Aggregated parameter update schemes for monitoring binary profiles.

Profile monitoring is one of the most important topics for statistical process control. Traditional self-starting profile monitoring schemes generally use all historical observations to estimate parameters. Because of the rapid increase in the complexity of modern statistical processes, the practitioners often need to deal with massive datasets in process monitoring. However, when observations of each period are of large sample size and the computation is of high complexity, the traditional method is not economical and urgently needs a parameter update strategy. Under the framework of binary profile monitoring, this paper proposes a novel recursive update strategy based on the aggregated estimation equation (AEE) for massive datasets and designs a self-starting control chart accordingly. Numerical simulation verifies that the proposed method performs better in parameter estimation and process monitoring. In addition, we give the asymptotic property of the proposed monitoring statistic and illustrate our method's superiority by a real-data example.