The U.K. company, which licenses its designs for use in chips made by companies such as Samsung and Nvidia, is betting that growing consumer interest in tablets will translate into a big jump in its market share. Chips based on its technology already power most of the leading tablets including Apple’s iPad, Samsung’s Galaxy Tab and Motorola’s Xoom.

“Today we have about 10 percent market share [in mobile PCs]. By the end of 2011 we believe we will have about 15 percent of that market share as tablets grow,” said Tudor Brown, president of the U.K.-based company, during a news conference at the Computex trade show in Taipei. “By 2015, we expect that to be over 50 percent of the mobile PC market.”

ARM-based chips already power most of the smartphones on sale today and its procesors can also be found in a majority of standard mobile phones.

Intel, the world’s biggest chip maker, was caught off guard by the sudden popularity in tablets — sparked by Apple’s iPad — and has been trying to catch up. Intel is expected to discuss its latest attempt to crack the smartphone market, with a chip code-named Medfield, later this week at the Computex show.

ARM’s chances in the mobile PC market got a boost in January when Microsoft CEO Steve Ballmer said the next version of the Windows operating system would be available in a version that runs on ARM-based chips. It was a nod to ARM’s lead in the tablet market, where Microsoft has also struggled.

But to maintain that lead and build on its current success, ARM will have to continue developing more advanced processors.

The company’s next processor design, the Cortex A15, promises a five-times performance improvement over current smartphone processors while drawing about the same amount of energy, the company said when the design was announced in September last year.

ARM has already begun licensing the design to chip makers, and the first prototypes of chips based around the A15 design could be out around the end of the year, Brown said. Commercial chips based on the A15 will likely follow in 2012.

The A15 is currently based on a 32 nanometer or 28 nanometer production process. The nanometer measurement defines the size of the smallest feature on the chip’s surface and a smaller number denotes a more advanced manufacturing process. It also typically means chips can be made more powerful and less power-hungry.

ARM, which works on chip production technology with IBM, is also planning more advanced chips.

“We’ve been working at 20 nanometer and we’ve had test chips at 20 nanometer for over a year,” Brown said. Earlier this year the company said its partnership with IBM will be extended to 14 nanometer.