Unfortunately most of "The Evil of the Daleks" (Second Doctor) was lost when the BBC did an archive purge. But the novelization and Tardis Wiki entry both speak of a conversion arch rigged by the Doctor to implant the Human Factor in Daleks. Maybe a bit-Dalek got shoved through a conversion arch by accident during a mission? Or one of the humanized Daleks from that episode "got lost" when the episode tapes were junked and wound up in HQ?

(Link: http://tardis.wikia.com/wiki/Evilofthe_Daleks)

Exterminate! http://www.youtube.com/watch?v=SKhtP62RE1E

Both of them have been given the Human Factor and... That's it, I guess.

So, you can make one with no worries.

Loved that episode.

Don't worry: I also find that Daleks have some sort of odd charm. There's something inherently funny about the way they scream "EXTERMINATE" in a semi-hysterical fashion. Or is it just me? Anyone?

The PPC can administer the Human Factor to a Dalek in order to create a Humanized Dalek which takes away the instinct to hate and destroy and replaces it with a more... well, human personality.

Agent Omicron is a humanized Dalek. There are no missions featuring him (I think), but he is a precedent. I, for one, would absolutely love seeing a Humanized Dalek scoot around PPC HQ and the reactions of Whovian agents...