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Chapter 19 Risk management 581
distinction between the three stages is less clear, with infant-mortality failure subsiding only
slowly and a gradually increasing chance of wear-out failure. Failure of the type shown in
curve B is far more difficult to manage in a planned manner. The failure of operations which
rely more on human resources than on technology, such as some services, can be closer to
curve C. They may be less susceptible to component wear-out but more so to staff complacency
as the service becomes tedious and repetitive.
Reliability
Reliability
Reliability measures the ability to perform as expected over time. Usually the importance
of any particular failure is determined partly by how interdependent the other parts of the
system are. With interdependence, a failure in one component will cause the whole system
to fail. So, if an interdependent system has n components each with their own reliability, R 1 ,
R 2 ,..., R n , the reliability of the whole system, R s , is given by:
R s = R 1 × R 2 × R 2 × ...× R n
where
R 1 = reliability of component 1
R 2 = reliability of component 2
etc.
Worked example
An automated pizza-making machine in a food manufacturer’s factory has five major
components, with individual reliabilities (the probability of the component not failing)
as follows:
Dough mixer Reliability = 0.95
Dough roller and cutter Reliability = 0.99
Tomato paste applicator Reliability = 0.97
Cheese applicator Reliability = 0.90
Oven Reliability = 0.98
If one of these parts of the production system fails, the whole system will stop working.
Thus the reliability of the whole system is:
R s = 0.95 × 0.99 × 0.97 × 0.90 × 0.98
= 0.805
The number of components
In the example, the reliability of the whole system was only 0.8, even though the reliability
of the individual components was significantly higher. If the system had been made up of
more components, then its reliability would have been even lower. The more interdependent
components an operation or process has, the lower its reliability will be. For one composed
of components which each have an individual reliability of 0.99, with 10 components the
system reliability will shrink to 0.9, with 50 components it is below 0.8, with 100 components
it is below 0.4, and with 400 components it is down below 0.05. In other words, with a process
of 400 components (not unusual in a large automated operation), even if the reliability
of each individual component is 99 per cent, the whole system will be working for less than
5 per cent of its time.
Mean time between
failures
Mean time between failures
An alternative (and common) measure of failure is the mean time between failures (MTBF)
of a component or system. MTBF is the reciprocal of failure rate (in time). Thus:
MTBF =
operating hours
number of failures