The current study proposes the explanatory cognitive diagnostic models (CDMs) incorporating response times (RTs) with item covariates on both the item response side and the RT side. There are two main contributions of the current study. One appealing usage of this model is that scored item covariates can be used to predict item parameters when item calibration is not feasible in diagnostic assessments while the other is that the cognitive theories underlying the test design can be evaluated. Model parameter estimation is explored using the Bayesian Markov chain Monte Carlo (MCMC) method. A Monte Carlo simulation study is conducted to examine the parameter recovery of the proposed model under different simulated conditions in comparison to a few competing models. The results indicate that model parameter could be well recovered using the MCMC approach. Further, the application of the proposed model is illustrated using the Programme for International Student Assessment (PISA) 2012 problem-solving items using both item response and item RT data.