'failure-related' originates from Modern English as a compound of the noun 'failure' and the past-participle/adjective 'related'.

'failure' comes from Old French 'faillir' (to fail) ultimately from Latin 'fallere' (to deceive, to fail); 'related' comes from Latin 'relatus' (past participle of 'referre', 're-' + 'ferre' meaning 'to carry/back') via Old French/Medieval Latin into Middle English 'relate'. The compound 'failure-related' is a modern formation combining the two words.

Individually the elements meant 'the act/state of failing' ('failure') and 'brought/connected' ('related'); combined they have a straightforward compositional meaning: 'connected to failure'.