12.1.2 Laws of reliability in complex systems
Measurement systems usually comprise
a number of components that are connected together in series, and hence it is
necessary to know how the reliabilities of individual components are aggregated
into a reliability figure for the whole system. In some cases, identical
measurement components are put in parallel to improve reliability, because the
measurement system then only fails if all of the parallel components fail.
These two cases are covered by particular laws of reliability.
Reliability of components in series
A measurement system consisting of
several components in series fails when any one of the separate components
develops a fault. The reliability of such a system can be quantified as the
probability that none of the components will fail within a given interval of
time. For a system of n series components, the reliability RS is the
product of the separate reliabilities of the individual components according to
the joint probability rule (Morris, 1997):
RS
= R1R2 ...Rn
Example 12.3
A measurement system consists of a
sensor, a variable conversion element and a signal processing circuit, for
which the reliability figures are 0.9, 0.95 and 0.99 respectively. Calculate
the reliability of the whole measurement system.
Solution
Applying (12.5), RS = 0.9
Reliability of components in parallel
One way of improving the reliability
of a measurement system is to connect two or more instruments in parallel. This
means that the system only fails if every parallel instrument fails. For such
systems, the system reliability RS is given by:
RS = 1 - FS
where FS is the unreliability of the
system. The equation for calculating FS is similar to (12.5). Thus,
for n instruments in parallel, the unreliability is given by:
FS
= F1F2 ...Fn
If all the instruments in parallel
are identical then (12.7) can be written in the simpler form:
FS
= (FX)n
where FX is the
unreliability of each instrument.
Example 12.4
In a particular safety critical
measurement system, three identical instruments are connected in parallel. If
the reliability of each instrument is 0.95, calculate the reliability of the
measurement system.
Solution
From (12.1), the unreliability of
each instrument FX is given by FX = 1 - RX = 1
- 0.95 = 0.05.
Applying (12.8), FS = (FX)3
= (0.05)3 = 0.000125.
Thus, from (12.6), RS = 1 -
FS = 1 - 0.000125 = 0.999875.
12.1.3 Improving measurement system
reliability
When designing a measurement system,
the aim is always to reduce the probability of the system failing to as low a
level as possible. An essential requirement in achieving this is to ensure that
the system is replaced at or before the time t2 in its life shown in
Figure 12.1 when the statistical frequency of failures starts to increase. Therefore,
the initial aim should be to set the lifetime T equal to t2 and
minimize the probability F (T) of the system failing within this specified
lifetime. Once all measures to reduce F (T) have been applied, the
acceptability of the reliability R (T) has to be assessed against the
requirements of the measurement system. Inevitably, cost enters into this, as
efforts to increase R (T) usually increase the cost of buying and maintaining
the system. Lower reliability is acceptable in some measurement systems where
the cost of failure is low, such as in manufacturing systems where the cost of
lost production, or the loss due to making out-of-specification products, is
not serious. However, in other applications, such as where failure of the
measurement system incurs high costs or causes safety problems, high
reliability is essential. Some special applications where human access is very
difficult or impossible, such as measurements in unmanned spacecraft,
satellites and nuclear power plants, demand especially high reliability because
repair of faulty measurement systems is impossible.
The various means of increasing R (T)
are considered below. However, once all efforts to increase R (T) have been
exhausted, the only solution available if the reliability specified for a
working period T is still not high enough is to reduce the period T over which
the reliability is calculated by replacing the measurement system earlier than
time t2.
Choice of instrument
The type of components and
instruments used within measuring systems has a large effect on the system
reliability. Of particular importance in choosing instruments is to have regard
to the type of operating environment in which they will be used. In parallel
with this, appropriate protection must be given (for example, enclosing
thermocouples in sheaths) if it is anticipated that the environment may cause
premature failure of an instrument. Some instruments are more affected than
others, and thus more likely to fail, in certain environments. The necessary
knowledge to make informed choices about the suitability of instruments for
particular environments, and the correct protection to give them, requires many
years of experience, although instrument manufacturers can give useful advice
in most cases.
Instrument protection
Adequate protection of instruments
and sensors from the effects of the operating environment is necessary. For
example, thermocouples and resistance thermometers should be protected by a
sheath in adverse operating conditions.
Regular calibration
The most common reason for faults
occurring in a measurement system, whereby the error in the measurement goes
outside acceptable limits, is drift in the performance of the instrument away
from its specified characteristics. Such faults can usually be avoided by
ensuring that the instrument is recalibrated at the recommended intervals of
time. Types of intelligent instrument and sensor that perform self-calibration
have clear advantages in this respect.
Redundancy
Redundancy means the use of two or
more measuring instruments or measurement system components in parallel such
that any one can provide the required measurement. Example 12.4 showed the use
of three identical instruments in parallel to make a particular measurement
instead of a single instrument. This increased the reliability from 95% to
99.99%. Redundancy can also be applied in larger measurement systems where
particular components within it seriously degrade the overall reliability of
the system. Consider the five-component measurement system shown in Figure
12.2(a) in which the reliabilities of the individual system components are R1
= R3 = R5 = 0.99 and R2 = R4 =
0.95.
Using (12.5), the system reliability
is given by RS = 0.99
Now, consider what happens if
redundant instruments are put in parallel with the second and fourth system
components, as shown in Figure 12.2(b). The reliabilities of these sections of
the measurement system are now modified to new values R’2 and R’4,
which can be calculated using (12.1), (12.6) and (12.8) as follows: F2
= 1 - R2 = 0.05. Hence, F’2 = (0.05)2 = 0.0025
and R’2 = 1 – F’2 = 0.9975. R’4 = R’2
since R4 = R2. Using (12.5) again, the system reliability
is now RS = 0.99
Thus, the redundant instruments have
improved the system reliability by a large amount. However, this improvement in
reliability is only achieved at the cost of buying and maintaining the
redundant components that have been added to the measurement system. If this
practice of using redundant instruments to improve reliability is followed,
provision must be provided for replacing failed components by the standby
units. The most efficient way of doing this is to use an automatic switching
system, but manual methods of replacement can also work reasonably well in many
circumstances.
The principle of increasing
reliability by placing components in parallel is often extended to other
aspects of measurement systems such as the connectors in electrical circuits,
as bad connections are a frequent cause of malfunction. For example, two
separate pairs of plugs and sockets are frequently used to make the same
connection. The second pair is redundant, i.e. the system can usually function
at 100% efficiency without it, but it becomes useful if the first pair of
connectors fails.
No comments:
Post a Comment
Tell your requirements and How this blog helped you.