Robustification is a form of
optimisation
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
whereby a
system
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...
is made less sensitive to the effects of
random variability
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rando ...
, or
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
, that is present in that system's input variables and
parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
s. The process is typically associated with
engineering systems
Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinking p ...
, but the process can also be applied to a
political policy, a
business strategy
In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of resources and an assessmen ...
or any other system that is subject to the effects of random variability.
Clarification on definition
Robustification as it is defined here is sometimes referred to as parameter design or
robust parameter design (RPD)
A robust parameter design, introduced by Genichi Taguchi, is an experimental design used to exploit the interaction between control and uncontrollable noise variables by robustification—finding the settings of the control factors that minimize ...
and is often associated with
Taguchi methods
Taguchi methods ( ja, タグチメソッド) are statistical methods, sometimes called robust design methods, developed by Genichi Taguchi to improve the quality of manufactured goods, and more recently also applied to engineering, biotechnology, ...
. Within that context, robustification can include the process of finding the inputs that contribute most to the random variability in the output and controlling them, or tolerance design. At times the terms design for quality or
Design for Six Sigma (DFFS) might also be used as
synonym
A synonym is a word, morpheme, or phrase that means exactly or nearly the same as another word, morpheme, or phrase in a given language. For example, in the English language, the words ''begin'', ''start'', ''commence'', and ''initiate'' are all ...
s
Principles
Robustification works by taking advantage of two different principles.
Non-linearities
Consider the
graph
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
below of a relationship between an input variable ''x'' and the output ''Y'', for which it is desired that a value of 7 is taken, of a system of interest. It can be seen that there are two possible values that ''x'' can take, 5 and 30. If the tolerance for ''x'' is independent of the nominal value, then it can also be seen that when ''x'' is set equal to 30, the expected variation of ''Y'' is less than if ''x'' were set equal to 5. The reason is that the gradient at ''x'' = 30 is less than at ''x'' = 5, and the random variability in ''x'' is suppressed as it flows to ''Y''.
This basic principle underlies all robustification, but in practice there are typically a number of inputs and it is the suitable point with the lowest gradient on a multi-dimensional surface that must be found.
Non-constant variability
Consider a case where an output ''Z'' is a function of two inputs ''x'' and ''y'' that are multiplied by each other.
''Z'' = ''x y''
For any target value of ''Z'' there is an infinite number of combinations for the nominal values of ''x'' and ''y'' that will be suitable. However, if the standard deviation of ''x'' was proportional to the nominal value and the standard deviation of ''y'' was constant, then ''x'' would be reduced (to limit the random variability that will flow from the right hand side of the equation to the left hand side) and ''y'' would be increased (with no expected increase random variability because the standard deviation is constant) to bring the value of ''Z'' to the target value. By doing this, ''Z'' would have the desired nominal value and it would be expected that its standard deviation would be at a minimum: robustified.
By taking advantage of the two principles covered above, one is able to optimise a system so that the nominal value of a systems output is kept at its desired level while also minimising the likelihood of any deviation from that nominal value. This is despite the presence of random variability within the input variables.
Methods
There are three distinct methods of robustification, but a
practitioner
Practitioner may refer to:
*Health practitioner
*Justice and public safety practitioner
*Legal practitioner
*Medical practitioner
*Mental health professional or practitioner
*Theatre practitioner
Spiritual Practitioner
*Solitary practitioner in ...
might use a mix that provides the best in results, resources and time.
Experimental
The experimental approach is probably the most widely known. It involves the identification of those variables that can be adjusted and those variables that are treated as
noises
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
. An experiment is then designed to investigate how changes to the nominal value of the adjustable variables can limit the transfer of noise from the noise variables to the output. This approach is attributed to
Taguchi and is often associated with
Taguchi methods
Taguchi methods ( ja, タグチメソッド) are statistical methods, sometimes called robust design methods, developed by Genichi Taguchi to improve the quality of manufactured goods, and more recently also applied to engineering, biotechnology, ...
. While many have found the approach to provide impressive results, the techniques have also been criticised for being statistically erroneous and inefficient. Also, the time and effort required can be significant.
Another experimental method that was used for robustification is the Operating Window. It was developed in the
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
before the wave of quality methods from
Japan
Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...
came to the
West
West or Occident is one of the four cardinal directions or points of the compass. It is the opposite direction from east and is the direction in which the Sunset, Sun sets on the Earth.
Etymology
The word "west" is a Germanic languages, German ...
, but still remains unknown to many.
[See Clausing (2004) reference for more details] In this approach, the noise of the inputs is continually increased as the system is modified to reduce sensitivity to that noise. This increases robustness, but also provides a clearer measure of the variability that is flowing through the system. After optimisation, the random variability of the inputs is controlled and reduced, and the system exhibits improved quality.
Analytical
The analytical approach relies initially on the development of an analytical model of the system of interest. The expected variability of the output is then found by using a method like the
propagation of error
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of ex ...
or functions of random variables.
[See the 'Probabilistic Design' link in the external links for more information.] These typically produce an algebraic expression that can be analysed for optimisation and robustification. This approach is only as accurate as the model developed and it can be very difficult if not impossible for complex systems.
The analytical approach might also be used in conjunction with some kind of surrogate model that is based on the results of experiments or numerical simulations of the system.
Numerical
In the numerical approach a model is run a number of times as part of a
Monte Carlo simulation
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determini ...
or a numerical propagation of errors to predict the variability of the outputs. Numerical optimisation methods such as hill climbing or evolutionary algorithms are then used to find the optimum nominal values for the inputs. This approach typically requires less human time and effort than the other two, but it can be very demanding on computational resources during simulation and optimization.
See also
*
Sensitivity analysis
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty anal ...
Footnotes
References
* Clausing (1994) ''Total Quality Development: A Step-By-Step Guide to World-Class Concurrent Engineering.'' American Society of Mechanical Engineers.
* Clausing, D. (2004) ''Operating Window: An Engineering Measure for Robustness'' Technometrics. Vol. 46
pp. 25–31.
* Siddall (1982) ''Optimal Engineering Design.'' CRC.
* Dodson, B., Hammett, P., and Klerx, R. (2014) ''Probabilistic Design for Optimization and Robustness for Engineers'' John Wiley & Sons, Inc. {{ISBN, 978-1-118-79619-1
External links
Probabilistic design
Reliability engineering
Quality