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Robustification
Robustification is a form of optimisation whereby a system is made less sensitive to the effects of random variability, or noise, that is present in that system's input variables and parameters. The process is typically associated with engineering systems, but the process can also be applied to a political policy, a business strategy 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) and is often associated with Taguchi methods. 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 synonyms Principles Robustification works by taking advantage of two different principles. Non-linearities Conside ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Robust Parameter Design (RPD)
A robust parameter design, introduced by Genichi Taguchi, is an Design of experiments, experimental design used to exploit the interaction between control and uncontrollable noise variables by robustification—finding the settings of the control factors that minimize response variation from uncontrollable factors. Control variables are variables of which the experimenter has full control. Noise variables lie on the other side of the spectrum. While these variables may be easily controlled in an experimental setting, outside of the experimental world they are very hard, if not impossible, to control. Robust parameter designs use a naming convention similar to that of FFDs. A 2''(m1+m2)-(p1-p2)'' is a 2-level design where ''m1'' is the number of control factors, ''m2'' is the number of noise factors, ''p1'' is the level of fractionation for control factors, and ''p2'' is the level of fractionation for noise factors. Consider an RPD cake-baking example from Montgomery (2005), where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Taguchi Methods
Taguchi methods () 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, marketing and advertising. Professional statisticians have welcomed the goals and improvements brought about by Taguchi methods, particularly by Taguchi's development of designs for studying variation, but have criticized the inefficiency of some of Taguchi's proposals. Taguchi's work includes three principal contributions to statistics: *A specific loss function *The philosophy of ''off-line quality control''; and *Innovations in the design of experiments. Loss functions Loss functions in the statistical theory Traditionally, statistical methods have relied on mean-unbiased estimators of treatment effects: Under the conditions of the Gauss–Markov theorem, least squares estimators have minimum variance among all mean-unbiased linear estimators. The emphasis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Design For Six Sigma
Design for Six Sigma (DFSS) is a collection of best-practices for the development of new products and processes. It is sometimes deployed as an engineering design process or business process management method. DFSS originated at General Electric to build on the success they had with traditional Six Sigma; but instead of process improvement, DFSS was made to target new product development. It is used in many industries, like finance, marketing, basic engineering, process industries, waste management, and electronics. It is based on the use of statistical tools like linear regression and enables empirical research similar to that performed in other fields, such as social science. While the tools and order used in Six Sigma require a process to be in place and functioning, DFSS has the objective of determining the needs of customers and the business, and driving those needs into the product solution so created. It is used for product or process ''design'' in contrast with process ''imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Optimisation
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Optimization problems can be divided into two categories, depending on whether the variables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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. This involves estimating sensitivity indices that quantify the influence of an input or group of inputs on the output. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem. Motivation A mathematical model (for example in biology, climate change, economics, renewable energy, agronomy...) can be highly complex, and as a result, its relationships between inputs and outputs may be faultily understood. In such cases, the model can be viewed as a black box, i.e. the output is an "opaque" function of its inputs. Quite often, some or all of the model inputs are subject to sources of uncertainty, including errors of measurement, er ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Monte Carlo Method
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 deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function. The uncertainty ''u'' can be expressed in a number of ways. It may be defined by the absolute error . Uncertainties can also be defined by the relative error , which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, , which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval . However, the most general way of characterizing uncertainty is by specifying its probability distribution. If the probability distribution of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Western World
The Western world, also known as the West, primarily refers to various nations and state (polity), states in Western Europe, Northern America, and Australasia; with some debate as to whether those in Eastern Europe and Latin America also constitute the West. The Western world likewise is called the Occident () in contrast to the Eastern world known as the Orient (). Definitions of the "Western world" vary according to context and perspectives; the West is an evolving concept made up of cultural, political, and economic synergy among diverse groups of people, and not a rigid region with fixed borders and members. Some historians contend that a linear development of the West can be traced from Greco-Roman world, Ancient Greece and Rome, while others argue that such a projection constructs a false genealogy. A geographical concept of the West started to take shape in the 4th century CE when Constantine the Great, Constantine, the first Christian Roman emperor, divided the Roman Em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Japan
Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea in the south. The Japanese archipelago consists of four major islands—Hokkaido, Honshu, Shikoku, and Kyushu—and List of islands of Japan, thousands of smaller islands, covering . Japan has a population of over 123 million as of 2025, making it the List of countries and dependencies by population, eleventh-most populous country. The capital of Japan and List of cities in Japan, its largest city is Tokyo; the Greater Tokyo Area is the List of largest cities, largest metropolitan area in the world, with more than 37 million inhabitants as of 2024. Japan is divided into 47 Prefectures of Japan, administrative prefectures and List of regions of Japan, eight traditional regions. About three-quarters of Geography of Japan, the countr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 contiguous states border Canada to the north and Mexico to the south, with the semi-exclave of Alaska in the northwest and the archipelago of Hawaii in the Pacific Ocean. The United States asserts sovereignty over five Territories of the United States, major island territories and United States Minor Outlying Islands, various uninhabited islands in Oceania and the Caribbean. It is a megadiverse country, with the world's List of countries and dependencies by area, third-largest land area and List of countries and dependencies by population, third-largest population, exceeding 340 million. Its three Metropolitan statistical areas by population, largest metropolitan areas are New York metropolitan area, New York, Greater Los Angeles, Los Angel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Genichi Taguchi
was an engineer and statistician. From the 1950s on, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods. Taguchi methods have been controversial among some conventional Western statisticians, but others have accepted many of the concepts introduced by him as valid extensions to the body of knowledge. Biography Taguchi was born and raised in the textile town of Tokamachi, in Niigata prefecture. He initially studied textile engineering at Kiryu Technical College with the intention of entering the family kimono business. However, with the escalation of World War II in 1942, he was drafted into the Astronomical Department of the Navigation Institute of the Imperial Japanese Navy. After the war, in 1948 he joined the Ministry of Public Health and Welfare, where he came under the influence of eminent statistician Matosaburo Masuyama, who kindled his interest in the design of experiments. He also worked at the Institute of Statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
