The following table shows the time between failures (in hours) observed for a piece of software:

Error number	1	2	3	4	5
Time since last failure (hours)	6	4	8	5	6

Assuming an exponential reliability model, what is the reliability of the system for one hour of operation?

Explanation

Under the exponential reliability model, the failure rate λ is estimated as 1/MTBF, where MTBF is the mean of the observed inter-failure times: (6+4+8+5+6)/5 = 29/5 hours, giving λ = 5/29 failures per hour. Reliability over t hours is R(t) = e^(−λt); for t = 1 hour this gives R(1) = e^(−5/29), option (iii). The other options would result from mistakenly using 9, 7, or 3 as the numerator instead of the correctly computed failure count parameter 5.