To follow up:
As noted K>1 says stability but give no hint at how far outside the smith chart the stability circles are. Similarly if you get K<1 it doesn't give you much insight as to what to do, or where to do it.
On the other hand Mu and Muprime have direct relation and give great insight.
Mu is the distance from the center of the Smith Chart to nearest point of instability on the INPUT stability circles. Muprime is the same, but for the OUTPUT stability circles. Hence a mu or muprime of 1 means that a stability circle just brushes the edge of the smith chart.
Here's the real cool thing about plotting both Mu and Muprime that blows K-Factor stability analysis out of the water:
Lets say you get a Mu of 0.9, a Muprime of 0.2, and a K of 0.5.
The large Mu says you only have to do a little work at the INPUT to stabilize the circuit, and the small Muprime says that fixing it at the output is near futile (counter intuitive at first). If you then go plot the stability circles at the offending frequency (or range of frequencies) you can immediately see if adding series resistance, shunt resistance, or both is the correct path. Stability circles on the left indicates the need for series resisance, while stability circles on the right indicates shunt resistance. Stability circles on the top or bottom are best solves with both a series and shunt resistance.