Measurement Uncertainty Research Articles

Characterizing Vehicle-Induced Distributed Acoustic Sensing Signals for Accurate Urban Near-Surface Imaging

Abstract Continuous seismic monitoring of the near-surface structure is crucial for urban infrastructure safety, aiding in the detection of sinkholes, subsidence, and other seismic hazards. Utilizing existing telecommunication optical fibers as distributed acoustic sensing (DAS) systems offers a cost-effective method for creating dense seismic arrays in urban areas. DAS leverages roadside fiber-optic cables to record vehicle-induced surface waves for near-surface imaging. However, the influence of roadway vehicle characteristics, such as vehicle weight, size, and driving speed, on their induced surface waves and the resulting imaging of near-surface structures is poorly understood. In this study, we investigate surface waves generated by vehicles of varying weights and speeds to provide insights into accurate and efficient near-surface characterization. We first classify vehicles into light, midweight, and heavy based on the maximum amplitudes of quasi-static DAS records. Vehicles are also classified by their traveling speed (slow, medium, and fast) using their arrival times at DAS channels. To investigate how vehicle characteristics influence the induced surface waves, we extract phase velocity dispersion and invert the subsurface structure for each vehicle class by retrieving virtual shot gathers. Our results reveal that heavy vehicles produce higher signal-to-noise ratio surface waves, and a sevenfold increase in vehicle weight can reduce uncertainties in phase velocity measurements from dispersion spectra up to 3 × , particularly at lower frequencies. Thus, data from heavy vehicles better constrain structures at greater depths. In addition, with driving speeds ranging from 5 to 30 m per second in our study, differences in the dispersion curves due to vehicle speed are less pronounced than those due to vehicle weight. Our results suggest judiciously selecting and processing surface-wave signals from certain vehicle types can improve the quality of near-surface imaging in urban environments.

Design methodology and uncertainty estimation of a wireless sensor network for surface strain and shape measurements

Abstract A sensor network has been developed consisting of wireless sensor nodes, that are interconnected by mechanical distance sensors. This approach makes it possible to precisely measure strain and shape of an object. The total number of probes and their positions will vary depending on the shape of the individual object that shall be measured. We developed a design procedure of optimally distributing the network on the surface with respect to the minimum number of sensors to be used taking into account the mechanical boundary conditions. Furthermore, two possible evaluations are shown to determine the measurement uncertainty of the sensor network. This can be used to select the network with the minimum uncertainty. Both methods developed will be illustrated using an artificial surface. Although the example was chosen specifically to achieve the greatest possible clarity, the results can be regarded as generally applicable.

An isotope dilution-liquid chromatography-tandem mass spectrometry-based candidate reference measurement procedure for the quantification of cortisone in human serum and plasma.

Cortisone is an inert precursor/metabolite of the potent steroid hormone cortisol. Measurement of serum cortisone levels and the cortisol-cortisone ratio can be useful for the diagnosis of dysfunction in the regulation of cortisol levels (i.e.,severe and subtle apparent mineralocorticoid excess, low-renin primary aldosteronism). Therefore, an isotope dilution-liquid chromatography-tandem mass spectrometry (ID-LC MS/MS)-based candidate reference measurement procedure (RMP) to quantify cortisone in human serum/plasma was developed and validated. Quantitative nuclear magnetic resonance (qNMR) was utilized to assign absolute content (g/g) and SI-traceability to reference materials used as primary calibrators. A supported liquid extraction sample preparation protocol as well as a two-dimensional heart-cut LC approach for LC-MS/MS analysis were employed to mitigate matrix effects and prevent co-elution of interferences. Selectivity was determined by analyzing a matrix sample containing the analyte, the internal standard and six potential interferents. A post-column infusion experiment and a comparison of standard line slopes were performed to evaluate matrix effects. An extensive protocol over five days was applied to determine precision, accuracy and trueness. Measurement uncertainty (MU) was evaluated in compliance with current guidelines. This RMP is suitable for analyzing cortisone within the 0.0800-120 ng/mL (0.222-333 nmol/L) range, demonstrating selectivity, sensitivity and matrix independence. Intermediate precision was ≤3.4 %, repeatability was ≤2.9 % across all concentration levels and relative mean bias ranged from -3.7 to 2.8 % across all tested matrices and concentrations. Expanded MU (k=2) for target value assignment (n=6) ranged from 2.1 to 5.5 %, irrespective of concentration or sampletype. This RMP allows for accurate and reproducible determination of cortisone in human serum and plasma. Implementation of this method supports routine assay standardization and patient sample measurement with confirmed traceability.

Accurate measurements and error analysis of Bi2Te3-based low-temperature thermoelectrics

Abstract The accurate characterization of thermoelectric properties at low temperatures is crucial for the development of high-performance thermoelectric cooling devices. While measurement errors of thermoelectric properties at temperatures above room temperature have been extensively discussed, there is a lack of standard measurement protocols and error analyses for low-temperature transport properties. In this study, we present a measurement system capable of characterizing all three key thermoelectric parameters, i.e. Seebeck coefficient, electrical conductivity, and thermal conductivity for a single sample across a temperature range of 10 K to 300 K. We investigated six representative commercial Bi2Te3-based samples (three N-type and three P-type). Using an error propagation model, we systematically analyzed the measurement uncertainties of the three intrinsic parameters and the resulting thermoelectric figure of merit. Our findings reveal that measurement uncertainties for both N-type and P-type Bi2Te3-based materials can be effectively maintained below 5% in the temperature range of 40 K to 300 K. However, the uncertainties increase to over 10% at lower temperatures, primarily due to the relatively smaller values of electrical resistivity and Seebeck coefficients in this regime. This work establishes foundational data for Bi2Te3-based thermoelectric materials and provides a framework for broader investigations of advanced low-temperature thermoelectrics.

Macroeconomic-Energy-Related Uncertainty and Economic Complexity as Drivers of Renewable Energy Investment

Abstract The United Kingdom (U.K.) has set ambitious climate goals, aiming for a net-zero target in carbon emissions by 2050 and planning to leverage green energy technologies and innovation. This study explores the key factors influencing investments in renewable energy within the United Kingdom. Specifically, the study applies the recently constructed interest rate uncertainty measure alongside economic complexity, energy security risk, financial development and load capacity factor as new determinants of renewable energy investment. Innovative econometric methods, including the bivariate quantile-on-quantile regression (QQR) technique and the nonparametric Granger causality in quantiles (NGCinQ) methods were employed. The study's findings reveal that interest rate uncertainty depresses investment in renewable energy in the lower to median quantiles. Economic complexity negatively affects renewable energy investment across all quantiles, while energy security risks stimulate renewable energy investment in the U.K. The impact of financial development and load capacity are positive across all quantiles, reflecting the well-developed financial system, as well as the efficiency of renewable energy projects and their appeal to investors in the U.K. The results of the NGCinQ provide strong evidence of a hump-shaped pattern of causality across a broad range of quantiles. The findings are supported by the robustness tests. The findings highlight the importance of the new determinants in leveraging green energy innovation and technology.

An Uncertainty Based Approach for Dealing With Selection Bias in Non‐Probability Samples

SummaryThe main issue with non‐probability samples is that the standard design‐based approach cannot be applied as the selection mechanism is unknown. In this paper, the concept of uncertainty on data generating model, resulting from the lack of knowledge of the sampling design acting in the non‐probability sample, is discussed. Furthermore, the effect on uncertainty due to the availability of extra‐sample information is evaluated. First of all, the class of plausible distributions for the variable of interest is defined, a measure of uncertainty is introduced and its asymptotic properties are analysed. Next, a plausible estimate of the distribution of the variable of interest is constructed and its accuracy is evaluated. Finally, a simulation study is performed, and an application to a real case is provided.

A Ship Emission Monitoring Option for Fuel Sulphur Content Measurement in Complex Environments

Limiting the fuel sulphur content (FSC) of ships can significantly reduce the harm caused by ship emissions, and analyzing ship exhaust gas to estimate FSC is a rapid, efficient, and low-cost monitoring method. To solve the difficulty in measuring FSC using sniffer equipment in a complex port area, a ship emission monitoring option for FSC measurement in complex environments is proposed here. First, the exhaust gas measurement data of a time series collected using the sniffer equipment were examined to determine the dataset that could be used to estimate FSC. Second, the background value of polluted gases in the environment was dynamically calculated to suppress the interference of various pollution sources. The gas-measured value series was then converted into a mean value series, and the peak points in the mean value series were automatically selected for the calculation of FSC. Finally, the wind speed, wind direction, automatic identification system information, plume diffusion model, and FSC results of ship targets around the equipment were correlated. Between June and August 2023, we conducted a field observation campaign at Ningbo Port, China, where 2624 ships were monitored. A comparison of the real and measured FSC values of eight ships showed that the system could accurately measure FSC at 0.10% (m/m) and 0.50% (m/m) levels despite measurement uncertainty that may be greater at a 0.01% (m/m) FSC level. The FSC statistics of 2624 ships showed that the FSC of small seagoing ships was relatively higher than that of other types of ships. This study proposes a monitoring option for ship emissions, designs and develops an associated system, and collects data to validate the effectiveness and accuracy of this option. This approach has been integrated into daily business operations within the maritime sector, significantly enhancing the efficiency of supervision in this field.

Graph2Mat: universal graph to matrix conversion for electron density prediction

Abstract The electron density is a fundamental observable of an atomic system from which all ground-state properties can be computed. As a prediction target for machine learning (ML) models, electron density is often represented on a dense real space grid, which is data heavy, or through density fitting approximations. In this work, we show the power of targeting the density matrix (DM), a linear-scaling sparse SE(3) equivariant matrix that encodes the exact density. We introduce Graph2Mat, a universal function for converting molecular graphs into equivariant matrices. We demonstrate how a ML model that combines this Graph2Mat approach with state-of-the-art molecular graph representations can accurately predict the DM of molecular systems. The models achieve state-of-the-art performance on electron density prediction by matching the accuracy of grid-based methods, while using datasets that are at least one order of magnitude smaller. Accurately predicted electron densities can also accelerate density functional theory (DFT) calculations by reducing the number of self-consistent field (SCF) iterations needed to converge. In this work, we get an average 40% reduction on the number of SCF steps in DFT calculations of QM9 molecules with SIESTA. The novel prediction model also allows for two new and promising measures of uncertainty (total charge error and self-consistency error) that will facilitate its practical usage, e.g. within active learning workflows. These results open the door for many applications using hybrid ML-accelerated DFT methodologies, and uncertainty aware single iteration ab initio molecular dynamics.

On suitability of measures of amplitude for quality assurance of vibration sensing systems in structural health monitoring

AbstractAccelerometers play a crucial role in measurement systems utilized for structural health monitoring (SHM) in the field of civil engineering. Structural vibrations are analyzed to gather data that helps evaluate the integrity, performance, and safety of infrastructure. Their accurate measurements allow for early identification of abnormalities, support proactive maintenance, and guarantee the resilience of civil constructions. Yet, practical conditions encountered in the field produce variations in signal response that impact the precision and performance of sensor responses. This highlights the necessity for a quality assurance approach for SHM measurements. This report systematically investigates the sources of variation contributing to measurement uncertainty in sensor responses. To study the factors causing these variations, data were collected from two accelerometers using a shaker table apparatus and a factorial design of experiments. Amplitude, a fundamental signal feature, was evaluated in eight different ways to characterize measurement uncertainty, study static characteristics such as repeatability and linearity, and perform in situ calibration. The characteristics were compared over both short and long time‐windows as well as between two sensors. The findings reveal that amplitude, depending on how one calculates it, is a simple feature that effectively demonstrates both linearity and proportionality when correlated with shaker acceleration. This makes them exceptionally suitable for fast, efficient quality assurance (QA) tasks. Such analyses help evaluate uncertainties caused by environmental, operational, instrumentation, and human factors affecting sensing systems. The presented methodologies for evaluating measurement uncertainty contribute to the essential set of tools needed for QA of sensing systems.

Extending the Traceability of Dynamic Calibration to the High-Pressure Regime Using a Shock Tube

In this paper, a development of the shock tube at RISE, the National Metrology Institute of Sweden, to extend its capability to the high-pressure regime is presented. The shock tube was developed to be operated in three different configurations: conventional, with an amplification system and with a converging cone. In the conventional and with the amplification system, the well-established shock tube analytical solution was used to calculate the reference pressure, while in the converging cone, a numerical simulation was applied. To demonstrate the capabilities and limitations of each configuration, a device under test (DUT) was characterized. The results show a good agreement in the DUT dynamic response calculated using the three configurations in the overlap regions between them. The uncertainty in measurements was estimated for each configuration. The three configurations complement each other to reach a pressure range from 0.1 MPa to 25 MPa and a frequency range from 0.5 kHz to 500 kHz.

Assessing the Metrological Reliability of Static Firing Tests of Rocket Motors Through the Evaluation of Thrust and Total Impulse Measurement Uncertainty

A solid propellant rocket motor is a propulsion system used in missiles and rockets that burns a propellant, typically composed of a mixture of fuel and an oxidizer, to generate the thrust necessary to propel the vehicle. During both the development and quality assurance phases, static firing tests of rocket motors are conducted to verify whether the system requirements meet the product specifications. These tests aim to produce two main types of graphs, “thrust versus burn time” and “pressure versus burn time,” both generated by the rocket motor during the burn. While thrust and pressure are important parameters in the design of a rocket motor, total impulse is the quantity that incorporates the crucial element of time, measuring how high a rocket can be launched. To ensure greater metrological reliability in static tests of rocket motors, it is important to carefully evaluate the uncertainty levels in the measurement chain of the data acquisition system. This work aims to assess the uncertainty levels expressed in the calculated total impulse values during a static firing test of a rocket motor at the Propulsion Jets Testing Laboratory of the Brazilian Army Technological Center. To estimate the measurement uncertainty of the chain in question, approaches based on combined and expanded uncertainty theories were adopted. These methodologies consider Type A and Type B uncertainties, providing a comprehensive and rigorous analysis. In addition to the uncertainties previously mentioned, the oscillation of the measured signal should also be recognized as a contributing factor to the overall uncertainty in the calculation of total impulse. By incorporating these various sources of uncertainty, we can achieve a more comprehensive and reliable understanding of the uncertainty associated with the measurements obtained from the measurement chain. This analysis yields a measurement uncertainty of 0.24% for thrust and 0.007% for impulse, both calculated at a confidence level of 95.45%.

Suggested Method for Prediction Using Gaussian Process Regression Kernel Regression

Accurately predicting children's weight is challenging due to measurement inconsistencies. To address this, a hybrid kernel function, combining the squared exponential kernel and the Gaussian kernel with a mixture parameter, is proposed for developing a fuzzy Gaussian process regression model. The integration of fuzzy set theory and a triangular membership function helps handle weight measurement inaccuracies by determining the degrees of membership for each element in the weight vector. The model is estimated using the spider monkey optimization (SMO) algorithm and implemented in MATLAB Ver. 2023a. The fminunc function is used for optimization, while the fitrgp function applies fuzzy set theory for regression. A dataset consisting of 191 observations from Al-Elwiya Maternity Teaching Hospital in Baghdad (collected between June 1, 2022, and December 31, 2022) is used for evaluation. The dataset is divided into 70% training data (n_train = 129) and 30% testing data (n_test = 55). The standard deviation of explanatory variables is f = 0.9234, and the smoothing parameter l = 0.8 is selected through optimization. Model performance is assessed using root mean square error (RMSE), mean square error (MSE), and mean absolute percentage error (MAPE). Results indicate a significant difference between actual and predicted values for the squared exponential kernel function, whereas the Gaussian kernel function produces closer predictions. The hybrid kernel function achieves the most accurate predictions, aligning more closely with actual child weight values than the individual kernel functions. The proposed fuzzy Gaussian process regression model with a hybrid kernel function outperforms both the squared exponential and Gaussian kernel functions in predictive accuracy. By effectively handling measurement uncertainties through fuzzy set theory, the model provides a more reliable approach for predicting children's weights.

Supporting prioritization efforts of higher-order reference providers using evidence from the Joint Committee for Traceability in Laboratory Medicine database.

The Joint Committee for Traceability in Laboratory Medicine (JCTLM) database represents a valuable resource for implementing metrological traceability in laboratory medicine. Three main database users can be identified: (a) invitro diagnostic (IVD) manufacturers, using the database information for meeting ISO 17511:2020 requirements, (b)laboratory professionals, for defining the quality of their test results, and (c)providers of higher-order certified reference materials (CRM) and reference measurement procedures (RMP), to be helped in improving the suitability of their products, if needed, and assistance with prioritizing their future efforts. In this report, we focus on the utility of the information provided (or still not provided) by the JCTLM database on this last category of users. Two types of information are discussed: (a)the use of listed CRMs as common calibrators intended to transfer trueness from the top of the calibration hierarchy to commercial IVD calibrators, and (b)the measurement uncertainty (MU) of CRM certified values and the reproducibility characteristics of RMP measurements, considering their impact on the MU of clinical samples, when compared to maximum allowable MU (MAU). The discussion output is a recommendation for suppliers to respond urgently to the need to provide higher-order references (CRMs and/or RMPs) for a number of key analytes that are currently lacking or do not yet fully meet quality criteria related to: (a)commutability assessment, (b)contribution to MAU fulfilment, and (c)demonstration of the extent of equivalence to an already listed higher-order reference.

A Monte Carlo method for the quantitative analysis of triage algorithms in mass casualty events.


In mass casualty scenarios, efficient triage algorithms are used to prioritize medical care when resources are outnumbered by victims. This research proposes a computational approach to quantitatively analyze and optimize triage algorithms by developing a Monte Carlo code which is subsequently validated against the few quantitative data.
Approach:
The developed Monte Carlo code is used to simulate several mass casualty events, namely car accidents, burns, shootings, sinking ships and a human stampede. Four triage algorithms- mSTART, PRIOR, CareFlight, and FTS-are evaluated using metrics like mortality, overtriage, undertriage, sensitivity, and specificity.
Main results:
Results indicate that, on average, the analyzed algorithms achieve about 30% accuracy in classifying critical casualties when compared to a perfect algorithm, with FTS being the less accurate. However, when all casualties are considered, algorithm performance improves to around 63% of a perfect algorithm, except for FTS. The study identifies an increased probability of false positives for red categorization due to comorbidities and a higher tendency for false negatives in casualties with burns or internal trunk injuries.
Significance:
Despite variations in vital sign measurements, triage classification results do not depend on the measurement uncertainties of the paramedics. The ethically challenging decision, of withholding medical care from low-survival probability victims, leadsto a 63% reduction in mortality among critical casualties. This research establishes a quantitative method for triage algorithm studies, highlighting their robustness to measurement uncertainties.&#xD.

Inlet Preswirl Effects on the Leakage and Dynamic Characteristics of a Labyrinth Seal: Experimental Results and Computational Fluid Dynamics Analysis

Abstract In this paper, a rotordynamic test rig based on the mechanical impedance method has been developed to measure the leakage and dynamic coefficients of annular gas seals. Test results are presented for a labyrinth seal with a rotor diameter of 170 mm, a radial clearance of 0.3 mm, and a length-to-diameter ratio of 0.38 at zero and high preswirl conditions. The tests were conducted at three pressure ratios (PR = 0.2, 0.25, and 0.33) and three rotor speeds (ω = 3000, 6000, and 8500 rpm) in an atmospheric backpressure environment. The measurement uncertainty analysis is also performed, including the propagation of instrument errors and the analysis of dynamic repeatability. The results show that the high inlet preswirl has little effect on the sealing capability of the labyrinth seal, but severely deteriorates its rotordynamic performance. For high preswirl conditions, the labyrinth seal possesses negative centering forces due to the negative direct stiffness and negligible cross-coupled damping. The tangential forces resulting from the negative effective damping also have a destabilizing effect on the rotor system, which is more pronounced at low frequencies and pressure ratios. Furthermore, comparisons are made between test data and predictions from both the computational fluid dynamics (CFD) method and the bulk-flow method (BFM) to assess the reliability of published prediction methods.

Efficient Online Training for Zero-Shot Time-Lapse Microscopy Denoising and Super-Resolution

In time-lapse microscopy, inherent noise significantly limits imaging sensitivity and increases measurement uncertainty. Due to the scarcity of clean data, zero-shot approaches have emerged as highly data-efficient solutions for microscopy denoising. However, existing methods typically process video frames independently, resulting in long training times and issues such as temporal noise and over-smoothing. In this paper, we introduce MDSR-Zero, a zero-shot online learning method designed for plug-and-play noise suppression and super-resolution of microscopy videos. Our approach leverages an efficient online training strategy that reuses denoising models from previous frames. By treating the video as a continuous stream, our model significantly reduces training time and ensures temporally consistent denoising. Additionally, we propose a novel loss function tailored for denoising in the context of super-resolution, which enhances the detail in the denoised results. Extensive experiments on both synthetic and real-world noise demonstrate that our method achieves state-of-the-art performance among zero-shot denoising approaches and is competitive with self-supervised methods. Notably, our method can reduce training time by up to 10x compared to the previous SOTA method.

Batch Selection for Multi-Label Classification Guided by Uncertainty and Dynamic Label Correlations

The accuracy of deep neural networks is significantly influenced by the effectiveness of mini-batch construction during training. In single-label scenarios, such as binary and multi-class classification tasks, it has been demonstrated that batch selection algorithms preferring samples with higher uncertainty achieve better performance than difficulty-based methods. Although there are two batch selection methods tailored for multi-label data, none of them leverage important uncertainty information. Adapting the concept of uncertainty to multi-label data is not a trivial task, since there are two issues that should be tackled. First, traditional variance or entropy-based uncertainty measures ignore fluctuations of predictions within sliding windows and the importance of the current model state. Second, existing multi-label methods do not explicitly exploit the label correlations, particularly the uncertainty-based label correlations that evolve during the training process. In this paper, we propose an uncertainty-based multi-label batch selection algorithm. It assesses uncertainty for each label by considering differences between successive predictions and the confidence of current outputs, and further leverages dynamic uncertainty-based label correlations to emphasize instances whose uncertainty is synergistically expressed across multiple labels. Empirical studies demonstrate the effectiveness of our method in improving the performance and accelerating the convergence of various multi-label deep learning models.

Multiregional Population Forecasting: A Unifying Probabilistic Approach for Modelling the Components of Change

In this article, we extend the multiregional cohort-component population projection model developed by Andrei Rogers and colleagues in the 1960s and 1970s to be fully probabilistic. The projections are based on forecasts of age-, sex- and region-specific fertility, mortality, interregional migration, immigration and emigration. The approach is unified by forecasting each demographic component of change by using a combination of log-linear models with bilinear terms. This research contributes to the literature by providing a flexible statistical modelling framework capable of incorporating the high dimensionality of the demographic components over time. The models also account for correlations across age, sex, regions and time. The result is a consistent and robust modelling platform for forecasting subnational populations with measures of uncertainty. We apply the model to forecast population for eight states and territories in Australia.

Designing circular fixed-area plots in large-scale forest inventories: effect of horizontal distance measurement uncertainty and tree position pattern

Plot design is one of the key elements that must be defined in forest inventories. This is particularly challenging in large-scale inventories, as both forest variability and measurement uncertainty generally increase with scale. Nonetheless, plot design is usually based exclusively on targeting i) an average minimum number of trees to reduce the random measurement errors, and ii) an average maximum number of trees to optimize the efficiency of fieldwork, while ignoring the uncertainty in tree position measurement. The present study focused on the effect of horizontal distance measurement errors on stand level estimates in large-scale forest inventories including circular fixed-area plots. The error was characterized in forests with non-regular (natural stands) and regular (plantations) patterns of tree positions. The effect on stand volume, stand basal area and stand density estimates was simulated using Monte Carlo techniques. Different horizontal distance measurement uncertainty was observed in natural stands and plantations. However, similar effects were observed in the three stand variables estimates for both tree spacing patterns, with stabilization of errors for radii between 12m and 20m. Doubling or halving the error uncertainty yielded similar results. The proposed method can help with selecting plot size in forest inventories based on circular fixed-area plots.

Measurement problems of conformity assessment in the quality infrastructure

A brief description of the problems that arise in the measurement problems of assessing compliance with established requirements in the quality infrastructure is given, including in connection with the requirements of ISO/IEC 17025:2017(E) “General requirements for the competence of testing and calibration laboratories” for documenting and applying decision-making rules for determinative and control tests, taking into account possible risks. These problems are conventionally divided into two groups: problems of methods for solving measurement problems, on which discussions are still ongoing, and problems of conformity assessment procedures, for which the experience of control theory can be used. The first group includes the problems of uncertainty and precision of measurement, the inadequacy of measurement equations in the indirect measurement method, the loss of the property of freedom from distribution by the criteria of agreement in the statistical verification of complex hypotheses, the exclusion of outliers in measurement protocols and terminological contradictions. It is shown that the measurement tasks of assessing compliance with established requirements in the quality infrastructure can be formulated as typical problems of the theory of control. Therefore, the second group consists of problems that can be solved by methods for determining the completeness of control, setting tolerance limits for controlled parameters, and selecting the confidence level. Then it becomes possible to assess the risks of statistical assumptions, false positive and false negative decisions about compliance with established requirements based on mathematical models of control objects.