Re-establishing control limits in statistical process control analyses: the stable shift algorithm

Statistical process control (SPC) charts provide a natural approach to analysing time series data for healthcare quality improvement (QI) initiatives. A problem arising in practice is that having established baseline control limits, there is no accepted objective and transparent approach to deciding when to establish new control limits for a given chart. We present the Stable Shift Algorithm, a new algorithm to aid analysts by identifying when control limits should be re-established, partitioning a control chart of time series data into distinct time periods. The algorithm aims to achieve this while (1) using only the theory of SPC, familiar to many QI practitioners, (2) avoiding re-establishing limits prematurely and (3) remaining flexible to choice of basic parameters of typical control chart use in QI. This is achieved through the commonly used shift rule of control charts, applied to establish whether shifts warrant new control limits or not. We conducted a simulation study to evaluate the effectiveness of the algorithm in achieving its aims, and a case study demonstrating application of the algorithm to 557 time series of accident and emergency care measures for providers in England and Scotland. Simulation results show that the algorithm avoids premature re-establishment of limits more often than simply re-establishing at every shift rule break. Application of the algorithm to the accident and emergency measures demonstrates this is not achieved at the cost of excessive additional rule breaks that might indicate control limits do not represent the underlying process. The Stable Shift Algorithm offers a potentially highly valuable tool for QI practitioners and researchers undertaking SPC analyses, providing an automated, consistent and rigorous approach facilitating large-scale analyses.