Estimating operating room utilisation rate for differently distributed surgery times

A method is developed to determine the required sample size to estimate utilisation rate (UR) of a facility, where blocks of work processes/jobs with i.i.d execution times are consecutively executed, and different blocks possibly pursuing different distributions. It is assumed that within-block processes may be repetitive (constant work-content; execution time normally distributed), semi-repetitive (work-content somewhat varies between cycles) or memoryless (no characteristic work-content; exponentially distributed). Surgeries are known to comprise all three types of work processes. In this article, we use operating theatres as prototype facility to estimate UR, assuming that surgeries are allocated in blocks, in conformance with the specified scenario. A recently developed model for surgery duration, bridging the gap between duration models for repetitive and memoryless processes, is used to estimate UR. A database of ten thousand surgeries serve to compare sample sizes, calculated under normality (the traditional method) or lognormality, with the correct model-based values. The latter deviate appreciably from the former, corroborating the need for the new methodology. Abbreviations: OF: objective function; OR: operating room; SD: Surgery duration; SDD: Surgery duration distribution; UR: utilisation rate