Digital Signal Processing Reference
In-Depth Information
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(a)
(b)
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Closed
-
form solution
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0
−
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(c)
Figure 2.9 Functions of random variables
In this case we could find out the desired pdf but it is only because we have a
closed-form solution for x
h
as
2
ð
=
g
Þ
sin 2
:
v
2.3.2 Reliability of Systems
Systems are designed from components having different failure probabilities. A
complex system is a function of many random variables and the study of these
interconnected subsystems constitute an important branch of engineering. This
must always be borne in mind by every product designer and practising engineer.
Reliability can be achieved only at the product design stage, not at the end, hence
product designers should pay attention to reliability.
In the case of software, system failures occur due to existence of many paths due
to different input conditions and it behaves as a finite-state automaton. It is almost
impossible to exhaust all the outcomes for all conditions. In fact, this is why many
practices have been introduced in testing at each level. Reliability of the software
improves with use whereas the reliability of a mechanical system degrades with use.
Figure 2.10 shows the reliability graph of any generic system. Notice there are three
phases in the graph: infantile mortality, random failures and aging. In the case of
software there are only two phases exist; the aging phase doesn't exist.
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