real life data set.