Orthogonal Arrays

Hedayat, A.; Sloane, N. J. A.; Stufken, John

doi:10.1007/978-1-4612-1478-6

Cited by 991 publications

(481 citation statements)

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“…The use of orthogonal arrays in statistically designed experiments are discussed Hedayat et al (1999).…”

Section: Combinatorial Designsmentioning

confidence: 99%

Test Algebra for Concurrent Combinatorial Testing

Tsai

2017

Combinatorial Testing in Cloud Computing

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A new algebraic system, Test Algebra (TA), is proposed for identifying faults in combinatorial testing for SaaS (Software-as-a-Service) applications. In the context of cloud computing, SaaS is a new software delivery model, in which mission-critical applications are composed, deployed, and executed on cloud platforms. Testing SaaS applications is challenging because new applications need to be tested once they are composed, and prior to their deployment. A composition of components providing services yields a configuration providing a SaaS application. While individual components in the configuration may have been thoroughly tested, faults still arise due to interactions among the components composed, making the configuration faulty.When there are k components, combinatorial testing algorithms can be used to identify faulty interactions for t or fewer components, for some threshold 2 ≤ t ≤ k on the size of interactions considered. In general these methods do not identify specific faults, but rather indicate the presence or absence of some fault. To identify specific faults, an adaptive testing regime repeatedly constructs and tests configurations in order to determine, for each interaction of interest, whether it is faulty or not. In order to perform such testing in a loosely coupled distributed environment such as the cloud, it is imperative that testing results can be combined from many different servers. The TA defines rules to permit results to be combined, and to identify the faulty interactions. Using the TA, configurations can be tested concurrently on different servers and in any order. The results, using the TA, remain the same.

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“…The use of orthogonal arrays in statistically designed experiments are discussed Hedayat et al (1999).…”

Section: Combinatorial Designsmentioning

confidence: 99%

Test Algebra for Concurrent Combinatorial Testing

Tsai

2017

Combinatorial Testing in Cloud Computing

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“…In designing a fractional factorial experiment care must be given so that all factors have an undeviating weight on other factors, at all levels that the may take, and orthogonal arrays [6] [7] [8] [9] are used to that effect. In these arrays, each factor is equally influenced by the effects of the factors under study.…”

Section: Designing Experimentsmentioning

confidence: 99%

Designing experiments to study welding processes: using the Taguchi method

Vairis¹,

Petousis²

2009

JESTR

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Identification of significant process parameters using experiments needs to be carefully formulated as it can be a resource demanding process. Using appropriate statistical techniques such as the Taguchi method of factorial design of experiments, the number of necessary experiments can be reduced and the statistical significance of parameters can be safely identified. In the case of linear friction welding it was found that the frequency of oscillation, power input and forging pressure are statistically insignificant for the range of friction pressures studied.Keywords: taguchi method, factorial design of experiments, friction welding. An experiment can be considered as a process seeking to answer one or more carefully formulated questions. It should have carefully described goals which will be used to choose the appropriate factors and their range, as well as the relevant procedure. The factors studied should not be covered by other variables, with the chosen experimental sequence removing the effects of the uncontrolled variables. Replication of the experiments will help to randomise the results taken, to limit bias from the experiments. While replication ensures a measure of precision, randomisation provides validity of the measure of precision. By using this technique, many evaluations are usually needed to get sufficient information which can be a time-consuming process. Journal of EngineeringThe term "design of experiments" was originated around 1920 by Ronald A. Fisher, a British scientist who studied and proposed a more systematic approach in order to maximize the knowledge gained from experimental data [1] nce then, design of experiments has become an important methodology that maximizes the knowledge gained from experimental data by using a smart positioning of points in the space. This methodology provides a strong tool to design and analyze experiments; it eliminates redundant observations and reduces the time and resources to make experiments.In general, we can say that a good distribution of points achieved through a DOE (design of experiments) technique will extract as much information as possible from a system, based on as few data points as possible. Ideally, a set of points made with an appropriate DOE should have a good distribution of input parameter configurations. This equates to having a low correlation between inputs. The DOE approach is important to determine the behavior of the objective function we are examining because it is able to identify which factors are more important. The choice of DOE depends mainly on the type of objectives and on the number of variables involved. Usually, only linear or quadratic relations are detected. However and fortunately, higher-order interactions are rarely important and for most purposes it is only necessary to evaluate the main effects of each variable. This can be done with just a fraction of the runs, using only a "high" and "low" setting for each factor and some center points when necessary.Therefore DOE statistical techniques are especia...

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“…[32] The properties of Hadamard matrices (especially the above mentioned 4k-conjecture) is an intensively studied topic in combinatorics, and its complexity is impressive given the simple definition. [11,17,27,28,29] In 1933, Raymond Paley proved the existence of two families of Hadamard matrices that are very different from Sylvester's 2 n -construction. Proof: See the original article [24], or any other standard text on combinatorial objects [11,22,29].…”

Section: Definition 1 (Hadamard Matrix In Combinatorics)mentioning

confidence: 99%

Quantum Algorithms for Weighing Matrices and Quadratic Residues

Dam

2002

Algorithmica

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In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is significantly lower than the classical one. It is pointed out that this scheme captures both Bernstein & Vazirani's inner-product protocol, as well as Grover's search algorithm.In the second part of the article we consider Paley's construction of Hadamard matrices, which relies on the properties of quadratic characters over finite fields. We design a query problem that uses the Legendre symbol χ (which indicates if an element of a finite field Fq is a quadratic residue or not). It is shown how for a shifted Legendre function fs(i) = χ(i + s), the unknown s ∈ Fq can be obtained exactly with only two quantum calls to fs. This is in sharp contrast with the observation that any classical, probabilistic procedure requires more than log q + log( 1−ε 2 ) queries to solve the same problem.

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Orthogonal Arrays

Cited by 991 publications

References 0 publications

Test Algebra for Concurrent Combinatorial Testing

Test Algebra for Concurrent Combinatorial Testing

Designing experiments to study welding processes: using the Taguchi method

Quantum Algorithms for Weighing Matrices and Quadratic Residues

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