To start this series, we should first define what "success" is in socialism, and from there we can see the obvious conclusion.
I would argue that there are two fundamental aims under socialism:
1) In the ultimate utopia, we have the elimination of all authority. Authority ranges from family authority, to religion, to the traditional university (history), to money, personified in your boss and in the market.
Authority is a sort of "structural oppression" in the socialist mind. Further, authority is the thing that prevents the entrance into a state of either absolute equality, or into a state where people discard "exploitation based economics" and collectively work for the betterment of everybody.
This aim is at the root of both economic and cultural Marxism. In the cultural case, the world is seen in terms of oppressors and oppressed, and like the economic case, whenever a distinction exists between two groups, one group must have authority over the other, also called "privilege."
2) Once there is no authority, the idea is that we would have something of an equality, or to use the Marxist line, "from each according to his ability, to each according to his needs."
This state of equality is supposed to be achieved through the creation of the "socialist new man," in which the basic nature of mankind is changed. Also, this is where we get to communism, or the common ownership of the means of production.
To make the above happen, there are (at least) two schools of thought:
1) Having a revolution and violently destroying the old system all at once. This would be Leninism or revolutionary socialism/communism.
2) Using the central state to gradually but systematically eliminate all other forms of authority, at which point "equality" can be enforced through legislation. This would include both nationalism and globalism (same goal, for different sizes of territory), and of course, democratic socialism.
The end game for either is still the same - eliminate all authority while bringing mankind into a new state of existence, which Marx thought to be the final state of existence.
As we go through the series, we're going to see how, once the "success" aims are reached, certain human and economic forces will turn the supposed success into failure. But first, we need to understand what "success" is.