How long a modern warship could operate in World War II

How long could a modern warship sent back to World War II remain useful without its normal supply chain?

It might operate for months on adaptable fuels and replacement lubricants, but missiles would probably last one engagement while spare parts became the decisive constraint.

Fuel might be less restrictive than expected because many NATO and Russian marine engines can tolerate a broad range of distillates. Spare parts and specialist lubricants would become the harder long-term problem, although some substitutes might be found. A modern missile outfit could be exhausted in one major engagement, while gun ammunition and a close-in weapon system supplied with compatible 20 mm rounds could remain useful much longer. A 1960s ship sent to the 1930s might therefore offer a more sustainable technological advantage than the newest possible vessel.