Sequential-Based Approach for Estimating the Stress-Strength Reliability Parameter for Exponential Distribution

In this paper, two-stage and purely sequential estimation procedures are considered to construct fixed-width confidence intervals for the reliability parameter under the stress-strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the stopping rule under the purely sequential procedure is approximated using the law of large numbers and Monte Carlo integration. For the two-stage sequential procedure, explicit formulas for the distribution of the total sample size, the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress-strength model are provided. Moreover, it is shown that both proposed sequential procedures are finite, and in exceptional cases, the exact distribution of stopping times is degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally using real data, the procedures are clearly illustrated.