An accurate evaluation of adaptive exponentially weighted moving average schemes

As a natural generalization of the conventional Exponentially Weighted Moving Average (EWMA) monitoring scheme, the Adaptive EWMA (AEWMA) scheme has received a great deal of attention. The Markov chain method was originally used to approximate the average run length performance of the AEWMA chart; however, this method may suffer from the issue of slow convergence and unstable approximation due to kernel discontinuity. In order to overcome this issue, this article extends the piecewise collocation method and the Clenshaw–Curtis (CC) quadrature (method) to the evaluation of AEWMA chart performance. It is shown that both the collocation and CC quadrature methods are very competitive and can provide more accurate and fast approximation to the run length performance of AEWMA charts than the conventional Markov chain approach.