When two solenoid valves are used in series with a common cause beta factor of 0.001, what is the PFDavg of the valve subsystem?

When two solenoid valves are used in series with a common cause beta factor of 0.001, what is the PFDavg of the valve subsystem?

• A. 0.0009
• B. 0.001
• C. 0.000009
• D. 0.0000017

Answer: (D)

To determine the average probability of failure on demand (PFDavg) for a subsystem involving two solenoid valves in series with a common cause beta factor, it is essential to apply the formulas and concepts related to reliability and failure rates. In a series system, the failure of any component will lead to the failure of the entire system. The formula for PFDavg in such cases is often calculated by combining the individual failure probabilities of each component as well as accounting for the common cause failures. The common cause beta factor indicates the likelihood of simultaneous failure due to a shared cause. Given that the system consists of two solenoid valves with a common cause beta factor of 0.001, you first calculate the PFDavg for both valves. If each solenoid valve has a PFDavg of 0.001, the series configuration means their individual probabilities would be added (assuming they are identical for simplicity), leading to an additive component for the beta factor. Thus, the overall PFDavg can be represented as: PFDavg = PFD1 + PFD2 + β In this case, since both valves are treated equally, we have: PFDavg = 0.001 + 0.001 + 0.001

To determine the average probability of failure on demand (PFDavg) for a subsystem involving two solenoid valves in series with a common cause beta factor, it is essential to apply the formulas and concepts related to reliability and failure rates.

In a series system, the failure of any component will lead to the failure of the entire system. The formula for PFDavg in such cases is often calculated by combining the individual failure probabilities of each component as well as accounting for the common cause failures. The common cause beta factor indicates the likelihood of simultaneous failure due to a shared cause.

Given that the system consists of two solenoid valves with a common cause beta factor of 0.001, you first calculate the PFDavg for both valves. If each solenoid valve has a PFDavg of 0.001, the series configuration means their individual probabilities would be added (assuming they are identical for simplicity), leading to an additive component for the beta factor.

Thus, the overall PFDavg can be represented as:

PFDavg = PFD1 + PFD2 + β

In this case, since both valves are treated equally, we have:

PFDavg = 0.001 + 0.001 + 0.001