The older strings {I was appointed bad bulb seeker in my youth...Uggg!!} were a true series circuit...one bulb dies, they all die. The newer ones are still wired in series, though a bit better. I still have my old 1980, handy dandy Radio Shack christmas bulb tester....still works.
String Faults
The most common problem with these strings is that a bulb can burn out. Most strings come with a couple of replacement bulbs which may be enough for a few weeks of operation. But if we want to keep a string running for years, we are well advised to purchase an additional identical string simply to provide replacement bulbs.
It is interesting to note that each year the bulb bases seem to differ, and typically it is impossible to get direct replacements another year. Probably we could remove the bad bulb from its base, and re-use that base with a new bulb. But using a bulb from a different set often has sad consequences.
These lights are designed to be wired in series, and so drop the 120V line voltage to typically 2.4V (120V/50bulbs=2.4V/bulb) without using an expensive transformer. As a result, any single bulb failure could darken an entire circuit. To avoid this, each bulb has a "shunt" of several turns of tiny wire inside the bulb near the bead. The shunt is intended to conduct current when the filament fails, but the shunts often do not work.
When a shunt does operate, it takes on a low resistance. As a result, each bulb in the rest of that circuit takes slightly more voltage, gets slightly brighter, and lasts less long. So it is important to replace bad lights promptly.
Beyond bad bulbs, some socket connections may become intermittent (especially outside). Even less commonly, a fuse in the plug may also become intermittent. But it is very common to overload the fuses.
http://www.ciphersbyritter.com/RADELECT/LITES/XMSLITES.HTM