How does your team organize their work? In a restaurant or retail shop the customer is standing and waiting, so over time we learn how to organize the work to get the product to them quickly. But when you are processing information or other computer based production work, how do you do it?
First, as the leader, you are the one person who must understand the entire design. How does information or work request come into your group? How is everyone else alerted? How is the workflow on that request established? You probably have already done this.
But second, what is the protocol for a problem order or a mistake in how the information is processed? This is where I often see a variety of "recovery methods" that become isolated and prone to being ignored. Every mistake/problem must be transparent to everyone who can do something about it.
Third, test the system often. Plant an order or request that will be a problem and see how your system and your team responds. As the manager it is your job not to just make sure things run smoothly but to also be on hand and on point when they don't.
The more your entire team can do that then it will become less important for you to be at the helm in a storm.