In statistical software like MINITAB and SAS, the default alpha value (critical p-value) is set as 0.15. I would like to know (1) if there is any statistic basis to set it as 0.15
Not really. To my vague recollection (I have no reference to offer), it was originally just presented as a value that seemed to work fairly well, because 0.05 was too strict.
I have found that in this question, the critical p-value of 0.15 in R is actually based on AIC. So is AIC the basis to set 0.15 as default value?
I think the suggestion preceded wide awareness of the AIC (but it's possible that the idea to use it originally came via the AIC, it's nearly old enough). So I think it's more coincidental (though that "a value that seems to work fairly well" would come up close to AIC is hardly surprising).
and (2) if this is a common accepted value in statistics.
It was fairly widely accepted once (many decades ago). The whole idea (no matter what cutoff value is used) is now well understood to be pretty bad.
If I dig up any more precise information, I'll come back and add it.