What is the probability of failure on demand for a control valve with a dangerous failure rate of once in five years, tested every five years?

What is the probability of failure on demand for a control valve with a dangerous failure rate of once in five years, tested every five years?

• A. 0.22
• B. 0.52
• C. 0.63
• D. 0.85

Answer: (C)

To determine the probability of failure on demand for a control valve with a given dangerous failure rate, we need to consider the rate of failure and the testing frequency. In this case, the valve has a dangerous failure rate of one failure every five years, meaning it is expected to fail once in that timeframe. When a component is tested every five years, it has a certain probability of not failing between tests. If we define the dangerous failure rate as a constant, the probability of failure on demand can be calculated using the formula: P(failure on demand) = 1 - e^(-λt) Where λ is the failure rate (in this case, 1/5 years = 0.2 failures per year) and t is the time between tests (5 years). Plugging in these values gives: P(failure on demand) = 1 - e^(-0.2 * 5) = 1 - e^(-1) = 1 - 0.3679 ≈ 0.6321 This computation reveals that the probability of failure on demand for the control valve, when tested every five years and with a dangerous failure rate of one every five years, is approximately

To determine the probability of failure on demand for a control valve with a given dangerous failure rate, we need to consider the rate of failure and the testing frequency. In this case, the valve has a dangerous failure rate of one failure every five years, meaning it is expected to fail once in that timeframe.

When a component is tested every five years, it has a certain probability of not failing between tests. If we define the dangerous failure rate as a constant, the probability of failure on demand can be calculated using the formula:

P(failure on demand) = 1 - e^(-λt)

Where λ is the failure rate (in this case, 1/5 years = 0.2 failures per year) and t is the time between tests (5 years). Plugging in these values gives:

P(failure on demand) = 1 - e^(-0.2 * 5)

= 1 - e^(-1)

= 1 - 0.3679

≈ 0.6321

This computation reveals that the probability of failure on demand for the control valve, when tested every five years and with a dangerous failure rate of one every five years, is approximately