Algorithms for detecting endotracheal intubation and/or misplacement of endotracheal tubes in child patients during anesthesia for use with anesthesia machines, mechanical ventilators, and/or respiratory function monitors. An algorithm uses end-tidal carbon dioxide (EtCO2), and tidal volume (TV) or peak inspiratory pressure (PIP) to detect exact intubation time. Another algorithm uses respiratory parameters to identify and/or confirm the type of airway device used during mechanical ventilation, and to detect if and when an issue has arisen with use of a specific airway device to provide real-time decision support to attending medical care professionals.