It's hard to quote a "number of missiles to kill a ship" in the modern world. The size and strength of both the variety of Anti-ship missiles and the size (and relative technology) of the ship in question both count.

Loooking at modern examples: Both the USS Stark and the HMS Sheffield took Exocet missile strikes, but a decade apart. The Stark survived handily, while the Sheffield died. Both ships are relatively equal in size, but the Stark is a full generation ahead of the Sheffield, both in defenses and in construction. The major cause of the Sheffield's death was the "new" aluminum superstructure, which proved to be unable to resist the high-temperature fires the Exocet hit caused. The Stark's all-steel superstructure (a lesson learned from the Sheffield disaster) didn't melt, allowing this ship to control the fires and survive.

Given the new lighweight armoring of DDG and CG ships these days (usually 100-200 tones of Kevlar-like materials), and the massive damage-control of big ships, a one-hit, one-kill is unlikely (direct magazine hits being the exception). If I was a gambling man these days, I'd go with these generations:

a) small ASM vs sub-frigate: mission-kill & 75% chance total kill
b) small ASM vs frigate: 25% total kill, 50% mission-kill, 25% partial mission-kill
c) large ASM vs frigate: 50% total kill, 50% mission-kill
d) small ASM vs dest/cruiser: 5% total kill, 10% mission-kill, 30% partial mission-kill
e) large ASM vs dest/cruiser: 10% total kill, 50% mission-kill, 40% partial mission-kill
f) small ASM vs CV/BB: 10% partial mission kill
g) large ASM vs CV/BB: 5% total kill, 15% mission kill, 30% partial mission-kill

Small ASMs are the Harpoon/Exocet class, while large ASMs include Tomahawk and Kingfisher.

Modern US carriers and BBs have undergone accidents equivalent to multiple heavy ASM hits, and still remained completely operational. The USS Iowa turret explosion in 1989 was equivalent to at least 2 Kingfisher-stlyle strikes, and it only knocked out the turret. A pod of ZUNI ground-attack rockets blew up on the USS Enterprise's deck in 1969, causing a hole in the flight deck. While it impeded operations, it didn't stop them or cripple the ship.

As an aside, modern torpedos are much more of a danger - one hit is a virtually guarrantied mission-kill on anything smaller than a carrier, and carriers are unlikely to survive more than 2 hits. A total kill is highly likely for FF and smaller craft with just one hit, while DD and CGs run a significant chance of sinking with a single hit.


Oh, and real-life CIWS effectiveness is classified by virtually all countries. Claimed accuracy of 3rd-generation stuff like the Phalanx and Goalkeepers is 100% under test conditions against current generation ASMs. However, no one has any idea how they'd really work in conditions like partial squall, 15-foot seas, multiple vector attack scenarios.

Keep-out Ranges With 1.65 lbs. (0.75 kg) AHEAD Shell
Fighter aircraft/attack helicopters 3,830 yards (3,500 m)
Guided missiles/cruise missiles 2,190 yards (2,000 m)
Anti-radiation and sea-skimmer missiles 1,640 yards (1,500 m)
Note: Flight time for AHEAD at a muzzle velocity of 3,445 fps (1,050 mps):
1.05 seconds for 1,090 yards (1,000 m)
2.34 seconds for 2,190 yards (2,000 m)
3.98 seconds for 3,280 yards (3,000 m)

Lockheed Martin has become the U.S. licensee to Oerlikon Contraves for sale and manufacture of the gun systems. The USN is currently performing evaluation testing of this weapon system.