Some Considerations on the Statistical Error Analysis in Holographic Interferometry with Application to an Optimized Interferometer

Re: Hoffer et al.: Update on intraocular lens power calculation study protocols: the better way to design and report clinical trials (Ophthalmology. 2020; Jul 9 [Epub ahead of print

In mechanical assemblies, the performance, quality, cost and assemblability of the product are significantly affected by the geometric errors of the parts. This paper develops the statistical error analysis approach for dimensional control in automotive body multi-station assembly process. In this method, the homogeneous transformation matrices are used to describe the location and orientation of part and assembly features and the small homogeneous transformation matrices are used to model the errors. In this approach, the effective errors in automotive body assembly process are classified in three categories: manufacturing errors (dimensional and geometric tolerances), locating errors (fixture errors) and process errors (joining errors). In a mechanical assembly, small variations due the errors propagate according to a complex mechanism that in this approach it formulated in error analysis procedure. The propagation chain of geometric errors is described based on CAD models. The estimation of the error accumulation and the percent contributions of individual errors are based on the statistical model (root-sum-square method). The application of the proposed method is illustrated through presenting an example problem.

The thermodynamic properties of hydrophobic hydration processes can be represented in probability space by a Dual-Structure Partition Function {DS-PF} = {M-PF} · {T-PF}, which is the product of a Motive Partition Function {M-PF} multiplied by a Thermal Partition Function {T-PF}. By development of {DS-PF}, parabolic binding potential functions α) RlnKdual = (−ΔG°dual/T) ={f(1/T)*g(T)} and β) RTlnKdual = (−ΔG°dual) = {f(T)*g(lnT)} have been calculated. The resulting binding functions are “convoluted” functions dependent on the reciprocal interactions between the primary function f(1/T) or f(T) with the secondary function g(T) or g(lnT), respectively. The binding potential functions carry the essential thermodynamic information elements of each system. The analysis of the binding potential functions experimentally determined at different temperatures by means of the Thermal Equivalent Dilution (TED) principle has made possible the evaluation, for each compound, of the pseudo-stoichiometric coefficient ±ξw, from the curvature of the binding potential functions. The positive value indicates convex binding functions (Class A), whereas the negative value indicates concave binding function (Class B). All the information elements concern sets of compounds that are very different from one set to another, in molecular dimension, in chemical function, and in aggregation state. Notwithstanding the differences between, surprising equal unitary values of niche (cavity) formation in Class A <Δhfor>A = −22.7 ± 0.7 kJ·mol−1 ·ξw−1 sets with standard deviation σ = ±3.1% and <Δsfor>A = −445 ± 3J·K−1·mol−1·ξw−1J·K−1·mol−1·ξw−1 with standard deviation σ = ±0.7%. Other surprising similarities have been found, demonstrating that all the data analyzed belong to the same normal statistical population. The Ergodic Algorithmic Model (EAM) has been applied to the analysis of important classes of reactions, such as thermal and chemical denaturation, denaturation of proteins, iceberg formation or reduction, hydrophobic bonding, and null thermal free energy. The statistical analysis of errors has shown that EAM has a general validity, well beyond the limits of our experiments. Specifically, the properties of hydrophobic hydration processes as biphasic systems generating convoluted binding potential functions, with water as the implicit solvent, hold for all biochemical and biological solutions, on the ground that they also are necessarily diluted solutions, statistically validated.

Accurate estimation of crude oil bubble point pressure plays a vital role in many petroleum engineering calculations, such as reserve estimation, material balance, reservoir simulation, production equipment design, and optimization of well performance. The Pb can be measured in the pressure-volume-temperature (PVT) experiments. Nonetheless, the PVT measurements have limitations, such as being costly and time-consuming. In this paper, the Al-Marhoun correlation for bubble point pressure for black oil reservoirs is improved using the linearization of non-linear regression techniques to fit Libyan crudes accurately. A total of 62 PVT data reports taken from various Libyan oil fields were used in the study. The PVT data consist of an oil gravity range of 24.7 ºAPI to 46.8 ºAPI and bubble point pressures of 123 psig to 6100 psig. Statistical error analyses and graphical methods were used to evaluate the original and modified Al-Marhoun correlations. The results showed that the improved Al-Marhoun correlation exhibits significantly lower average absolute error and deviation than the published ones. The correlation coefficient of R2 of the improved Al-Marhoun correlation is 96.70%, and the average percent error (APE) is 0.70% with a standard deviation (SD) of 14.70.

PII: S0965-2299(02)00111-5

Statistical analysis of astrometric errors for the most productive asteroid surveys

Uncertainty calculation for spacecraft thermal models using a generalized SEA method

Determination of uncertainty characteristics for the satellite data-based estimation of fractional snow cover

To provide a reference for study design comparing intraocular lens (IOL) power calculation formulas, to show that the standard deviation (SD) of the prediction error (PE) is the single most accurate measure of outcomes, and to provide the most recent statistical methods to determine P values for type 1 errors. Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California, USA. Retrospective consecutive case series. Two datasets comprised of 5200 and 13 301 single eyes were used. The SDs of the PEs for 11 IOL power calculation formulas were calculated for each dataset. The probability density functions of signed and absolute PE were determined. None of the probability distributions for any formula in either dataset was normal (Gaussian). All the original signed PE distributions were not normal, but symmetric and leptokurtotic (heavy tailed) and had higher peaks than a normal distribution. The absolute distributions were asymmetric and skewed to the right. The heteroscedastic method was much better at controlling the probability of a type I error than older methods. (1) The criteria for patient and data inclusion were outlined; (2) the appropriate sample size was recommended; (3) the requirement that the formulas be optimized to bring the mean error to zero was reinforced; (4) why the SD is the single best parameter to characterize the performance of an IOL power calculation formula was demonstrated; and (5) and using the heteroscedastic statistical method was the preferred method of analysis was shown.

Estimation of age is one of the important medico legal works where medical knowledge is applied in rendering Justice to the public and to the state. Assessment of age is often required in civil and criminal litigations. Assessment of age of an individual by examination of teeth is one of the universally accepted methods of age estimation. In a developing country like India, a large number of people are illiterate and have no knowledge or records of their date of birth which is required by law enforcing agencies in matters like, criminal responsibilities, identification, judicial punishment, consent, rape, criminal abortion, employment, attainment of majority, kidnapping and prostitution (Pathak et al, 1999). Age estimation is also required for admission purposes at the time of schooling, joining services and during retirement. Estimation of age is also required for giving old age benefits. Hence, scientific determination of age is very important.

Surgical Revascularization Versus Endovascular Therapy to Treat Chronic Limb-Threatening Ischemia: Perhaps Less Invasive Is Not Always Better

Digital implementations of neural nets must consider finite wordlength effects. For large sized nets, it is particularly important to investigate the roundoff errors in order to realize low-cost hardware implementations while satisfying precision constraints. This paper presents output error expressions for a large feedforward neural net, which are based on statistical error analysis. Weight quantization errors as well as arithmetic errors due to rounding of multiplier output and sigmoid output are modeled. The results indicate that for equal wordlengths, multiplier roundoff errors exceed weight quantization errors by about an order of magnitude.

In order to assess the uncertainties in the experimental measurements, the use of statistical error analysis is essential for a reliable technical diagnosis on structural safety in reinforced concrete of bridges. Two non-destructive techniques (ultrasound and rebound hammer) were performed, resulting in conflicting technical diagnostics when analyzed without the study of the variability of experimental errors. It was evident that physically the only use of arithmetic average means nothing. The obtained results also demonstrated the lack of correlations between those ones driven by the ultrasound and the impact hammer on the four tested bridges. &nbsp; Key words: Rebound hammer, ultrasound, compressive strength, nondestructive tests, statistical error analysis.

Optimal the tilt angles for photovoltaic modules using PSO method with nonlinear time-varying evolution

The derivation of Cloud Motion Vectors (CMVs) using infrared data has been started from Kalpana-1 in April 2003 and from INSAT-3A recently. In the present technique, the quality check of CMVs was carried out with LAM Model forecast data, which covers the area 40° E - 129° E and 29° S - 45° N). The CMVs derived below the 29° south were rejected due to non availability of LAM Model forecast data. Recently, the LAM Model forecast is replaced by global forecast and therefore CMVs are now derived over larger area (40° E - 129° E and 45° S - 45° N) resulting a significant increase in the number of good quality CMVs. These CMVs are put on GTS for end users. The Integrated Satellite Wind Monitoring NWP SAF site has recently started storing and monitoring of Kalpana-1 and INSAT-3A derived CMVs. The statistical error analysis has been carried out for the CMVs with different NWP models in order to identify and distinguish error contributions from satellite winds and NWP models. Further, in this paper, we have examined the impact of these data in the MM5 NWP model for a cyclone case study. This study demonstrates the impact of these data in the model to capture wind circulation, surface pressure and rainfall. The impact of additional CMVs data in the model is found positive and beneficial.