In 2008, Toyota faced an embarrassing problem: The Imperial Family's luxury Century Royal, used to carry Crown Prince Naruhito around Japan, was a dud. Memos flew back and forth between managers and senior engineers trying to find the cause of what appeared to be a speed-control fault. "This is a very difficult situation," fretted one engineer. "The Imperial Household Agency feels there is risk if it should recur."

The unspoken concern was clear: What if a crash hurt or even killed Japan's heir to the Imperial throne?

The problem seemed rooted in electronics — but its solution was elusive, even to all those trained minds. Toyota replaced the gas pedal, the throttle system and the engine computer at its own expense.