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In a technology-rich world, digital problem-solving skills (DPS) are crucial to meet the demands of educational context and 21st century workplace environments. The aim of this study is to understand the prevalence and nature of the challenges adults face when engaging with digital assessments in the context of problem-solving skills and identify the most demanding subskills to support DPS trainings tailored to adults in different demographic and competence groups. To do so, we explored both response and process data collected in the assessment of Problem-Solving in Technology-Rich Environment (PSTRE) of the Program for the International Assessment of Adult Competencies survey (PIAAC) in the 2012 cycle. To accurately estimate adults’ DPS, this study proposes to develop a joint cognitive diagnosis model incorporating comprehensive information from item response data, response time, and response sequences. The parameters of the proposed model are estimated using the Bayesian Markov Chain Monte Carlo (MCMC) method. We will carefully examine the model fit to the data in real practice and conduct a simulation study to evaluate the stability and viability of the proposed model under different conditions. The implications of the proposed method will be discussed regarding the examination of adults’ DPS and extended to a general measurement on problem-solving skills in interactive scenario-based environments.