A company produces a product consisting of two components arranged as follows: If both components must function for the product to function, then the two components would need individual reliabilities of _______ to achieve an overall reliability of 0.90.
A) R1 = 0.90 and R2 = 0.90
B) R1 = 0.95 and R2 = 0.95
C) R1 = 0.80 and R2 = 0.80
D) R1 = 0.85 and R2 = 0.85

Question

A company produces a product consisting of two components arranged as follows:    If both components must function for the product to function, then the two components would need individual reliabilities of _______ to achieve an overall reliability of 0.90.
A) R1 = 0.90 and R2 = 0.90 
B) R1 = 0.95 and R2 = 0.95 
C) R1 = 0.80 and R2 = 0.80 
D) R1 = 0.85 and R2 = 0.85

Quizplus · Accepted Answer

To calculate the overall reliability of the product, we use the formula R = R1 x R2, where R1 and R2 are the individual reliabilities of the two components. 
We need R = 0.90, so we have:
0.90 = R1 x R2
Taking the square root of both sides gives:
√0.90 = √(R1 x R2)
0.95 ≈ R1 x R2
Since both R1 and R2 have to be greater than 0 (otherwise the component would not function at all), we can assume that R1 = R2 = 0.95. 
Therefore, the answer is B.

A Company Produces a Product Consisting of Two Components Arranged