Sequential fixed-accuracy confidence intervals for the stress–strength reliability parameter for the exponential distribution: two-stage sampling procedure

Abstract

In this paper, a two-stage sequential estimation procedure is considered to construct fixed-accuracy confidence intervals of the reliability parameter R under the stress–strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the total sample size, explicit formulas for the expected value, and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Performances of the proposed methodology are investigated with the help of simulations. Finally, using three pairs of real datasets, the procedure is clearly illustrated. We used MATLAB in order to implement computations, simulation studies, and real data analysis.