Dysarthria is a name given to a group of speech disorders. Our research focuses on developing an automated system for dysarthric speech assessment. Being different from traditional speech assessments which normally rely on human-perceptual analyses, this paper proposes an indicator called modified speech clarity index (ψ†). By incorporating a speech overlapped factor (φ) into the previous version of the speech clarity index (ψ), the ψ† achieves a better performance as a speech severity index and speech recognition rate predictor for people with dysarthria. A number of experiments are made to compare predicted recognition rates, generated by ψ†, with the recognition rates from HMM and ANN system. The effectiveness of the indicator is evaluated in terms of (i) root-mean-square distance, (ii) correlation coefficient, and (iii) rank-order inconsistency. The experiments on a control set and an unknown set of eight dysarthric speakers show that ψ† achieves the outstanding results when compared to the standard assessments.