“Supply chains, broadly defined, are still challenging,” Mr. Culp said in an interview Monday, highlighting challenges at both the aerospace and healthcare divisions. “You might have success here. You might make progress there, but I don’t think we’re anywhere close to declaring victory.”

Mr. Culp said the company is streamlining its manufacturing processes and working with suppliers to help keep down costs.

“We’re continuing to spend a great deal of time, both on supply chain and relatedly inflation,” he said, noting the need to be mindful of the connection between the two. “In talking to other CEOs, it continues to be a daily battle for them as well.”

Mr. Culp is approaching his four-year anniversary of taking over as CEO. Since that time, he has overhauled manufacturing practices, sold off divisions, paid down debt and made GE’s far-flung divisions responsible for covering their own costs. Last November, Mr. Culp announced that GE would break up.

Mr. Culp’s new role at the healthcare business adds to his existing titles, chief executive of the aerospace division and CEO and chairman of GE. He played down the idea that the numerous titles would become a distraction, saying that he has been working in similar roles for years and that healthcare will require less of his time as his role evolves.

“That has allowed and will continue to allow me to spend more time at aerospace, which is what I’ve been doing for the last couple of months here,” he said.

The planned healthcare board includes eight additional members, including three from GE’s current board. The members include Cleveland Clinic CEO

Tomislav Mihaljevic

;

Lloyd W. Howell,

finance chief of

Booz Allen Hamilton Holding Corp.

; and

Anne Madden,

general counsel at

Honeywell International Inc.

GE hasn’t said what valuation it will seek for GE Healthcare, which has about $18 billion in annual revenue. Overall, GE has a market capitalization of around $80 billion as investors await the breakup. The shares have fallen about 20% so far this year, compared with a 16% drop in the S&P 500 index. GE’s healthcare division plans to hold an investor day in early December.

GE’s power and renewables business will combine and form a separate company in early 2024, while GE Aviation will be the surviving unit. Existing GE shareholders will get new shares in the two companies after they are spun off.

Write to Thomas Gryta at thomas.gryta@wsj.com