In my view reliable test is always valid.
Is it possible for an operational definition to be valid but not reliable
A test may be reliable but not valid. A test may not be valid but not reliable. For example, if I use a yard stick that is mislabeled to measure the distance from tee to hole in golf on different length holes, the results will be neither reliable nor valid. If you use the same stick to measure football fields that are the same length the result will reliable (repeatable, consistent) but not valid (wrong numbers of yards). There is no test that is unreliable (repeatable, consistent) and valid (measures what we are looking for).
A reliable measure is consistent and yields consistent results, so it may not be measuring the intended construct accurately (lack validity). On the other hand, a valid measure accurately assesses the intended construct, but it must be consistent and produce stable results (reliable) to ensure that the measurements are dependable and trustworthy.
this board is not valid
Reliable indicates that each time the experiment is conducted, the same results are obtained (accuracy). Valid indicates the experiment (or test) has controlled variables and used an appropriate method/model.
A test may be reliable yet not valid, The results can end up being reliable, in other words certain to have yielded properly based on input. But the results may not be trustworthy.
Social and Medical sciences uses these statistical concepts. ideally, we have to measure the same way each time, but intrasubject, interobserver and intraobserver variance occur, so we have to anticipate and evaluate them. In short, it is the repeatability of a measurement, by you, myself and everybody person or instrument. Validity is how much the mean measure that we got is near of the true answer or value. So, an instrument can be reliable but not valid, valid but not reliable, both valid and reliable, nor valid neither reliable. I suggest that you imagine a target: you can aim and 1) always get the center (both valid and reliable) 2) always get the same distant point (reliable but not valid) 3) err much around the true center (valid but not reliable - the mean and median of your arrow's shot will get the center) 4) err much around the another center, false one (nor valid neither reliable) I did not understood exactly what selection criteria have to do with the rest of question, so, left in blank ;-)
ANSWER that the information should have evidence and proof to back up the research and not just some peoples opinions on paper that there are people who can corroborate its authenticity, people who were involved, people who its used/worked/based on that its not correct once and never again yet used as correct in general
It is reliable because it can be replicated. Always remember if it can be repeated it is most likely reliable.
A reliable experiment is one that can be proven or has been worked out several times giving valid or dependable results.
valid