Design of double CUSUM quality control schemes

The simultaneous use of two standard CUSUM schemes is shown to result in a quality control scheme with a high performance in detecting an arbitrary out-of-control state. The parameters of the (so called) double CUSUM scheme are found by adapting the average run length to the ones of a set of locally optimal standard CUSUM schemes in a best way. First the run length distribution is evaluated with the help of an efficient extrapolation method. Second an optimization problem is stated and solved. Use is made of some monotonicity results considerably reducing the computational effort.