Statistical Considerations for Improved Signal Identification from Repeated Measurements at Low Signal-to-background Ratios

Abstract

Continuously repeated or frequent periodic measurements of the radiation environment in the absence of an identified source of ionizing radiation provide large data sets on the ambient background. Statistical evaluation of these data allows for the identification and quantification of the relevant background distribution parameters paramount to establishing a well characterized background distribution. Given this distribution, the determination of characteristic limits, such as the decision threshold, follows standard procedures. However, the data used to establish these characteristic limits contain additional information on the probabilities for future individual measurement results, which can be employed to improve the detection system capabilities for signal identification at low signal-to-background ratios. In particular, a statistical evaluation of the time history of individual, independent measurements allows for the establishment of new decision thresholds with the same prescribed probability of error of the first kind but with a lower value than the decision threshold obtained from standardized procedures. A rigorous mathematical and statistical treatment of multiple data from a well characterized background distribution is presented, together with an analysis of the relevant operational restrictions and statistical conditions for which an improved lower decision threshold can be obtained. A set of initial projections toward the application of appropriate statistical algorithms is intended to provide a basis for further investigation of these statistical considerations for their implementation in continuous scanning or screening operations or in individual or environmental monitoring programs.