What is the reliability for a twenty year mission for a system with an unreliability of 0.02 for a one year mission time?

• A. 0.40
• B. 0.60
• C. 0.668
• D. 0.332

Answer: (C)

To determine the reliability of a system over a twenty-year mission, given an annual unreliability of 0.02, one must first calculate the annual reliability. Reliability is defined as the probability that a system will perform its intended function without failure for a specified time.

The unreliability over one year is 0.02, which indicates that the reliability can be calculated as:

Reliability for one year = 1 - Unreliability for one year

Reliability for one year = 1 - 0.02 = 0.98

For a mission lasting twenty years, the system is assumed to operate independently over each year. Therefore, the reliability over the entire twenty-year period can be calculated by raising the annual reliability to the power of the number of years:

Reliability over twenty years = (Reliability for one year) ^ (number of years)

Reliability over twenty years = (0.98) ^ 20

When this calculation is performed, it results in approximately 0.6676, which can be rounded to 0.668. This aligns with the selected answer, confirming that for a twenty-year mission, the system has a reliability of approximately 0.668, indicating that there is a