SPC scheme to monitor surgery duration

A unified statistical process control (SPC) scheme is developed to monitor work-process duration of repetitive processes (constant work content), semi-repetitive (work content somewhat varies between cycles) and memoryless (no typical work content). As a basic paradigm to develop the new scheme, we monitor surgery duration (SD), known to represent durations of all three types of work processes. Recently, a new bi-variate model for SD was developed and empirically validated. Based on the new model, we derive an approximation to the distribution of SD sample average and use it to construct a two-stage SPC scheme (for a medically specified subcategory of surgeries). In the first stage, SD distributional shape, as reflected in third and fourth moments, is monitored to determine that no shape-changing assignable causes are active (e.g., work-content variation is stable); in the second stage, location and scale parameters are separately monitored via a traditional Shewhart scheme. Using an existent database of surgery times, application of the new scheme is demonstrated, and average-run-length properties explored. Extensions (like incorporating co-variates) and generalizations are addressed.