It comes from an old SAE paper by Arthur Bender (1960s?). The 1.5 coefficient is not based on any theory -- instead, it was empirically derived by doing case studies of actual manufactured parts, and comparing them to the theory of RSS. He found that there tended to be a correction factor of 1.5, and that's what is often used to this day. But it's flexible; some companies use 1.4 or 1.6.
His paper was called "Statistical Tolerancing as is Relates to Quality Control and the Designer," and the paper number seems to be 680490.
John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems