How to go from "particles / second" to "corresponding measurement time"?

[willend]

A popular and relevant question posed by McStas and McXtrace users is how to translate a simulated, discrete statistic to a "corresponding measurement time" - and our documentation on this topic is admittedly limited.

Relevant background information can be found in chapter 2 of your McStas or McXtrace manual

• Use the Docs button on the gui or
• use mcdoc -m / mxdoc -m in your terminal

The best / most thorough explanation of the problem and its solution is found in this PDF note written by Anette Vickery with help from Erik Knudsen and Peter Willendrup. PLEASE DO ACTUALLY READ IT.

The TLDR; explanation is this one:
For a given monitor with recorded "McStas/McXtrace time-averaged intensity" $I$ and RMS error bar $I_{err}$, a “maximum counting time” $t$ for each (non-zero) bin $i$ can be estimated, such that the RMS error bar is always less than the Poisson error-bar of the corresponding "measured" intensity of that given bin:

From this expression we can assess that

which must hold for every (non-zero) bin of the monitor -> requiring use of the lowest $t$ estimated across the monitor. In addition, one should in fact add noise, see the PDF note for details.