  In this paper, the improvement about the generalized Kolmogorov-type three
series theorem, in the case of NQD random variables, is obtained by different
method. Furthermore, the generalized Kolmogorov-type three series theorem is
simplified. From the simplified theorem, related results in Wu (Acta. Math.
Sinica. 45(3), 617-624, 2002) and some main results in Shi (Acta. Math. Appl.
Sin., 34(1), 122-130, 2011) and Li et al. (J. Math. Anal. Appl., 344, 741-747,
2008) are also discussed or improved in the article.
