A spontaneous breathing trial is a test for patients on mechanical ventilation, before they can be weaned from the ventilator, i.e. return to normal breathing.
The weaning process depends closely on the patient's pathology, but the final common pathway to ventilator independence always includes at least one trial of spontaneous breathing.
The RSBI ("Riz-bee") is simply the ratio of respiratory frequency in respirations per minute to tidal volume in liters (f/Vt).
Certainly, other measures such as patient's mental status should be considered.
E.g., a Glasgow Coma Scale score of less than 8 is an independent indication for intubation in traumatic brain injury.