Hewlett-Packard Co.’s decision to fire CEO Leo Apotheker after just 11 months and replace him with former eBay chief Meg Whitman is another dizzying turn of the executive merry-go-round at a company whose leadership issues are straining a sprawling technology empire.

Swapping Apotheker, who has now been ousted from two high-profile CEO jobs in two years, for Whitman is a decision designed to stem investor fury over a series of questionable strategy moves.

Apotheker was doomed by disappointing earnings and his fumbled announcement that HP’s personal computer division is for sale. HP’s chairman, Ray Lane, said the dismissal was caused by several factors.

“You don’t deliver a quarter, you don’t deliver another quarter, then you make some important announcements that are communicated poorly — it was incremental,” Lane said on a conference call. Whitman was on the call, but Apotheker was not. “Then you have to make the tough call of, how long do you go along with that? Do you help? Do you surround? Or do you replace?”

Whitman is a billionaire who is best known for the decade she spent building eBay and her unsuccessful run last year for California governor.

Her star power could be an asset for a company that struggled to gain credibility under Apotheker, who was previously little-known outside of the business-software world. HP is no stranger to celebrity CEOs. But Carly Fiorina’s run at the company’s helm, from 1999 to 2005, ended in shambles.

Despite Whitman’s success at eBay, she is untested when it comes to running a company that is in as many businesses as HP. Another turnaround effort earlier in her career, at FTD, the iconic flower-delivery company, ended with Whitman quitting after two years and declaring that the company is “not fixable.” Many analysts have said the same thing about HP in its current form.