Morgan Stanley analyst Katy Huberty, just back from a trip to Asia to meet with suppliers, says she expects orders on launch for the yet-to-be released iPhone 6 to surpass those of Apple’s flagship iPhone 5s when it was launched and that the larger smartphone could help Apple gain 11 percent in U.S. market share.

Huberty, in a note to investors, said that based on her supply chain sources, sales for the iPhone 6 are expected to be 20 percent higher than last year’s iPhone 5s launch. If true, Apple’s next iPhone launch could be the biggest in its history. She was previously expecting only a 12 percent increase in orders for the new smartphone.

She also thinks that launch of the iPhone 6 will likely go more smoothly than last year’s iPhone 5s launch, which was plagued by worldwide inventory shortages, which some analysts blamed on production constraints on the Touch ID fingerprint sensor.

“At this point, we see no major bottleneck in iPhone 6 production and an earlier production ramp could improve volumes early in the cycle,” Business Insider quoted Huberty as saying.

Apple saw a 7 percent increase in iPhone sales during the last quarter of 2013, said senior vice president and chief financial officer Peter Oppenheimer during the company’s fiscal first quarter earnings call in January. 

“Despite supply constraints on iPhone 5S, we sold 51 million iPhones compared to 47.8 million in the year ago quarter. That’s an increase of over 3 million phones, or 7%, and a new quarterly record,” Oppenheimer said during the call.

Since Apple doesn’t break out sales figures for individual phones, its hard to know what percentage of its sales can be attributed to the iPhone 5s.

Business Insider says that analysts are expecting the iPhone 6 to have a bigger screen, which will lead to “a monster upgrade cycle for Apple.” 

“There are a lot of iPhone users with a 3.5-inch iPhone 4 or iPhone 4S. Analysts like [Morgan Stanley’s Katy] Huberty believe those people are going to ditch their old, tiny iPhones as soon as the iPhone 6 is out,” the web site notes.

Huberty thinks that while total worldwide shipments for smartphones will decline slightly to 1.24 billion units, from 1.25 billion, North American shipments will rise to 163 million units, from her previous estimate of 156 million.