Should they stay or should they go?

The typical investor may not think in such stark terms when she votes for corporate directors at companies’ annual meetings. At most of these confabs, director re-elections are noncontroversial.

But that’s not the case this year at Tempur Sealy International, the mattress manufacturer based in Lexington, Ky. When its shareholders convene in Boston on May 8, they will decide whether three of the company’s top officials, including its chief executive, should be ousted.

Agitating for change at Tempur Sealy is H Partners, a low-profile New York investment firm that happens to be the company’s largest shareholder. H Partners wants three people overseeing the company to get the boot: Mark A. Sarvary, Tempur’s chief executive since 2008 and a director; and two longer-term directors, Christopher A. Masto and P. Andrews McLane, the chairman of the board.

Some of H Partners’ complaints about the Tempur board and its oversight are familiar. The firm contends that the company’s long-tenured directors don’t own enough stock and are not open to giving a large shareholder a seat at the table.