This season “House” has reached as many as 17.5 million viewers a week. And those numbers were scored before the show enjoyed what it will enjoy again, starting this Tuesday — the adjacency to “Idol.”

Along with those stellar ratings, “House” is bucking the current trend in serialized dramas. It tells a complete story every week, which means that its repeats are far more valuable. All this success comes from a series that at first seemed to belong on a different network, that struggled so much in its early weeks that Fox cut back its order of episodes, and that at one point defied what sounded like a fix-or-be-canceled order from executives.

That it all worked out so well is a testament mainly to the show’s consistently high quality. But as its top producers, David Shore and Katie Jacobs, noted in an interview in their offices here on the Fox Studio lot, it also took some preposterous luck in casting and some exquisite timing in scheduling.

Things might never have worked out had a largely unknown British actor named Hugh Laurie not sent in an audition tape at just the right time. Or had all of Fox’s other new series in the fall of 2004 not failed so quickly that by the time “American Idol” came the next January, “House” was the show selected to be placed immediately behind it.

“Probably the only reason we’re still around,” Mr. Shore said, “is because they had nothing else.” What “House” really had was a creative team committed to its vision of a singular lead character. “What they pitched was a doctor who hates people but solves insoluble medical mysteries,” said Craig Erwich, executive vice president of programming at Fox.

That was how Mr. Shore and Ms. Jacobs, along with her husband and producing partner, Paul Attanasio, conceived their show in the summer of 2003 — although there was one critical difference in the character. At first, Dr. House was in a wheelchair.

“The idea was that this was not only a doctor who didn’t want to see patients, he didn’t want to be seen by patients,” Ms. Jacobs said.

Gail Berman, who headed Fox Entertainment, loved the idea, but she had one caveat. “Gail decreed that he not be in a wheelchair,” Mr. Shore said. “That’s when the cane came in.” But Fox did not object to House’s other quirks, like calling patients idiots and popping Vicodin like M&M’s to stave off pain in a damaged leg.

Everyone at Fox also got the unmistakable allusions that Mr. Shore was making to a classic character: the brilliant mind for connecting obscure scientific clues, the drug habit, the antisocial behavior and, of course, the best friend who was his outlet to the real world. It was all easy to spot — especially when the friend’s name was Dr. James Wilson instead of Dr. John Watson.

“The Sherlock Holmes thing was part of it from the beginning,” Mr. Shore said. It is also the reason the character is called House. “That was our little joke,” Mr. Shore said. “Holmes, as in ‘home,’ becomes House.”

It became the title of the show, though that initiated another issue because “House” sounded like a family show, not a medical show. (Mr. Erwich said one title considered was “Jagged Little Pill.”)

The title problem was addressed in two ways: first, adding “m. d.” in tiny letters after the title, and then, in what Ms. Jacobs called a clever touch by the Fox graphics department, putting a square around the first letter in “House” to signal the setting of the hospital.

Mr. Laurie, who was in Namibia shooting a film when he made the initial audition tape, had received only a few pages of the script and thought that House, as nasty as he was, must surely be a supporting character. Mr. Shore knew Mr. Laurie from his comic work in England in shows like “Black Adder.” “I knew him as a British twit,” he said.

After an appearance that Mr. Erwich called “one of the great auditions of all time” no one else needed to apply.

Before “House” had its premiere, in November 2004, the producers had heard great things about the quality of their pilot, and endless questions about why this show was on Fox. “This is such an NBC show, everyone was telling us,” Ms. Jacobs said.

One reason everyone thought of NBC may have been that by that time NBC owned the show because it had acquired Universal, the show’s original studio. But Fox had already secured the rights to the series, not that it seemed a coup at first. Its ratings in the fall, before “Idol” started, were puny. The producer began to worry when they finished up shooting their first 13 shows and no order came for more.

Just before breaking for the Christmas holidays, Fox called the producers in for a meeting. “They were demanding changes,” Mr. Shore said. “They wanted a bad guy.” The character was meant to be in constant conflict with House.

“There was the clear implication that your show is gone if you don’t accede to these demands,” Mr. Shore said. Nevertheless, he was opposed. “I said no,” he recalled. “I said it was a bad idea. They sat there and nodded and agreed.”

Mr. Shore left for Israel on vacation. He had barely landed when he got what he called a “panicked phone call” from Ms. Jacobs saying Fox had asked when the outline for the new character would arrive. “I realized things aren’t going so well,” Ms. Jacobs said. “It was very stressful.”

What neither producer knew was that Ms. Berman had called Jeff Zucker, who as head of NBC television was in charge of the Universal studio, and asked that the show’s original order for a full 22-episode season be cut back to just 16.

Eventually, Mr. Shore relented just enough to create a character, a hospital administrator, who would clash with House in a story arc. Chi McBride signed to do the part. Five episodes with Mr. McBride were shot. But even before they got on the air, the episodes the series had completed before vacation made it onto the air — behind “American Idol.”

The ratings soared. Mr. Shore ended the McBride character after just those five episodes. “House” was on its way.

Mr. Laurie has since won two Golden Globe awards as best actor. Mr. Shore gave Fox credit for appreciating down deep what the show was all about.

“There was a reason a network should have been scared” of this character, he said, adding, “Fox was never scared. The phone call I expected to get from Day 1 I never got: ‘Everything is great, great; but you’ve got to make the character more likeable.’ You always get that call, and we never got that call.”

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