Yes and no is the only possible answer. It failed in a lot of things and succeeded in a lot of things.
From a gaming community perspective it was a great success. It brought us some fantastic games and it is the 4th best selling console of all time, and in many countries it is the 2nd best selling only behind PS2.
From a corporate perspective it failed to turn a profit, and it failed to capitalise on the amazing success of the PS2. Though it did manage maintain a decent degree of popularity of the PS brand. And it did help to win the HDDVD/Bluray format war. While Bluray isn't as dominant as DVD became, because of the rise of digital distribution, it's still an important medium, and losing the format war to HDDVD would have been a failure of a different sort for Sony. Still the cost/benefit of that winning the format war is probably debatable.
Ultimately, though, PS3 was successful enough despite many failings. In later years it helped keep Sony alive, it ensured there would be an 8th generation Playstation console, and it carried the best momentum of the 7th generation into the 8th generation (which I predicted back in 2009).
“The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.” - Bertrand Russell
"When the power of love overcomes the love of power, the world will know peace."
Jimi Hendrix
