In a one-out-of-two voting arrangement for transmitters, what is the common cause failure rate if the failure rate is 0.03 failures per year?

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In a one-out-of-two voting arrangement, there are two transmitters operating simultaneously, and the system requires at least one of them to function correctly for the system to operate effectively. To determine the common cause failure rate, we need to understand how the failure rate of each individual transmitter contributes to the overall failure of the system.

Given that the failure rate for each transmitter is 0.03 failures per year, we need to consider the possibility that both transmitters could fail due to a common cause. In a one-out-of-two configuration, if both transmitters fail simultaneously (e.g., due to a shared fault or external condition), the system will fail.

To calculate the probability that both transmitters fail together (the common cause failure), we can multiply the individual failure rates of the two transmitters. For a common cause failure, we use the formula:

[

\text{Common Cause Failure Rate} = \text{Failure Rate} \times \text{Failure Rate}

]

Thus:

[

\text{Common Cause Failure Rate} = 0.03 \times 0.03 = 0.0009 \text{ failures/year}

]

However, since the options provided are cumulative rates over the chosen period,