Security and dependability of computer systems - esercitazione affidabilità

Exercise 1

A processing system for a helicopter

Exercise 1

The reliability block diagram of the system.

CPU INS BUS A BUS B

Remote c.

CPU AHRS BUS A BUS B

Remote c. Doppler AHRS

AHRS

Exercise 1

First i calculated the reliability of every single block, for a

 one hour period

EQ MTTF λ r

CPU 2000 0,0005000 0,9995001249793

Remote 3500 0,0002857 0,9997143265268

AHRS 1000 0,0010000 0,9990004998335

INS 1000 0,0010000 0,9990004998335

Doppler 700 0,0014286 0,9985724484941

BUS 5000 0,0002000 0,9998000199987

Then i calculated the total reliability by partial semplifications,

 using a Spreadsheet: R = 0,99999816169

sys

Finally i calculated the needed coverage to obtain a reliability

 of 0,99999: c = 0,98367

Exercise 2

The skip-ring network

Exercise 2

I assumed that the network is working when cycles are

 possible.

A necessary and sufficient condition for this, is that there

 shouldn't be consecutive falied nodes.

After a certain period of observation, there could be 7

 different situations: 0 nodes have failed, 1 node has failed, ...,

6 nodes have failed.

Since these situation are mutually exclusive, and they cover

 all the possible results, we can use the law of total

probability:

P(system fails) = P(system fails | 0 nodes have failed) +

P(system fails | 1 node has failed) +

...

P(system fails | 6 nodes have failed)

Exercise 2

There are 6 There are 2

 

combination combination

on 15 that on 20 that DO

cause a NOT cause a

system failure system failure

when n = 2 when n = 3

Exercise 2

Thus, the expression for the reliability r of the system results

 s

to be:

If r = e

-0,002*10

 r = 0,99769447147626

s Exercise 3

Self-diagnostic in a symplex system

The failure rate is increased by a factor of α because of self-

 diagnostics

If the self-diagnostics detect a fault, the time required to

 repair the system is 24 hours, instead of 72

We need the value of α at which including the self

 diagnostics begins to degrade the availability of the system.

First, i calculated the MTTF of a sistem with self-diagnostic

 =24c721−c=26,4

MTTF sd

Exercise 3

Thus the avaibility of the system with sd is

 1

=

A sd 

1 MTTF sd

Thus, there is a degeneration if

 

A A

sd 1 1





1 MTTF 1 MTTF

sd

MTTR

 =2,73

MTTR sd Exercise 4

Parallel of series vs serie of parallels

Wich one has the highest reliability?

 Exercise 4

Parallel of series

The reliability of this implementation of redundancy is easily

 calculated, and it results to be: s m

=1−1−r 

R sp

Exercise 4

Serie of parallels

For this one, the reliability results to be

 s m

=1−1−r  

R sp