Assignment 1 - Courses

approximate fault coverage value that is required to obtain reliability (at the end of one
hour) of 0.99999.
Problem 2 (5 points)
Calculate the reliability of this system using the success diagram approach described in class.
Derive the Question upper boundary 2: Non-series/Non-Parallel for the system reliability System using the Redundancy formula:
Using an approach described in class, calculate the reliability of the system below.
Calculate an upper bound on Rsysthe reliability usingR the path independent i path assumption.
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Question 3: Software fault-tolerance and coverage
Problem 3 (5 points)
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A. A system design uses N-­‐Version programming for reliability. There are 3
Suppose versions that a simplex of the (no software redundancy) andcomputer the decision system has algorithm a failure generates rate of (assume output that ifat the
exponential least failure 2 out law ofapplies) the 3 versions and a fault agree detection and coverage generatesfactor a failure of C. condition The fault detection if they
capability don't is the match. result of a self-diagnostics that are run continuously. If the self-diagnostics detect a
fault, the time required to repair the system is 24 hours because the faulty board is identified,
obtained overnight • Theand probability easily replaced. that Version If, however, 1 generates the self-diagnostics incorrect output do not on detect a random the faults, input the
time required to is repair 0.0002. the system is 72 hours because a repair person must visit the site, determine
the problem, • and The perform probability the repair. that The Version disadvantage, 2 generates however, incorrect is that output the on inclusion a random of the input selfdiagnostics
results is 0.0023. in the failure rate becoming . In other words, the failure rate is increased by a
factor of because • The of the probability self-diagnostics. that Version Determine 3 generates the value incorrect of , for output a coverage on afactor random of 0.95, inputat
which including is the 0.0001 self-diagnostics begins to degrade the availability of the system.
Assume that failures of versions are independent. There is also a bug in the decision
algorithm that is triggered only when all three versions agree and causes it to
Problem generate 4 (5 points) a failure condition with probability 0.0000002. Assuming that incorrect
outputs do not match, what is the probability that the system works?
The architecture of a network of computers in a banking system is shown below. The architecture is
called a B. skip-ring How would network the answer and is designed to part Ato differ allow if the processors systemto uses communicate the three modules even after in anode
failures have recovery occurred. blockFor likeexample configuration. if node In 1 other fails, node words, 6 can version bypass (i + the 1) failed is activated node by if and routing
data over only the if alternative version i fails link and connecting the decision nodes algorithm 6 and 2. Assuming detects the the failure links or are if the perfect decision and the
nodes each algorithm have a reliability generatesof a false Rm , failure derive an condition. expression (assume for the that reliability the decision of the mechanism network. If Rm
has the same bug as in part A, but that it is otherwise perfect).
Question 4: Skip Ring Network
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The architecture of a network of computers in a system is shown below. The architecture
is called a skip-ring network and is designed to allow processors to communicate even
after node failures have occurred. For example if node 1 fails, node 6 can bypass the
failed node by routing data over the alternative link connecting nodes 6 and 2. Assuming
the links are perfect and the nodes each have a reliability of Rm , derive an expression for
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