If a system consists of a transmitter, a controller, and a valve, what is the probability of system success over five years if their failure rates are 0.15, 0.008, and 0.19 respectively?

If a system consists of a transmitter, a controller, and a valve, what is the probability of system success over five years if their failure rates are 0.15, 0.008, and 0.19 respectively?

• A. 0.683
• B. 0.348
• C. 0.652
• D. 0.352

Answer: (A)

To determine the probability of system success over five years for the given components, it's essential first to compute the failure probabilities for each part of the system and then evaluate the overall system success. 1. **Identify Failure Rates**: - Transmitter failure rate = 0.15 - Controller failure rate = 0.008 - Valve failure rate = 0.19 2. **Calculate the Probability of Success for Each Component**: The probability of success for each component can be determined by subtracting its failure rate from 1: - Probability of success for the transmitter = 1 - 0.15 = 0.85 - Probability of success for the controller = 1 - 0.008 = 0.992 - Probability of success for the valve = 1 - 0.19 = 0.81 3. **Overall System Success**: If we consider the system to be a series connection (where the failure of any single component leads to system failure), the total probability of system success is the product of the individual probabilities of success: \[ P(\text{system success}) = P(\text{transmitter success}) \times P

To determine the probability of system success over five years for the given components, it's essential first to compute the failure probabilities for each part of the system and then evaluate the overall system success.

1. Identify Failure Rates:

• Transmitter failure rate = 0.15

• Controller failure rate = 0.008

• Valve failure rate = 0.19

2. Calculate the Probability of Success for Each Component:

The probability of success for each component can be determined by subtracting its failure rate from 1:

• Probability of success for the transmitter = 1 - 0.15 = 0.85

• Probability of success for the controller = 1 - 0.008 = 0.992

• Probability of success for the valve = 1 - 0.19 = 0.81

3. Overall System Success:

If we consider the system to be a series connection (where the failure of any single component leads to system failure), the total probability of system success is the product of the individual probabilities of success:

[

P(\text{system success}) = P(\text{transmitter success}) \times P