X-ray counting statistics plays a key role in establishing confidence
limits in composition determination by X-ray microanalysis. The process
starts with measurements of intensity on one or more samples and standards
as well as related background determinations. Since each individual
measurement is subject to variability associated with counting statistics,
it is necessary to combine all of the counting variability according to
established mathematical procedures. The next step is to apply propagation
of error calculations to equations for quantitative analysis and determine
confidence limits in reported composition. Similar concepts can also be
applied to trace element determination. This approach can then be combined
with spectral simulation modeling, making it possible to predict
detectability limits without additional measurements.