The number claim is correct in the context of nuclear power stations.
The "440" reactors from the claim indicate, that we are talking about nuclear reactors for power generation in power plants. Therefore I won't include reactors used on submarines or vessels.
According to the International Atomic Energy Agency (IAEA) there are currently (May 2019) 452 nuclear reactors in operation. 173 reactors have been decommissioned. This means a total of 625 nuclear reactors have been built and operated to date. These do not include research reactors.
According to Shrader-Frechette (not a peer reviewed paper, but an open-peer commentary) there have been a number of apparent melt downs (emphasis added, list has been cleared of vessels and submarines).
To provide a best-estimate answer, the list below excludes: (a)serious non-melt accidents; (b) intentional or deliberate melts; and (c) supposed melts, not documented in reliable scientific literature.
Regarding (a), the lists below exclude fuel-loss or criticality accidents, however serious, if they do not partially melt the core. Thus, many damaging US-reactor accidents — such as the criticality catastrophe in Charlestown, Rhode Island; the fire near Chicago; the loss of cooling in New York; or the Nebraska and Connecticut reactor explosions — are not included in the lists below (see Pollack, 2011). Regarding (b), the lists also exclude melts that have been intentional or experimental, not the result of apparent accidents or negligence — such as those at Borax-1, SPERT, and TREAT reactors in Idaho. Regarding (c), the lists below exclude meltdowns for which detailed accounts are not available in refereed scientific literature, such as at the WTR reactor in Pennsylvania. Given the previous three caveats, (a)–(c), at least five unintentional, nuclear-core melts — all resulting in radiation releases, death, and injury — appear to have occurred in the US:
- EBR-1 in Idaho, 1955.
- Santa Susana in Los Angeles, 1959.
- SL-1 in Idaho, 1960–1961.
- Fermi 1 in Michigan, 1966.
- Three Mile Island in Pennsylvania, 1979.
Given the same three caveats, at least 21 unintentional nuclear-core melts appear tohave occurred outside the US—all resulting in radiation releases, death, and injury:
- Mulvihill Windscale in the UK, 1957.
- Chalk River in Canada, 1958.
- Chapelcross in Scotland, 1967.
- Saint-Laurent in France, 1969.
- Lucens in Switzerland, 1969.
- Greifswald in Germany, 1975.
- Saint-Laurent in France, 1980.
- Chernobyl in Ukraine, 1986.
- Fukushima #1 (dai-ichi) Reactors 1,2 & 3, Japan 2011.
Of these EBR-1, Santa Susana, SL-1, Fermi-1, Chalk River were research reactors, Mulvhill was a fast breeder for plutonium and not intended to generate power. If we take the as actual meltdowns in scope, 10 meltdowns have happened in nuclear power stations world wide since the 1950s. This would results in 1.6% of all reactors ever built for power generation melting down. If we only regard the three worst incidents at Three Mile Island, Chernobyl and Fukushima we have 5 major meltdowns (0.8% of reactors). So a lower bound on the estimate would be 0.8%.
Given this source the number seems to be in the right range. Shrader-Frechette notes, though, that public information about nuclear accidents is rare and it is difficult to get accurate information. Furthermore, the IAEA does not classify nuclear accidents in terms of whether a meltdown happened or not, but in terms of consequences in the INES scale.
The claim is correct in the context in which it was provided (nuclear power stations). In the context of all nuclear reactors (power stations, research reactors, submarines and vessels, space craft, etc.) the claim is most likely not correct, but it is hard to verify, because independent information on reactor accidents in the military (e.g. US and Russian submarines) is limited.
The claim uses the 1.5% number as a means to question the safety of nuclear reactors. It is highly questionable if this is the right way to assess the safety or if other metrics are better. If one reactor is built and has a meltdown after 100 years, 100% of reactors had a meltdown. If 100 reactors are built and after 1 year one melts down, 1% of reactors had a meltdown. The percentages are totally different, although the cumulative reactor time and power output of operation is the same (given all reactors having equal output).
Additionally, just because there was a certain risk in the past does not necessarily mean that this risk will be the same in the future. Most of the accident in this study were in the 1950s - 1980s. Since then the incident rate has declined. With a new generation of plants being built, there may also potentially be more accidents. It is difficult to infer future risks from past risks.
A meltdown does not necessarily mean a catastrophic accident, because what matters more is, whether (and how much) radioactive material escaped into the environment. In risk assessment the commonly used metric is the number of severe accidents (e.g. after the INE Scale) per reactor year of operation.