Is it permissible to perform the prayer immediately upon the entry of its time, without waiting for the completion of the Adhan, in the case of work that necessitates rotation among individuals due to time constraints and the continuous operation of production lines?

If your work schedule, based on shifts, does not permit you to attend congregational prayers at the mosque, then it is permissible for you to establish and perform the prayer as soon as you verify the entry of the legitimate time for prayer, even if the muezzin has not yet raised the adhan. The crucial point is the entry of the time that the Lawgiver made a condition for the validity of the prayer, not the adhan. The entry of the time can be verified by observing the signs, or by the adhan of a trustworthy muezzin, or by reliable calendars.