Efficient control chart calibration by simulated stochastic approximation

The accurate determination of control limits is crucial in statistical process control. The usual approach consists in computing the limits so that the in-control run-length distribution has some desired properties; for example, a prescribed mean. However, as a consequence of the increasing complexity of process data, the run-length of many control charts discussed in the recent literature can be studied only through simulation. Furthermore, in some scenarios, such as profile and autocorrelated data monitoring, the limits cannot be tabulated in advance, and when different charts are combined, the control limits depend on a multidimensional vector of parameters. In this article, we propose the use of stochastic approximation methods for control chart calibration and discuss enhancements for their implementation (e.g., the initialization of the algorithm, an adaptive choice of the gain, a suitable stopping rule for the iterative process, and the advantages of using multicore workstations). Examples are used to show that simulated stochastic approximation provides a reliable and fully automatic approach for computing the control limits in complex applications. An R package implementing the algorithm is available in the supplemental materials.