Second-order efficiency of fully sequential designs for estimating the product of two means with application in reliability estimation

The problem of estimating system reliability is the same as estimating the product of means of independent Bernoulli populations. We use independent Beta priors for the means and propose a sequential design that is second order efficient, it converges faster to the optimal ratio than the first order designs. Second order sequential designs are sought and show the optimality of the fully sequential design through an application of reliability estimation using Monte Carlo simulation.