In his 30 years at International Business Machines Corp., incoming Chief Executive Arvind Krishna has witnessed what works in corporate turnarounds and, more recently, what doesn’t.

Mr. Krishna, 57 years old, is only the 10th chief executive in IBM’s 108-year history. He takes over a company that has been in transition for almost the entirety of his predecessor Ginni Rometty’s eight-year run in the job.

The…

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