China has become a global manufacturing powerhouse thanks to the many domestic and foreign companies that produce goods there and sell them to consumers throughout the world. Most global leaders are producing and selling products in China. Despite intense competition, the Chinese market—particularly for consumer electronics and domestic appliances—is dominated by homegrown giants that have built a strong awareness of their brands inside their own country. Outside it, however, the story is different. Many Chinese companies, finding the challenge of building their own brands and channels in the United States and Europe daunting, have opted for the OEM route, producing goods for global brands rather than their own. Glanz, for example, makes microwave ovens for more than 80 brands around the world.

But now a few large Chinese companies, encouraged by their government, are intent on creating truly international brands. First off the mark is the Haier Group, a diversified manufacturer of more than 80 products ranging from refrigerators, washing machines, and air conditioners—a few of the core products that make it the world’s fifth-largest maker of white goods—to cell phones and televisions. As China’s domestic markets have mushroomed over the past two decades, Haier has built a reputation...