A double sequential procedure for detecting a change in distribution

Let X₁, X₂,... be such that X₁,... X_T-1, have the distribution F₀, while X_T, X_T+1,... have the distribution F₁. Think of X₁, X₂,... as samples from large batches and suppose T has a prior geometric distribution. Sampling from each batch is assumed to give rise to a Brownian motion process and we are interested in both an optimal sampling scheme and an optimal stopping time to detect the changepoint T. The suggested procedure may roughly be described as a sequence of sequential probability ratio tests. A comparison of our procedure with the fixed size sampling procedure, with the same level of false alarms and the same average sample size per batch, shows that our procedure is significantly superior in that it detects the changepoint much faster.