For the overall reliability of the following system to be 0.975 or greater the reliability of the backup component, Rb, must be
A) at least 1.00.
B) at least 0.896.
C) at least 0.736.
D) at least 0.534.

Question

For the overall reliability of the following system to be 0.975 or greater the reliability of the backup component, Rb, must be       
A) at least 1.00. 
B) at least 0.896. 
C) at least 0.736. 
D) at least 0.534.

Quizplus · Accepted Answer

To calculate the overall reliability, we use the formula R = 1 - ((1 - R1) x (1 - R2) x ... x (1 - Rn)), where R1 - Rn are the reliability of the individual components. Let the reliability of the main component be Rm, which can be expressed as Rm = 0.975 / (1 - Rb).

Substituting the given values, we get

0.975 / (1 - Rb) = Rm 
=> 1 - Rb = 0.975 / Rm 
=> Rb = 1 - 0.975 / Rm

We need to find the minimum value of Rb that satisfies the condition Rm >= Rb.

Substituting the expression for Rm in terms of Rb, we get

0.975 / (1 - Rb) >= Rb 
=> 0.975 / Rb - 1 >= 1 
=> Rb <= 0.975 / 2

Therefore, the minimum value of Rb that satisfies the condition is Rb = 0.4875.

The answer is B) at least 0.896 because it is the minimum value of Rb among the options given that satisfies the condition Rm >= Rb.

For the Overall Reliability of the Following System to Be