Decision Sciences Journal
Volume 31, Number 1
Winter 2000
Fitting the Lognormal Distribution to Surgical Procedure
Times
Jerrold H. May
Joseph M. Katz Graduate School of Business, University of Pittsburgh,
Pittsburgh, PA 15260, email: jerrymay@katz.pitt.edu
David P. Strum
Department of Anesthesiology, Department of Anesthesiology, Queen’s
University, Kingston General Hospital, 76 Stuart St., Kingston,
Ontario K7L 2V7, email: strumd@post.queensu.ca
Luis G. Vargas
Joseph M. Katz Graduate School of Business, University of Pittsburgh,
Pittsburgh, PA 15260, email: vargas@katz.pitt.edu
ABSTRACT. Minimum surgical times are positive and often
large. The lognormal distribution has been proposed for modeling
surgical data, and the three-parameter form of the lognormal,
which includes a location parameter, should be appropriate for
surgical data. We studied the goodness-of-fit performance, as
measured by the Shapiro-Wilk p-value, of three estimators of
the location parameter for the lognormal distribution, using
a large data set of surgical times. Alternative models considered
included the normal distribution and the two-parameter lognormal
model, which sets the location parameter to zero. At least for
samples with n > 30, data adequately fit by the normal had
significantly smaller skewness than data not well fit by the
normal, and data with larger relative minima (smallest order
statistic divided by the mean) were better fit by a lognormal
model. The rule “If the skewness of the data is greater
than 0.35, use the three-parameter lognormal with the location
parameter estimate proposed by Muralidhar & Zanakis (1992),
otherwise, use the two-parameter model” works almost as
well at specifying the lognormal model as more complex guidelines
formulated by linear discriminant analysis and by tree induction.
Subject Areas: Hospital Management, Planning and Scheduling,
Probability Models, and Statistics. |