The phrase "approach the standard of" is correct and usable in written English.
It can be used when discussing the level of quality or performance in relation to a specific benchmark or expectation.
Example: "The new software update aims to approach the standard of excellence set by its predecessor."
Alternatives: "meet the standard of" or "align with the standard of".
England, for their part, will know that they have managed to win three of four Tests in this series without approaching the standard of cricket they produced in Australia last time.
Only a total restructuring of what government does, how it does it, and how we pay for it and a serious reappraisal of the institutional structure of our private sector can save us and provide any hope that the next generation can enjoy anything approaching the standard of living of its predecessors or the access to opportunity hitherto fundamental to the American way of life.
Lymphatic mapping and identification of the sentinel lymph node in patients with breast cancer is rapidly approaching the standard of care.
And that has given writers new ways to approach the standard mix of sitcom characters.
Table 5 shows the integral model-fit effectiveness of Model RT by such evaluation indexes as χ /df = 4.557, GFI = 0.908, NFI = 0.904, IFI = 0.912, CFI = 0.911, RMR = 0.053, and RMSEA = 0.077, all of which approached the standards of experience value.
Furthermore, the apparent activation energy of such a reaction approaches the standard enthalpy of reaction (ΔH0), rather than the true activation energy of the chemical reaction.
It approached the standard tropes of the police procedural with a lighthearted twist, pairing the tough, slobby tomboy detective Jane Rizzoli (Angie Harmon) with the sweet, faintly awkward lab nerd Maura Isles (Sasha Alexander).
And the hard-working, perfectly likable fellows who have replaced them, Brad Oscar and Steven Weber, don't begin to approach the same standards of teamwork.
In reviewing a May 2002 performance featuring Mr. Oscar and Steven Weber, Ben Brantley wrote in The New York Times that they "don't begin to approach the same standards of teamwork" established by Mr. Lane and Mr. Broderick.
