What is the reliability of a system with a constant failure rate of 0.002 failures per year if operated for 10 years?

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Multiple Choice

What is the reliability of a system with a constant failure rate of 0.002 failures per year if operated for 10 years?

To determine the reliability of a system over a specified period of time with a constant failure rate, the formula to calculate this is: Reliability (R) = e^(-λt) Where: - λ (lambda) is the failure rate, in this case, 0.002 failures per year. - t is the time of operation, which is 10 years. Using this formula, we first calculate the product of the failure rate and time: λt = 0.002 failures/year * 10 years = 0.02 Now we can substitute this value back into the reliability formula: R = e^(-0.02) Using a calculator or mathematical software to find e raised to the power of -0.02 gives approximately: R ≈ 0.9802 The closest value to this in the given choices is 0.9801. While there may be slight discrepancies depending on rounding, this choice is a reasonable approximation of the calculated reliability. Thus, B is the correct choice, representing the expected reliability of the system over 10 years given the specified constant failure rate.

To determine the reliability of a system over a specified period of time with a constant failure rate, the formula to calculate this is:

Reliability (R) = e^(-λt)

Where:

  • λ (lambda) is the failure rate, in this case, 0.002 failures per year.

  • t is the time of operation, which is 10 years.

Using this formula, we first calculate the product of the failure rate and time:

λt = 0.002 failures/year * 10 years = 0.02

Now we can substitute this value back into the reliability formula:

R = e^(-0.02)

Using a calculator or mathematical software to find e raised to the power of -0.02 gives approximately:

R ≈ 0.9802

The closest value to this in the given choices is 0.9801. While there may be slight discrepancies depending on rounding, this choice is a reasonable approximation of the calculated reliability.

Thus, B is the correct choice, representing the expected reliability of the system over 10 years given the specified constant failure rate.

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