A maximum likelihood method is used to deal with the combined estimation of multi-measurements of a branching ratio, where each result can be presented as an upper limit. The joint likelihood function is constructed using observed spectra of all meas
urements and the combined estimate of the branching ratio is obtained by maximizing the joint likelihood function. The Bayesian credible interval, or upper limit of the combined branching ratio, is given in cases both with and without inclusion of systematic error.
