Project success and project failure are NOT absolutes. It may not be possible to be a little bit pregnant, but you can be a little bit successful.
Every project has multiple success criteria related to business results, product/service results, and project delivery results (cost, schedule, scope, and quality).
Some criteria are absolute, meaning they must be completed on or before the original planned date, and some are relative, meaning they must be completed by a date acceptable to the client.
Project success is determined by how many of your success criteria are satisfied, and how well.
Whether or not a project is successful depends on who you ask. The very happy project manager that implemented the SAP project as scoped on time and below budget (I know, this will NEVER happen), the end users who absolutely hate the complexity and slowness of the new system, and the COO that has seen IT costs double whilst none of the expected savings materialized may all have very different opinions on the success of the project.
Project success also depends on when you ask. Twelve months after go live the users will have a better grasp of the system and initial performance problems will have been solved. And slowly but steadily, the expected savings will often start to materialize as well.
In a nutshell: In order to determine project success, you must define all the criteria relevant to your project, define how you will measure them, and define when you will measure them.