The probability of the closing of the i th relay in the circuits shown is given by pi, i=1,2,3,4

The probability of the closing of the i th relay in the...

Key Concepts

Parallel Circuit Reliability

In a parallel configuration, the overall system functions as long as at least one of the components is working. The probability of system success is therefore calculated by first determining the probability that all components fail—by multiplying their individual failure probabilities—and then subtracting this number from one. This approach is key to understanding systems that are designed with redundancy to increase reliability.

Circuit Reliability Analysis

Circuit reliability analysis involves applying probability theory to assess the performance of electrical circuits. This includes the use of series and parallel reliability formulas to determine the overall probability of current flow in a circuit, and is a critical tool in designing robust circuits that can tolerate individual component failures.

Independent Events

In probability theory, when events are independent, the occurrence of one does not affect the likelihood of the others. This concept allows for the computation of joint probabilities by taking the product of the individual event probabilities, which is essential in analyzing systems where multiple components operate without mutual interference.

Series Circuit Reliability

A series configuration in a circuit implies that all components must function for the overall system to work. Consequently, the reliability of a series circuit is computed by multiplying the probabilities of each individual component's successful operation. This concept is fundamental in determining the probability of success when components are arranged in a sequential, interdependent fashion.

Transcript

00:01 In problem 6 s xx we have a portion of a circuit with 5 relays the probability of closing of the ieth relay equals p i which means we have the probability 1 for closing relay 1 probability 2 here probability 3 probability 4 and finally we have probability 5 for closing all the 5 relays we want to calculate the probability that the current flows from point a to point b we can consider this as a portion of a circuit then we have at least one both from a to b the different both is we have both a which is 1 to 5 relay 1 then relay 2 then relay 5 the second bus b is relay 3 relay 4 relay 5 then to get the probability of part a we want to get the probability of a union b the probability of a union b is the probability of a the probability of a is the multiplication for their probabilities probability of 1 multiplied by relative 2 multiplied by probability of 5 because they act independently plus the probability of b as previous is the probability of 3 multiplied by 4 multiply by 5 minus the probability of the intersection between a and b the intersection is all relays are activated b1 b2 b3 b4 and b5 this is the answer for circuit number a for circuit b near we have fifth we have five relays and it has a different orientation from party to answer this we want to get the probability that the current flows from a to b let's see what is the buzzes that can part a the the current flows from a to b it can go from a to b from the first bus here one four this is a a one four the second bus b from 2 to 5 to 5 to 5 c is 234 2 3 4 and d is 1 3 5 the more direct way is to use the inclusion property which says that the current flows for the union of these buses a union union b, union c, union d.

03:30 As previous here, it's a union b.

03:34 Here, a, union b, union c, union d.

03:38 We can't get it using the inclusion.

03:42 It's the probability of a plus b plus c plus c plus d...

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