According to James Letts' article "A field guide to critical thinking," the method of critical thinking can be distilled into an acronym, "FiLCHeRS." The letters stand for the rules of Falsifiability, Logic, Comprehensiveness, Honesty, Replicability, and Sufficiency. The method itself is based on formulating a claim, and then applying the six rules to it.
Falsifiability means that if the claim is false, the evidence will prove it false; and if the claim is true, the evidence will not disprove it. Hence, it can be assumed to be true for the time being.
It can be problematic to determine if a claim is logically sound. You must be able to infer the claim from the premises --- preconditions and assumptions --- you have set. If you can provide a counterexample, a single imaginable instance whereby the conclusion would not necessarily follow from the premises you have set for your claim, even if the premises were true, then the argument is invalid.
The important thing about the comprehensiveness rule is to consider all the evidence available. To consider only the evidence that supports a theory and to discard the evidence that contradicts it means that you have already decided that the claim is true, and is not attempting to find evidence disproving it, which breaks the first rule.
This rule simply means you must accept the conclusion that is drawn from the evidence. If the only conclusion you can make from the evidence is that your claim is false, then you must accept that. In science as well as engineering, this is not particularly strenuous, but in everyday life, especially where religious or ideological beliefs clash with available evidence, it may lead to self-deception if you prefer your claim over the conclusion from the evidence.
A coin toss has a 50 percen chance of coming up tails. Any experiment may lead to random results which seem to fit the claim. Only if an experiment consistently leads to the same result can the claim be accepted. In civil engineering, this would apply to different soil types: If mud consistently does not support a 100-tonne bridge, the claim that the bridge will sink if it is built on mud alone can be assumed to be true.
Is there enough evidence to draw the conclusion that the evidence proves the claim? And is the evidence complete? Is there bedrock under the mud, and is that why the bridge did not sink? Is the bridge actually lighter than what is claimed, perhaps because it is made of wood? Considering everything that is needed to support the claim means the evidence is sufficient. In practice, this means there is always a small probability that a claim which is held to be true is actually false, especially in disciplines where evidence is scarce, such as cosmology.
Lionel M. Claris and Donna M. Riley attempted to create a curriculum that encouraged critical thinking in, as well as about, engineering. The curriculum included reading an essay by Focault as well as a module on the thermodynamics of everyday life. As a result, students demonstrated improved critical thinking "in" and "about" engineering.
There is no checklist where you can tick off the critical questions. There is not even a unified definition of critical thinking. For their study on critical thinking in engineering, Claris and Riley drew on Engineering Reasoning by Paul, Niewoehner, and Elder, as well as the reflective judgment model King and Kitchener developed based on the work of John Dewey. However, the main source of critical thinking and self-reflection in their study were the philosophers Focault and Derrida, as well as Harraway's critical and reflexive relationality. He asks engineers and scientists to look in the mirror and see how power operates in their life and work, and to be mindful of their actions in relation to one another and the planet.