If a failure rate is given as 0.2 failures per year, which is the probability of failure for a Markov model with a one-hour time increment?

If a failure rate is given as 0.2 failures per year, which is the probability of failure for a Markov model with a one-hour time increment?

• A. 0.0002
• B. 0.2
• C. 0.028
• D. 0.0000228

Answer: (D)

To understand the correct answer, it's important to first relate the failure rate to the probability of failure over a specified time increment. The failure rate of 0.2 failures per year can be expressed in terms of smaller time increments. First, we find the failure rate per hour by dividing the annual failure rate by the number of hours in a year. Since a typical year has 365 days, that results in: 0.2 failures/year ÷ (365 days/year × 24 hours/day) = 0.2 / 8760 hours = approximately 0.0000228 failures per hour. This value represents the probability of a failure occurring in one hour. The calculation shows that the probability of failure in a time increment of one hour is indeed approximately 0.0000228. The other options represent different interpretations of failure probability and do not match the calculated probability based on the specified time increment and given failure rate.

To understand the correct answer, it's important to first relate the failure rate to the probability of failure over a specified time increment.

The failure rate of 0.2 failures per year can be expressed in terms of smaller time increments. First, we find the failure rate per hour by dividing the annual failure rate by the number of hours in a year. Since a typical year has 365 days, that results in:

0.2 failures/year ÷ (365 days/year × 24 hours/day) = 0.2 / 8760 hours = approximately 0.0000228 failures per hour.

This value represents the probability of a failure occurring in one hour. The calculation shows that the probability of failure in a time increment of one hour is indeed approximately 0.0000228.

The other options represent different interpretations of failure probability and do not match the calculated probability based on the specified time increment and given failure rate.