Question 17084 – NTA UGC NET JUNE-2023 Paper-2

To calculate the reliability of the system for one hour of operation using an exponential model, you can use the formula:

Reliability (R) = e^(-λt)

Where:

λ (lambda) is the failure rate, which can be calculated as the reciprocal of the mean time between failures (MTBF), and
t is the time of interest, which in this case is 1 hour.
First, let’s calculate λ. The MTBF is the average time between failures, which can be calculated as the sum of the time since the last failure divided by the number of failures.

MTBF = (6 + 4 + 8 + 5 + 6) / 5 = 29/5 hours

Now, calculate λ:

λ = 1 / MTBF = 5 / 29 per hour

Now, calculate the reliability for 1 hour of operation:

R = e^(-λt) = e^(-(5/29) * 1) = e^(-5/29)

So, the reliability of the system for one hour of operation assuming an exponential model is approximately e^(-5/29).