Social Security Commissioner John A. Svahn announced yesterday that the agency will spend $479 million over the next five years to improve its outmoded computer system.

The computers are so out of date, Svahn said, that it took almost six months of work to assure that the first checks with last July's cost-of-living increase went out on time--and then with only an 18-hour margin of safety. A good system, he said, could have done the work in a few days.

A generation ago the Social Security Administration had one of the best systems in the world. But today, for want of updating, it grinds out overpayments of $1.2 billion a year and many underpayments as well, Svahn said.

He said people who died as long as 16 years ago are still getting checks, while computer-produced letters keep telling a living beneficiary that he died in 1975. Unable to get that bug out of the system, officials take care of his benefits by hand. Moreover, Svahn said, the computer system performs so badly that officials must "circumvent the system in 25 percent of the cases." Wage records and recalculations are often not up to date.

Without a complete overhaul, he added, the system might soon face "the ultimate disaster: the checks don't go out."

Svahn said the computers keep records on hundreds of millions of workers and employer wage reports, 36 million beneficiaries, 4.1 million Supplemental Security Income recipients, 120 million health bills and queries, 7.5 million new claims applications and 10 million requests for Social Security cards.

Svahn said the five-year plan includes a new software system, improved security of records, substantially improved hardware and a goal of achieving a modern, near-state-of-the-art system by 1987 and then keeping it that way with annual improvements. The money will come out of Social Security administrative funds. He said the General Services Administration has been working with SSA to plan the overhaul.