Let me present a scenario I can solve, and then the one I cannot: A system is considered operational if K out of N lighbulbs work. All the lightbulbs are connected to a power source. System reliability is the reliability of the power source times the reliability of the K out of N lightbulb system (binomial).
What about if I use multiple power sources and make that each power source supplies only a subset of the lightbulbs? It can be assumed that all the power sources will supply the same number of lightbulbs. From intuition, I know that increasing the number of power sources will decrease the probability of loosing all the lightbulbs, but should increase the probability of loosing a group of them. Is there a model (series or parallel I don't think that work) for this scenario?
For example, imagine I have 10 lightbulbs connected to 2 power sources. How can I get the reliability of the system if the criteria for success is that 7 or more lightbulbs are operative?