Nuclear-decay data: The statement of uncertainties

Nuclear-decay data: The statement of uncertainties

Nuclear-decay data: The statement of uncertainties

Nuclear-decay data: The statement of uncertainties

At the annual general meeting of the International Committee for Radionuclide Metrology (ICRM) held last June at the Physikalisch-Technische Bundesanstalt, it was suggested that letters should be sent to the editors of journals that publish nucleardecay data, drawing attention to the need for specific statements of the uncertainties that are associated with such data. Authors frequently fail to state clearly the nature of their estimates of uncertainty, and not all editors insist on such clarity, so that evaluators of nuclear-decay data often f'md that it is necessary to consult with the individual authors to arrive at the weighting factors appropriate to their data. If uncertainties could be dearly characterized in the abstracts or in the text of papers reporthag values of nuclear parameters, there would be a corresponding shortening of the time required for the data to be evaluated and tabulated. There are many methods of stating estimates of conventional random and systematic uncertainties that are acceptable, provided that the methods used are described. Thus random error may be stated as: (i) the estimate of the standard deviation (or the square root of the variance), which is in the same units as the observed data and indicates the order of magnitude of the spread of the data: (ii) the standard error (or the estimated standard deviation of the mean of the distribution); and (ri) the estimated limits for the mean at stated levels of confidence (C1) (e.g. limits at the 99-percent CI define the range within which there is a 99:percent probability of ineluding the mean of a population). Provided that the author states the number of independent measurements made of the given parameter, or the number of degrees of freedom, these statements of random uncertainty are related uniquely to each other. The other component of the overall uncertainty is the estimate of possible systematic error. The significance, or meaning, of the estimate of systematic uncertainties should be dearly stated and also related to the method chosen to state the random uncertainties. Thus an estimate of maximum conceivable systematic uncertainties would logically be combined with a random uncertainty at a 99-percent confidence level. An appropriate fraction of the estimate of maximum conceivable systematic uncertainty would be chose to match smaller random confidence levels. The methods used to combine random and systematic uncertainties should also be stated by authors, and an explicit listing of all components of these uncertainties will allow an evaluator of nuclear data to unravel the statements of uncertainty and to choose

A method is suggested to decompose the statistical and systematic uncertainties from the residues between the calculation of a theoretical model and the observed data. The residues and the parameters of the model can be obtained through the standard statistical fitting procedures. The present work concentrates on the decomposition of the total uncertainty, of which the distribution corresponds to that of the residues. The distribution of the total uncertainty is considered as two normal distributions, statistical and systematic uncertainties. The standard deviation of the statistical part, ${\ensuremath{\sigma}}_{\mathrm{stat}}$, is estimated through random parameters distributed around their best fitted values. The two normal distributions are obtained by minimizing the moments of the distribution of the residues with the fixed ${\ensuremath{\sigma}}_{\mathrm{stat}}$. The method is applied to the liquid drop model (LD). The statistical and systematic uncertainties are decomposed from the residues of the nuclear binding energies with and without the consideration of the shell effect in LD. The estimated distributions of the statistical and systematic uncertainties can well describe that of the residues. The normal assumption of the distribution of the statistical and systematic uncertainties is examined through various approaches. The comparison between the distributions of the specific nuclei and those of the statistical and systematic uncertainties are consistent with the physical considerations, although the latter two can be obtained without the knowledge of these considerations. Such as, the LD are more suitable to describe the heavy nuclei. The light and heavy nuclei are indeed distributed mostly inside the distributions of the systematic and statistical uncertainties, respectively. A similar situation is also found for the nuclei close to and far from shell. The present method is also performed for nuclei around the stability line. The results are used to investigate all measured nuclei, which show the usefulness of the uncertainty decomposition method in the exploration of the unmeasured nuclei.

Uncertainties are typically assumed to be constant or a linear function of the measured value; however, this is generally not true. Particle image velocimetry (PIV) is one example of a measurement technique that has highly nonlinear, time varying local uncertainties. Traditional uncertainty methods are not adequate for the estimation of the uncertainty of measurement statistics (mean and variance) in the presence of nonlinear, time varying errors. Propagation of instantaneous uncertainty estimates into measured statistics is performed allowing accurate uncertainty quantification of time-mean and statistics of measurements such as PIV. It is shown that random errors will always elevate the measured variance, and thus turbulent statistics such as . Within this paper, nonlinear, time varying errors are propagated from instantaneous measurements into the measured mean and variance using the Taylor-series method. With these results and knowledge of the systematic and random uncertainty of each measurement, the uncertainty of the time-mean, the variance and covariance can be found. Applicability of the Taylor-series uncertainty equations to time varying systematic and random errors and asymmetric error distributions are demonstrated with Monte-Carlo simulations. The Taylor-series uncertainty estimates are always accurate for uncertainties on the mean quantity. The Taylor-series variance uncertainty is similar to the Monte-Carlo results for cases in which asymmetric random errors exist or the magnitude of the instantaneous variations in the random and systematic errors is near the ‘true’ variance. However, the Taylor-series method overpredicts the uncertainty in the variance as the instantaneous variations of systematic errors are large or are on the same order of magnitude as the ‘true’ variance.

Seawater carbonate chemistry observations are increasingly necessary to study a broad array of oceanographic challenges such as ocean acidification, carbon inventory tracking, and assessment of marine carbon dioxide removal strategies. The uncertainty in a seawater carbonate chemistry observation comes from unknown random variations and systematic offsets. Here, we estimate the magnitudes of these random and systematic components of uncertainty for the discrete open‐ocean carbonate chemistry measurements in the Global Ocean Data Analysis Project 2022 update (GLODAPv2.2022). We use both an uncertainty propagation approach and a carbonate chemistry measurement “inter‐consistency” approach that quantifies the disagreement between measured carbonate chemistry variables and calculations of the same variables from other carbonate chemistry measurements. Our inter‐consistency analysis reveals that the seawater carbonate chemistry measurement community has collected and released data with a random uncertainty that averages about 1.7 times the uncertainty estimated by propagating the desired “climate‐quality” random uncertainties. However, we obtain differing random uncertainty estimates for subsets of the available data, with some subsets seemingly meeting the climate‐quality criteria. We find that seawater pH measurements on the total scale do not meet the climate‐quality criteria, though the inter‐consistency of these measurements improves (by 38%) when limited to the subset of measurements made using purified indicator dyes. We show that GLODAPv2 adjustments improve inter‐consistency for some subsets of the measurements while worsening it for others. Finally, we provide general guidance for quantifying the random uncertainty that applies for common combinations of measured and calculated values.

This paper discusses the effect of statistical uncertainties present in Monte Carlo (MC) calculated dose distributions on the evaluation of a ‘cost function’ that expresses the suitability of a treatment plan for the intended treatment. The mathematical derivations given are valid for any ‘well-behaved’ cost function. The validity of the general expressions is demonstrated using numerical examples. It is shown that random dose uncertainties lead to statistical and systematic uncertainties on the cost function. The balance between the two types of uncertainty and the desired accuracy on the cost function presents a clear criterion for the maximum acceptable MC dose uncertainties. It is demonstrated that it is possible to remove the systematic cost function uncertainty. Finally, it is shown that when the dose distribution is close to a true optimum, MC calculations of the cost function converge to the true result as one over the number of particles simulated, i. e. much faster than the individual dose uncertainties.

PurposeThe purpose of this paper is to present a novel Kriging meta-model assisted method for multi-objective optimal tolerance design of the mechanical assemblies based on the operating conditions under both systematic and random uncertainties.Design/methodology/approachIn the proposed method, the performance, the quality loss and the manufacturing cost issues are formulated as the main criteria in terms of systematic and random uncertainties. To investigate the mechanical assembly under the operating conditions, the behavior of the assembly can be simulated based on the finite element analysis (FEA). The objective functions in terms of uncertainties at the operating conditions can be modeled through the Kriging-based metamodeling based on the obtained results from the FEA simulations. Then, the optimal tolerance allocation procedure is formulated as a multi-objective optimization framework. For solving the multi conflicting objectives optimization problem, the multi-objective particle swarm optimization method is used. Then, a Shannon’s entropy-based TOPSIS is used for selection of the best tolerances from the optimal Pareto solutions.FindingsThe proposed method can be used for optimal tolerance design of mechanical assemblies in the operating conditions with including both random and systematic uncertainties. To reach an accurate model of the design function at the operating conditions, the Kriging meta-modeling is used. The efficiency of the proposed method by considering a case study is illustrated and the method is verified by comparison to a conventional tolerance allocation method. The obtained results show that using the proposed method can lead to the product with a more robust efficiency in the performance and a higher quality in comparing to the conventional results.Research limitations/implicationsThe proposed method is limited to the dimensional tolerances of components with the normal distribution.Practical implicationsThe proposed method is practically easy to be automated for computer-aided tolerance design in industrial applications.Originality/valueIn conventional approaches, regardless of systematic and random uncertainties due to operating conditions, tolerances are allocated based on the assembly conditions. As uncertainties can significantly affect the system’s performance at operating conditions, tolerance allocation without including these effects may be inefficient. This paper aims to fill this gap in the literature by considering both systematic and random uncertainties for multi-objective optimal tolerance design of mechanical assemblies under operating conditions.

We present a method for formally assessing random and systematic uncertainties in the Aquarius salinity retrievals. The method is based on performing multiple retrievals by perturbing the various inputs to the retrieval algorithm. This results in calculating the sensitivity of the Aquarius salinity to these inputs. Together with an error model for the uncertainties in the input parameters it is possible to calculate the uncertainty in the retrieved SSS. It is important to distinguish between random uncertainties, which get suppressed when computing weekly or monthly averages and systematic uncertainties, which do not get suppressed by taking averages. We compare the results of the formal uncertainty estimates with uncertainty estimates based on comparing the Aquarius salinities with those from external validation sources finding excellent agreement.

The DSSC (DEPFET Sensor with Signal Compression) is a new instrument with non-linear response and parallel signal processing (filtering, linear amplification, and 8bit digitization) for all pixels. The DSSC will serve as ultrafast megapixel imaging detector at the European XFEL (Xray Free Electron Laser) in Schenefeld, Germany, which began science operation in September this year. The DSSC detector needs to be calibrated for each of a set of twelve predefined operation modes before being employed in scientific experiments. A crucial step in the calibration of the response of each individual detector pixel is the calibration of offset and gain. We present a study of both systematic and statistical uncertainty in the determination of offset, noise, and gain. The best possible calibration of offset and gain requires that these two quantities can be determined with an uncertainty that is less than half the finite resolution of the respective read-out ASIC calibration settings. The study is based on simulated calibration data, which were then analyzed using our calibration tools. Systematic and statistical uncertainty in offset, noise, and gain determination was quantified by comparing analysis results with the actual values employed in the simulations. A review of all results identified the most suitable calibration approaches. Their ability for providing the best possible offset and gain calibration is discussed.

Abstract. A new reference occultation processing system (rOPS) will include a Global Navigation Satellite System (GNSS) radio occultation (RO) retrieval chain with integrated uncertainty propagation. In this paper, we focus on wave-optics bending angle (BA) retrieval in the lower troposphere and introduce (1) an empirically estimated boundary layer bias (BLB) model then employed to reduce the systematic uncertainty of excess phases and bending angles in about the lowest 2 km of the troposphere and (2) the estimation of (residual) systematic uncertainties and their propagation together with random uncertainties from excess phase to bending angle profiles. Our BLB model describes the estimated bias of the excess phase transferred from the estimated bias of the bending angle, for which the model is built, informed by analyzing refractivity fluctuation statistics shown to induce such biases. The model is derived from regression analysis using a large ensemble of Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) RO observations and concurrent European Centre for Medium-Range Weather Forecasts (ECMWF) analysis fields. It is formulated in terms of predictors and adaptive functions (powers and cross products of predictors), where we use six main predictors derived from observations: impact altitude, latitude, bending angle and its standard deviation, canonical transform (CT) amplitude, and its fluctuation index. Based on an ensemble of test days, independent of the days of data used for the regression analysis to establish the BLB model, we find the model very effective for bias reduction and capable of reducing bending angle and corresponding refractivity biases by about a factor of 5. The estimated residual systematic uncertainty, after the BLB profile subtraction, is lower bounded by the uncertainty from the (indirect) use of ECMWF analysis fields but is significantly lower than the systematic uncertainty without BLB correction. The systematic and random uncertainties are propagated from excess phase to bending angle profiles, using a perturbation approach and the wave-optical method recently introduced by Gorbunov and Kirchengast (2015), starting with estimated excess phase uncertainties. The results are encouraging and this uncertainty propagation approach combined with BLB correction enables a robust reduction and quantification of the uncertainties of excess phases and bending angles in the lower troposphere.

Exploring the dosimetric impact of systematic and random setup uncertainties in robust optimization of head and neck IMPT plans

The proper choice of a measurement technique that minimizes systematic and random uncertainty is an essential part of experimental physics. These issues are difficult to teach in the introductory laboratory, though. Because most experiments involve only a single measurement technique, students are often unable to make a clear distinction between random and systematic uncertainties, or to compare the uncertainties associated with different techniques. In this paper, we describe an experiment suitable for an introductory college-level (or advanced high school) course that uses velocity measurements to clearly show students the effects of both random and systematic uncertainties.

Tokai to Kamioka (T2K) is an accelerator long baseline experiment that measures the neutrino oscillation parameters by observing $\nu_\mu$ ($\bar{\nu}_\mu$) disappearance and $\nu_e$ ($\bar{\nu}_e$) appearance from a $\nu_\mu$ ($\bar{\nu}_\mu$) beam. The experiment has both near and far detectors situated at 280 m and 295 km respectively from the beam production target. The far detector Super-Kamiokande where $\nu$ and $\bar{\nu}$ interact is a water Cherenkov detector. The dominant interactions at ∼0.6 GeV where T2K flux peaks are charged current quasi-elastic which result in single ring events. The next largest charged current interaction at T2K energy is resonant $1\pi$ production. The addition of charged current $\nu_\mu1\pi^+$ samples to the T2K analysis is expected to improve the precision on $\sin^{2}\theta_{23}$ and $|\Delta{m^2}_{32}|$. Studies on the selection of $\nu_\mu$ charged current $1\pi^+$ like events accumulated in forward horn current operation corresponding to a proton on target of $1.9663\times10^{21}$ are performed. The estimation of systematic uncertainty is important in the studies of sensitivity to neutrino oscillation parameters. One source of uncertainty is the impact of shortcomings in the detector model on the event selection. In our study, far detector systematic uncertainty is estimated via a fit to atmospheric neutrinos events collected in Super-Kamiokande, using a Markov Chain Monte Carlo Framework. We present the selection of $\nu_\mu$ charged current $1\pi^+$ multi-ring events and the process of estimation of detector systematic uncertainty.