What is the probability of success for a system with a failure probability of 0.01 over a ten-year mission?

What is the probability of success for a system with a failure probability of 0.01 over a ten-year mission?

• A. 0.1
• B. 0.9
• C. 0.9044
• D. 0.99

Answer: (C)

To determine the probability of success for a system with a failure probability of 0.01 over a ten-year mission, you need to calculate the probability that the system does not fail at all during that period. The failure probability of 0.01 means that the system has a 1% chance of failing in one year, which implies it has a 99% chance of succeeding in that same year. To find the probability of success over ten years, we raise the success probability for one year to the power of the number of years. This can be expressed mathematically as: P(success over 10 years) = P(success in one year) ^ number of years So, substituting the probabilities: P(success over 10 years) = 0.99^10 Calculating this gives approximately: P(success over 10 years) ≈ 0.9044 This result indicates that there is about a 90.44% chance that the system will not fail over the course of ten years. This understanding reflects the essence of reliability calculations in functional safety, where assessing the cumulative effects of small probabilities over time is crucial for predicting overall system performance. Understanding this approach can help grasp how reliability and safety are quantified in system

To determine the probability of success for a system with a failure probability of 0.01 over a ten-year mission, you need to calculate the probability that the system does not fail at all during that period. The failure probability of 0.01 means that the system has a 1% chance of failing in one year, which implies it has a 99% chance of succeeding in that same year.

To find the probability of success over ten years, we raise the success probability for one year to the power of the number of years. This can be expressed mathematically as:

P(success over 10 years) = P(success in one year) ^ number of years

So, substituting the probabilities:

P(success over 10 years) = 0.99^10

Calculating this gives approximately:

P(success over 10 years) ≈ 0.9044

This result indicates that there is about a 90.44% chance that the system will not fail over the course of ten years. This understanding reflects the essence of reliability calculations in functional safety, where assessing the cumulative effects of small probabilities over time is crucial for predicting overall system performance.

Understanding this approach can help grasp how reliability and safety are quantified in system