Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Joint X̄ and R charts with variable parameters

Recent studies have shown that the X̄chart with variable parameters (Vp X̄ chart) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both, X̄ and R charts. Basically, the X̄ and R values establish if the control should or should not be relaxed. When the X̄ and R values fall in the central region the control is relaxed because one will wait more to take the next sample and/or the next sample will be smaller than usual. When the X̄ or R values fall in the warning region the control is tightened because one will wait less to take the next sample and the next sample will be larger than usual. The action limits are also made variable. This paper proposes to draw the action limits (for both charts) wider than usual, when the control is relaxed and narrower than usual when the control is tightened. The Vp feature improves the joint X̄ and R control chart performance in terms of the speed with which the process mean and/or variance shifts are detected. © 1998 IIE.

Study on period search methods of variable stars: Application to ASAS and CRTS databases

Study on variable stars is an important topic of modern astrophysics. After the invention of powerful telescopes and high resolving powered CCD’s, the variable star data is accumulating in the order of peta-bytes. The huge amount of data need lot of automated methods as well as human experts. This thesis is devoted to the data analysis on variable star’s astronomical time series data and hence belong to the inter-disciplinary topic, Astrostatistics. For an observer on earth, stars that have a change in apparent brightness over time are called variable stars. The variation in brightness may be regular (periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and are caused by various reasons. In some cases, the variation is due to some internal thermo-nuclear processes, which are generally known as intrinsic vari- ables and in some other cases, it is due to some external processes, like eclipse or rotation, which are known as extrinsic variables. Intrinsic variables can be further grouped into pulsating variables, eruptive variables and flare stars. Extrinsic variables are grouped into eclipsing binary stars and chromospheri- cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae, supernovae, etc., which rarely occurs and are not periodic phenomena. Most of the other variations are periodic in nature. Variable stars can be observed through many ways such as photometry, spectrophotometry and spectroscopy. The sequence of photometric observa- xiv tions on variable stars produces time series data, which contains time, magni- tude and error. The plot between variable star’s apparent magnitude and time are known as light curve. If the time series data is folded on a period, the plot between apparent magnitude and phase is known as phased light curve. The unique shape of phased light curve is a characteristic of each type of variable star. One way to identify the type of variable star and to classify them is by visually looking at the phased light curve by an expert. For last several years, automated algorithms are used to classify a group of variable stars, with the help of computers. Research on variable stars can be divided into different stages like observa- tion, data reduction, data analysis, modeling and classification. The modeling on variable stars helps to determine the short-term and long-term behaviour and to construct theoretical models (for eg:- Wilson-Devinney model for eclips- ing binaries) and to derive stellar properties like mass, radius, luminosity, tem- perature, internal and external structure, chemical composition and evolution. The classification requires the determination of the basic parameters like pe- riod, amplitude and phase and also some other derived parameters. Out of these, period is the most important parameter since the wrong periods can lead to sparse light curves and misleading information. Time series analysis is a method of applying mathematical and statistical tests to data, to quantify the variation, understand the nature of time-varying phenomena, to gain physical understanding of the system and to predict future behavior of the system. Astronomical time series usually suffer from unevenly spaced time instants, varying error conditions and possibility of big gaps. This is due to daily varying daylight and the weather conditions for ground based observations and observations from space may suffer from the impact of cosmic ray particles. Many large scale astronomical surveys such as MACHO, OGLE, EROS, xv ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke- pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even though their primary intention is not variable star observation. Center for Astrostatistics, Pennsylvania State University is established to help the astro- nomical community with the aid of statistical tools for harvesting and analysing archival data. Most of these surveys releases the data to the public for further analysis. There exist many period search algorithms through astronomical time se- ries analysis, which can be classified into parametric (assume some underlying distribution for data) and non-parametric (do not assume any statistical model like Gaussian etc.,) methods. Many of the parametric methods are based on variations of discrete Fourier transforms like Generalised Lomb-Scargle peri- odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi- sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994) etc. Even though most of the methods can be brought under automation, any of the method stated above could not fully recover the true periods. The wrong detection of period can be due to several reasons such as power leakage to other frequencies which is due to finite total interval, finite sampling interval and finite amount of data. Another problem is aliasing, which is due to the influence of regular sampling. Also spurious periods appear due to long gaps and power flow to harmonic frequencies is an inherent problem of Fourier methods. Hence obtaining the exact period of variable star from it’s time series data is still a difficult problem, in case of huge databases, when subjected to automation. As Matthew Templeton, AAVSO, states “Variable star data analysis is not always straightforward; large-scale, automated analysis design is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of xvi huge amount of data in these databases is quite challenging, even when looking at seemingly small issues such as period determination and classification”. It will be beneficial for the variable star astronomical community, if basic parameters, such as period, amplitude and phase are obtained more accurately, when huge time series databases are subjected to automation. In the present thesis work, the theories of four popular period search methods are studied, the strength and weakness of these methods are evaluated by applying it on two survey databases and finally a modified form of cubic spline method is intro- duced to confirm the exact period of variable star. For the classification of new variable stars discovered and entering them in the “General Catalogue of Vari- able Stars” or other databases like “Variable Star Index“, the characteristics of the variability has to be quantified in term of variable star parameters.

Gráficos de controle de EWMA e de X-barra para monitoramento de processos autocorrelacionados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Joint conomic design of x̄ and R charts under Weibull shock models

This paper deals with the joint economic design of x̄ and R charts when the occurrence times of assignable causes follow Weibull distributions with increasing failure rates. The variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as tool wear-out, overheating, or vibration). One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimum design parameters. Finally, a sensitivity analysis of the model is conducted, and the cost savings associated with the use of non-uniform sampling intervals instead of constant sampling intervals are evaluated.

Preliminary results concerning the VSS X- chart with unknow in-control parameters

The VSS X- chart is known to perform better than the traditional X- control chart in detecting small to moderate mean shifts in the process. Many researchers have used this chart in order to detect a process mean shift under the assumption of known parameters. However, in practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS X- control chart when the process parameters are estimated and we compare them in the case where the process parameters are assumed known. We draw the conclusion that these performances are quite different when the shift and the number of samples used during the phase I are small. ©2010 IEEE.

Planejamento econômico de gráficos de controle X para monitoramento de processos autocorrelacionados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gráficos de controle de X para monitoramento de processos autocorrelacionados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Nature of the X(3872) from QCD

We have studied some possible four-quark and molecule configurations of the X(3872) using double ratios of sum rules, which are more accurate than the usual simple ratios often used in the literature to obtain hadron masses. We found that the different structures ((3) over bar - (3) over bar and (6) over bar - 6 tetraquarks and D - D(*) molecule) lead to the same prediction for the mass (within the accuracy of the method), indicating that the alone prediction of the X mass may not be sufficient to reveal its nature. In doing these analyses, we also find that (within our approximation) the use of the (MS) over bar running (m) over bar (c)(m(c)(2)), rather than the on-shell mass, is more appropriate to obtain the J/psi and X meson masses. Using vertex sum rules to roughly estimate the X(3872) hadronic and radiative widths, we found that the available experimental data does not exclude a lambda - J/psi-like molecule current.

Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD sum rules

We use QCD sum rules (QCDSR) to calculate the width of the radiative decay of the meson X(3872), assumed to be a mixture between charmonium and exotic molecular [c (q) over bar][q (c) over bar] states with J(PC) = 1(++). We find that in a small range for the values of the mixing angle, 5 degrees <= theta <= 13 degrees, we get the branching ratio Gamma(X -> J/psi gamma)/Gamma(X -> J/psi pi(+)pi(-)) = 0.19 +/- 0.13, which is in agreement, with the experimental value. This result is compatible with the analysis of the mass and decay width of the mode J/psi(n pi) performed in the same approach.

QCD sum rules for the X(3872) as a mixed molecule-charmonium state

We use QCD sum rules to test the nature of the meson X(3872), assumed to be a mixture between charmonium and exotic molecular [c (q) over bar][q (c) over bar] states with J(PC) = 1(++). We find that there is only a small range for the values of the mixing angle theta that can provide simultaneously good agreement with the experimental value of the mass and the decay width, and this range is 5(0) <= theta <= 3(0). In this range we get m(X) = (3.77 +/- 0.18) GeV and Gamma(X -> J/psi pi(+)pi(-)) = (9.3 +/- 6.9) MeV, which are compatible, within the errors, with the experimental values. We, therefore, conclude that the X(3872) is approximately 97% a charmonium state with 3% admixture of similar to 88% D(0)D*(0) molecule and similar to 12% D(+)D*(-) molecule.

SU(5) x SU(5) unification revisited

The idea of grand unification in a minimal supersymmetric SU(5) x SU(5) framework is revisited. It is shown that the unification of gauge couplings into a unique coupling constant can be achieved at a high-energy scale compatible with proton decay constraints. This requires the addition of minimal particle content at intermediate energy scales. In particular, the introduction of the SU(2)(L) triplets belonging to the (15, 1)+((15) over bar, 1) representations, as well as of the scalar triplet Sigma(3) and octet Sigma(8) in the (24, 1) representation, turns out to be crucial for unification. The masses of these intermediate particles can vary over a wide range, and even lie in the TeV region. In contrast, the exotic vector-like fermions must be heavy enough and have masses above 10(10) GeV. We also show that, if the SU(5) x SU(5) theory is embedded into a heterotic string scenario, it is not possible to achieve gauge coupling unification with gravity at the perturbative string scale.

Sampling strategies for tropical forest nutrient cycling studies: a case study in São Paulo, Brazil

The precise sampling of soil, biological or micro climatic attributes in tropical forests, which are characterized by a high diversity of species and complex spatial variability, is a difficult task. We found few basic studies to guide sampling procedures. The objective of this study was to define a sampling strategy and data analysis for some parameters frequently used in nutrient cycling studies, i. e., litter amount, total nutrient amounts in litter and its composition (Ca, Mg, Κ, Ν and P), and soil attributes at three depths (organic matter, Ρ content, cation exchange capacity and base saturation). A natural remnant forest in the West of São Paulo State (Brazil) was selected as study area and samples were collected in July, 1989. The total amount of litter and its total nutrient amounts had a high spatial independent variance. Conversely, the variance of litter composition was lower and the spatial dependency was peculiar to each nutrient. The sampling strategy for the estimation of litter amounts and the amount of nutrient in litter should be different than the sampling strategy for nutrient composition. For the estimation of litter amounts and the amount of nutrients in litter (related to quantity) a large number of randomly distributed determinations are needed. Otherwise, for the estimation of litter nutrient composition (related to quality) a smaller amount of spatially located samples should be analyzed. The determination of sampling for soil attributes differed according to the depth. Overall, surface samples (0-5 cm) showed high short distance spatial dependent variance, whereas, subsurface samples exhibited spatial dependency in longer distances. Short transects with sampling interval of 5-10 m are recommended for surface sampling. Subsurface samples must also be spatially located, but with transects or grids with longer distances between sampling points over the entire area. Composite soil samples would not provide a complete understanding of the relation between soil properties and surface dynamic processes or landscape aspects. Precise distribution of Ρ was difficult to estimate.

Anion-directed synthesis of metal-organic frameworks based on 2-picolinate Cu(II) complexes: a ferromagnetic alternating chain and two unprecedented ferromagnetic fish backbone chains

Three new polynuclear copper(II) complexes of 2-picolinic acid (Hpic), {[Cu-2(pic)(3)(H2O)]ClO4}(n) (1), {[Cu-2(pic)(3)(H2O)]BF4}(n) (2), and [Cu-2(pic)3(H2O)(2)(NO3)](n) (3), have been synthesized by reaction of the "metalloligand" [Cu-(pic)(2)] with the corresponding copper(II) salts. The compounds are characterized by single-crystal X-ray diffraction analyses and variable-temperature magnetic measurements. Compounds 1 and 2 are isomorphous and crystallize in the triclinic system with space group P (1) over bar, while 3 crystallizes in the monoclinic system with space group P2(1)/n. The structural analyses reveal that complexes 1 and 2 are constructed by "fish backbone" chains through syn-anti (equatorial-equatorial) carboxylate bridges, which are linked to one another by syn-anti (equatorial-axial) carboxylate bridges, giving rise to a rectangular grid-like two-dimensional net. Complex 3 is formed by alternating chains of syn-anti carboxylate-bridged copper(II) atoms, which are linked together by strong H bonds involving coordinated nitrate ions and water molecules and uncoordinated oxygen atoms from carboxylate groups. The different coordination ability of the anions along with their involvement in the H-bonding network seems to be responsible for the difference in the final polymeric structures. Variable-temperature (2-300 K) magnetic susceptibility measurement shows the presence of weak ferromagnetic coupling for all three complexes that have been fitted with a fish backbone model developed for 1 and 2 (J = 1.74 and 0.99 cm(-1); J' = 0.19 and 0.25 cm(-1), respectively) and an alternating chain model for 3 (J = 1.19 cm(-1) and J' = 1.19 cm(-1)).

Syntheses, structural analyses, and magneto-structural correlations of three polymeric Fe(II) complexes with azide ligand

Three new metal-organic polymeric complexes, [Fe(N-3)(2)(bPP)(2)] (1), [Fe(N-3)(2)(bpe)] (2), and [Fe(N-3)(2)(phen)] (3) [bpp = (1,3-bis(4-pyridyl)-propane), bpe = (1,2-bis(4-pyridyl)-ethane), phen = 1,10-phenanthroline], have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature magnetic measurements in the range 300-2 K. Complexes 1 and 2 crystallize in the monoclinic system, space group C2/c, with the following cell parameters: a = 19.355(4) Angstrom, b = 7.076(2) Angstrom, c = 22.549(4) Angstrom, beta = 119.50(3)degrees, Z = 4, and a = 10.007(14) Angstrom, b = 13.789(18) Angstrom, c = 10.377(14) Angstrom, beta = 103.50(1)degrees, Z = 4, respectively. Complex 3 crystallizes in the triclinic system, space group P (1) over bar, with a = 7.155(12) Angstrom, b = 10.066(14) Angstrom, c = 10.508(14) Angstrom, alpha = 109.57(1)degrees, beta = 104.57(1)degrees, gamma = 105.10(1)degrees, and Z = 2. All coordination polymers exhibit octahedral Fe(II) nodes. The structural determination of 1 reveals a parallel interpenetrated structure of 2D layers of (4,4) topology, formed by Fe(II) nodes linked through bpp ligands, while mono-coordinated azide anions are pendant from the corrugated sheet. Complex 2 has a 2D arrangement constructed through 1D double end-to-end azide bridged iron(11) chains interconnected through bpe ligands. Complex 3 shows a polymeric arrangement where the metal ions are interlinked through pairs of end-on and end-to-end azide ligands exhibiting a zigzag arrangement of metals (Fe-Fe-Fe angle of 111.18degrees) and an intermetallic separation of 3.347 Angstrom (through the EO azide) and of 5.229 Angstrom (EE azide). Variable-temperature magnetic susceptibility data suggest that there is no magnetic interaction between the metal centers in 1, whereas in 2 there is an antiferromagnetic interaction through the end-to-end azide bridge. Complex 3 shows ferro- as well as anti-ferromagnetic interactions between the metal centers generated through the alternating end-on and end-to-end azide bridges. Complex I has been modeled using the D parameter (considering distorted octahedral Fe(II) geometry and with any possible J value equal to zero) and complex 2 has been modeled as a one-dimensional system with classical and/or quantum spin where we have used two possible full diagonalization processes: without and with the D parameter, considering the important distortions of the Fe(II) ions. For complex 3, the alternating coupling model impedes a mathematical solution for the modeling as classical spins. With quantum spin, the modeling has been made as in 2.