In this paper, novel mathematical approach for evaluation of probability density function (PDF) of instantaneous signal-to-interference ratio (SIR) at the receiver output in interference-limited environment is proposed. Dual-branch selection combining (SC) receiver operating over correlated Weibull fading channels applying SIR algorithm is considered. Analytical expression for joint PDF of desired signal and interference at the receiver output is derived and used for evaluation of PDF of instantaneous SIR. The expression for PDF of SIR is used for system performance analysis via outage probability, average bit error probability (ABEP) and average output SIR as system performance measures. Numerical results are graphically presented showing the effects of fading severity, average SIR at the input and level of correlation on the diversity receiver performance. In addition, results obtained for the PDF of instantaneous SIR in this paper, are compared to the results when the PDF of instantaneous SIR is directly calculated.