The chromatic quasisymmetric functions, which were invented by Stanley and Shareshian-Wachs, play a central role in the theory of symmetric functions. They has many connection with other mathematical areas. There is a famous conjecture related to the chromatic quasisymmetric function, so-called the e-positivity conjecture. In this talk, we introduce a combinatorial operation, called a local flip. This gives a refinement of the chromatic quasisymmetric function of a natural unit interval order P, and is useful to resolve the e-positivity conjecture. Also we define noncommutative P-analogues of symmetric functions which reflect information about the chromatic quasisymmetric function. Using these, we give a general framework for establishing positivity of the chromatic quasisymmetric function. Also, we present some partial results for the e-positivity conjecture.