I suggest a new system complexity notation: Big-UhOh() notation.

A system that is UhOh(n) means that n failures cause n propagated problems in other systems. For example, n errors in your service = n crashes in the client.

A system that is UhOh(n²) means that each error causes n downstream issues. For example, if one shard goes down for a short time period that can cause errors across all clients.

A system that is UhOh(n³) means that each error causes n² downstream issues. For example, pushing a single bad configuration can break every client for an arbitrary amount of time: n * n.

A system that is UhOh(1) can absorb the errors.