Question

A given component has an MTBF of 106 hr, what is the reliability for an operating period of 10 hr for 5 such components in series ?

Answer 1

The reliability for 5 components in series is e^-50/10^6, given the MTBF and operating period.

Step-by-step explanation:

To calculate the reliability for 5 components in series, we need to consider the reliability of each component and use the formula for components in series. The reliability of a component is given by the formula: R = e-t/MTBF, where t is the operating period and MTBF is the mean time between failures. Given that the MTBF is 10^6 hours and the operating period is 10 hours, the reliability of one component is e-10/10^6. To calculate the reliability for 5 components in series, we multiply the individual reliabilities: (e-10/10^6)^5 = e-50/10^6.

Answer 2

To calculate the reliability of 5 components in series with an MTBF of 106 hours for a 10-hour operation period, you must first calculate the reliability of a single component and then raise that to the power of 5.

Step-by-step explanation:

The student is asking about the reliability of components in series given a Mean Time Between Failures (MTBF). For components in series, the overall system reliability is the product of the individual reliabilities of each component. First, to find the reliability of a single component with an MTBF of 106 hours over a 10-hour period, we use the exponential reliability function:

R(t) =
`e^(-t/MTBF)`

For one component over 10 hours:

R(10) =
`e^(-10/106)`

Once we have the reliability of a single component, we must raise that number to the power of the number of components in series (in this case, 5) to find the overall system reliability, since:

System Reliability =
`(Component Reliability)^(number of components)`

This yields the answer to the student's question.