scholarly journals Determination of the Uncertainties in S-Curve Logistic Fits

2022 ◽  
Author(s):  
THEODORE MODIS
Keyword(s):  
General Result ◽  
Confidence Level ◽  
Simulated Data ◽  
Historical Period ◽  
Confidence Levels ◽  
Minimization Technique ◽  
Data Points ◽  
S Curve ◽  
Better Than

Look-up tables and graphs are provided for determining the uncertainties during logistic fits, on the three parameters M, α and to describing an S-curve of the form: S(t) = M/(1+exp(-α(t-t0))).The uncertainties and the associated confidence levels are given as a function of the uncertainty on the data points and the length of the historical period. Correlations between these variables are also examined; they make “what-if” games possible even before doing the fit.The study is based on some 35,000 S-curve fits on simulated data covering a variety of conditions and carried out via a χ2 minimization technique. A rule-of-thumb general result is that, given at least half of the S-curve range and a precision of better than 10% on each historical point, the uncertainty on M will be less than 20% with 90% confidence level.

scholarly journals Comparison of several non-linear-regression methods for fitting the Michaelis-Menten equation

1985 ◽  
Vol 231 (1) ◽  
pp. 171-177 ◽  
Author(s):  
L Matyska ◽  
J Kovář
Keyword(s):  
Simulated Data ◽  
Confidence Regions ◽  
Parameter Estimates ◽  
Interval Parameter ◽  
Variance Matrix ◽  
Regression Methods ◽  
Parameter Estimations ◽  
Data Points ◽  
Relative Weighting

The known jackknife methods (i.e. standard jackknife, weighted jackknife, linear jackknife and weighted linear jackknife) for the determination of the parameters (as well as of their confidence regions) were tested and compared with the simple Marquardt's technique (comprising the calculation of confidence intervals from the variance-co-variance matrix). The simulated data corresponding to the Michaelis-Menten equation with defined structure and magnitude of error of the dependent variable were used for fitting. There were no essential differences between the results of both point and interval parameter estimations by the tested methods. Marquardt's procedure yielded slightly better results than the jackknives for five scattered data points (the use of this method is advisable for routine analyses). The classical jackknife was slightly superior to the other methods for 20 data points (this method can be recommended for very precise calculations if great numbers of data are available). The weighting does not seem to be necessary in this type of equation because the parameter estimates obtained with all methods with the use of constant weights were comparable with those calculated with the weights corresponding exactly to the real error structure whereas the relative weighting led to rather worse results.

On Determination of Sample Size to Evaluate Reliability Growth Plans

2011 ◽  
Author(s):  
X. Jin ◽  
P. Woytowitz ◽  
T. Tan
Keyword(s):  
Sample Size ◽  
Confidence Level ◽  
Semiconductor Manufacturing ◽  
Field Performance ◽  
Reliability Growth ◽  
Confidence Levels ◽  
Equipment Reliability ◽  
Margin Of Error ◽  
Reliability Performance

The reliability performance of Semiconductor Manufacturing Equipments (SME) is very important for both equipment manufacturers and customers. However, the response variables are random in nature and can significantly change due to many factors. In order to track the equipment reliability performance with certain confidence, this paper proposes an efficient methodology to calculate the number of samples needed to measure the reliability performance of the SME tools. This paper presents a frequency-based Statistics methodology to calculate the number of sampled tools to evaluate the SME reliability field performance based on certain confidence levels and error margins. One example case has been investigated to demonstrate the method. We demonstrate that the multiple weeks accumulated average reliability metrics of multiple tools do not equal the average of the multiple weeks accumulated average reliability metrics of these tools. We show how the number of required sampled tools increases when the reliability performance is improved and quantify the larger number of sampled tools required when a tighter margin of error or higher confidence level is needed.

Single-point likelihood method to determine a generalized S-N surface

2006 ◽  
Vol 220 (10) ◽  
pp. 1519-1529 ◽  
Author(s):  
J J Xiong ◽  
R A Shenol
Keyword(s):  
Confidence Level ◽  
Single Point ◽  
Small Sample ◽  
Likelihood Method ◽  
Fatigue Reliability ◽  
Reliability Design ◽  
S Curve ◽  
A New Technique ◽  
Economic Use

This paper outlines a new technique to address the paucity of data in determining a generalized S-N surface on the basis of fatigue reliability design. A new single-point likelihood method (SPLM) is presented for estimating a P-S-N curve, dealing with small sample numbers of data. A confidence level formula for P-S-N curve estimated by SPLM is also given. The concepts are then applied for the determination of a generalized S-N surface. Finally, contrast tests for the P-S curve are conducted to examine the presented method, demonstrating the practical and economic use of the proposed technique. It is shown from the results that the P-S-N curve can be obtained realistically using small sample numbers and that the required number of test specimens in this case is less than those for the conventional method.

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

Determination of the International Sensitivity Index of a New Near-Patient Testing Device to Monitor Oral Anticoagulant Therapy

1997 ◽  
Vol 78 (02) ◽  
pp. 855-858 ◽  
Author(s):  
Armando Tripodi ◽  
Veena Chantarangkul ◽  
Marigrazia Clerici ◽  
Barbara Negri ◽  
Pier Mannuccio Mannucci
Keyword(s):  
Linear Relationship ◽  
Whole Blood ◽  
Oral Anticoagulant ◽  
Oral Anticoagulant Therapy ◽  
Oral Anticoagulants ◽  
Calibration Model ◽  
Testing Device ◽  
Data Points ◽  
Near Patient Testing

SummaryA key issue for the reliable use of new devices for the laboratory control of oral anticoagulant therapy with the INR is their conformity to the calibration model. In the past, their adequacy has mostly been assessed empirically without reference to the calibration model and the use of International Reference Preparations (IRP) for thromboplastin. In this study we reviewed the requirements to be fulfilled and applied them to the calibration of a new near-patient testing device (TAS, Cardiovascular Diagnostics) which uses thromboplastin-containing test cards for determination of the INR. On each of 10 working days citrat- ed whole blood and plasma samples were obtained from 2 healthy subjects and 6 patients on oral anticoagulants. PT testing on whole blood and plasma was done with the TAS and parallel testing for plasma by the manual technique with the IRP CRM 149S. Conformity to the calibration model was judged satisfactory if the following requirements were met: (i) there was a linear relationship between paired log-PTs (TAS vs CRM 149S); (ii) the regression line drawn through patients data points, passed through those of normals; (iii) the precision of the calibration expressed as the CV of the slope was <3%. A good linear relationship was observed for calibration plots for plasma and whole blood (r = 0.98). Regression lines drawn through patients data points, passed through those of normals. The CVs of the slope were in both cases 2.2% and the ISIs were 0.965 and 1.000 for whole blood and plasma. In conclusion, our study shows that near-patient testing devices can be considered reliable tools to measure INR in patients on oral anticoagulants and provides guidelines for their evaluation.

Determination of trace concentrations of copper by FIA-FAAS after preconcentration on chelating sorbents

1989 ◽  
Vol 54 (7) ◽  
pp. 1785-1794 ◽  
Author(s):  
Vlastimil Kubáň ◽  
Josef Komárek ◽  
Zbyněk Zdráhal
Keyword(s):  
Sampling Frequency ◽  
Copper Determination ◽  
Flow Rates ◽  
Sample Injection ◽  
Injection Flow ◽  
Chelating Sorbents ◽  
Set Up ◽  
Trace Concentrations ◽  
Better Than

A FIA-FAAS apparatus containing a six-channel sorption equipment with five 3 x 26 mm microcolumns packed with Spheron Oxin 1 000, Ostsorb Oxin and Ostsorb DTTA was set up. Combined with sorption from 0.002M acetate buffer at pH 4.2 and desorption with 2M-HCl, copper can be determined at concentrations up to 100, 150 and 200 μg l-1, respectively. For sample and eluent flow rates of 5.0 and 4.0 ml min-1, respectively, and a sample injection time of 5 min, the limit of copper determination is LQ = 0.3 μg l-1, repeatability sr is better than 2% and recovery is R = 100 ± 2%. The enrichment factor is on the order of 102 and is a linear function of time (volume) of sample injection up to 5 min and of the sample injection flow rate up to 11 ml min-1 for Spheron Oxin 1 000 and Ostsorb DTTA. For times of sorption of 60 and 300 s, the sampling frequency is 70 and 35 samples/h, respectively. The parameters of the FIA-FAAS determination (acetylene-air flame) are comparable to or better than those achieved by ETA AAS. The method was applied to the determination of traces of copper in high-purity water.

A novel GNSS deformation feature extraction method based on ensemble improved LMD threshold denoising

2020 ◽  
Vol 14 (4) ◽  
pp. 445-453
Author(s):  
Qian Fan ◽  
Yiqun Zhu
Keyword(s):  
Feature Extraction ◽  
Spline Interpolation ◽  
Simulated Data ◽  
Mining Area ◽  
Deformation Monitoring ◽  
Denoising Method ◽  
Feature Extraction Method ◽  
Deformation Feature ◽  
Mode Decomposition ◽  
Better Than

AbstractIn order to solve the problem that the moving span of basic local mean decomposition (LMD) method is difficult to choose reasonably, an improved LMD method (ILMD), which uses three cubic spline interpolation to replace the sliding average, is proposed. On this basis, with the help of noise aided calculation, an ensemble improved LMD method (EILMD) is proposed to effectively solve the modal aliasing problem in original LMD. On the basis of using EILMD to effectively decompose the data of GNSS deformation monitoring series, GNSS deformation feature extraction model based on EILMD threshold denoising is given by means of wavelet soft threshold processing mode and threshold setting method in empirical mode decomposition denoising. Through the analysis of simulated data and the actual GNSS monitoring data in the mining area, the results show that denoising effect of the proposed method is better than EILMD, ILMD and LMD direct coercive denoising methods. It is also better than wavelet analysis denoising method, and has good adaptability. This fully demonstrates the feasibility and effectiveness of the proposed method in GNSS feature extraction.

scholarly journals Measuring the quartic Higgs self-coupling at a multi-TeV muon collider

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
M. Chiesa ◽  
F. Maltoni ◽  
L. Mantani ◽  
B. Mele ◽  
F. Piccinini ◽  
...  
Keyword(s):  
Higgs Boson ◽  
Center Of Mass ◽  
Mass Energy ◽  
Simple Analysis ◽  
Proton Proton ◽  
Coupling Interaction ◽  
Center Of Mass Energy ◽  
Muon Collider ◽  
Better Than

Abstract Measuring the shape of the Higgs boson potential is of paramount importance, and will be a challenging task at current as well as future colliders. While the expectations for the measurement of the trilinear Higgs self-coupling are rather promising, an accurate measurement of the quartic self-coupling interaction is presently considered extremely challenging even at a future 100 TeV proton-proton collider. In this work we explore the sensitivity that a muon collider with a center of mass energy in the multi-TeV range and luminosities of the order of 1035cm−2s−1, as presently under discussion, might provide, thanks to a rather large three Higgs-boson production and to a limited background. By performing a first and simple analysis, we find a clear indication that a muon collider could provide a determination of the quartic Higgs self-coupling that is significantly better than what is currently considered attainable at other future colliders.

scholarly journals Performance of the SoLid reactor neutrino detector

2019 ◽  
Vol 219 ◽  
pp. 08003
Author(s):  
Maja Verstraeten
Keyword(s):  
Quality Control ◽  
Energy Resolution ◽  
Neutrino Detector ◽  
Channel Response ◽  
In Situ Calibration ◽  
Reactor Neutrino ◽  
Li Isotope ◽  
Better Than

The SoLid Collaboration is currently operating a 1.6 ton neutrino detector near the Belgian BR2 reactor. Its main goal is the observation of the oscillation of electron antineutrinos to previously undetected flavour states. The highly segmented SoLid detector employs a compound scintillation technology based on PVT scintillator in combination with LiF-ZnS(Ag) screens containing the 6Li isotope. The experiment has demonstrated a channel-to-channel response that can be controlled to the level of a few percent, an energy resolution of better than 14% at 1 MeV, and a determination of the interaction vertex with a precision of 5 cm. This contribution highlights the major outcomes of the R&D program, the quality control during component manufacture and integration, the current performance and stability of the full-scale system, as well as the in-situ calibration of the detector with various radioactive sources.

A Generic Method to Generate AS-Curve Profile in Commercial Motion Controller

2017 ◽  
Author(s):  
Youdun Bai ◽  
Xin Chen ◽  
Zhijun Yang
Keyword(s):  
Motion Controller ◽  
Residual Vibration ◽  
Practical Applications ◽  
Analytic Polynomial ◽  
Acceleration And Deceleration ◽  
Special Knowledge ◽  
Curve Profile ◽  
S Curve ◽  
Motion Profile ◽  
Better Than

It is well believed that S-curve motion profiles are able to reduce residual vibration, and are widely applied in the motion control fields. Recently, a new asymmetric S-curve (AS-curve) motion profile, which is able to effectively adjust the acceleration and deceleration periods, is proposed to enhance the performance of S-curve motion profile, and proved to be better than the traditional symmetric S-curve in many cases. However, most commercial motion controllers do not support the AS-curve motion profiles inherently. Special knowledge or expensive advanced controlling systems, such as dSPACE system, are required to generate the AS-curve motion command, which limits the applications of the AS-curve motion profile in many practical applications. In this paper, a generic method based on the Position-Velocity-Time (PVT) mode move supported by most commercial motion controllers is proposed to generate exact AS-curve motion command in real machines. The analytic polynomial functions of AS-curve motion profile are also derived to simplify the further application, and the effectiveness of the proposed method is verified by numerical simulation.

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