Shareholders in a 75-year-old investment bank become nervous and begin to flee, causing the bank’s stock price to plummet from $100 to $2 in one month. A surgeon at a hospital in Minneapolis removes a patient’s healthy kidney rather than the cancerous one. A 20-story crane collapses at a New York construction site and kills seven people.

Sometimes it looks as though the world of business is an accident waiting to happen. To help monitor and manage such risk, companies are becoming more creative about setting up management-level risk and compliance committees.

The structure, composition, and methods of these committees vary ...