For me I class my own writing success as not only finishing the piece I was working on, but finishing it to a standard where I am happy with it.
I didn't start writing initially to be published, in fact, when I sat down and began to write my first book, I was actually intending to write a role play scenario (the table top dice rolling kind) for myself and some friends to try. Yet it took on such depth it became a novel in its own right which took about a year to fully write (and never did become an rpg scenario). I then spent 5 years (on and off due to work and commitments) editing and revising it until I thought it was finished, put it aside for another 4 years whilst I finished the series. Then I went back to it last year, improved on writing style and plot slightly until now, finally after ten years, it is ready to go. That for me is a writing success, bringing something up to the place where it is everything I want it to be and more
A secondary success would be that when I gave it to a selection of people to beta read, I got very positive results. I was really happy about his because by the end, I had written a story I wanted to read, thus as I wrote it for me and my own enjoyment, I was concerned other people wouldn't like it, especially since it is a rather large book, so when I started to receive feedback it really felt like I had succeeded.
I don't think success is gauged on whether or not the work is published, it's how you feel about what you have done and achieved, and thus, your success is something only you can measure.