Statistical Errors of Texture Entities Based on EBSD Orientation Measurements

2005 ◽  
Vol 495-497 ◽  
pp. 179-184 ◽  
Author(s):  
K.Gerald van den Boogaart
Keyword(s):  
Measurement Errors ◽  
Shear Plane ◽  
Confidence Limits ◽  
Standard Measurement ◽  
Spatially Correlated ◽  
Dependent Observations ◽  
Statistical Errors ◽  
General Statistical ◽  
Incomplete Sampling

The determination of an ODF, C-coefficients, property tensors and portions of texture components from EBSD orientation measurements is afflicted with statistical errors introduced by incomplete sampling of the grains. Since the measurements are highly spatially correlated and stochastically dependent, classical sampling theory does not apply. A general statistical method for error estimation in the presence of stochastically dependent observations has been developed and applied to the most important quantities of texture analysis. The method is based on the assumption of a finite range of dependence between different measurements and on the estimation of the covariance in the observed set of orientation. The methods allows the computation of standard measurement errors and confidence limits for the mentioned texture quantities. It can be used for an objective decision whether two textures are statistically equal or not, based on the comparison of estimated ODFs. Further we can decide statistically whether the ODF obeys certain types of symmetry (e.g. whether it is a girdle textures or whether it is symmetric about the shear plane observed in the field).

Molar Absorptivity Values for Aflatoxins and Justification for Their Use as Criteria of Purity of Analytical Standards

1970 ◽  
Vol 53 (1) ◽  
pp. 96-101 ◽  
Author(s):  
J V Rodricks ◽  
L Stoloff ◽  
W A Pons ◽  
J A Robertson ◽  
L A Goldblatt
Keyword(s):  
Thin Layer ◽  
Statistical Study ◽  
Molar Absorptivity ◽  
Confidence Limits ◽  
Components Of Variance ◽  
Significant Difference ◽  
Single Determination ◽  
Comparison Measurements ◽  
Analytical Standards

Abstract Measurements of molar absorptivities in methanol were carried out by two laboratories on samples of anatoxins Bi and Gi prepared and purified independently in four laboratories and on samples of aflatoxins B2 and G2 prepared and purified independently in three laboratories. Molar absorptivities of pure aflatoxins Bi, B2, G1, and G2 in benzene-acetonitrile (98 + 2) were determined at two laboratories. With the exception of aflatoxin G2, no significant difference between aflatoxin samples could be demonstrated. Molar absorptivity values and absorbance ratios for each aflatoxin, based on these data, are given. Statistical 95% confidence limits were established for a single determination of molar absorptivity. A statistical study was made of the components of variance which contribute to the accuracy of the determination of molar absorptivity. A comparison of the fluorescence intensities of spots of various aflatoxin preparations, developed on silica gel-coated thin layer plates, with the amount of aflatoxin in each spotting solution as determined by absorbance measurements, demonstrated the validity of using absorbance and fluorescence comparison measurements for aflatoxin quantitation.

scholarly journals Quantification of Fructans in Bioethanol Stillage Based On a Simplified Analytical Method

2021 ◽  
Author(s):  
Andreas Zimmermann ◽  
Martin Kaltschmitt
Keyword(s):  
Analytical Method ◽  
Measurement Errors ◽  
Process Development ◽  
Stationary Phases ◽  
New Approach ◽  
Sample Matrix ◽  
Sample Throughput ◽  
Complex Sample ◽  
Potential Substrate

Abstract Bioethanol stillage, the main by-product of industrial bioethanol production, is a potential substrate for fructans. However, the determination and quantification of fructans in such complex sample matrices is still a challenge for the corresponding analytics to be overcome in order to allow for the identification and utilisation of such unused fructan sources. Especially a possible utilisation or rather the corresponding process development requires appropriate analytics first. Thus, this paper aims to illuminate the basics of fructan quantification in stillage and the corresponding challenges particularly arising with widely used HPLC-RID systems. On this basis, a new approach for fructan quantification is presented based on such HPLC-RID systems allowing for a reliable and especially simple fructan determination in bioethanol stillage for comparably high sample throughput. The developed method performs fructan quantification by determination of fructose and glucose equivalents after a targeted acidic hydrolysis adapted to the respective sample matrix. By means of two different stationary phases, the problem of limited resolution in case of HPLC-RID is overcome and thus measurement errors are reduced. The approach towards the adapted analytical method can be transferred easily to comparable complex sample matrices.

Monte Carlo method for the reduction of measurement errors in the material parameter estimation with cavities

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ronny Peter ◽  
Luca Bifano ◽  
Gerhard Fischerauer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Measurement Errors ◽  
Input Data ◽  
Material Parameter ◽  
Cavity Resonator ◽  
Calculation Algorithm ◽  
The Monte Carlo Method ◽  
Electromagnetic Resonances

Abstract The quantitative determination of material parameter distributions in resonant cavities is a relatively new method for the real-time monitoring of chemical processes. For this purpose, electromagnetic resonances of the cavity resonator are used as input data for the reverse calculation (inversion). However, the reverse calculation algorithm is sensitive to disturbances of the input data, which produces measurement errors and tends to diverge, which leads to no measurement result at all. In this work a correction algorithm based on the Monte Carlo method is presented which ensures a convergent behavior of the reverse calculation algorithm.

scholarly journals High-resolution fiber-coupled interferometric point sensor for micro- and nano-metrology

2015 ◽  
Vol 82 (7-8) ◽  
Author(s):  
Markus Schake ◽  
Markus Schulz ◽  
Peter Lehmann
Keyword(s):  
High Resolution ◽  
Measurement Errors ◽  
Surface Profile ◽  
Optical Measurements ◽  
High Demand ◽  
Force Microscopy ◽  
Atomic Force ◽  
Measurement Object ◽  
Contact Free

AbstractThe determination of surface roughness is a common challenge in industrial quality assurance. Because tactile techniques like the stylus method or atomic force microscopy run the risk of damaging the measurement object there is a high demand for contact-free optical measurements. In this contribution we demonstrate the feasibility of a high resolution fiber-coupled interferometric point sensor with periodical path length modulation to determine the surface profile of rough surfaces. Measurements on two specimens characterized by different roughness parameters are presented and corrections for common measurement errors, due to phase ambiguity are discussed.

scholarly journals The accuracy of FOM instrument used in on-line pig carcass classification in the Czech Republic

2008 ◽  
Vol 52 (No. 6) ◽  
pp. 149-158 ◽  
Author(s):  
M. Šprysl ◽  
J. Čítek ◽  
R. Stupka ◽  
L. Vališ ◽  
M. Vítek
Keyword(s):  
Czech Republic ◽  
Measurement Errors ◽  
Muscle Thickness ◽  
The Czech Republic ◽  
High Agreement ◽  
Lean Meat ◽  
Depth Measurement ◽  
Operator Error ◽  
On Line

The objective of this study was to document the accuracy of the classification equipment used in the Czech Republic with respect to measurement errors in lean meat percentage prediction such as point of measurement error, equipment error as well as operator error. To this end, a total of 720 pigs were measured in one abattoir. One can say from the results that the correlations between correct and surrogate measurements of fat depth are high (0.95&minus;0.98), for muscle thickness they are lower ranging from 0.49 to 0.88, and for lean meat percentage they are in the range of 0.85&minus;0.95. The lowest correlation (0.49) was calculated for muscle depth measurement between the 2nd and 3rd last rib when the place of measurement was moved 1 cm in the caudal direction, which influenced the level of the FOM correlation. It was further demonstrated that for the second insertion the differences in lean meat percentage prediction ranged from &minus;6.07% to +9.29%. It was also demonstrated that various instruments provided identical measurements of fat depth (<i>r</i> = 0.57&minus;0.97), while for muscle depth the performance was worse (<i>r</i> = 0.38–0.78), which caused a fluctuation in the prediction of lean meat percentage with differences ranging from &minus;2.56% to +2.81%. It can also be concluded that a high agreement between operators was demonstrated for the determination of lean meat percentage (<i>r</i> = 0.71&minus;0.80).

Collaborative Study of the Ion-Pair Column Partition Method for the Determination of Phenylephrine.HC1 in Drug Formulations

1970 ◽  
Vol 53 (1) ◽  
pp. 120-122
Author(s):  
Michel Margosis
Keyword(s):  
Collaborative Study ◽  
Colorimetric Method ◽  
Ion Pair ◽  
Confidence Limits ◽  
Drug Formulations ◽  
Three Solutions ◽  
The Mean ◽  
Partition Method ◽  
Collaborative Evaluation

Abstract Three solutions containing varying amounts of phenylephrine.HC1 were subjected to a collaborative evaluation of the ion-pair column partition method of Levine and Doyle. Results submitted by 20 collaborators were evaluated statistically. Recoveries averaged 99.0, 100.8, and 103.5% with 95% confidence limits of the mean of ±0.71, ±0.53, and ±0.85%, respectively. The method is recommended for adoption as official first action. The colorimetric method approved last year is recommended for adoption as official final action.

The determination of layer charge by curve-fitting of Lorentz- and polarization-corrected X-ray diagrams

Clay Minerals ◽  
1986 ◽  
Vol 21 (2) ◽  
pp. 183-190 ◽  
Author(s):  
H. Stanjek ◽  
R. Friedrich
Keyword(s):  
Charge Distribution ◽  
Curve Fitting ◽  
Clay Fraction ◽  
Layer Charge ◽  
Confidence Limits ◽  
High Charge ◽  
X Ray ◽  
Symmetrical Distribution

AbstractThe clay fraction from the B horizon of a Psammentic Hapludalf containing vermiculite and smectite was treated with n-alkylammonium chloride ranging from nc = 6 to nc = 16. X-ray data were obtained by step-scanning, stored in a computer, corrected with the Lorentz and polarization factors and then fitted with a deconvolution programme. The layer charge was determined from the uncorrected, the corrected and the fitted diagrams, respectively. The evaluated confidence limits of ξ decreased in the same order revealing the vermiculite to be a high-charge type. The computed charge distribution of the smectite changed from an unlikely bimodal to a nearly symmetrical distribution.

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