Some ways of combining optimum interval upper limits

When backgrounds are not well enough controlled to measure the value of some physical parameter, one may still obtain an upper limit on the parameter. A single experiment may have several detectors, each of which can alone be used to derive an upper limit from the set of detected events, and the experiment can be run during multiple periods. There can also be more than one experiment which produces an upper limit. Six methods are discussed for producing a combined upper limit. These methods all assume use of either the optimum interval method or the maximum gap method for finding an upper limit in the face of poorly known background.