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Orthogonal Array
In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a "table" (array) whose entries come from a fixed finite set of symbols (for example, ), arranged in such a way that there is an integer ''t'' so that for every selection of ''t'' columns of the table, all ordered ''t''-tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times. The number ''t'' is called the ''strength'' of the orthogonal array. Here are two examples: The example at left is that of an orthogonal array with symbol set and strength 2. Notice that the four ordered pairs (2-tuples) formed by the rows restricted to the first and third columns, namely (1,1), (2,1), (1,2) and (2,2), are all the possible ordered pairs of the two element set and each appears exactly once. The second and third columns would give, (1,1), (2,1), (2,2) and (1,2); again, all possible ordered pairs each appearing once. The same st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuples
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An -tuple can be formally defined as the image of a function that has the set of the first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an -tuple can be identified with the ordered pair of its first elements and its th e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first meaning is the six permutations (orderings) of the set : written as tuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Anagrams of a word whose letters are all different are also permutations: the letters are already ordered in the original word, and the anagram reorders them. The study of permutations of finite sets is an important topic in combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of distinct objects is factorial, us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software System
A software system is a system of intercommunicating software component, components based on software forming part of a computer system (a combination of Computer hardware, hardware and software). It "consists of a number of separate Computer program, programs, configuration files, which are used to set up these programs, system documentation, which describes the structure of the system, and user documentation, which explains how to use the system". A software system differs from a computer program or software. While a computer program is generally a set of instructions (source code, source, or object code) that perform a specific task, a software system is more or an encompassing concept with many more components such as specification, Software test automation, test results, end-user documentation, maintenance records, etc.' The use of the term software system is at times related to the application of systems theory approaches in the context of software engineering. A software sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Box Testing
Black-box testing, sometimes referred to as specification-based testing, is a method of software testing that examines the functionality of an application without peering into its internal structures or workings. This method of test can be applied virtually to every level of software testing: unit, integration, system and acceptance. Black-box testing is also used as a method in penetration testing, where an ethical hacker simulates an external hacking or cyber warfare attack with no knowledge of the system being attacked. Test procedures Specification-based testing aims to test the functionality of software according to the applicable requirements. This level of testing usually requires thorough test cases to be provided to the tester, who then can simply verify that for a given input, the output value (or behavior), either "is" or "is not" the same as the expected value specified in the test case. Specific knowledge of the application's code, internal structure and programmin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Statistical Institute
The Indian Statistical Institute (ISI) is a public research university headquartered in Kolkata, India with centers in New Delhi, Bengaluru, Chennai and Tezpur. It was declared an Institute of National Importance by the Government of India under the Indian Statistical Institute Act, 1959. Established in 1931, it functions under the Ministry of Statistics and Programme Implementation of the Government of India. Primary activities of ISI are research and training in statistics, development of theoretical statistics and its applications in various natural and social sciences. Key areas of research at ISI are statistics, mathematics, theoretical computer science and mathematical economics. It is one of the few research oriented Indian institutes offering courses at both the undergraduate and graduate level. Apart from the degree courses, ISI offers a few diploma and certificate courses, special diploma courses for international students via ISEC, and special courses in collaborati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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] |
Fractional Factorial Design
In statistics, a fractional factorial design is a way to conduct experiments with fewer experimental runs than a full factorial design. Instead of testing every single combination of factors, it tests only a carefully selected portion. This "fraction" of the full design is chosen to reveal the most important information about the system being studied ( sparsity-of-effects principle), while significantly reducing the number of runs required. It is based on the idea that many tests in a full factorial design can be redundant. However, this reduction in runs comes at the cost of potentially more complex analysis, as some effects can become intertwined, making it impossible to isolate their individual influences. Therefore, choosing which combinations to test in a fractional factorial design must be done carefully. History Fractional factorial design was introduced by British statistician David John Finney in 1945, extending previous work by Ronald Fisher on the full factorial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial Experiment
In statistics, a factorial experiment (also known as full factorial experiment) investigates how multiple factors influence a specific outcome, called the response variable. Each factor is tested at distinct values, or levels, and the Experimental unit, experiment includes every possible combination of these levels across all factors. This comprehensive approach lets researchers see not only how each factor individually affects the response, but also how the factors interaction (statistics), interact and influence each other. Often, factorial experiments simplify things by using just two levels for each factor. A 2x2 factorial design, for instance, has two factors, each with two levels, leading to four unique combinations to test. The interaction between these factors is often the most crucial finding, even when the individual factors also have an effect. If a full factorial design becomes too complex due to the sheer number of combinations, researchers can use a fractional fact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secrecy
Secrecy is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret. Secrecy is often controversial, depending on the content or nature of the secret, the group or people keeping the secret, and the motivation for secrecy. Secrecy by government entities is often decried as excessive or in promotion of poor operation; excessive revelation of information on individuals can conflict with virtues of privacy and confidentiality. It is often contrasted with social transparency. Secrecy can exist in a number of different ways: encoding or encryption (where mathematical and technical strategies are used to hide messages), true secrecy (where restrictions are put upon those who take part of the message, such as through government security classification) and obfuscation, where secrets are hidden in plain sight behind complex idiosyncrat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secret Sharing
Secret sharing (also called secret splitting) refers to methods for distributing a secrecy, secret among a group, in such a way that no individual holds any intelligible information about the secret, but when a sufficient number of individuals combine their 'shares', the secret may be reconstructed. Whereas ''insecure'' secret sharing allows an attacker to gain more information with each share, ''secure'' secret sharing is 'all or nothing' (where 'all' means the necessary number of shares). In one type of secret sharing scheme there is one ''dealer'' and ''n'' ''players''. The dealer gives a share of the secret to the players, but only when specific conditions are fulfilled will the players be able to reconstruct the secret from their shares. The dealer accomplishes this by giving each player a share in such a way that any group of ''t'' (for ''threshold'') or more players can together reconstruct the secret but no group of fewer than ''t'' players can. Such a system is called a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
