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Recent studies show that cognitive diagnosis can be more accurate if additional information such as response time can be incorporated with response data. This study accommodates response time measures in GDINA (generalized deterministic inputs, noisy "and" gate) framework to enhance the cognitive diagnosis modeling and proposes a novel RT-GDINA model. The study also develops a parameter estimation algorithm through the Bayesian Markov Chain Monte Carlo method. The RT-GDINA model is applied to real-life test data, and the model can estimate individual ability parameters, individual speed parameters, item parameters, and covariance structure between ability and speed parameters. The proposed RT-GDINA joint model will aid examiners and test developers to improve test quality and design, test timing, individual assessment, and overall parameter estimation process in complex testing environments.