pinecone/core-2020-05-10-deduplication huggingface dataset:
Synthetic and runs-rules charts combined with an X chart : theoretical discussion

A synthetic and a runs-rules X charts that are combined with a basic X chart are called a Synthetic-X and an improved
runs-rules X charts, respectively. This paper gives the zero-state and steady-state theoretical results of the Synthetic-X
and improved runs-rules X monitoring schemes. The Synthetic-X and improved runs-rules schemes can each be classified
into four different categories, that is, (i) non-side-sensitive, (ii) standard side-sensitive, (iii) revised side-sensitive, and (iv)
modified side-sensitive. In this paper, we first give the operation and, secondly, the general form of the transition
probability matrices for each of the categories. Thirdly, in steady-state, we show that for each of the categories, the three
methods that are widely used in the literature to compute the initial probability vectors result in different probability
expressions (or values). Fourthly, we derive the closed-form expressions of the average run-length (ARL) vectors for each
of the categories, so that, by multiplying each of these ARL vectors with the zero-state and steady-state initial probability
vectors, yield the zero-state and steady-state ARL expressions. Finally, we formulate the closed-form expressions of the
extra quadratic loss function for each of the categories.Part of
this work was supported by the South African Researchers Chair Initiative (SARChI) Chair at the University of Pretoria. Sandile Shongwe’s
research was supported in part by the National Research Foundation and Department of Science and Technology’s Innovation Doctoral
scholarship (SFH14081591713, Grant number: 95208) as well as Department of Statistics’ STATOMET, and Marien Graham’s research was supported in part by the National Research Foundation (Thuthuka program: TTK14061168807, Grant number: 94102).http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-16382018-02-26hb2016Statistic
On cost-effective reuse of components in the design of complex reconfigurable systems

Design strategies that benefit from the reuse of system components can reduce costs whilst maintaining or increasing dependability—we use the term dependability to tie together reliability and availability. D3H2 (aDaptive Dependable Design for systems with Homogeneous and Heterogeneous redundancies) is a methodology that supports the design of complex systems with a focus on reconfiguration and component reuse. D3H2 systematises the identification of heterogeneous redundancies and optimises the design of fault detection and reconfiguration mechanisms, by enabling the analysis of design alternatives with respect to dependability and cost. In this paper, we extend D3H2 for application to repairable systems. The method is extended with analysis capabilities allowing dependability assessment of complex reconfigurable systems. Analysed scenarios include time-dependencies between failure events and the corresponding reconfiguration actions. We demonstrate how D3H2 can support decisions about fault detection and reconfiguration that seek to improve dependability whilst reducing costs via application to a realistic railway case study
Training for design of experiments using a catapult

Design of experiments (DOE) is a powerful approach for discovering a set of process (or design) variables which are most important to the process and then determine at what levels these variables must be kept to optimize the response (or quality characteristic) of interest. This paper presents two catapult experiments which can be easily taught to engineers and managers in organizations to train for design of experiments. The results of this experiment have been taken from a real live catapult experiment performed by a group of engineers in a company during the training program on DOE. The first experiment was conducted to separate out the key factors (or variables) from the trivial and the second experiment was carried out using the key factors to understand the nature of interactions among the key factors. The results of the experiment were analysed using simple but powerful graphical tools for rapid and easier understanding of the results to engineers with limited statistical competency
Evaluation of a maintenance strategy by the analysis of the rate of repair

The evaluation of maintenance strategies is a problem which has been widely tackled. However, it remains a topic worthy of consideration since the economic stakes peculiar to this activity are huge. The work presented in this paper deals with this problem under the point of view of data feedback. A statistical analysis is made from the examination of the forms of the failure rate distribution. The laws resulting from the implementation of a given maintenance strategy inform us about the relevance of the choices representative of this strategy. The construction of these laws from a raw time of repair is a global approach which tends to hide the induced phenomenon. A decomposition of the repair process into phases allows us to better identify the influence of the strategy parameters. The analysis of each elementary phase distribution is interesting since it givesinformation about the performance of the implemented maintenance strategy
Implementing evaluation of the measurement process in an automotive manufacturer: a case study

Reducing process variability is presently an area of much interest in manufacturing organizations. Programmes such as Six Sigma robustly link the financial performance of the organization to the degree of variability present in the processes and products of the organization. Data, and hence measurement processes, play an important part in driving such programmes and in making key manufacturing decisions. In many organizations, however, little thought is given to the quality of the data generated by such measurement processes. By using potentially flawed data in making fundamental manufacturing decisions, the quality of the decision-making process is undermined and, potentially, significant costs are incurred. Research in this area is sparse and has concentrated on the technicalities of the methodologies available to assess measurement process capability. Little work has been done on how to operationalize such activities to give maximum benefit. From the perspective of one automotive company, this paper briefly reviews the approaches presently available to assess the quality of data and develops a practical approach, which is based on an existing technical methodology and incorporates simple continuous improvement tools within a framework which facilitates appropriate improvement actions for each process assessed. A case study demonstrates the framework and shows it to be sound, generalizable and highly supportive of continuous improvement goals
Ordered samples control charts for ordinal variables

The paper presents a new method for statistical process control when ordinal variables are involved. This is the case of a quality characteristic evaluated by an ordinal scale. The method allows a statistical analysis without exploiting an arbitrary numerical conversion of scale levels and without using the traditional sample synthesis operators (sample mean and variance). It consists of a different approach based on the use of a new sample scale obtained by ordering the original variable sample space according to some specific ‘dominance criteria' fixed on the basis of the monitored process haracteristics. Samples are directly reported on the chart and no distributional shape is assumed for the population (universe) of evaluations. Finally, a practical application of the method in the health sector is provided
An application of Six Sigma to reduce waste

Six Sigma has been considered a powerful business strategy that employs a well-structured continuous improvement methodology to reduce process variability and drive out waste within the business processes using effective application of statistical tools and techniques. Although there is a wider acceptance of Six Sigma in many organizations today, there appears to be virtually no in-depth case study of Six Sigma in the existing literature. This involves how the Six Sigma methodology has been used, how Six Sigma tools and techniques have been applied and how the benefits have been generated. This paper presents a case study illustrating the effective use of Six Sigma to reduce waste in a coating process. It describes in detail how the project was selected and how the Six Sigma methodology was applied. It also shows how various tools and techniques within the Six Sigma methodology have been employed to achieve substantial financial benefits
Winning customer loyalty in an automotive company through Six Sigma: a case study

Six Sigma is a disciplined approach to improving product, process and service quality. Since its inception at Motorola in the mid 1980s Six Sigma has evolved significantly and continues to expand to improve process performance, enhance business profitability and increase customer satisfaction. This paper presents an extensive literature review based on the experiences of both academics and practitioners on Six Sigma, followed by the application of the Define, Measure, Analyse, Improve, Control (DMAIC) problem-solving methodology to identify the parameters causing casting defects and to control these parameters. The results of the study are based on the application of tools and techniques in the DMAIC methodology, i.e. Pareto Analysis, Measurement System Analysis, Regression Analysis and Design of Experiment. The results of the study show that the application of the Six Sigma methodology reduced casting defects and increased the process capability of the process from 0.49 to 1.28. The application of DMAIC has resulted in a significant financial impact (over U.S. $110 000 per annum) on the bottom-line of the company
A multivariate analysis on non-nucleoside HIV-1 reverse transcriptase inhibitors and resistance induced by mutation

This paper describes the use of multivariate statistical procedure PCA as a tool to explore the inhibitory activity of classes of NNRTIs against HIV-1 viruses (wild type and more frequent mutants, Y181C, V106A, K103N, L100I) and against RT enzyme. The analysis of correlations between biological activity and molecular descriptors or similarity indexes allowed a reliable classification of the fifty five derivatives considered in this study. The best results were obtained in the case of L100I and K103N mutants for which the higher number of assignments was found when the principal components derived from the descriptors were used. On this basis this statistical approach is proposed as a reliable method for the prediction of the activity of NNRTIs, for which the data against mutant strains have not been reported
Orthogonal Linear Combinations of Gaussian Type Orbitals

The set of Gaussian Type Orbitals g(n1,n2,n3) of order (n+1)(n+2)/2, of
common n=n1+n2+n3<=7, common center and exponential, is customized to define a
set of 2n+1 linear combinations t(n,m) (-n<=m<=n) such that each t(n,m) depends
on the azimuthal and polar angle of the spherical coordinate system like the
real or imaginary part of the associated Spherical Harmonic. (Results cover
both Hermite and Cartesian Gaussian Type Orbitals.) Overlap, kinetic energy and
Coulomb energy matrix elements are presented for generalized basis functions of
the type r^s*t(n,m) (s=0,2,4,...). In addition, normalization integrals int
|g(n1,n2,n3)|d^3r are calculated up to n=7 and normalization integrals int
|r^s*t(n,m)|d^3r up to n=5.Comment: 13 pages, no figures, REVTeX4. Corrected eqs. (23) and (C4
MIKA: a multigrid-based program package for electronic structure
  calculations

A general real-space multigrid algorithm MIKA (Multigrid Instead of the
K-spAce) for the self-consistent solution of the Kohn-Sham equations appearing
in the state-of-the-art electronic-structure calculations is described. The
most important part of the method is the multigrid solver for the Schr\"odinger
equation. Our choice is the Rayleigh quotient multigrid method (RQMG), which
applies directly to the minimization of the Rayleigh quotient on the finest
level. Very coarse correction grids can be used, because there is in principle
no need to represent the states on the coarse levels. The RQMG method is
generalized for the simultaneous solution of all the states of the system using
a penalty functional to keep the states orthogonal. Special care has been taken
to optimize the iterations towards the self-consistency and to run the code in
parallel computer architectures. The scheme has been implemented in multiple
geometries. We show examples from electronic structure calculations employing
nonlocal pseudopotentials and/or the jellium model. The RQMG solver is also
applied for the calculation of positron states in solids.Comment: To appear in a special issue of Int J. Quant. Chem. devoted to the
  conference proceedings of 9th International Conference on the Applications of
  the Density Functional Theory in Chemistry and Physic
Optical excitations of Si by time-dependent density-functional theory
  based on the exact-exchange Kohn-Sham band structure

We calculate the imaginary part of the frequency-dependent dielectric
function of bulk silicon by applying time-dependent density-functional theory
based on the exact-exchange (EXX) Kohn-Sham (KS) band structure and the
adiabatic local-density approximation (ALDA) kernel. The position of the E2
absorption peak calculated with the EXX band structure at the
independent-particle level is in excellent agreement with experiments, which
demonstrates the good quality of EXX `KS quasiparticles'. The excitonic E1 peak
that is missing at the independent-particle level remains absent if
two-particle interaction effects are taken into account within the
time-dependent LDA, demonstrating the incapability of the ALDA kernel to
describe excitonic effects.Comment: 6 pages, 2 figures; contribution to "DFT 2001", Sep. 10-14, San
  Lorenzo de El Escorial, Spain; to be published in Int. J. Quantum. Che
Theory of strongly correlated f and d-electron systems. I. Exact
  Hamiltonian, Hubbard-Anderson models and perturbation theory near atomic
  limit within non-orthogonal basis set

The theory of correlated electron systems is formulated in a form which
allows to use as a reference point an ab initio band structure theory (AIBST).
The theory is constructed in two steps. As a first step the total Hamiltonian
is transformed into a correlated form. In order to elucidate the microscopical
origin of the parameters of the periodical Hubbard-Anderson model (PHAM) the
terms of the full Hamiltonian which have the operator structure of PHAM are
separated. It is found that the matrix element of mixing interaction includes
ion-configuration and number-of-particles dependent contributions from the
Coulomb interaction. In a second step the diagram technique (DT) is developed
by means of generalization of the Baym-Kadanoff method for correlated systems.Comment: 40 pages, 6 figure
Control of Decoherence: Dynamical Decoupling versus Quantum Zeno Effect
  - a case study for trapped ions

The control of thermal decoherence via dynamical decoupling and via the
quantum Zeno effect (Zeno control) is investigated for a model of trapped ion,
where the dynamics of two low lying hyperfine states undergoes decoherence due
to the thermal interaction with an excited state. Dynamical decoupling is a
procedure that consists in periodically driving the excited state, while the
Zeno control consists in frequently measuring it. When the control frequency is
high enough, decoherence is shown to be suppressed. Otherwise, both controls
may accelerate decoherence.Comment: 24 pages, 8 figure
Two-step method for precise calculation of core properties in molecules

Precise calculations of core properties in heavy-atom systems which are
described by the operators heavily concentrated in atomic cores, like to
hyperfine structure and P,T-parity nonconservation effects, usually require
accounting for relativistic effects. Unfortunately, completely relativistic
treatment of molecules containing heavy elements is very consuming already at
the stages of calculation and transformation of two-electron integrals with a
basis set of four-component spinors.
  In turn, the relativistic effective core potential (RECP) calculations of
valence (spectroscopic, chemical etc.) properties of molecules are very popular
because the RECP method allows one to treat quite satisfactory the correlation
and relativistic effects for the valence electrons of a molecule and to reduce
significantly the computational efforts. The valence molecular spinors are
usually smoothed in atomic cores and, as a result, direct calculation of
electronic densities near heavy nuclei is impossible.
  In the paper, the methods of nonvariational and variational one-center
restoration of correct shapes of four-component spinors in atomic cores after a
two-component RECP calculation of a molecule are discussed. Their efficiency is
illustrated in correlation calculations of hyperfine structure and parity
nonconservation effects in heavy-atom molecules YbF, BaF, TlF, and PbO.Comment: 20 pages, 3 tables, lecture on the Fock school-conference
  (Novgorod-the-Great, Russia, April 2004
Construction of accurate Kohn-Sham potentials for the lowest states of
  the helium atom: Accurate test of the ionization-potential theorem

Accurate local Kohn-Sham potentials have been constructed for the ground
$1s^2 ^1S$ state and, in particular, for the lowest triplet $1s2s ^{3}S$ state
of the helium atom, using electron densities from many-body calculations and
the procedure of van Leeuwen and Baerends (Phys. Rev. A{\bf49}, 2138 (1994)).
The resulting Kohn-Sham orbitals reproduce the many-body densities very
accurately, and furthermore we have demonstrated that the negative of the
energy eigenvalue of the outermost electron orbital agrees with the
corresponding ionization energy with extreme accuracy. The procedure is also
applied to the Hartree-Fock density of the $1s2s ^{3}S$ state, and the
Kohn-Sham eigenvalue of the $2s$ orbital is found to agree very well with the
corresponding Hartree-Fock eigenvalue, which is the negative of the ionization
energy in this model due to Koopmans' theorem. The results for the $1s2s ^{3}S$
state clearly demonstrate that there is no conflict between the locality of the
Kohn-Sham potential and the exclusion principle, as claimed by Nesbet (Phys.
Rev. A{\bf58}, R12 (1998)).Comment: 10 pages, 7 figures and 2 table
On the Original Proof by Reductio ad Absurdum of the Hohenberg-Kohn
  Theorem for Many-Electron Coulomb Systems

It is shown that, for isolated many-electron Coulomb systems with Coulombic
external potentials, the usual reductio ad absurdum proof of the Hohenberg-Kohn
theorem is unsatisfactory since the to-be-refuted assumption made about the
one-electron densities and the assumption about the external potentials are not
compatible with the Kato cusp condition. The theorem is, however, provable by
more sophisticated means and it is shown here that the Kato cusp condition
actually leads to a satisfactory proof.Comment: 14 pages. Int. J. Quantum Chem. to appea
Energy lowering of current-carrying single-particle states in open-shell
  atoms due to an exchange-correlation vector potential

Current-density-functional theory is used to perturbatively calculate
single-particle energies of open-shell atoms prepared in a current-carrying
state. We focus on the highest occupied such energy, because its negative is,
in principle, the exact ionization energy. A variety of different density
functionals and calculational schemes are compared with each other and
experiment. When the atom is prepared in a current-carrying state, a
current-dependent exchange-correlation functional is found to slightly lower
the single-particle energy of the current-carrying orbital, as compared to a
calculation using standard (current independent) density functionals for the
same system. The current-dependent terms in the exchange-correlation functional
thus provide additional stabilization of the current-carrying state.Comment: 13 pages, accepted by Int. J. Quantum Che
Studies on some singular potentials in quantum mechanics

A simple methodology is suggested for the efficient calculation of certain
central potentials having singularities. The generalized pseudospectral method
used in this work facilitates {\em nonuniform} and optimal spatial
discretization. Applications have been made to calculate the energies,
densities and expectation values for two singular potentials of physical
interest, {\em viz.,} (i) the harmonic potential plus inverse quartic and
sextic perturbation and (ii) the Coulomb potential with a linear and quadratic
term for a broad range of parameters. The first 10 states belonging to a
maximum of $\ell=8$ and 5 for (i) and (ii) have been computed with good
accuracy and compared with the most accurate available literature data. The
calculated results are in excellent agreement, especially in the light of the
difficulties encountered in these potentials. Some new states are reported here
for the first time. This offers a general and efficient scheme for calculating
these and other similar potentials of physical and mathematical interest in
quantum mechanics accurately
Assessment of Various Density Functionals and Basis Sets for the
  Calculation of Molecular Anharmonic Force Fields

In a previous contribution (Mol. Phys. {\bf 103}, xxxx, 2005), we established
the suitability of density functional theory (DFT) for the calculation of
molecular anharmonic force fields. In the present work, we have assessed a wide
variety of basis sets and exchange-correlation functionals for harmonic and
fundamental frequencies, equilibrium and ground-state rotational constants, and
thermodynamic functions beyond the RRHO (rigid rotor-harmonic oscillator)
approximation. The fairly good performance of double-zeta plus polarization
basis sets for frequencies results from an error compensation between basis set
incompleteness and the intrinsic error of exchange-correlation functionals.
Triple-zeta plus polarization basis sets are recommended, with an additional
high-exponent $d$ function on second-row atoms. All conventional hybrid GGA
functionals perform about equally well: high-exchange hybrid GGA and meta-GGA
functionals designed for kinetics yield poor results, with the exception of of
the very recently developed BMK functional which takes a middle position along
with the HCTH/407 (second generation GGA) and TPSS (meta-GGA) functionals. MP2
performs similarly to these functionals but is inferior to hybrid GGAs such as
B3LYP and B97-1.Comment: Int. J. Quantum Chem., in press (special issue on vibrational
  spectroscopies
Symbolic Computation of Conservation Laws of Nonlinear Partial
  Differential Equations in Multi-dimensions

A direct method for the computation of polynomial conservation laws of
polynomial systems of nonlinear partial differential equations (PDEs) in
multi-dimensions is presented. The method avoids advanced
differential-geometric tools. Instead, it is solely based on calculus,
variational calculus, and linear algebra.
  Densities are constructed as linear combinations of scaling homogeneous terms
with undetermined coefficients. The variational derivative (Euler operator) is
used to compute the undetermined coefficients. The homotopy operator is used to
compute the fluxes.
  The method is illustrated with nonlinear PDEs describing wave phenomena in
fluid dynamics, plasma physics, and quantum physics. For PDEs with parameters,
the method determines the conditions on the parameters so that a sequence of
conserved densities might exist. The existence of a large number of
conservation laws is a predictor for complete integrability. The method is
algorithmic, applicable to a variety of PDEs, and can be implemented in
computer algebra systems such as Mathematica, Maple, and REDUCE.Comment: To appear in: Thematic Issue on ``Mathematical Methods and Symbolic
  Calculation in Chemistry and Chemical Biology'' of the International Journal
  of Quantum Chemistry. Eds.: Michael Barnett and Frank Harris (2006