This correspondence paper studies how correlation of the wiretap channel affects the secrecy rate of the artificial noise (AN) scheme. To this end, we first develop a simple but tight lower bound on the ergodic secrecy rate of the AN scheme on correlated multiple-input single-output wiretap channels. Then, utilizing the derived bound, we investigate the influence of correlation on the secrecy rate, which explicitly manifests how the channel correlation affects the optimal power allocation. Ultimately, this paper answers two fundamental questions: when is the AN signal beneficial? and how much power should be allocated for the AN signal to achieve a higher ergodic secrecy rate? in terms of channel correlation.