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A method is described, which computes from an observed sample of events upperlimits for production rates of particles, or, in case of appearance of asignal, the probability for an upwards fluctuation of the background. For anycandidate, a weight is defined, and the computation is based on the sum ofobserved weights. Candidates may be distributed over many decay channels withdifferent detection efficiencies, physical observables and different or poorlyknown background. Systematic errors with any possible correlations are takeninto account and they are incorporated into the weight definition. It isinvestigated, under which conditions a Bayesian treatment of systematic errorsis correct. Some numerical examples are given and compared with the results ofother methods. Simple approximate formulas for observed and expected confidencelevels are given for the limiting case of high count rates. A special procedureis introduced, which analyses input data in terms of polynomial distributions.It extracts confidence levels for a signal or background hypothesis on thebasis of spectral shapes only, normalizing the total rate to the number ofobserved events.Comment: 33 pages, 14 eps-figures, equ.(17) corrected, sect.6.3 and fig.12  replace

Computation of confidence levels for search experiments with fractional event counting and the treatment of systematic errors