3. 440 points DevoreStat9 2.E.081 My Notes Ask Your Teacher Consider the followi

Question

3. 440 points DevoreStat9 2.E.081 My Notes Ask Your Teacher Consider the following configuration of solar photovoltaic arrays consisting of crystalline silicon solar cells. 34 There are two subsystems connected in parallel, each one containing two cells. In order for the system to function, at least one of the two parallel subsystems must work. Within each subsystem, the two cells are connected in series, so a subsystem will work only if all cells in the subsystem work. Consider a particular lifetime value to, and suppose we want to determine the probability that the system lifetime exceeds to. Let A, denote the event that the lifetime of cell exceeds to (1, 2, . 4). We assume that the A's are independent events (whether any particular cell lasts more than to hours has no bearing on whether or not any other cell does) and that p(A) = 0.8 for every i since the cells are identical. Using P(A) = 0.8, the probability that system lifetime exceeds to is easily seen to be 0.8704. To what value would 0.8 have to be changed in order to increase the system lifetime reliability from 0.8704 to 0.92? [Hint: Let P(A,) = p, express system reliability in terms of p, and then let x -p2] (Round your answer to four decimal places.) Need Help? .ead. : to a Tutor i Talk to a Tutor Show My Work (Optional. @

Explanation / Answer

Let reliability of each cell = p

Reliability of one part working = p^2

Reliability of system working= 1-(1-p^2)^2

Solving,

1-(1-p^2)^2 = 0.92

(1-p^2)^2 = 0.08

1-p^2 = 0.2828

p^2 = 0.7172

p=sqrt(0.7172)=0.8468

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