Problem - For a truly Simple Automatic Teller Machine (SATM) a preliminary estimate of transitions probabilities a software specification amenable to Markov analysis is represented by the following finite state machine:
Assuming that above is indeed an adequate model for the real SATM and that estimated probabilities are matching realistic operational usage profile determine:
a) Set of all primary independent paths (not traversing any loop more than once- note two loops above).
b) Probabilities of primary test paths.
c) Devise (and for 50 points bonus: write and testa VB/C#/Java program) procedure to simulate 10.000.000 working hours using statistical testing (simulating at least100.000.000 ATM transaction) using random walks of up to 12 states length as paths according to the operational profile (for a bonus program make sure that average transaction simulation time in memory in the program need to take about1 sec/per 100 transaction or less).
d) What statistical conclusion about reliability (MTBF) we can draw from the statistical testing experiment above - without any faults detected (explain for example will the vendor be able to provide a 99.99999% warranty?)
e) How many (simulations as designed in part c above) as statistical tests one need to run to assure 99.99% reliable results (if you can make a statistical argument on that basis)?