'process-independent' originates from modern English, formed by combining the noun 'process' and the adjective 'independent'. The noun 'process' ultimately comes from Latin 'processus' (from 'pro-' meaning 'forward' and 'cedere' meaning 'to go'), while 'independent' comes from Latin 'independens' (from the prefix 'in-' meaning 'not' and 'dependere' meaning 'to hang from or depend').

'process' entered English via Old French/Medieval Latin forms such as 'proces' and 'processus' and became the English word 'process'. 'independent' came into English via Middle French/Latin 'independens' and Middle English adaptations, eventually forming the adjective 'independent'. The compound 'process-independent' is a modern English formation combining these two words to express lack of dependence on a process.

Individually, 'process' originally referred to a going forward or course of action and 'independent' originally meant 'not hanging from' (i.e., not depending). Over time their meanings stabilized as 'procedure/sequence' and 'not dependent', and the compound now specifically means 'not dependent on the process' in general or technical usage.