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The phrase "a failure to apply" is correct and usable in written English.
It can be used in contexts where you want to indicate that something was not implemented or executed as intended.
Example: "The report highlighted a failure to apply the new safety protocols, which led to several incidents."
Alternatives: "an inability to implement" or "a neglect to utilize".
Exact(12)
She had caught a failure to apply the knowledge science has to this particular situation.
His lack of lifelong ambition for the presidency translated into a failure to apply himself to the parts of the job that held less interest for him, often to disastrous effects.
According to the European commission, which sent the UK a warning letter on Thursday, a failure to apply the Habitats Directive to the cetaceans now could "seriously compromise their ecological character".
The report said the UN High Commissioner for Refugees (UNHCR) had identified a number of failings in the quality of the UK's asylum decision-making, including a failure to apply the correct methodology to assess an applicant's credibility.
This rapid rise could be said to follow from technological advances — the spread of automobiles, the advent of jet travel, the proliferation of appliances and electronic devices — or it could be seen as just the reverse: a failure to apply technology where it is needed.
As my old friend Bill Hanage put it in email, "[Graham's] biggest flaw is a failure to apply the same criticism to his own opinion as he does to others".
Similar(46)
The second-favourite, Steven Woolfe, isn't on the ballot either, following an equally mysterious failure to apply before the deadline.
Post hoc analysis 1 of the data from the Australian Quality and Health Care Study (AQHCS) 2 found that 'that misapplication of, or failure to apply a rule; or use of a bad or inadequate rule' and 'violation of a protocol or rule' together occurred in 13.6% of the adverse events identified in the AQHCS.
"The lack of documentation and failure to apply a formal procedure does not, of itself, evidence discrimination..
In its ruling the tribunal criticised the BBC for the "lack of documentation" about the decision making process that led to younger presenters being hired for Countryfile's peaktime move, and the "failure to apply a formal procedure".
The Achilles heel in catheter-based studies of renal denervation for severe hypertension is the almost universal failure to apply a confirmatory test for renal denervation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com