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.