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and what is your definition of Project success?
The answer in my view is both are important for the following reasons.1. projects tend to have multiple objectives while a product is only one of them. In this case, if the product was a success and the project wasn't then that means not all of the objectives were met, eg, org change management or knowledge transfer, etc.
2. Looking at it from a portfolio point of view, you could be doing things right, but not doing the right things. Meaning although a product was delivered, maybe it wasnt time for it, or its not high in priority. Ultimately this doesn't deliver much value to the organization
I tried to keep the answer as short as possible, i hope it helps.
Project success = All other side success including objectivity + Product Success.
Product Success = Project success - All other side success including objectivity.
That's means product success is partial success.