Try computing Cronbach’s alpha using the formula rather than a stats package. If I recall correctly, it only relies on having estimates of the variance–covariance matrix. You should be able to construct this even if not every user has seen question, though you need enough users for ecah pair of questions to get a reasonable measure of the pairwise covariances.

Thank you, I will look into that, my main concern is that the Stroop test is a test made of three parts then it produces a final interference score. Which raises concerns about how to calculate Cronbach alpha technically?