This paper presents a detailed framework for Condition Monitoring (CM) based on hydraulic systems and multi-sensor data. Nowadays, the CM technique is increasingly deployed for the optimization of quality and manufacturing processes. It is used as a decision-making support tool in maintenance operations or activities. In this environment, the diagnosis, prognosis, or monitoring of interconnected machines has become a crucial issue for improving the cost-effectiveness of manufacturing industries. Some models are available to monitor or predict the degradation of elements within a hydraulic system such as coolers, valves, internal pump leakage, or the condition of the hydraulic accumulator. In this case, we have focused on a data-driven approach, concentrating on the Deep Neural Networks (DNN) multi-class classification for imbalanced data that are adapted to predict the real operating states of the system. Despite their performance, questions remain concerning the reliability of the DNN as "black box" models when used in complex applications, notably regarding the decision-making processes and the possible ethical, socioeconomic, and transparency impacts upon stakeholders. Regarding the explanation approach, we have exploited the Deep SHapley Additive exPlanations (DeepSHAP) methodologies to provide trustworthy results, and to explain the importance (weight) or role that each sensor plays and its contribution to the DNN algorithm's decision-making. The obtained framework based on two principal modules illustrates that the DNN classifier model when evaluated by Accuracy, F1-Score, Recall, and Precision metrics are robust and perform efficiently. Finally, using the DeepSHAP technique provides an explanation of the results of the developed model, and helps humans to understand, interpret and trust the model, with an associated increase in the support or the stimulation of Artificial Intelligence (AI) models applications on large-scale problems including industrial sectors.