Computer Systems Question on Reliability

Question

(1) M1 has an availability of 96% and an MTBF of 2 minutes; (2) M2 has an availability of 90% and an MTBF of 5 minutes; and (3) M3 has an availability of 85% and an MTBF of 10 minutes. A request is considered correctly processed by your system if it is sent to a machine that is currently in operational state (up) and is stays that way until the request completes processing at that machine.

a) You want to ensure that any incoming request will be correctly processed with a probability of at least 60%. Which ones of three machines satisfy this requirement?

Answer 1

I believe the formula to determine this probability percentage is: a * e^(-t/MTBF)

where a is the availability percentage, t is the time needed to process a request, and t and MTBF are in the same units. I decided to multiply by a because that's what accounts for downtime, which isn't accounted for in the latter part of the formula.

There isn't enough information here to be able to answer the question, because I don't have a value for t.

Just for argument's sake, if I assume an average of 1 minute per request, I get:

1. M1: 96% * e^(-1/2) = 58.22%
2. M2: 90% * e^(-1/5) = 73.68%
3. M3: 85% * e^(-1/10) = 76.91%

On the other hand, if requests can be processed instantaneously, t is such a small quantity that it becomes of negligible importance, and the probability for each system approaches the availability percentage given.