Consider the following configuration of solar photovoltaic arrays consisting of crystalline silicon solar cells. 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 t0. Let Ai denote the event that the lifetime of cell i exceeds t0 (i = 1, 2, , 4). We assume that the Ai's are independent events (whether any particular cell lasts more than t0 hours has no bearing on whether or not any other cell does) and that P(Ai) = 0.6 for every i since the cells are identical. Using P(Ai) = 0.6, the probability that system lifetime exceeds t0 is easily seen to be 0.5904. To what value would 0.6 have to be changed in order to increase the system lifetime reliability from 0.5904 to 0.63? [Hint: Let P(Ai) = p, express system reliability in terms of p, and then let x = p2.] (Round your answer to four decimal places.)

Answered: express system reliability in terms of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Consider the following configuration of solar photovoltaic arrays consisting of crystalline silicon solar cells. 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 t₀. Let A_idenote the event that the lifetime of cell i exceeds t₀(i = 1, 2, , 4). We assume that the A_i's are independent events (whether any particular cell lasts more than t₀ hours has no bearing on whether or not any other cell does) and that P(A_i) = 0.6 for every i since the cells are identical. Using P(A_i) = 0.6, the probability that system lifetime exceeds t₀is easily seen to be 0.5904. To what value would 0.6 have to be changed in order to increase the system lifetime reliability from 0.5904 to 0.63? [Hint: Let P(A_i) = p, express system reliability in terms of p, and then let x = p².] (Round your answer to four decimal places.)

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