Good times for millionaires mean good times for high-fashion and that's what we've got today. As a consequence, the luxury sector worldwide is growing faster than many others, according to Interbrand, a respected brand consultancy based in New York that's been around since 1974.

Interbrand recently released its much-anticipated ranking of the world's 100 best brands for 2018. This ranking measures how much a brand name contributes to a consumer's decision to buy a product, which is especially true when it comes to luxury items. Think Louis Vuitton, Chanel, and Hermes, for example.

Individually, or on a brand-by-brand basis, Apple tops the list of the world's top brands. Its brand has an estimated value of $214.5 billion, an increase of 16 percent from 2017. Behind Apple is Google, another tech giant, which saw its brand equity jump 10 percent to $155.5 billion.

And third is Amazon, whose brand equity skyrocketed 56 percent to $100.8 billion, helped by the massive increase in its stock price and revenues since the start of the year. Amazon is also the fastest-growing brand on Interbrand's top 100 list.

But on an industry-by-industry basis, the luxury industry tops the Best Global Brands 2018 Index. Interbrand reported that luxury apparel is the top-performing sector in its list of 100 companies that includes the technology, financial, consumer goods, and automotive sectors.

The world's most valuable luxury fashion and accessories brands according to Interbrand (and the value of their brand name) are:

Louis Vuitton - $28.6 billion; Chanel - $20 billion; Hermes - $16.4 billion; Gucci - $12.9 billion; Cartier - $7.7 billion; Tiffany - $5.6 billion; Dior - $5.2 billion; Burberry - $5 billion and Prada - $4.8 billion.

Gucci and Louis Vuitton are among the world's fastest-growing luxury apparel brands. The luxury fashion and accessories sector reported an overall growth of 42 percent since 2017, according to Interbrand.

The report noted Gucci's brand value grew the most of any luxury fashion label on the list. The brand's value rose 30 percent to $12.9 billion. On the other hand, Louis Vuitton's grew 23 percent to $28.2 billion. The nine luxury brands on the list have a combined brand value of $105.8 billion.

Chanel, a new entrant to the list (number 23), has a brand value of $20 billion. It reported full-year earnings for the first time in a long time. It reported $9.62 billion in revenues for 2017, an 11 percent year-on-year increase. Profits rose 18.5 percent to $1.79 billion.

Interbrand said luxury apparel companies remain successful because of their ability to respond to cultural trends. These firms have managed to immerse themselves in street culture, which is one of the fastest segments of the industry.

They also provide levels of access that have made their brands more desirable to more customers, while retaining their authenticity and a level of exclusivity, said the report.

The ranking illustrates the premium a company can charge for brand-name goods compared to other factors such as price or convenience. It also looks at financial performance and how likely a company is to have future success.