From Wikipedia:

The W47 was the first warhead with a new, miniaturized pit.[3] The aerodynamic flare at the base provided stability of orientation during descent. Two small rocket motors were used to spin the warhead for better stability and symmetry during reentry…

The W47 is the only US ICBM or SLBM warhead to have been live fired in an atmospheric missile and warhead test, on May 6, 1962. This event took place during shot Frigate Bird which was part of the Dominic test series. While stationed off Johnston Island, the American submarine USS Ethan Allen fired a Polaris-A2 missile at an open ocean target point in the vicinity of Palmyra Atoll, south of Hawaii. The missile traveled a distance of 1,020 nmi (1,890 km; 1,170 mi). The test was observed by two submerged US submarines stationed approximately 30 miles from the target point, the USS Carbonero and the USS Medregal. The missile warhead detonated at 23:30 GMT on May 6, 1962, approximately 2 km from the designated target point, and at the target altitude of 11,000 ft (3,400 m). The detonation was successful and had the full design yield of approximately 600 kilotons

Failures of the W45, W47, and W52 warheads are still an active part of the debate about the reliability of the US nuclear weapons force moving into the future, without ongoing nuclear testing.

From Michael Lewis:

[T]he United States no longer tests its nuclear weapons. Instead, it relies on physicists at three of the national labs—Los Alamos, Livermore, and Sandia—to simulate explosions, using old and decaying nuclear materials.

From the Guardian in May:

The Missile Defense Agency said it was the first live-fire test against a simulated ICBM for the ground-based midcourse defense (GMD) and hailed it as an “incredible accomplishment”…

A 2016 assessment released by the Pentagon’s weapons testing office in January said that US ground-based interceptors meant to knock out any incoming ICBM still had low reliability, giving the system a limited capability of shielding the United States.

From The Heritage Foundation:

[T]he U.S. has elected to maintain nuclear warheads—based on designs from the 1960s and 1970s—that were in the stockpile when the Cold War ended rather than take advantage of technological developments to field new warheads that could be designed to be safer and more secure and could give the United States improved options for guaranteeing a credible deterrent…

Presidential Decision Directive-15 (PDD-15) requires the U.S. to maintain the ability to conduct a nuclear test within 24 to 36 months of a presidential decision to do so.4 However, successive governmental reports have noted the continued deterioration of technical and diagnostics equipment and the inability to fill technical positions supporting nuclear testing readiness.5 A lack of congressional support for improving technical readiness further undermines efforts by the National Nuclear Security Administration (NNSA) to comply with the directive.

The weapons labs are beset by demographic challenges of their own. Thomas D’Agostino, former Under Secretary of Energy for Nuclear Security and Administrator of the NNSA, has stated that it is quite plausible that by 2017, the United States will not have a single active engineer who had “a key hand in the design of a warhead that’s in the existing stockpile and who was responsible for that particular design when it was tested back in the early 1990s.”6 This is a significant problem because for the first time since the dawn of the nuclear age, the U.S. will have to rely on the scientific judgment of people who were not directly involved in nuclear tests of weapons that they designed, developed, and are certifying…

Former NNSA spokesman Bryan Wilkes said, “We know that plutonium pits have a limited lifetime.”21 A plutonium pit is a crucial component of a nuclear weapon,22 and with life-extension programs introducing new components to warheads whose radiological effects are not fully known, the level of uncertainty has increased…

Absent nuclear weapons testing, the assessment of weapons reliability becomes more subjective, albeit based on experience and non-nuclear tests rather than fact. While certainly an educated opinion, it is not a substitute for the type of objective data obtained through nuclear testing. Testing was used to diagnose potential problems and to certify the effectiveness of fixes to those problems. Given that modern simulation is based on nuclear tests that were conducted primarily in the 1950s and 1960s, using testing equipment of that era, there is a great deal that modern testing equipment and computer capability could teach about nuclear physics…

Secretary of Defense Robert Gates warned in October 2008 that, “[t]o be blunt, there is absolutely no way we can maintain a credible deterrent and reduce the number of weapons in our stockpile without either resorting to testing our stockpile or pursuing a modernization program.”..

Today, the United States is focused on sustaining the existing stockpile, not on developing new warheads, even though all of its nuclear-armed adversaries are developing new nuclear warheads and capabilities and accruing new knowledge in which the U.S. used to lead…

The Navy is fully funding its programs to replace the Ohio-class submarine and to life extend and eventually replace the Trident SLBM, but existing ICBMs and SLBMs are expected to remain in service until 2032 and 2042, respectively, and new bombers are not planned to enter into service until 2023 at the earliest…

As Bradley Thayer and Thomas Skypek have noted, “Using 2009 as a baseline, the ages of the current systems of the nuclear triad are 39 years for the Minuteman III, 19 years for the Trident II D-5 SLBM, 48 years for the B-52H, 12 years for the B-2, and 28 years for the Ohio Class SSBNs.”..

The existing nuclear weapons complex is not fully functional. The U.S. cannot produce more than a few new warheads per year. There are limits on the ability to conduct life-extension programs. Dr. John Foster has reported that the U.S. no longer can “serially produce many crucial components of our nuclear weapons.”..

Currently, the U.S. can produce no more than about 10 plutonium pits a year at the Los Alamos PF-4 facility. Infrastructure modernization plans for PF-4, if funded, will boost that number to about 20 by the middle of the next decade and to between 50 and 80 by the end of the next decade. Russia can produce around 2,000 pits a year…

Because many scientists and engineers with practical nuclear weapon design and testing experience are retired, nuclear warhead certifications will therefore rely on the judgments of people who have never tested or designed a nuclear weapon.

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