Thomas Edison's most memorable invention was the light bulb, which purportedly took him 1,000 tries before he developed a successful prototype: “How did it feel to fail 1,000 times?” a reporter asked. “I didn’t fail 1,000 times,” Edison responded. “The light bulb was an invention with 1,000 steps.”

The prevailing school of thought in progressive companies—such as Intuit, General Electric, Corning and Virgin Atlantic—is that great success depends on great risk, and failure is simply a common byproduct. Executives of such organizations don’t mourn their mistakes but instead ...