When is a project successful?

This seems a fairly straightforward and easy question. However, we will show that there are multiple ways of looking at this and that an answer may not always be so straightforward.
Is a project successful when it:
  • is on time?
  • is on budget?
  • delivered a quality product?
  • satisfies the users of the project deliverable(s)?
  • ...?
The answer is, it depends!
It depends on the success criteria that were (or were not) established at the beginning of the project.
If the only criterion their was was to build a machine that goes "bleeb" when you turn it on and it just does that when you turn it on, success!
If the criteria were to build said machine within a year and it still had to go "bleeb" when you turn it on and you did that, success.
If you were late a day, partial success.
It depends on the business/organizational objective(s) the project is to achieve.
If the objective of the project is for instance, to reduce wait times and thus increasing customer satisfaction within three months after the project, by replacing the call centre system at a call centre operator, then the project is a success if the customer satisfaction indeed goes up.
If the above project had the additional success criterion that the project is not to cost more than a X the project is a success if it did not cost more than X. If it did  cost more than X but still was able to satisfy the project objective than the project was a partial success.
When there is more than one criterion and when some of those criteria are related to the project objectives, as there should be, then you can see the question of project success becomes rather complicated.
For instance, in the above example of the call centre it is assumed (by the project owner) that there is a direct correlation and even causation between wait times and customer satisfaction. That seems an okay assertion. On the other hand, what if the new call centre system did indeed decrease wait times but also added one of those automated messages where you have to go through a slew of options before reaching (if ever) a real person and as a result decreased customer satisfaction?
What if there are no success criteria established at the start or during the project?
It is difficult if not impossible to measure something if you do not know what it is your are supposed to be measured against.
In other words, it is very important to clearly define what constitutes success but also to be very clear and specific on cause and effect including any assumptions you make with respect to causation and correlation.
As you can see there are many ways of looking at project (mangement) success.
Key point to note is that the sooner you, as the project manager or the project owner, establish the specific criteria for the project you are responsible for the better.
Having established the success criteria is of course no guarantee for success, it is merely an important first step!
See also: