I'm not sure about this but it may mean your computer is faulty, you might be able to return and get a replacement it if it's new or something and the pixel was dead when you got it.
Your computer isn't faulty, no. However most LCD monitors have a dead pixel warrenty of which you will need to check your manufacturers handbook, usually it's 2 or 3 dead pixels round the edge of the screen or one or two in the center.