When the federal government chose Bart M. Schwartz to watch over New York City’s troubled public housing system, home to more than 360,000 residents, he knew the job would be difficult. The agency, after all, had been caught lying about lead inspections, faced several other scandals, and was routinely criticized for mismanagement.

Since he started in 2019, he has dealt with leaking sewage raining down from a ceiling and hundreds of meetings with frustrated tenants. He helped uncover a sprawling bribery and corruption scheme that broke a record for the Justice Department.

And yet, he remains optimistic that change is possible for the New York City Housing Authority. On Wednesday, Mr. Schwartz, 77, released his final report on NYCHA’s progress toward meeting the terms of a federal settlement, in which the agency agreed to improve its handling of persistent problems residents face.

Some successes from the past five years include a 40 percent drop in complaints about heat, a 50 percent drop in mold cases and a rapid uptick in lead abatement, which occurred at 700 apartments in all of 2019 and takes place at an average of 400 per month now.

In an interview, Mr. Schwartz talked about some of the highs and lows of his term, and said there was more work to do. The conversation has been edited and condensed for clarity.

Say all the problems were solved in NYCHA buildings. Why would that be beneficial to the city?

The people who live there deserve to live in a safe, clean environment. Especially, you know, in the richest country, the richest city. We should be able to do better.

How did you know this would be a tough job?

I’ll give you an example. Very early on, our field investigators were up in the Bronx, and they went into the laundry room in one of the buildings and sewage was pouring out of a pipe in the ceiling. A maintenance worker was doing the best he could with a mop.

Our field investigator said, “How long has this been going on?” He said, “Four weeks.” The investigator said, “Why isn’t it being repaired?” The response was, “Well, I’ve reported it and we’re waiting for the carpenters.”

“Why are you waiting for the carpenters to fix the pipe ceiling?” “Well, they’re going to build a scaffold so that we can get to the ceiling.”

It was a Saturday night. I called the chief operating officer. I told him the story and they got a ladder over there and they fixed it.

Do you think having more authority would have made solving these problems easier?

A very important element of being a successful monitor is for the entity being monitored to learn how to do it on its own. If I were to take over and make all the day-to-day decisions, then they’d always be leaning on something and someone. And when you leave, it would go back to the old ways.

Dozens of NYCHA employees were recently arrested and accused of taking bribes for giving out low-level, no-bid contracts, also known as “micro-purchasing.”

The micro-purchasing was a known problem. It was obvious it was subject to abuse.

I hoped to find some examples of this, because I felt that we could have the most immediate impact on residents if we could get the inspections done and the work done honestly. So when we gathered this information, we turned it over right away to the Southern District Criminal Division and to the Department of Investigation. And they ran with it.

It took a longer but it became a bigger project. If they had taken two people out in handcuffs in the first month, it would have been very helpful to me. But I understand why they did it.

Why did such a big issue persist for so long?

Because they focused on numbers and not values. The report came in that the plumber was there and did three drains. But did they do a good job? Did anybody care about what they were doing?

Will the arrests solve the problem?

You can’t say every 10 years, we’ll have a roundup of corrupt employees. That’s not a solution. They’ve got to build on this.

You say NYCHA needs to do much more work on its “values-based compliance.” What is that and why?

There are basically two kinds of compliance.

There is the regulatory, which is strictly numbers, the law, getting to the line without going over.

Then there’s value-based compliance. What is the best thing? What is the right thing? What are you trying to accomplish?

You can’t have a rule for everything. But if you have values, it’s like a safety net. People will think about being more conscientious, having more respect for the residents, not assuming that failure is acceptable and trying to do a better job.

How satisfied are you?

I’m pleased with the progress that we’ve made, because we’ve influenced the operations, and the numbers demonstrate that. But even more so, we started to influence the culture. When I got there, failure was always an alternative.