Quality is a set of characteristics that are ultimately decided by the user, and not every user will agree on what those characteristics should be. This is why user testing of all sorts is very valuable.
You have to go back to Walter Shewhart's work and writings while at Bell Labs. In 1931's 'Economic Control of Quality of a Manufactured Product' he draws a line between 'a thing' and the human experience of it, drawing heavily from the philosophy of C.I. Lewis:
"There are two common aspects of quality: one of them has to do with the consideration of the quality of a thing as an objective reality independent of the existence of man. The other has to do with what we think, feel or sense as a result of the objective reality. In other words, there is a subjective side of quality."
He draws a line between objective quality (the measurable, physical things) and subjective quality (the human relationship to those properties).
Later in 1939's 'Statistical Method from the Viewpoint of Quality Control' he gives a good example:
"Let us take a very simple example. Suppose we consider the quality of a glass of water. We may list some of its characteristics as follows: temperature, volume, chemical purity, taste, clarity, and color. If we look at any one of these characteristics, say temperature, we see that it is impossible to specify the temperature of a glass of water to the last degree of accuracy."
I would argue this is the standard to go for when looking for a definition. Ask yourself what makes a quality glass of water and you'll immediately realize you need to ask 'according to who?'.