Validation: Are we building the right product?
Verification: Are we building the product right?
Validation is the process of making sure that you have objective evidence that user needs and intended uses are met. ... Verification is typically making sure that you have objective evidence that specified requirements are met. It is usually done by tests, inspections, and in some cases analysis as well.
i.e. when you are designing something, you will write a series of requirements relating to user needs. Validation is the check that those requirements actually meet the users needs, and then Verification is the check that you've actually met the requirements that you set out for yourself.
For example, a requirement might be "This device must be light enough for all users to pick up".
You might then write a reqirement, such as "The device must weigh < 30kg"
You could Validate this, to show that your specified requirement actually meets the user need by doing research to find out how much weight your users could acutally lift, or by referencing some existing research if the grip etc. is comparable. There will of course be other requirements (e.g. size, grip features), that also need to be included in order to ensure that the user need is met.
Once you've manufactured your device, you then Verify that it meets your requirements, by performing a physical test - weigh the device, and check that against your specification.
In some cases, certain features e.g. "the device must be <1m long" can be verified through a technical report (e.g. drawing review) without the need for a physical test. In this case e.g. if the device is supplied with a Certificate of Conformity confirming that it matches the drawings.
In the example that you wrote, you are performing a real world test, and then comparing this information to a value that was set by your previous research would be Verification
Checking whether or not your mathematical model actually shows you something useful with regard to a user need would be Validation.
Source: ASME https://www.asme.org/topics-resources/content/validation-verification-for-medical-devices