For a module with an MTTF of 100 years, what is its reliability over six years?

For a module with an MTTF of 100 years, what is its reliability over six years?

• A. 0.9999
• B. 0.9433
• C. 0.9417
• D. 0.9402

Answer: (C)

To determine the reliability of a module with a Mean Time To Failure (MTTF) of 100 years over a period of six years, we can use the exponential reliability function. The reliability function R(t) for a constant failure rate can be expressed mathematically as: R(t) = e^(-t/MTTF) In this case, t is the duration of interest (in years) and MTTF is given as 100 years. Plugging in the values: R(6) = e^(-6/100) Calculating: -6/100 = -0.06 Now, we can compute the exponential: R(6) = e^(-0.06) Using the value of e (approximately equal to 2.71828), we find: R(6) ≈ 2.71828^(-0.06) ≈ 0.9417 (rounded to four decimal places). This calculation shows that the reliability of the module over a six-year period is approximately 0.9417. Therefore, the choice that matches this calculation is the correct one. Understanding this helps in assessing how likely a system is to function without failure over a specified period, which is crucial in

To determine the reliability of a module with a Mean Time To Failure (MTTF) of 100 years over a period of six years, we can use the exponential reliability function. The reliability function R(t) for a constant failure rate can be expressed mathematically as:

R(t) = e^(-t/MTTF)

In this case, t is the duration of interest (in years) and MTTF is given as 100 years. Plugging in the values:

R(6) = e^(-6/100)

Calculating:

-6/100 = -0.06

Now, we can compute the exponential:

R(6) = e^(-0.06)

Using the value of e (approximately equal to 2.71828), we find:

R(6) ≈ 2.71828^(-0.06) ≈ 0.9417 (rounded to four decimal places).

This calculation shows that the reliability of the module over a six-year period is approximately 0.9417. Therefore, the choice that matches this calculation is the correct one.

Understanding this helps in assessing how likely a system is to function without failure over a specified period, which is crucial in