This paper presents a novel quality assessment approach for the prediction of the subjective haptic experience in time-delayed teleoperation. With the rapid development of haptic technology in remote robot control and virtual reality, new control schemes and hardware systems are developed to provide high quality human-in-the-loop teleoperation service. Our subjective experiments indicate that the existing objective quality assessment metrics do not sufficiently correlate with the subjective haptic experience of the users. This gap requires expensive and time-consuming subjective experiments to be conducted. To avoid time-consuming experiments and provide a fast and accurate subjective experience prediction, we make an attempt to analyze and explain the mismatch between the subjective and objective haptic signal quality metrics. To this end, extensive subjective experiments and case studies have been conducted for teleoperation with time delay and haptic data reduction. Based on our experimental results, we propose a quality assessment approach that predicts the subjective quality of experience using multiple objective metrics. For the one-dimensional spring model, the Spearman's rank-order, Kendall's rank-order and Pearson's Linearity correlation coefficient (SROCC, KLOCC and PLCC) between the predictions of our model and the results of subjective experiment show remarkable improvement on the correlation between subjective and objective quality assessment.