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Orthogonal design

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Orthogonal design is a statistical methodology used in experimental design that ensures the independence of factors by arranging them in a way that their effects can be estimated without confounding. This approach facilitates the analysis of variance and enhances the efficiency of experiments by minimizing the number of runs needed to obtain reliable results.
lightbulbAbout this topic
Orthogonal design is a statistical methodology used in experimental design that ensures the independence of factors by arranging them in a way that their effects can be estimated without confounding. This approach facilitates the analysis of variance and enhances the efficiency of experiments by minimizing the number of runs needed to obtain reliable results.

Key research themes

1. How can projection uniformity and discrepancy measures optimize orthogonal and extended two-level experimental designs?

This theme investigates augmentation strategies of orthogonal and nearly orthogonal two-level factorial designs through projection discrepancy and uniformity measures, notably the centered L2-discrepancy. These approaches are critical to ensure high-quality experimental runs, especially when designs are extended with additional runs, while maintaining desirable statistical properties in lower-dimensional factor projections.

Key finding: This paper develops lower bounds on projection discrepancy for extended U-type and nearly U-type designs obtained by augmenting optimally few runs to an initial design, based on the centered L2-discrepancy. It introduces a... Read more
Key finding: By employing a greedy coffee-house algorithm restricted to fractional factorial candidate sets, this work constructs nested two-level designs with guaranteed 50% packing and covering efficiencies even in high dimensions... Read more
Key finding: This study introduces fractional word length concepts and extended word length patterns using indicator functions to analyze and select optimal foldover plans for non-regular two-level orthogonal designs. It proves that a... Read more

2. How can orthogonal arrays and product constructions facilitate efficient mixture and factorial designs in constrained, high-dimensional experimental settings?

This research area focuses on constructing efficient mixture and factorial designs using orthogonal arrays generated via difference schemes or product methods, addressing constraints inherent in mixture experiments and structural design complexity. These methods reduce experimental runs without sacrificing coverage or design strength, well-suited for high-dimensional or constrained design spaces common in practical applications.

Key finding: The paper presents an algorithm (OABMD) that uses orthogonal arrays based on difference schemes to generate efficient mixture designs that respect component proportion constraints, transforming design points into the simplex... Read more
Key finding: This work advances combinatorial design theory by proposing novel product techniques for constructing mutually orthogonal graph squares (MOGS), a generalization of orthogonal Latin squares. It develops new large sets of... Read more
Key finding: Extending the construction of uniform designs from discrete lattice points to continuous domains, this study implements coordinate descent methods with a threshold accepting-based initialization to minimize centered... Read more

3. What theoretical and algorithmic innovations enable flexible and orthogonal response surface designs for second-order models in moderate to high dimensional settings?

This theme centers on constructing and generalizing classical response surface designs like Box-Behnken via cyclic generators and developing computational algorithms to generate orthogonally blocked and rotatable designs with improved properties. These advancements support efficient parameter estimation in second-order models while addressing design flexibility, blocking, and prediction variance characteristics in scenarios with 3 to 16 factors.

Key finding: Introducing cyclic BBDs (CBBDs), the paper provides an algorithm to generate Box-Behnken type three-level second-order designs with enhanced flexibility in radii and run allocation. The CBBDs improve over classical BBDs by... Read more

All papers in Orthogonal design

Antenna spacings, the angle spread and the Rice factor significantly affect the correlation of fading coefficients in a multi-antenna system. In this paper we study the effect of these parameters on the performance of different types of... more
Constructions of square, maximum rate complex orthogonal space-time block codes (CO STBCs) are well known, however codes constructed via the known methods include numerous zeros, which impede their practical implementation. By modifying... more
Skew-Hadamard matrices are of special interest due to their use, among others, in constructing orthogonal designs. In this paper, we give a survey on the existence and equivalence of skew-Hadamard matrices. In addition, we present some... more
In the present study, laser cutting of cotton fiber composite laminate is experimented using a modified DVD writer drive. A 250 mW diode laser is initially extracted from a DVD writer drive, and then regulated by a custom-made laser... more
The allocation of combinations of attribute levels to choice situations in stated choice (SC) experiments can have a significant influence upon the resulting study outputs once data is collected. Recently, a small but growing stream of... more
Symmetric designs are used to construct binary extremal self-dual codes and Hadamard matrices and weighing matrices are used to construct extremal ternary self-dual codes. In this paper, we consider orthogonal designs and related matrices... more
A single-carrier quasi-orthogonal distributed block space-time coding scheme for a wireless collaborative network with one relaying stage composed of four nodes is proposed. This block quasi-orthogonal design can attain full diversity and... more
This paper describes the dynamic investigation of a 3-component and a 6-component force- moment sensors using the facilities in the PTB (Physikalisch-Technische Bundesanstalt) in Germany. The 3-component sensor has the transverse forces... more
We show that the classical algebra of quaternions is a commutative Z 2 ×Z 2 ×Z 2 -graded algebra. A similar interpretation of the algebra of octonions is impossible. This note is our "private investigation" of what really happened on the... more
The success of applying generalized complex orthogonal designs as space-time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space-timepolarization block codes. This paper... more
Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditional analysis focuses on main... more
Apple juice inoculated with Staphylococcus aureus (SST 2.4) was processed by a hurdle sequence including ultraviolet irradiation (UV; 30 min, 20 °C), pre-heating and pulsed electric fields (PEF). Four different levels of pre-heating... more
Apple juice inoculated with Staphylococcus aureus (SST 2.4) was processed by a hurdle sequence including ultraviolet irradiation (UV; 30 min, 20 °C), pre-heating and pulsed electric fields (PEF). Four different levels of pre-heating... more
In this paper, the prediction of a soot model [J. Appel, H. Bockhorn, M. Frenklach, Combust. Flame 121 (2000) 122-136] is compared to a recently published set of highly detailed soot particle size distributions [B. Zhao, Z. Yang, Z. Li,... more
Common ratio-based approaches for analyzing gene expression microarray data do not provide a framework for handling replication, although replication is clearly desirable for these noisy data. In contrast, replication fits naturally into... more
This article describes and illustrates how to produce modular .NET software solutions by the use of Decorator design pattern and AspectOriented Programming (AOP) tool PostSharp. We applied both techniques for modularizing crosscutting... more
Ultraviolet-visible (UV-VIS) and near-infrared (NIR) spectroscopy coupled to artificial neural networks (ANNs) was used as a nondestructive technique to quantify ethanol, glucose, glycerol, tartaric acid, malic acid, acetic acid and... more
The paper examines multi-modulation schemes (MMSs) to increase the rate of our two new Complex Orthogonal Designs (CODs) proposed for eight transmit antennas, namely C 1 and C 2 , corresponding to the Amicable Orthogonal Designs (AODs)
Wireless communication system is rapidly enhancing using various techniques by many researcher & to meet the requirement of accurate and fast data communication in fading environment. The MIMO technique plays an important role in this... more
In this paper, we consider efficient blind decoder design for orthogonal space-time block codes (OSTBCs). A general decision rule for blind OSTBC decoding is derived assuming a quasi-static flat multiple-input multiple-output (MIMO)... more
A Hadamard matrix of side n is an n × n matrix with every entry either 1 or −1, which satisfies HH T = nI. Two Hadamard matrices are called equivalent if one can be obtained from the other by some sequence of row and column permutations... more
Many construction methods for (nearly) uniform designs have been proposed under the centered L 2-discrepancy, and most of them are only suitable for constructing designs with small size. This paper proposes a new method, called mixture... more
Experimental designs are very important in chemometrics, since chemistry, until now, is still essentially a field of science strongly dependent on chemical experiments. So, for a long time, chemists have been trying to use the techniques... more
The common methods used by chemists to obtain the estimates of the kinetic rate constants are deterministic ones. The Ž. statistical methods, such as D-optimum design DOD , can offer a better way to deal with this problem. But the kinetic... more
The common methods used by chemists to obtain the estimates of the kinetic rate constants are deterministic ones. The Ž. statistical methods, such as D-optimum design DOD , can offer a better way to deal with this problem. But the kinetic... more
Experimental designs are very important in chemometrics, since chemistry, until now, is still essentially a field of science strongly dependent on chemical experiments. So, for a long time, chemists have been trying to use the techniques... more
Conjoint analysis studies involving many attributes and attribute levels often occur in practice. Because such studies can cause respondent fatigue and lack of cooperation, it is important to design data collection tasks that reduce those... more
The wrist force/torque sensors has been increasinly used in variety of robotic fields which the most important one is human-computer interactions. Applied features of the force/torque sensors have motivated scientists to investigate novel... more
Plastic materials are used in automobile, electrical and electronic applications, agricultural utilization, household and furniture products, and medical equipments. Among various plastic manufacturing process, injection molding is one of... more
Plastic materials are used in automobile, electrical and electronic applications, agricultural utilization, household and furniture products, and medical equipments. Among various plastic manufacturing process, injection molding is one of... more
Data shuffling is one of the fundamental building blocks for distributed learning algorithms, that increases the statistical gain for each step of the learning process. In each iteration, different shuffled data points are assigned by a... more
Conjoint Analysis (CA) is a very popular class of methods for measuring consumer preferences, both in research and practice. However, since a couple of years, the Analytic Hierarchy Process (AHP) is being discussed in this field as well.... more
In this paper, we propose a generalized code index modulation (CIM) technique for direct sequence-spread spectrum (DS-SS) communication. In particular, at the transmitter, the bit stream is divided into blocks in which each block is... more
Page 1. Uniform Design: Theory and Application Kai-Tai FANG ... h(xl,...,x,) can be expressed as : iki(2l : s), optimal design theory can provide the most efficient de-sign. If Model (1.3) cannot be expressed as (1.2), an ap-proximately... more
Theory development is a very complex process that requires creativity and highly specialized analytical skills. This article presents a new algorithm, based on causal mapping, for assisting in the creation of qualitative theories. This... more
Space-time block codes based on orthogonal designs (ODs) are used for wireless communications with multiple transmit antennas which can achieve full transmit diversity along single-symbol maximum-likelihood decodability. Single-Symbol... more
The purpose of this paper is to model the desires, expectations and priorities of the inhabitants of Istanbul, a city with a population of about 15 million, from a multidimensional perspective. In this way, effective allocation of the... more
The performance of space-time block codes for transmission over Quasi-static Rayleigh flat fading channels using multiple transmit antennas is considered. Data is prearranged using a space-time block code, which is split in to parallel... more
The present paper discusses the selection of process parameters for obtaining optimal magnetic properties in strontium ferrite sintered magnets. The magnetic properties have several quality characteristics, such as remanence, coercivity... more
From time immemorial, human beings have used pigments made from vegetables, fruits, superior plants, animal tissues and cereals. One of the greatest sources of pigments is the bacterium that, with the use of the modern technology, has... more
The consumer market has changed drastically in recent times. Consumers are becoming more demanding, and many companies are competing to be market leaders. Therefore, companies must reduce rejects and minimize their operating costs. One... more
Orthogonal designs and their special cases such as weighing matrices and Hadamard matrices have many applications in combinatorics, statistics, and coding theory as well as in signal processing. In this paper we generalize the definition... more
The present work deals with surface roughness characteristics of electroless Ni-P coatings. The optimised process parameters have been determined based on L27 Taguchi Orthogonal array. Bath concentration of nickel sulphate, concentration... more
It is shown that the complement of a universally optimal design derivable from a triangular design is again universally optimal in a class of connected designs. Furthermore, some series of universally optimal designs for diallel cross... more
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