When it comes to safety for Jack Ups, there is a rigorous process in place including International Bodies (International Codes), Class Societies (Class Rules), National Legislation (Shelf States), and National Maritime Legislation (Flag States). Although they don’t require a flag, having one enables them to move freely across international waters. When this is planned, the Maritime Authority regulations must be adhered to according to the Flag State (the country whose flag they are flying).
Normally, each drilling unit will be registered with a Flag State Governmental Administration. Essentially, the role of this administration is to set the requirements for each registering unit and these requirements generally follow the lead of the International Maritime Organization (IMO) since these are internally-agreed suggestions. More recently, the responsibility of verifying compliance has been awarded to classification societies and they also issue Marpol certificates, Loadline, and Tonnage.
Moving away from the flag, there are some governments who also request all drilling units to adhere to their own safety regulations when working in their waters. For example, the United Kingdom has a Health and Safety Offshore Division which ensures the safety of all drilling equipment in UK waters.
In terms of classification societies, these are largely independent and have no relation to any other party and this is important because their sole priority is the quality of the Jack Ups. In addition to authorities, these societies could be the owners, insurance underwriters, charterers, sub-contractors, building yards, and finance institutions.