Proceedings of the 2011 Winter Simulation Conference
S. Jain, R.R. Creasey, J. Himmelspach, K.P. White, and M. Fu, eds.
THE CONSEQUENCES OF HOW SUBJECT MATTER EXPERT ESTIMATES ARE
INTERPRETED AND MODELLED, DEMONSTRATED BY AN EMERGENCY DEPARTMENT
DES MODEL COMPARING TRIANGULAR AND BETA DISTRIBUTIONS
Lene Berge Holm Mathias Barra
Akershus University Hospital Akershus University Hospital
Health Service Research Centre Health Service Research Centre
P.O. Box 95 P.O. Box 95
Lorenskog, 1478, NORWAY Lorenskog, 1478, NORWAY
ABSTRACT
The aim of this paper is to demonstrate empirically the consequences of misinterpreting estimates from
subject matter experts (SMEs), and to study the differences between modeling this with triangular and be-
ta distributions. Three estimates which describe the duration of a process; minimum, maximum, and
mode, is ideally sufficient as a proxy for the empirical distribution. However, these estimates might be bi-
ased when the SMEs confuse the difference between mean and mode. The analysis are performed in an
ED model of a Norwegian hospital. When comparing the model output with data from the electronic pa-
tient record we see that a model with beta distributions based on the SME estimates outperforms a model
with the more frequently used triangular distributions. A triangular distribution will overestimate the
mean of the distribution compared to a beta distribution. We therefore encourage the use of beta distribu-
tions over triangular for activities with skewed distributions.
1 INTRODUCTION
Data acquisition is a crucial part of simulation modeling. However, when sufficient empirical data is not
available modelers often resort to estimates from so-called subject matter experts (SMEs) (Law 2007).
They typically provide the modeler with estimates on the duration of different processes included in the
model. To account for some variations in these estimates, it is common to have the SMEs give infor-
mation on the minimum (a), the maximum (b) and the most observed value (c) of time usage of each ac-
tivity in the model. The most observed value, the mode, is normally expressed by the term m. However in
this paper we will refer to it as c when referring to the SME estimate. The three SME estimates are then
usually used as parameters for a triangular distribution, the min, max and mode of the distribution.
Durations of processes, especially in health care, often exhibit a positive skew (tail to the right). That
this phenomenon recurs, is simply due to the fact that there is usually a natural lower bound on how fast
it is possible to perform some task, while there is no corresponding “natural” upper bound on time con-
sumption. Unforeseen delays, malfunctions, or lack of information may prolong a process ad infintium,
while on the other hand the time it takes to, e.g., transport a patient from A to B is clearly constrained be-
low by the laws of physics.
When using the estimates on min, mode and max from SMEs in a triangular distribution, one is likely
to overestimate the tail of the distribution, and hence the mean and, similarly, to underestimate the bulk of
the distribution (shown in Figure 1 below). This constitutes a major - and inherent - problem with the tri-
angular distribution, and its impact is evaluated in this paper.
3654 978-1-4577-2109-0/11/$26.00 ©2011 IEEE