For a start, the division of the company covering - in typical American fashion - Europe, the Middle East and Africa appointed Mr Crosswell, director of quality, reporting directly to the division president Brian McMahon. Not only that, they made some effort to ensure that they got a man who knew what he was talking about rather than pitching some unfortunate into the role as a sop to current thinking.
Prior to taking on the job Mr Crosswell had spent a dozen years at Mars, the deeply secretive confectionery company. Although little is known about the organisation it has a fearsome reputation for quality control.
Second, the main company, while driven by financial constraints as much as the next organisation, realises that real improvement in profitability relies on looking at other issues.
And here it becomes clear that Carrier is not dedicated to improvement - total quality, in the modern parlance - for the sake of it. It perceives a real need.
With a turnover of dollars 1bn ( pounds 526m) and 6,000 employees around the world, Carrier - named after Willis Carrier, the man credited with inventing air conditioning - makes products ranging from portable air coolers to the large engineering equipment chilling thousands of square feet of empty office space in the Canary Wharf tower. It has about 11 per cent of the global market and about twice as much of Europe's. But its position is threatened - by some fellow US companies, but increasingly by Japanese groups such as Toshiba and Mitsubishi.
Faced, in Mr Crosswell's words, with having to do 'something drastic' to ward off the attack, the company decided to concentrate on customer satisfaction since that was the offensive route the Japanese were thought likely to take.
This is another difference from the approach of many other companies. In the first flush of enthusiasm for total quality scores of organisations have sought to upgrade their processes without apparently considering the ultimate purpose.
This is particularly so in the US, where a year ago Fortune magazine suggested that applying for the Malcolm Baldrige quality award put the emphasis on processes of management rather than the product or service.
By concentrating on the customer, though, a quality programme is going to the heart of a business. And if the management then addresses any problems appropriately, any changes in the running of the company - so far as they are necessary - will follow.
But the key is the role of the managers - or leadership. In a recently published assessment of 42 British organisations using the criteria of the Baldrige award Rita Cruise O'Brien and Chris Voss, of the London Business School, made this quite clear.
'Leadership is probably the most crucial issue,' they wrote. 'Many organisations have declared quality aims and have incorporated quality into their corporate mission statements.' Although the concept of total quality management was being introduced to many British organisations three problems frequently arose, they added.
These were difficulties in obtaining the commitment of top managers, conflicts between company mission statements and actual actions and priorities of senior managers and, above all, a lack of understanding of leadership or management effectiveness.
Another problem is the notion that total quality is a 'total solution'. In fact, it is part of a big picture. The difficulty is that, as with much management training, there is a tendency to swing from one 'flavour of the month' to the next.
In addition, says Warren Kinston, of a consultancy called the Sigma Centre, 'in most organisations the people can't cope with ideology'. They are more concerned with preventing an organisation from failing than with degrees of success.
Though more positive in their view of the value of total quality, consultants at Coopers & Lybrand, the management consultants closely involved in the development of Carrier's programme, agree that the idea should not be seen as 'a quick fix'.
Anxious to refute the suggestion that because the concept has run into problems in the US it must be flawed, Bob Millar says: 'Total quality is a way of achieving things. It is not a programme.'
He adds that the Coopers approach - which he believes accounts for some of the success - is to stress that the concept should not be seen as a short-term solution. Instead, the firm tries to ensure that the concept is part of the management strategy for at least 10 years.
His colleague John Pendlebury goes so far as to say that companies need to make a 'paradigm shift to create an atmosphere of continuous change'. The logical extension of this is to go beyond total quality to establish an elite organisation.
And that is where 'benchmarking' comes in. Already popular in the US, it is the process by which companies identify 'world class' competitors and measure their own performance against them.
Rank Xerox, for instance, claims that it has a big part in regaining share of the photocopier market from the Japanese. Although it can be confined to particular sectors it is increasingly being thought to be most successful when it crosses boundaries, so that organisations pick up good practices from other types of business.
As interest grows in the European Quality Award, which has been set up as a sort of equivalent of the Baldrige award, benchmarking is certain to become more important on this side of the Atlantic.
Companies which, like Carrier, have Japanese competitors can expect to be in the vanguard. As Mr Crosswell says, his company has spent a lot of money finding out how to give customers greater satisfaction.
But it has recognised that actually to achieve that improvement it must have a clear idea of what it is doing. In the past there have been problems with concepts like quality because of difficulties in assessing their effect on the bottom line.
Now it is felt that quality is an essential element in achieving its aims of doubled market share and profits. To make the point, top executives have had their bonuses linked to improvements in quality. 'It is a way of showing that quality is as important as profit,' says Mr Crosswell.
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