Abstract
Benford's law is an empirical observation which predicts the expected frequency of
digits in naturally occurring datasets spanning multiple orders of magnitude, with
the law having been most successfully applied as an audit tool in accountancy. This
study investigated the sensitivity of the technique in identifying system output changes
using simulated changes in interventional radiology Dose-Area-Product (DAP) data,
with any deviations from Benford's distribution identified using z-statistics.
The radiation output for interventional radiology X-ray equipment is monitored annually
during quality control testing; however, for a considerable portion of the year an
increased output of the system, potentially caused by engineering adjustments or spontaneous
system faults may go unnoticed, leading to a potential increase in the radiation dose
to patients. In normal operation recorded examination radiation outputs vary over
multiple orders of magnitude rendering the application of normal statistics ineffective
for detecting systematic changes in the output. In this work, the annual DAP datasets
complied with Benford's first order law for first, second and combinations of the
first and second digits. Further, a continuous ‘rolling’ second order technique was
devised for trending simulated changes over shorter timescales. This distribution
analysis, the first employment of the method for radiation output trending, detected
significant changes simulated on the original data, proving the technique useful in
this case. The potential is demonstrated for implementation of this novel analysis
for monitoring and identifying change in suitable datasets for the purpose of system
process control.
Keywords
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Article info
Publication history
Published online: December 09, 2013
Accepted:
November 21,
2013
Received in revised form:
November 11,
2013
Received:
August 28,
2013
Identification
Copyright
© 2013 Associazione Italiana di Fisica Medica. Published by Elsevier Inc. All rights reserved.
