Sequential design for estimating the reliability of a series system under Linex-loss and cost

Abstract

We investigate a sequential allocation procedure to estimate the reliability of a non-repairable series system of two independent exponential components under linear-exponential loss function combined with sampling cost. Since the optimal fixed allocation depends on unknown parameters, we propose a two-stage design which dynamically assigns observations to each population based on initial pilot estimates. We establish that the proposed procedure is second-order asymptotically optimal as the sampling cost tends to zero. Finally, Monte Carlo simulations are conducted to validate the theoretical findings and demonstrate the efficiency of the proposed estimator in finite samples.