The phrase "firmly based on" is correct and usable in written English.
You can use it to describe something that has been strongly and securely established on a particular body of knowledge or evidence. For example, "This policy is firmly based on research which shows that it is the most effective approach."
One estimable American novelist pays peculiar tribute to another in "Terre Haute," a two-person drama by Edmund White that imagines a series of death row encounters between characters firmly based on Timothy J. McVeigh, the man convicted and executed for the bombing of the Oklahoma City Federal Building in 1995, and the novelist Gore Vidal.
He told Pienaar's Politics on BBC Radio Five Live: "The logic is that any decision about our future in the EU has got to be one firmly based on national interests.
Perhaps the relationship between stewards and jockeys is firmly based on the respect that one modern professional has for another.
In the 1940s and 50s, the scientist Sir Alan Cottrell, who has died aged 92, transformed the field of metallurgy, a subject that had previously been largely based on craft experience and scientific observations, into one that was firmly based on sound scientific principles, with predictive capabilities.
Since its beginnings in the 1960s, the design of modified atmosphere packaging (MAP) has progressed from a trial and error process to one that is firmly based on sound phenomenological models developed with a good understanding of the underlying mechanisms.
The above works, all of which are continuations of Ṣadrian philosophy, further elaborate the fine points of transcendentalist theo-sophy, which was firmly based on the principality of existence over essence, gradation, and the oneness that appears as multiplicity.
ART is just one component of Mexico's overall oral health strategy that is firmly based on prevention and on increasing access to oral care for all its citizens.
Before climbing on the ladder, make sure the feet are firmly based on the ground.
The Gunman fulfils all the requirements of genre, while remaining firmly based on fact.
The Guns of August reads like a novel but it was history, firmly based on the evidence.
All of their work is firmly based on the E.U. treaties which the U.K. decided to leave".
