Risk assessment is an integral part of an enterprise's quality management system. The risk of low quality products is the most significant risk, as it is directly related to the concept of enterprise competitiveness. The paper analyzes the scientific papers related to the assessment of the quality of products, processes and services, their disadvantages, possible limits of application. It is proposed to use mathematical dependences to obtain estimates of product quality indicators on a dimensionless scale. Knowing the density function of random variables of product quality indicators and knowing the mathematical dependence of their estimates on a dimensionless scale, it is proposed to obtain the density function of estimates. Knowing the function of the density of estimates of quality indicators, it is proposed to find the probabilities of risks of the assessment of quality indicators in any given interval on a dimensionless scale. A method for assessing the risks of low quality products has been developed

Indicators, different in terms of nature and grading scales, are used to recognise hazardous and harmful factors that affect human health. However, no single methodology is available for their assessment, and the variety of qualimetric assessment methods requires in-depth research, in part on optimality and efficiency. Therefore, this work aimed to conduct several scientific studies to obtain the results of the assessment in unified units of measurement, which would provide a generalised indicator of harmful factors at the workplace. The article proposes to use dependencies to assess indicators of harmful factors, considering the maximum, minimum, and optimal values as well as the shape parameter, the change of which produces various assessments in a dimensionless scale. A hierarchy analysis method was used to obtain reliable values with a small number of experts and determine the form parameter. These efforts resulted in the value of the overall index for harmful factors, which serves as grounds for decisions regarding further improvements in working conditions. The developed methodology was used to assess the safety of working conditions at a machine-building enterprise, and the results are presented in the article.

The article considers several modern scientific papers substantiating the need for assessing workplace safety and focusing on methods applied for the quantitative assessment of working conditions. The analysis found unsolved problems in qualimetry, which could lead to the development of new practical and generally applicable methods to effectively assess working conditions. The analysis proved the relevance of the topic and helped to determine the aim of the article, i.e., the development of a methodology for the quantitative assessment of working conditions in industries, considering harmful production factors. An exponential distribution, which belongs to the theory of extreme statistics, was proposed for the transition of heterogeneous single indicators of harmful factors into a dimensionless scale. Affine transformations were used to combine dissimilar scales, making it possible to divide segments on dissimilar scales into equal proportions. The article proposes a step-by-step method for determining a complex indicator of working conditions in industries. The proposed methodology allows management decisions that minimise the deviation in actual values of harmful factors from the optimal ones. The developed technique was tested at one specific metallurgical production site.

The subject of research in the article are methods and means of measurement and testing. The goal of the work is to analyze the metrological requirements of the ISO/IEC 17025:2017 standard for equipment and methods used to conduct tests in laboratories to ensure control of the metrological system processes, and to provide information on the practical application of the requirements of this standard, taking into account the provisions of other international standards. The following tasks are solved in the article: analysis of the position of international documents containing the requirements to the equipment and test methods for measurement in order to determine their practical implementation; analysis of ISO/IEC 17025:2017 on metrological requirements and proposed ways of implementation of these requirements. The following methods are used-analysis method. The following results have been obtained: the analysis of international requirements to the equipment, including measuring, testing (measurement) and standardization of these requirements has been carried out to implement the provisions of ISO/IEC 17025:2017. An important factor in the implementation of the standard in Ukraine is that currently there are no national standards that would regulate the general requirements for the use of measuring equipment and assess the accuracy of measurement results. This standard provides general approaches to the use of equipment and accuracy characteristics of the results obtained by appropriate methods. Fulfillment of the requirements of the methodology makes it possible to obtain a reliable result with the required accuracy. Conclusions: on the basis of the carried out analysis it is established that ISO/IEC 17025:2017 became a new perspective step towards application of metrological requirements to means and methods of testing and measurements defined by various other international documents in the field of metrology; the standard is a fundamental, in fact, reference book for metrologists on organization of work on assurance of reliability of measurement results and tests at the enterprise; assurance of conformity to the requirements of the international standard provides customers with confidence in the results of measurements.

The article studies the properties of textile materials filled with magnetite nanoparticles. These materials have great prospects for creating smart clothes. They have both magnetic and hygienic properties. Chemical transformations in the production of magnetic nanopowder are described. The end product of the process is a mixture of oxides of divalent and ferric iron. The resulting mixture has magnetic properties. Conducted micro and macro experiments showed sufficient adhesion retention strength of magnetite nanoparticles in a textile material. Microscopic studies of the attachment of magnetic particles to the fibers of a textile material have been conducted. The data obtained in express mode allow us to determine the average mass of a magnetic particle in a textile material, the total number of nanoparticles, and, accordingly, to predict the magnetic force that a textile material saturated with magnetite can possess. The existence of the magnetic properties of a textile material filled with magnetite nanoparticles has been proven. A mathematical model of the dependence of the magnetic attraction force of a textile material on the distance and the number of abrasion cycles has been developed. The directions of the use of magnetic textile materials for the creation of smart clothes are proposed. Potential uses for such materials include sportswear and textiles for the disabled. The developed methods can predict the magnetic strength of the obtained textile materials and evaluate their resistance, which is necessary in the development of smart clothing elements based on these materials.

The Covid-19 pandemic mainly affected those target groups who, due to the nature of their duties, were unable to isolate themselves. The consequences of such work are psychological tension with various symptoms. In this situation, the formation of a system for localizing its consequences becomes a very important task. Three parts are distinguished: a quantitative assessment of the scale and nature of the pandemic, a quantitative assessment of the need to localize the consequences and the analysis of current system; third, the formation of a monitoring system. The chosen system allows verbal assessments to be transformed into quantitative ones. Based on it, the aggregated values of seven essential signs of psychological stress in the target groups (medical and social workers, police, customs officers, educators, pharmacists, and entrepreneurs) were identified: anxiety (0.80), stress (0.78), aggression (0.63), insomnia (0.62), persistent fatigue (0.61), depression (0.56), sadness (0.49). The application of the methodology allows forming a monitoring system considering the scale of the pandemic impact and the psychological consequences. The mental distress caused by the COVID-19 pandemic has been shown to be characterized by such negative effects as anxiety, stress, insomnia, persistent fatigue, depression and persistent sadness. The study revealed that the major shortcomings in the system developed for localizing the negative effects are as follows: insufficient efforts of state institutions even in the case the negative effects are getting worse; inadequate provision of psychological assistance conditioned by unreasonably high prices and deficient legal framework.

Jelly and marmalade products are "lyophilic colloids" – lyophilic colloidal-dispersed, ie microheterogeneous (multi- or polyphasic) systems based on high molecular weight compounds (gelatin, pectin, agar, etc.). Therefore, the problem of stabilizing their polyphasic structure is relevant. In addition, the expansion and improvement of the production of jelly and marmalade products requires the search for simplified resource- and energy-saving technology, increasing the stability of the colloidal disperse system, improving the quality and extending the shelf life of finished products. Promising technological applications have food additives in the nanometer range, due to specific and stable physical and chemical parameters, a wide range of functional and technological properties. The paper proposes the solution of the problem of stabilization of the polyphase structure of jelly-marmalade products and the formation of their quality by using the food additive "Magnetofood" (based on double oxide of divalent and trivalent iron: FeO×Fe2O3). "Magnetofood" - highly dispersed powder with a particle size (70–80) nm, which has a fairly diverse functional and technological potential: high ζ-potential and surface activity; clusterophilicity and amphiphilicity; complexing, thickening, structuring, stabilizing, thixotropic properties. This allows us to recommend "Magnetofood" as a food additive of complex action to improve the quality and prolong the shelf life of jelly-marmalade products, in particular jelly-shaped marmalade. The surface-active properties of nanoparticles of the food additive "Magnetofood" are determined: a rather significant value of ζ-potential (34-44) mV, amphiphilicity (marginal wetting angle Q<90o by polar-nonpolar medium) - show signs of stability and stability on polyphasic colloidal-dispersed systems , which increases in acidic environments, in solutions of polysaccharides, proteins on average by (55±)%, which is due to clusterophilicity and self-organization of nanoparticles "Magnetofood" into electrostatic complexes with proteins, polysaccharides and their spatial structuring. It was found that the addition of "Magnetofood" in the mass fraction (0,10–0,20)% to the mass of the structurant increases the viscosity of aqueous solutions of gelling agents in (1,22–1,27) times for agar and in (1,24–1,29) times for pectin and the rate of structuring of gel masses in (1,73±0,01) times for agar and in (1,67±0,01) times for pectin due to the structure-forming action of nanoparticles "Magnetofood". In addition, the ability of the gel structure to thixotropy increases by (1,4–1,5) times and the mechanical strength of the gel well by (1,32–1,80) times for agar and (1,49–1,57) times for pectin due to the stabilizing action of Magnetofood nanoparticles, which allows to reduce the amount of gelling agent by (9.0–11.0)% for agar and by (7.0–9.0)% for pectin.

A mathematical model for the numerical determination of the quality indicator value allowing one to obtain non-dimensional values in the range from minus infinity to 1 (the maximum usable value) is proposed. Unlike the traditional system of tolerances, in which the suitability can take two values -0 or 1, the proposed model allows you to obtain intermediate values of the suitability, depending on the proximity of the actual parameter to the desired value. The model uses the suitability function suggested in the paper, and the shape indicator drives it. The characteristic ranges of the shape indicator of the suitability function have been considered. Those of practical importance has been highlighted. In addition to the general dependence, exceptional cases (linear and parabolic suitability functions, which are mathematically simpler) are also given. It is shown how the use of the proposed model allows sorting parts into quality grades and introducing a technological margin of accuracy. The mathematical model is illustrated by the example of the dimensional suitability of an engineering part. The traditional system of dimensional tolerances is a particular case of the proposed generalized system, which is recommended for high-precision manufacturing.