Is script execution time a decent source of pseudorandom number generation? This is for a PHP script for password generation.
Naturally there are other things being calculated before the password is generated.
But I figure the time it takes for the script to initialize and queue would make it decently pseudorandom.
Has there been studies on script execution time as a source of pseurandom number generation?

If not, any tips on how to conduct cryptanalysis on this?
AFAIK, there are papers that show, for example, that process times are not so random as they may seem. This is in the context of operating systems gathering entropy for devices like /dev/random. I've read this in many places but I can't provide any reference (if someone could it would be great ;-)).

Having said that, if you have other sources of entropy, script time could be an additional input, of course. Some considerations that come to my mind are:


Take care with the resolution of your time source: if the maximum resolution is minutes, it will probably return always 0.
Run some tests to see what results you get and how they are distributed. A usual distribution could be that 1 is returned 20% of the time, 2 30%, 3 30%, 4 20%, for example. 


Depending on how you plan to use these "random values" these considerations may alter the results one way or another.

My advice is that you use a decent entropy generation algorithm instead of trying to invent your own. You can start your quest, for instance, here:

https://en.wikipedia.org/wiki/Fortuna_(PRNG)

See the reference links for more algorithms.