Robustness can be defined as the strength of
a statistical models, tests, and procedures according to the specific
conditions of the statistical analysis. Many models have been approached to
justify ideal situations that do not exist when working with real world data
and as a result the model may provide correct results even if the conditions
are not met exactly 1.
1.
Breakdown Point
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The breakdown point is an estimator or a
way of measurement for robustness is the proportion of incorrect observations which
can handle before giving an incorrect result. The amount of robustness
required mainly depends on the strength of the data used. In this definition
the term “breakdown point” is approached to define robustness. System with
higher breakdown point causes higher robustness 2. There are manly two
breakdown points: finite sample breakdown point which is that fraction
of the data that can be given arbitrary values without making the estimator go
bad. This is however, a local breakdown point and asymptotic breakdown point
is the limit of the finite sample breakdown point as tends to infinity. For
example, for a data set there are three estimators: mean, pseudomedian and
median. Breakdown point for mean is 0, pseudomedian is 0.293 and median is 0.5,
then the sample mean is the worst estimator, the pseudomedian and median are
better, and since the median estimator has the highest breakdown point. it is
the best estimator 3.
2. Operating
Window: An Engineering Measure for Robustness.
The operating window is a way for measuring and improving the robustness of
system. The OW is the range in some input noise which produces a fixed failure
rate in the failure modes. It is an inverse method for measuring the ratio of
output variance to input variance. The OW is determined, keeping the magnitude
of some aggravating noise (the stressing noise) large and controlled. This
allows the OW to be measured quickly. This OW has proved in practice to be very
superior while trying to develop reliability. The Operating Window definition
makes the consideration both accuracy and variation of performance 4.
