Business continuity planning works better when business units own it, not just IT. The key is reframing it as a personal challenge: how would your team actually operate if systems went down for days? When IT can't help, your boss and customers will hold you accountable.
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I had a peer, and we kind of tag-teamed this conversation, and the one going, "Hey, don't call IT. We're busy. I'm not even sure I can participate in your BCP. Include that as part of your thought process," really helped to put that ownership back on the other side. It's not to avoid the work, but it's to help them think through, "This is really my story. This is my challenge to think through if some service or some technical function isn't going to be able to help us, at least not for a few days." Not like they won't come help. Again, that makes it personal and I think it makes it a little bit more approachable.
BCP, make it your story. That's a good tagline because I think that you're really speaking to ownership and the fact that they're going to be the one holding the bag when they don't have IT, but their boss or their customers are asking them for answers. It really, it's an organizational culture and ownership issue before it is anything to do with IT and who's coordinating what.