As VP for operations at Méndez-Pinero Engineering, you must decide which product

Question

As VP for operations at Méndez-Pinero Engineering, you must decide which product design, A or B, has the higher reliability. B is designed with backup units for components R3 and R4 Product Design A Rs=0.94 R1 0.98 R3 0.997 R40.992 Product Design B 0.98 0.94 0.982 0.96 0.92 0.96 2 The overall reliability of the system provided in Design A = % enter your response as a percentage rounded to two dec mal places The overall reliability of the system provided in Design B = | % enter your response as a percentage rounded to two decimal places)

Explanation / Answer

Reliability of the system

Product Design A

In a series connection, a failure of any product will result in the failure of the entire system. So, the overall reliability is given by the formula,

Rs = R1 x R2 x R3 x R4

We know that, R1 = 0.98, R2 = 0.94, R3 = 0.997, R4 = 0.992

Rs = R1 x R2 x R3 x R4 = 0.98 x 0.94 x 0.997 x 0.992 = 0.911 = 0.91

The overall reliability of the system provide in Design A = 0.91

Product Design B

Overall reliability for Design B is given by the formula,

Rs = R1 x R2 x R3 x R4

Where R3 = 1 – (1 – 0.982) x (1– 0.92) = 1 – 0.018 x 0.08 = 1 – 0.00144 = 0.99856

Similarly R4 = 1 – (1 – 0.96) x (1– 0.96) = 1 – 0.04 x 0.04 = 1 – 0.0016 = 0.9984

So, Rs = R1 x R2 x R3 x R4 = 0.98 x 0.94 x 0.99856 x 0.9984 = 0.918 = 0.92

The overall reliability of the system provide in Design B = 0.92

Therefore, Product Design B has higher reliability.

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