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.
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Published online: December 09, 2013
Accepted: November 21, 2013
Received in revised form: November 11, 2013
Received: August 28, 2013
© 2013 Associazione Italiana di Fisica Medica. Published by Elsevier Inc. All rights reserved.