  The frequentist definition of sensitivity of a search for new phenomena
proposed in arXiv:0308063 has been utilized in a number of published
experimental searches. In most cases, the simple approximate formula for the
common problem of Poisson counts with background has been deemed adequate for
the purpose. There are however many problems nowadays in which more complex
analysis is required, involving multiple channels. In this article, the same
approach of arXiv:0308063 is applied to a multichannel Poisson problem, and a
convenient formula is derived in closed form, generalizing the known result for
the simple counting experiment. An explicit solution is also derived for the
common case of a search for a Gaussian signal superimposed over a flat
background.

Data Analysis, Statistics and Probability;High Energy Physics - Experiment;Methodology