Estimating operating room utilisation rate for differently distributed surgery times

Abstract

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

KEYWORDS:

• Estimating surgery duration mean
• operating room utilisation
• predicting surgery duration
• semi-repetitive work processes
• work-content instability

Acknowledgements

The author is indebted to three reviewers for their useful comments. ® Wolfram Mathematica is a registered trade mark of Wolfram Research, Inc.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data of this study (a database of ten thousand surgery times) are confidential and cannot be made public.

Additional information

Notes on contributors

Haim Shore

Haim Shore is Professor Emeritus of the Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Israel (retired October, 2015). He owns five academic degrees and had published seven books (four in English) and over a hundred chapters and articles in books and in refereed international journals. In 1993–1994, he was a visitor at the Center for Quality and Productivity Improvement, University of Wisconsin–Madison, and in 2002–2003 he was a visitor in the Department of Mathematics and Statistics, McMaster University, Canada. Shore’s interests include quality and reliability engineering, stochastic modelling and simulation and distributional theory. He was an Associate Editor for Communications in Statistics and on the editorial boards of Quality Engineering, IIE Transactions (Quality & Reliability Engineering), International Journal of Operations and Quantitative Management (IJOQM), and Quality Technology and Quantitative Management (QTQM). His most recent research work has focused on modelling, monitoring and statistical control of surgery times.