Question

A product has four components A, B, C, and D. The finished product must have a reliability of at least .95. The first three components come from a supplier, and they have reliabilities of .99, .98, and .995, respectively. The fourth component is being designed now. What must the reliability of component D be in order to meet the product reliability condition?

Answer 1

The reliability of component D must be at least 97.914% to achieve the desired product reliability of at least .95 when the other component reliabilities are .99, .98, and .995.

Step-by-step explanation:

To achieve a finished product with a reliability of at least .95, we must calculate the necessary reliability of component D, given that components A, B, and C have reliabilities of .99, .98, and .995, respectively. The overall reliability of the system assuming independent components is the product of each component's reliability:

R_total = R_A x R_B x R_C x R_D

Inserting the known reliabilities, we get:

.95 = .99 x .98 x .995 x R_D

To find R_D, divide both sides by the product of the reliabilities of A, B, and C:

R_D = .95 / (.99 x .98 x .995)

After the calculation, we find that:

R_D = .95 / (.9702)

R_D ≈ .97914 or 97.914%

Therefore, the reliability of component D must be at least 97.914% to ensure that the finished product achieves the desired reliability level.