“Fresh set of eyes” was a phrase repeatedly mentioned in connection with Robert Nardelli’s hiring as chairman and chief executive officer of Chrysler LLC.

“He might be a contrarian and just what the doctor ordered,” said analyst of Global Insight in Lexington, Massachusetts, John Wokonowicz, following the news conference on Monday at which the 59-year-old Mr. Nardelli was introduced.

With staggering losses by the “Big Three” and Detroit’s market share of the American vehicle market falling in July below 50% for the first time, the industry’s usual band-aids such as bigger cash discounts and head-count reductions no longer work.

Mr. Nardelli is a seasoned operating executive who narrowly lost a competition to succeed Jack Welch at General Electric Co. He later guided Home Depot Inc. to stellar financial, if not stock market, performance. By contrast, he knows very little about how to build and sell automobiles.

“What I bring will be a fresh set of eyes, a new perspective, if you will,” Mr. Nardelli said.

Cerberus Capital Management LP, which closed a deal to buy 80.1% of Chrysler three days ago, views Mr. Nardelli’s inexperience in Detroit as an asset. Cerberus’s chief executive officer, Steve Feinberg, apparently thinks newly-independent Chrysler must be led by a tough, smart operator whose decisions won ‘t be influenced by the norms at Chrysler, Ford Motor Co., and General Motors Corp. American automakers are famously insular, and tend to whine about the unfairness of competitive conditions.

Big Three managers and factories, including those at Chrysler, are more lean, nimble and responsive to consumers than ever. Their vehicles have never been better. Yet the competition keeps outselling them. Mr. Nardelli has to close the gap with Toyota Motor Corp., the industry leader.

“He might be the best operating executive I’ve ever seen. He can smell cost a mile away,” said Ken Langone, the Home Depot co-founder who hired and later fired Mr. Nardelli, in an interview yesterday.

Ford Motor’s board last year also saw merit in going outside the auto-industry when it selected Boeing Co. executive Alan Mulally to succeed Bill Ford Jr. as chief executive. When will GM directors start wondering if a non-automotive executive might make a worthy successor or sidekick for GM’s chief executive Rick Wagoner?

Mr. Nardelli arrives at Chrysler with baggage, notably the dustup in early January with Home Depot investors who resented that he earned $225 million over six years while the stock fell 7.9%. His defenders say his pay was contractual and that he saved the retailer from ruin before directors saw need for a new leader with different skills.

As Mr. Nardelli begins his new job, the United Auto Workers union is facing demands for concessions from the Big Three, which complain that above-market labor costs, especially health care, are strangling them.

Ron Gettelfinger, president of the UAW, and the union’s rank-and-file will be less inclined to compromise the more that is said and written about Mr. Nardelli’s wealth. Mr. Nardelli, who acknowledged Monday that his compensation came up in an initial conversation with Mr. Gettelfinger, said his pay will be tied to Chrysler’s performance. Since May, Cerberus has sought to allay suspicions that it simply aims to “strip and flip” Chrysler — to borrow a phrase from the UAW — for a quick financial gain. John Snow, Cerberus chairman, insists the private-equity firm hopes “to help bring an American automotive icon back to a path for profitability and long-term success.”

That’s Plan A and one that might yield the best return on Cerberus’s $7.4 billion investment if it works. And no doubt there is a Plan B: dismember and sell Chrysler, no matter what Mr. Snow has said. That will happen if Mr. Nardelli can ‘t grow the automaker’s cash flow to a level that Cerberus believes will justify its investment.

In a liquidation sale, Chrysler’s Jeep brand, factories, blueprints, patents, and dealer network alone likely could yield enough to make the whole venture worthwhile.

Mr. Nardelli’s performance at Chrysler won ‘t be as visible as it was at GE or Home Depot because Chrysler, as a private company — owned 19.9% by former parent DaimlerChrysler AG — isn’t obligated to disclose financial reports.

Soon enough, though, Mr. Nardelli will show whether his non- automotive pedigree and his drive are sufficient to return Chrysler to sound footing.

Mr. Levin is a columnist for Bloomberg News.