When a product is not found to be infringing a patent literally then the doctrine of equivalence is used to determine infringement. By the doctrine of equivalence if
1. It performs substantially the same function
2. In substantially the same way
3. To yield substantially the same result

That is if one of the components in a patented invention is substituted by an obvious replacement which is performs a similar function in the same way to yield the same result. In Graver Tank & Manufacturing Co. v. Linde Air Products Co., (1950), an alloy of rare earths was substituted with magnesium and the court found that magnesium and the rare earths performed the same function, in the same way and yielded the same result.

Warner-Jenkinson Co. v. Hilton Davis Chem. Co. (1997), the the plaintiff Davis, a dyemaker, had developed an "ultrafiltration" process to purify dyes. An amendment to the patent had specified that a solution used in the process must have a pH level between 6.0 and 9.0. The amendment was filed in order to clarify that this patent did not overlap with a previously patented process that used a solution with a pH level above 9.0 - however, the plaintiff was unable to explain why the amendment stated a lower level of 6.0. The defendant had developed a process using a solution with a pH level of 5.0, which was outside the range of the plaintiff's patent.

The plaintiff sued for infringement, conceding that the defendant's process did not literally infringe, but relying on the doctrine of equivalents to support the claim of infringement. The defendant argued that the doctrine of equivalents was no longer appropriate for courts to use because Congress had made some changes to the patent statute after the Supreme Court's 1950 decision establishing the propriety of using the doctrine.

The court found in favor of Warner, though Warner’s process infringed Davis’s patent by the doctrine of equivalents however the court held that since Davis had altered the claims to invalidating his invention in view of the prior art, hence an equivalent of such a claim cannot be said to be infringed under doctrine of equivalents and prosecution history estoppel.