Answered: The article “Reliability Evaluation 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

See similar textbooks

Related questions

Question

. The article “Reliability Evaluation of Solar Photovoltaic Arrays”(Solar Energy, 2002: 129–141) presents various configurations of solar photovoltaic arrays consisting of crystalline silicon solar cells. Consider first the system illustrated in Figure 2.14(a).

Series-parallel Total-cross tied

There are two subsystems connected in parallel, each one containing three cells. In order for the system to function, at least one of the two parallel subsystems must work. Within each subsystem, the three cells are connected in series, so a subsystem will work only if all cells in the subsystem work. Consider a particular lifetime value t0, 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 5 1, 2, c, 6). 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) = .9 for every i since the cells are identical. Given this, what is the probability that

For the series-parallel circuit, the system works (5)

Next consider the total-cross-tied system shown in Figure 2.14(b), obtained from the series-parallel array by connecting ties across each column of junctions. Now the system fails as soon as an entire column fails, and system lifetime exceeds t0 only if the life of every column does so. Given this, what is the probability that