Use of mathematical methods in research. Methodological problems of applying mathematical methods in modern sociological research

These technologies have been developed and successfully used in industrialized countries whose economies are either export-oriented (Western Europe, Japan) or their domestic market is open to imports (USA).

The quality of manufactured products has always been a problem for the Russian national economy. In the quality management practice of Russian companies, an approach that is not related to quality management, but to the ability to control it, has now taken root. Companies implement an external quality control system consisting of several control points during the production process. This approach is hopelessly outdated. Now it has become obvious to everyone that quality is created at all stages of production and every employee of the company is responsible for quality.

As a result of the study “Priority tasks of Russian managers”, conducted by the Association of Russian Managers and the Ernst & Young CIS company, it was possible to find out that the managers of Russian enterprises consider their top priority to be “increasing the company’s market share”, and improving the quality of service was given only fourth place after “ attracting and retaining qualified specialists” and “controlling and reducing costs”. This means that even in a market economy, Russian managers decide on the “quality-quantity” alternative in favor of “quantity” - increasing production and increasing market share. This position of Russian managers is generally natural and understandable, since the Russian market is still at the stage of saturation and the level of competition is significantly lower compared to industrialized countries. In addition, the Russian consumer often does not have strict quality requirements, especially in the service sector.

Quality management technologies include the following management technologies:

Total quality management

Six Sigma technology

Benchmarking

Total quality management (tqm - Total Quality Management)

It is a method of organizing the production of high-quality, quality products, which is based on an employee who understands what quality is and strives to do his job well the first time. The introduction of TQM technology requires a lot of explanatory work so that every employee understands that the quality of the product depends on him too.

System "Diamond"

A special way of adapting TQM technology was done at Instrum-Rand, which became one of the suppliers of Mercedes-Benz, one of the most critical customers in the world. General Director of the Instrum-Rand joint venture Vadim Sorokin proceeds from the following position: “The quality of a product largely depends not only on who makes it. The employee is not responsible for most of the processes in the enterprise: he does not choose the supplier, equipment, technology, or processing mode. And if he made a defective part, it is important for all of us to understand why this happened, and not to punish the last one. This is how the concept of the “diamond” was born. Now no one hides the defective part, but carries it to the table for “diamonds”, accompanied by a tag with his data and information about why, in his opinion, there was a defect. And the master expresses gratitude to such a worker and issues a bonus for the fact that the part did not make it onto the assembly line... Three years of work have passed using the “diamond” system, and the level of defects has dropped to one percent.” And the “diamond” concept was adopted by David Clark, head of quality programs for the European division of the Ingersoll-Rand holding company, in order to build a similar system for collecting and analyzing information at factories in England, Germany, France and Italy. Thus, the company has coped with the human factor of quality management.

Six Sigma technology. The Six Sigma standard is a quality level at which for every million opportunities or operations there are slightly more than three defects (in statistics, three sigma is an almost reliable result). This technology was developed in the mid-80s. in the USA, by Motorola. Throughout the world, this system is used by no more than a few dozen particularly advanced companies, and in Russia there are only a few of them. The implementation of this technology in Russian conditions involves training the relevant employees at the Six Sigma Academy in France. The requirements for the quality management system are so high that there can be no alternatives in the form of adaptations (to national conditions (“six sigma” in Russian conditions is still “six sigma”!). However, quality improvement projects directly at the enterprise are developed by the program participants themselves "Six Sigma", and they come from existing resources, values and perceptions, and adaptation still occurs, perhaps in an implicit form.

Benchmarking (control comparison, certification). A database of benchmark indicators is being created, drawn from monitoring the activities of other departments and other companies. The simplest example of a benchmark: the number of typing errors. Where there are fewer errors, there is a standard. In Russian practice, comparisons with foreign companies are widely used.

Benchmarking technology was proposed to be used to assess quality back in Soviet times. Thus, the famous Soviet and Russian researcher in the field of economics and management of research and development K.F. Puzynya in the mid-70s of the twentieth century developed a method for assessing the scientific and technical level of the equipment being created. In this method, not just a specific foreign model was chosen as a standard for comparing equipment parameters, but an ideal analogue, formed from the best parameters of comparable equipment from several manufacturers.

This technology is based on the formation of a standard, that is, the decision about what is considered a standard is made by people, so there is the possibility of self-deception and deception of superiors. Russian enterprises are trying to use this technology, but they use it rather haphazardly, which does not always give the expected effect.

In addition, there is the problem of disclosing confidential information: it is not always possible to disclose the level of achievements of a particular organization (and even more so a competitor organization). Often, attempts to find out the achieved level of performance of operations or product parameters are perceived as an attempt at industrial espionage with all the ensuing consequences.

HR technologies

These technologies are of great practical importance, since theorists and thinkers in the field of management have repeatedly noted that in modern conditions the main resource of an organization is people and in achieving the goals of the organization, the primary role belongs to the personnel. HR technologies include:

Empowerment

Formation of teams

Job Guarantee Programs

Management by objectives (MBO - management by objectives)

Construction of feedback systems

Empowerment. This technology encourages employees to make certain decisions without consulting their management. This technology came from the USA. In an organization using empowerment technology, decisions are made at the level where all relevant information is concentrated.

In the “Big Economic Dictionary” (M.: Knizhny Mir, 2004. – P. 305) “quality is determined by the measure of compliance of goods, works, services with the conditions and requirements of standards, agreements, contracts, consumer requests. Distinguish between the quality of products, work, labor, materials, goods and services.”

The quality of a product (service) is characterized as a set of properties that ensure their suitability for meeting relevant production, social, and individual needs. The quality of a product or service in a modern market economy is becoming an important factor in competition and the achievement of commercial success of enterprises.

According to the ISO 9000 standard, quality is a set of characteristics of an object related to its ability to satisfy stated and intended needs. This definition applies to both goods and services and the processes of their production. Quality characterizes the compliance of a product (service) with consumer requirements. The properties of a product that characterize its suitability for meeting certain requirements are called its quality attributes (characteristics).

The quality management system in domestic literature (since the 70s of the last century) was defined as a set of measures at all levels of an enterprise (organization) aimed at producing products, goods or services of the highest quality. Moreover, this system goes beyond the boundaries of a specific organization, including also suppliers, distribution systems for finished products, and the provision of services to consumers in their practical use.

Quality management is closely related to a number of other management disciplines, for example, production management, corporate management, project management, investment management, etc. In Fig. Figure 3.11 shows the relationship between quality management and other management disciplines.

International quality standards (including the latest developments ISO 9000:2000) essentially repeat and develop the basic principles of the best domestic quality management systems (Saratov, Lvov, etc.):

1. Concern for product quality extends to all levels of the enterprise’s organizational structure.

Rice. 3.11. The relationship between quality management and other management disciplines

2. The quality of products is ensured at all stages of their life cycle (development, design, production, sales, after-sales service).
3. Quality is focused on meeting the requirements of consumers, not manufacturers.
4. Improving the quality of products, goods or services requires the use of modern equipment, technology and management.
5. Total quality improvement (TQM) can only be achieved through the committed participation of all personnel in the organization.

Quality means that any product (good) must comply with established regulatory requirements and standards. However, this is not the end result. According to modern concepts of quality management theory, true quality includes not only the production of products (goods) according to established standards, but also the process of distribution of goods, customer service, as well as compliance of standards with the requirements of a market economy.

Consequently, quality is ensured already at the stages of studying the market needs for a specific product, its development, production preparation, manufacturing of the product, its packaging and storage, sale and delivery of the product to the consumer, after-sales service and use of the product by the consumer, as well as disposal of the product at the end of its life. services.

In practice, the problem of ensuring the required quality is the most difficult for managers, who must continuously ensure and monitor all processes in the enterprise (organization) according to quality criteria at every stage, from receiving raw materials to delivering finished goods to consumers. At service sector enterprises, managers control the entire process of production and provision of a specific service, and its quality.

The service sector is one of the fastest growing sectors (spheres) of the modern economy. Many manufacturing businesses are actually active participants in the service industry. About half of production costs relate to the purchase of services (advertising, transportation, packaging, financial services, after-sales service, etc.). It should be emphasized that it is modern enterprises (companies) in the service sector that are the basis for creating new models of effective quality management.

We will be guided by the concept of “service” as an intangible product that is the result of activities carried out through the interaction of supplier and consumer. In this case, services may include activities carried out on the supplied material (for example, repair of a product) and intangible (for example, tax return) products, the supply of material (transportation, placement, etc.), the provision of various types of intangible products (information, knowledge and etc.), creating favorable conditions for clients (for example, tourism and hotel services). In the real economy, there are no clear distinctions between the sale of goods and services, since most manufacturers today provide many different services along with goods. Thus, services are provided by all enterprises and manufacturers; the question is the share of services offered, and this share in the future should increase significantly at domestic enterprises.

The quality of goods or services is the main thing that the modern market takes into account and perceives. If the customers of a given company are not satisfied with its products and services, then they will certainly look for other manufacturers or sellers of a similar product or service that can more effectively meet their needs.

From the above it follows that quality is built into the product from the very beginning and is controlled at all stages (stages) of its life cycle. Moreover, at each stage the necessary regulatory and other requirements must be met (“there are no trifles in quality”).

In modern ISO 9000 series standards, the focus has shifted from product quality to the quality of labor, fixed assets of enterprises, technology and management. The quality assessment of an object should cover all stages of the life cycle (“quality loop principle”).

In Fig. Figure 3.12 shows a diagram of the “quality loop”. The loop represents the product life cycle stages that contribute to quality. At each stage, an appropriate quality assessment must be made.

An integrated quality assurance system at an enterprise can be characterized as a set of organizational structure, methods, processes, resources, systematically carried out activities necessary to ensure that products, goods or services meet certain quality requirements. The latter refers to the requirements for characteristics inherent in products, goods, services, processes, and systems.

Quality management is essentially an integral part of general quality management as a coordinated activity for the management and management of an enterprise (organization) related to quality.

Rice. 3.12. “Quality loop” in the quality management system

A quality program is a document that describes the elements of a quality management system and the resources that will be used in a particular organization. The quality manual is a fundamental document describing the organization's quality management system, which sets out the enterprise's quality policy. This manual usually includes general provisions, characteristics of the enterprise (organization), elements of the quality system, policy in this area, and applications. An example of a quality manual for an enterprise that has implemented ISO 9000 international standards is given in the training manual.

Quality requirements are requirements for characteristics inherent in a product, service, process or system. A quality characteristic is one established by requirements and inherent in a given product, service or process. Structuring the quality function is a way of translating customer requirements into the above characteristics.

Quality management processes are influenced by many factors. Among them there are both external (the state of the external environment, the intensity of competition, the level of quality of raw materials, consumer requirements, etc.) and factors of the internal environment of enterprises engaged in the production of goods and services.

All internal factors are divided into three groups:

1) technical and technological (state of technology, technological equipment, production technology, etc.);
2) organizational and economic (the effectiveness of the quality management system in force at the enterprise, the possibility of incurring costs for quality assurance, updating equipment and applying new technology, initial quality materials, etc.);
3) social (the degree of interested participation of various groups of personnel in improving the level of quality of production of goods and services, the level of qualifications of workers, the creation of social conditions for achieving quality indicators).

It is obvious that many of the existing problems of quality assurance and management at enterprises are complex in nature (mainly technical and economic, but at the same time there is a social aspect). This especially concerns the nature of the interaction between personnel and quality management processes at an enterprise in modern conditions.

The corporate culture of an enterprise using Total Quality Management (TQM) assumes that short-term economic benefits obtained as a result of savings on quality will inevitably lead to huge losses for the enterprise in the future due to the loss of some consumers and the loss of market positions. Personnel management in a TQM environment should be considered as a multi-level management activity in an enterprise with an effective solution to quality problems.

In a developed market economy, current quality problems are solved on the basis of the following basic principles:

1) consideration of quality as one of the most important competitive advantages of an enterprise;
2) unconditional satisfaction of consumer requirements;
3) consistent increase in the warranty period for sold products.

It should be borne in mind that the more complex the technologically produced goods, the more difficult it is for the manufacturing enterprise to guarantee their quality. But nevertheless, an increase in the warranty period for consumers is proof of the high quality of the products offered, and therefore, one of the most important competitive advantages of the manufacturer.

Providing employees with opportunities for self-control of quality and open discussion of problems related to the quality of goods and services increases the effectiveness of their resolution. To implement TQM requirements, it is necessary that the majority of enterprise employees have the opportunity to influence all factors that determine the level of quality. It is obvious that providing employees of an enterprise with opportunities for self-control of quality is achievable only in conditions where they, to a certain extent, identify themselves with their enterprise and associate their future professional destiny with it.

In a TQM environment, entrepreneurs and managers must actively develop and implement ideas aimed at solving quality problems, taking responsibility for their implementation. At the same time, a high degree of staff trust in leaders and managers must be achieved.

Elements of goods and services constantly interact with each other and are in a dynamic relationship. The quality of goods and services now has the greatest impact on the viability of any production or service enterprise.

In a market economy, both producers and consumers find each other in the market. Moreover, consumers often play the role of “leading violin” in society, choosing the best goods and services from various manufacturers, thereby determining the main directions of production development.

When considering the essence of the principles of systematic and comprehensive quality assessment, 15 main conditions for the application of these principles are identified. These conditions, after appropriate adaptation, can be formulated as specific principles of quality management:

1) formation of management decisions taking into account production, economic, social and market factors;
2) balancing goals and resources, searching for ways to use them rationally;
3) completeness of accounting of resource needs;
4) taking into account the interaction of industry and regional factors;
5) taking into account the relationships and interactions between different levels of economic management;
6) consideration in the unity of natural-material and cost measurements of production volumes, consumption and costs;
7) taking into account the relationship between short-term problems and long-term development strategy;
8) taking into account the impact of management decisions on the social and environmental environment;
9) analysis of the motives of activity and interests of various social groups;
10) taking into account the foreign economic aspects of the problems under consideration;
11) use of quantitative and qualitative methods of analysis and assessment;
12) combining objective-subjective assessments with the exception of the subjectivist approach when solving problems;
13) a combination of assessments: internal (from the performer) and external (from the control bodies);
14) a combination of continuity and phasing in the implementation of quality assessments;
15) development of quality management systems.

Our analysis showed that a system-integrated approach to quality management in our country since the 60s. until the mid-90s of the 20th century. actively used and developed in various sectors of the economy, especially in industry and the military-industrial complex (MIC). For several decades, enterprises of domestic industry (including defense industries) have been implementing the practice of improving quality work, characterized by an intensive search for new forms and methods of their organization and quality management at all levels.

In domestic integrated quality systems, as an analysis of the theory and practice of their application shows, there are great opportunities and reserves for their systematic improvement. Further development of such systems can be based on taking into account an increasing number of factors and reasonable restrictive conditions that influence the formation of the quality of the object, improving the structure and elements of these systems, expanding their goals and functions. When implementing such complex systems at leading domestic enterprises, a combination of areas for increasing production efficiency and work quality (including assessing the work of departments and performers) is valuable.

It can be noted that a number of leading Russian enterprises are currently painlessly carrying out work to bring previously implemented quality systems to the level of requirements of generally recognized modern international standards ISO 9000 for quality management. This suggests that domestic experience in integrated quality management is a good basis for mastering ISO 9000 standards.

The main provisions and requirements enshrined in GOSTs for quality management were a significant scientific and practical contribution to the methodology for improving modern management. Most of these provisions and requirements are still difficult to overestimate, taking into account modern trends in the production of competitive products, goods and services.

The quality management system, which domestic enterprises should implement in the future (as defined by GOST R ISO 9000-2008), is a management system for leading and managing an organization in relation to quality. It is a set of organizational structure, distribution of powers and responsibilities, methods, procedures and resources necessary to establish, maintain and improve quality. Any quality system, despite the characteristics of enterprises (organizations), is aimed at achieving the following main goals: improving quality and efficiency; increased customer satisfaction; cost reduction; increasing competitiveness; improving the production and psychological climate in the team; environmental protection.

Currently, Russian enterprises in a market economy must use advanced foreign experience in quality management at enterprises, primarily Japanese, American and European countries, which have gone far ahead in their development over the past 20 years.

Domestic enterprises will have to master the achievements of global quality management, implement international standards ISO 9000 family, TQM principles, learn how to manage personnel in a TQM environment, i.e. achieve an approach to managing an organization that is focused on quality, based on the participation of all its members and directed to achieve long-term success through customer satisfaction and benefit to organizational members and society.

The peculiarity of total quality management (TQM) is that in the activities of enterprises, quality is placed at the forefront, and all personnel are involved in ensuring the required quality of goods or services.

In general, the functioning of an enterprise under conditions of total quality management requires the fulfillment of the following basic requirements:

active quality management on the part of the management (administration) of the enterprise;
the main purpose of the enterprise is to satisfy customer needs for quality goods and services;
the quality strategy is aimed at continuous improvement and achieving results that ensure stable operation of the enterprise;
development and implementation of quality management systems taking into account international standards ISO 9000;
creation of a system for training and advanced training of personnel, involving employees in quality assurance work, “quality circles”;
provision of necessary resources with minimal reserves and their rational use (according to the principles of logistics);
implementation of a “just in time” inventory management system;
certification of goods, services and quality systems at the modern level;
creation of an information support system for work in the field of quality.

An increasing number of Russian enterprises and companies are aware of the problems of implementing TQM, studying advanced foreign experience in this area. Enterprise management needs to quickly solve the problem of understanding the methodological foundations of ISO 9000 standards and implementing their requirements.

According to the ideas of TQM developers, the main responsibility for quality rests with the management system and its creators, managers. At many of our enterprises, as is known, the situation is almost exactly the opposite. The second main problem for Russian enterprises is the missed stages of quality management development (including probabilistic, qualimetric, statistical methods of quality control and management).

At our enterprises, it is often necessary to solve four main problems from scratch in a scientifically sound, rational manner:

1) master the production of goods that are in high demand;
2) create a trade network for sales, distribution of goods and information about them;
3) minimize total costs;
4) learn to manage finances and quality costs by organizing an effective management accounting system.

Having completed these tasks, enterprises can begin to create and certify a quality management system that meets the requirements of ISO 9000 and the TQM concept.

In Fig. Figure 3.13 shows a model of a quality management system based on a process approach. This approach is aimed at continuous improvement, which requires not only long-term special training, but also well-organized work of the enterprise.

Let us note the main advantages of the new version of international standards:

1. ISO 9000-2000 standards are significantly reduced in comparison with the 1994 version and are easier to use.
2. The ISO 9004 standard, which contains recommendations for improving the activities of the enterprise, is aimed at developing a quality management system containing the requirements of the ISO 9001 standard.

Rice. 3.13. Model of the quality management process (according to R ISO 9000-2000)

3. The standards are suitable for all types of products, services, all industries and organizations.
4. The standards establish a connection between the quality management system and organizational processes and other management systems.
5. The standards address the needs and benefits of all interested parties.
6. Standards are focused on continuous improvement and customer satisfaction.

The listed advantages allow you to choose the right quality management system for an enterprise, but it should be taken into account that the most effective modern quality systems are integrated today and in the future into a single concept, Total Quality Management (TQM). The TQM system is comprehensive, focused on continuous quality improvement, cost minimization and just-in-time delivery. This system should be considered as part of the overall enterprise management system.

The international standards of the ISO 9000-2000 version are based on the following eight principles of quality management (TQM):

1. Customer focus.
2. Leadership of a manager who ensures the unity of purpose and directions of activity of the organization (enterprise).
3. Involvement of workers at all levels.
4. Approach the system as a process.
5. Systematic approach to quality management.
6. Continuous improvement as a constant goal.
7. Making decisions based on the analysis of facts, process data and information.
8. Mutually beneficial relationships with suppliers and all partners.

A process is understood as a set of interrelated and interacting activities that transform inputs into outputs (Fig. 3.14).

Rice. 3.14. Process description

The peculiarity of building a quality system based on a process approach is the organization of management taking into account the benefits of all stakeholders in an integrated supply chain with a main focus on the consumer. The basic ideology of TQM is based on the principle “there is no limit to improvement, constant improvement of quality.” Moreover, the complex process at the enterprise should be considered as a continuous logistics flow.

The philosophy of ISO 9000, the latest version, is based on the effective application of the “rule of trust”, which allows for a more rational use of the resources of both each enterprise individually and the economy as a whole. The universality of these international standards lies in the fact that they do not offer specific quality criteria for each individual type of goods and services, but only set the methodology for the functioning of the quality system, ensuring the highest quality of these goods and services with a high degree of consumer satisfaction.

Thus, due to their progressive nature, the international standards ISO 9000-2000 should be the basis of the modern concept of total or total quality management (TQM).

The TQM concept provides for the comprehensive, targeted and well-coordinated application of quality management systems and methods in all areas of activity, from research and development to after-sales service, with the participation of management and employees at all levels and the rational use of technical capabilities. The TQM concept is interdisciplinary in nature. This is a set of principles, methods, means and forms of quality management with the aim of increasing the efficiency and competitiveness of the organization. This concept allows for a broad interpretation of quality (Figure 3.15).

Total quality management is not a theoretical discipline; it represents a specific technology for managing all quality improvement processes. The TQM concept is implemented at the enterprise through the use of a set of techniques and means (Table 3.3).

For total quality management at enterprises, it is necessary to manage not only production, but also marketing, information, logistics, organizational, economic, labor, innovation and other processes, i.e. the use of a system-integrated approach.

Figure 3.15. Broad understanding of total quality management (TQM)

Table 3.3

TQM techniques and methods

Control quality	Control processes	Control staff	Control resources

1. Definition of quality	Stability process	Management team	Quality Spending Program
2. Quality policy	Statistical control methods	Total Quality Training	Execution control indicators
3. Total quality training	Opportunity process	Organization of working groups	Cost indicators
4. Relations with internal consumers	Solving technological problems	Methods and means of motivation	Conservation of resources
5. Quality systems	Process improvement	Links	Improvement of the environment
6. Quality mugs	Analysis of the nature and consequences of failures	Theories of intensification	Working according to the “just in time” system
7. Taguchi and Deming principles	Analysis of the nature and consequences of failures at the production stage	Training	Minimization resource costs

Enterprises using TQM are characterized by high quality and competitiveness, team spirit in the organization, justice as the basis of motivation and faith as the basis of optimism, high moral, ethical and guiding principles in the organization, flat organizational structure with process and project management styles, effective management.

Advantages of introducing the TQM concept at domestic enterprises:

improving quality and competitiveness;
increasing the degree of consumer satisfaction with products, goods and services;
improving the image of enterprises;
ensuring the financial and economic sustainability of enterprises;
rational use of all types of resources;
introduction of achievements of social progress and scientific and technical progress;
improving the quality of management decisions and technical and economic performance indicators of enterprises.

At enterprises it is necessary to combine internal audit and self-assessment (Table 3.4).

Successful application of this approach allows enterprises to provide managers with the necessary information on self-assessment, increase the efficiency of quality checks, determine their own potential and availability of resources, and select the best quality model for themselves.

Table 3.4

Comparative characteristics of internal audit and self-assessment

Internal audit	Self-esteem
Advantages
General approach	Increasing staff responsibility Everyone determines their own potential for improvement.
The technique is clearly proven	Better understanding of TQM Same tools for assessing the quality system and the new model
Flaws
Two different assessment methods (quality system and new model)	In relation to ISO 9000, inspections are carried out randomly. Additional training is required for department managers
	No methodology for general approach

Today, it should be clear to all domestic enterprises that it is necessary not only to ensure the quality of processes, but also a systematic view of the entire complex of relationships between enterprises and each stakeholder. When starting to implement the requirements of international standards ISO 9000:2000, and then to create a TQM model, the enterprise should:

study the relevant regulatory and technical documents (NTD);
determine what benefits the enterprise will have if a new quality management system is implemented;
prepare the necessary personnel and ensure the participation of managers in the process of preparing the system for implementation;
develop and implement a new quality standard document;
conduct self-assessment and audit;
carry out a preliminary assessment of the effectiveness of the new system;
reorganize the organizational structure of the enterprise, ensuring a transition to horizontal structures and a process approach;
implement the eight basic principles of TQM quality management (customer focus, leading role of management, employee involvement, implementation of process and system approaches to management, continuous improvement, fact-based decision-making, mutually beneficial relationships with suppliers);
carry out activities for certification of products and quality systems.

In accordance with the Law of the Russian Federation “On Technical Regulation”, standardization is defined as the activity of establishing rules and characteristics for the purpose of their voluntary repeated use, aimed at achieving orderliness in the areas of production and circulation of products and increasing the competitiveness of products, works or services.

Standardization performs three main socially significant functions:

1) ordering of objects (products, works, services, processes);
2) fixation in regulatory documents (ND) of optimal requirements for ordered objects;
3) establishment of rules for the application of ND.

Standardization has the following goals:

interchangeability (using one product, service or process as a substitute for another to fulfill the same requirements);
compatibility;
unification (bringing to uniformity);
safety, including environmental;
competitiveness;
efficiency.

Technical regulation (TR) is the legal regulation of relations in the field of establishment, application and execution of mandatory requirements for products or for products and the processes of design (including surveys), production, construction, installation, commissioning, operation, storage, transportation associated with product requirements , sales and disposal, as well as in the field of establishing and applying on a voluntary basis requirements for products, design processes (including surveys), production, construction, installation, adjustment, operation, storage, transportation, sales and disposal, performance of work or provision of services and legal regulation of relations in the field of conformity assessment.

Technical regulations - a document that is adopted by an international treaty of the Russian Federation, subject to ratification in the manner established by the legislation of the Russian Federation, or in accordance with an international treaty of the Russian Federation, ratified in the manner established by the legislation of the Russian Federation, or a federal law, or a decree of the President of the Russian Federation, or a decree of the Government of the Russian Federation, or a regulatory legal act of the federal executive body for technical regulation and establishes mandatory requirements for application and execution for objects of technical regulation (products or for products and processes of design (including surveys), production, construction, installation, adjustment, operation related to product requirements , storage, transportation, sales and disposal);

As you know, there is a distinction between certification of production, products, goods, services and quality systems. In the process of quality system certification, two main stages should be distinguished:

1) preliminary check and assessment of the quality system;
2) final inspection, assessment and issuance of a certificate of conformity of the enterprise’s quality system.

Based on the results of the first stage, the certification body (CB) draws up an appropriate conclusion. In case of a positive conclusion, when the contract is signed, the deadlines for the work on the second stage are established. If, when performing this stage, the OS detects a discrepancy between the quality system at the enterprise and the requirements of the relevant standard, then, together with this enterprise, a deadline for its revision and a new deadline for re-inspection are established. If the decision is positive, the certificate is issued for a period of up to three years.

Certification is carried out according to schemes, the classification of which is given by ISO and which are listed in the Rules for Certification in the Russian Federation (approved by Resolution of the State Standard of the Russian Federation dated May 10, 2000 No. 26). In the process of certification of services (works), seven schemes are used (Table 3.5).

Table 3.5

Certification schemes for services (works)

Object of assessment	Object of inspection (tests)	Inspection control
Performer skill	Results of services (works)	Monitoring the skill of the service (work) performer
Process of providing services (performing work)	Results of services (works)	Monitoring the process of providing services (performing work)
Production status	Results of services (works)	Production status monitoring
Enterprise (organization)	Results of services (works)	Compliance monitoring
Quality system	Results of services (works)	Quality system control
Quality of services (works)		Quality control of service provision (work performance)
Quality system	Review of the declaration of conformity (with attached documents)	Quality system control

For example, scheme 1 is used for services and work, the safety and quality of which are determined by the qualifications of the performer (for example, a teacher, hairdresser, seamstress). Scheme 3 is used for certification of production services. Scheme 5 is intended for certification of services (works) directly related to the health and life of consumers (for example, medical, transport services). The assessment of the quality system according to schemes 5 and 7 is carried out by quality system certification experts in accordance with the requirements of international standards ISO 9000.

Russia has finally joined the World Trade Organization (WTO). This accession requires compliance with the fundamental international document on services - the General Agreement on Trade in Services (GATS), aimed at developing world trade, legal and regulatory assurance of quality, and compliance of services with established requirements. Although many legislative acts have been introduced in the service sector in recent years, the system of standardization and certification of services in the Russian Federation requires significant reform. Russia needs to comply with the international conditions of the GATS, established by such documents as the “Agreement on Technical Barriers to Trade”, “Agreement on Sanitary and Phytosanitary Measures”, as well as the rules and principles governing trade in services on a commercial basis, regardless of ownership.

The general obligations of the GATS establish the most favored nation regime for trade in services, transparency of legislation in the service sector, and mutual recognition of requirements for supplier qualifications. At the same time, for each important type of service, Russia must clearly indicate the method of delivery of the service according to the GAT classification. Specific obligations for access to the Russian services market can be introduced by special decisions, measures and acts that define restrictive conditions for the activities of foreign service providers in the domestic market.

When developing quality management systems at enterprises operating in the service sector, one should be guided by the international standards ISO 9000:2000 (both the general Guidelines and the Service Guidelines). The selection of elements and the degree of their use depend on many factors (sales market, service characteristics, customer satisfaction, etc.). Requirements for a service and the processes for its delivery must be defined through characteristics that can be quantitative (measurable) or qualitative (comparable for quality, depending on how and by whom the assessments are carried out - the consumer or the service organization).

Top management has direct responsibility and obligations of the service organization for the quality policy and its implementation. Managers must translate the priority goals and objectives in this area into a specific program of action for the service enterprise team. At the same time, management needs to carry out the correct selection of employees based on their ability to satisfy precisely formulated requirements; provide the necessary working conditions; realize the potential of each employee through stimulation, creative work methods and wider involvement in solving the quality problem; achieve awareness of the involvement of all personnel in influencing the quality of services provided to consumers; Constantly train employees on the service organization’s quality policy and obtain relevant knowledge and skills.

Service quality indicators can be classified into quantitative and qualitative. The first include such indicators as waiting time and service delivery, reliability of its provision, completeness of service provision, etc. Qualitative indicators are accessibility, sensitivity, politeness, trust, competence, sociability, effectiveness of contacts between performers and clients.

Service quality indicators can be grouped into such groups as functionality, reliability and safety, aesthetics, environmental friendliness, social significance, professionalism, service culture, image of the service enterprise and its employees. In relation to specific types of services, the composition and nomenclature of indicators (their groups) can be differentiated and even unique.

In conclusion of this section, we note that from the theory and practice of management it is known that stimulating the “struggle” for better quality has a significant impact on the efficiency of enterprises. Standards for quality systems (ISO 9000, etc.) and TQM principles can be called the main tools of quality management. It is necessary to develop and implement incentive systems for quality indicators of goods and services at enterprises.

Of course, solving most quality problems in Russia requires the interaction of scientists, university teachers, and managers. Experience in the development of quality systems is gradually accumulating as a result of a fairly long and at the same time dynamic process of improving the market economy.

Nesterenko Denis Nikolaevich, Student, Volgograd State Agrarian University, Volgograd [email protected]

Kadina Irina Viktorovna, Ph.D., Associate Professor, Volgograd State Agrarian University, Volgograd [email protected]

The use of mathematical methods in solving psychological problems of the modern world

Annotation. The article substantiates the use of mathematical methods in psychological research. The statistical processing of the results of psychological testing is considered. The study identified and substantiated the effectiveness indicators of the applied methods, which are characterized, in turn, by a set of criteria for each component; the main connections between mathematics and psychology are revealed, presented in the form of a theoretical model built on the basis of a structural analysis of psychological research. Key words: mathematical methods, psychological problem, test, experiment, statistics.

“The maturity of a science is usually measured by the extent to which it uses mathematics. Mathematics itself is not a science in the empirical sense, but is a formal logical, symbolic system, a kind of game of signs and rules,” this is how S. S. Stevens begins his major work “Experimental Psychology,” which had a great influence on the formation of psychology not only for abroad, but also in our country. How do psychologists use mathematics?

There are two opposing points of view on the issue of studying mathematics in psychology. Supporters of one of them, perceiving mathematics as some kind of universal means, see in the mathematization of psychological knowledge the only way to overcome the difficulties that lie in the way of studying various problems of psychology. Proponents of another point of view, on the contrary, argue that research in mathematics, due to the specific nature of psychological research, is in principle impossible, because in practice, modeling and formalizing mathematical phenomena turns into an empty game with mathematical symbols. The groundlessness of both points of view is obvious. One cannot demand more from mathematics than what it can give, but what it can really give must be used to the fullest. The use of mathematical methods for diagnosing the mental qualities of an individual at different stages of its development is the subject of numerous discussions. Thus, the relevance of the study is explained by the fact that psychological problems (aggression, depression, neuropsychiatric disorders, computer, gaming, drug and other addictions) are very acute in modern society, and they can be solved with the help of specialists using effective techniques developed taking into account the results of processing experimental data using mathematical methods. The object of the research is mathematical methods for processing experimental data obtained as a result of psychological research. The subject of the research is mathematical and psychological methods that have certain requirements and influence the results of psychological research. The purpose of the research is to determine the influence of the results of processing experimental data using mathematical methods on the quality of psychological research. In accordance with The purpose and subject of the study were the following tasks: 1. Assess the current state of psychological problems in society.2. Based on an analysis of scientific literature, determine the requirements for mathematical methods for processing the results of psychological research. 3. Determine the classification of psychological problems solved using methods of mathematical statistics.4. Assess the extent to which mathematical methods influence the results of psychological research. The research hypothesis consists of the assumption that processing the results of psychological research using mathematical statistics methods allows us to determine the effectiveness of a particular technique. Research methods: study and analysis of psychological and scientific literature on the problem under study; methods for analyzing products of psychological activity; modeling, questioning, observation, testing; methods of statistical processing of research materials. The reliability of the research results is determined by the validity of the initial theoretical positions, including reference to related sciences; sufficient sample size to conduct the experiment; using a set of research methods adequate to the subject and objectives; correct organization of experimental work; variety of information sources; stable repeatability of results over a long period; positive feedback from specialists who use research materials in their activities. The scientific novelty of the research results is that:

it explores the importance of the problem and reveals the relationships between mathematics and psychology;

the psychological problem of modern society and methods for solving it are analyzed;

a comparison was made of various methods for solving certain psychological problems;

the effectiveness indicators of the applied methods have been identified and justified, which are characterized, in turn, by a set of criteria for each component;

The main connections between mathematics and psychology are revealed, presented in the form of a theoretical model built on the basis of a structural analysis of psychological research. The theoretical significance of the research results lies in the fact that the ideas about the essence of psychological research and their effectiveness are theoretically determined depending on the results of processing experimental data by methods of mathematical statistics. The practical value of the research results lies in the fact that the feasibility of using mathematical methods for processing experimental data from psychological research and using these results to select methods that have the most effective impact on solving psychological problems of the individual in modern society are substantiated. The results of this study have a beneficial effect on the formation of positive motivation in high school students, both when studying mathematics and psychology. Psychology as an independent scientific discipline is not that ancient, although the main object of its research is man, who has occupied philosophical thought since humanity learned to think. However, it took centuries of work by many scientists for psychological research to appear. Since the time of Wolf, psychology began to be called empirical, but it was not such, because the main method of its research remained the introspective method, with the help of which no precise measurements could be made. But if in the 18th century Kant argued that psychology could never become an exact science, since measurements in it were impossible, then already at the beginning of the 19th century the impossible became possible. In any case, the works of the German philosopher, psychologist and teacher Johann Herbert date back to this time, who in 1822 first gave a report in Berlin “On the impossibility and necessity of applying mathematics in psychology.” The most important milestone in the further development of psychology was the work of Weber and Fechner, who, while studying human sensations, were the first to use the experimental method in their research. The twentieth century introduced several unexpected features into the “relationship” between man and mathematics. So, if at the beginning of the century some aspects of this issue were widely discussed by many scientists, including A. Poincaré, I.P. Pavlov, A. Einstein, etc., then in 3040. they no longer arouse keen interest. This can be judged at least because in psychological research of this period very little attention is paid to quantitative methods; the formalization of quantitative phenomena prefers qualitative descriptions. However, just a few years pass, and interest in the use of mathematics in psychology flares up with new, unprecedented force. The reason for this was the emergence and rapid development of a number of technical sciences, primarily cybernetics. It contributed to the desire to improve many mathematical methods, which, in connection with new problems that arose in psychology, could be used in it much more effectively than before. But the main distinguishing feature of the interaction between psychology and mathematics of this period was the appeal of mathematics to psychology. This is explained by the fact that in the middle of the twentieth century, in connection with the development of electronic computing technology and achievements in psychology, neurology and physiology, a real opportunity arose to “pose” the problem of “improving” thought processes. Speaking in this regard about the interaction of psychology and mathematics, we can give another example that characterizes the two-way connection between these subjects. “Thanks to the enormous structural and functional complexity,” notes the author of the book “Fundamentals of Mathematical Statistics for Psychologists” V.G. Sukhodolsky – “mental, social, pedagogical phenomena have long served for the development of mathematical statistics itself; it is enough to mention F. Golton, who developed the initial ideas of correlation and regression, C. Stermin, who created rank correlation and univariate analysis, L. Furston, who developed multifactor analysis.” Thus, the assumption of N. Winner, who noted the connection between physics and biology: “I foresee that not only will the biological sciences move closer to physics, but that physics will also assimilate some biological ideas,” is to some extent true of the relationship between psychology and mathematics. But if we are still talking about this connection from the position what psychology has given to mathematics, now let us consider what mathematics gives to psychology? Let us dwell on one problem, which, without any exaggeration, can be called a general obstacle to the more effective use of mathematics in all areas of psychology without exception. This is a "language" problem. The fact is that the use of mathematical methods to sense psychological phenomena, as well as the use of psychological knowledge in the design of complex systems, requires a unified terminological language for its description. The absence of such a language sometimes leads to rather disastrous results. However, communication between psychologists and mathematicians sometimes seems absurd. Thus, even if psychologists manage to formulate the meaning of the problem posed for mathematicians, then mathematicians most often fail to convey to psychologists the meaning of mathematical results. It is well known from the history of psychology that, for example, psychophysics began its development with the establishment of mathematical laws (the famous Weber-Fechner formula). At present, mathematical procedures are necessarily included in such branches of psychology as psychometrics, psychodiagnostics, differential psychology. Modern psychogenetics, for example, widely uses such a branch of higher mathematics as structural modeling, etc. At the same time, the main difference between branches of psychological knowledge that use mathematical methods is that their subject of research can not only be described, but also measured. The ability to measure a particular psychological phenomenon (properties, characteristics, traits, etc.) opens up access to the use of quantitative analysis methods, and therefore corresponding computational procedures. In his work, a psychologist is often faced with the problem of measuring individual psychological characteristics, such as, for example, creativity, neuroticism, impulsiveness, properties of the nervous system, etc. For this purpose, various measurement procedures are being developed - tests, models (of cognitive processes, features of motivation, value orientations of an individual), etc. Numerical representation of objects or events allows one to operate with complex concepts in a more abbreviated form. This is precisely the reason for the use of measurements in any science. Measurement is a procedure by which the measured object is compared with some standard and receives a numerical expression on a certain scale or scale. The most natural way in which mathematics “penetrates” psychology is mathematical statistics . Modern statistics is a branch of mathematics. At the same time, many statistical procedures are quite simple and easy to implement. The correct use of statistics allows the psychologist to: 1. Prove the correctness and validity of the methodological techniques and methods used; 2. Strictly justify experimental plans;3. Summarize the experimental data;4. Find the relationship between experimental data;5. Identify the presence of significant differences between groups of subjects (for example, experimental and control);6. Make statistical predictions;7. Avoid logical and substantive errors and much more. We must not forget, however, that statistics itself is only a toolkit that helps a psychologist effectively understand a complex experiment: a clear statement of the problem, careful planning of the experiment, and the construction of consistent hypotheses. However, statistics itself is only a tool that helps a psychologist effectively understand complex experimental material. The most important thing in any experiment is a clear goal setting, careful planning of the experiment, construction of consistent hypotheses. Scheme of a psychologist’s research work. RESEARCHER (psychologist) ↓ Subject of research (mental properties, processes, functions, etc.) ↓ Experiment (measurement) ↓ Experiment data (numerical codes)↓Statistical processing of experimental data↓Result of statistical processing (numerical codes)↓CONCLUSIONS Mathematical statistics allows a psychologist not only to successfully navigate the sea of experimental data, but also contributes to the development of his objective thinking. Despite the noted difficulties, mathematical methods today cover a fairly wide area of psychological research. To verify this, it is enough to name three main forms of studying mathematics in psychology: the first of them is the statistical processing of observation results; the second is the search for equations that describe the relationship between the variables involved in the experiment; the third is the creation and testing of a mathematical model. On the initial development of statistical methods Their origins were influential: statistics had a "mother" who had to submit regular reports to government departments, and a "father" who was an honest card player who relied on mathematics to enhance his dexterity in taking decisive tricks in gambling. From the “mother” come the origin of reporting, measurement, description, tabulation, that is, everything that led to modern descriptive statistics. From the enterprising intellectual “father” arose, ultimately, the modern theory of statistical inference, directly based on the theory of probability. A recent addition called "design of experiments" relies mainly on a combination of probability theory with somewhat elementary but "amazing" logic. Let us now consider how these branches of statistical methods are used in psychology. Descriptive statistics serves as a tool for describing, summarizing, or reducing data sets to a desired form. The theory of statistical inference allows one to infer the properties of large amounts of this data by examining a sample. The third branch, planning and analysis of experiments, designed to discover and test causal relationships between variables, is of particular importance for psychological research, since psychology is more than any other. The application of all three main forms of using mathematical methods in psychology allows us to mathematically approach the most important question of modern psychological research: the construction of a scientific theory, its quantitative description, since a bad quantitative theory is much easier to refute than a poor quality one.

The mathematical interpretation also gives an advantage when deciding on the choice between two opposing theories. Analysis allows us to determine which predictions of one theory contradict those of another. An experiment is then set up to show which predictions are confirmed. Sometimes we become convinced that the predictions of completely different axioms unexpectedly turn out to be similar and even identical. This counterintuitive view can be derived deductively. Thus, the use of mathematics can save us from making experiments that are not capable of giving us the information we need. The mathematical approach helps the theorist even when his predictions are not confirmed, that is, when a qualitative theory turns out to be untenable, the theorist sometimes cannot resist the temptation to try to save her, stating that the theory is essentially correct, but requires only minor amendments to reconcile it with the results of observations. It’s another matter if this same theory is expressed in a mathematical formula. It will be much easier for the theorist to establish such a fact, how another trick will help eliminate the difficulties that have arisen, or how, without questioning the entire theory, one can localize the source of the difficulty by establishing what lies in one or another initial axiom. Let us emphasize again that before perform any psychological experiment. It is necessary to clearly formulate its tasks, define the experimental hypothesis and all stages of its statistical testing, as well as select the appropriate statistical method that is most effective for solving the problems posed in the study. The vast majority of problems solved by a psychologist in an experiment involve some kind of comparison. These can be comparisons of the same indicators in different groups or, conversely, different indicators in the same group. To determine the degree of effectiveness of any influences (education, training, coaching, instruction, etc.), the indicators “before” and “after” these influences are compared. For example, indicators of the level of aggressiveness in adolescents before and after psychotraining are compared, which makes it possible to determine its effectiveness. Sometimes the task arises of comparing individual indicators obtained under different external conditions in order to identify the connection between them. Two sample distributions are compared with each other or with a theoretical distribution law in order to identify differences or, on the contrary, similarities in the types of distribution. For example, a comparison of the time distributions for solving simple and complex problems will allow us to construct a classification of problems and a typology of subjects. In general, psychological problems solved using methods of mathematical statistics can be divided into several groups: 1. Problems that require establishing similarities or differences. 2. Problems , requiring grouping and classification of data. 3. Tasks aimed at analyzing the sources of variability in the obtained psychological characteristics. 4. Tasks involving the possibility of forecasting based on available data. Having examined, in the most general terms, various aspects of the use of mathematical methods in psychology, we will now try, as far as possible, to concentrate their use in some psychological research. In this regard, the use in psychology of such a “purely mathematical” theory, such as “game theory,” may be of undoubted interest. . According to the author of the book G.E. Zhuravlev, this theory has become one of the fundamental means of modern mathematical psychology. In this regard, there is an urgent need to clarify the role and place of game-theoretic description in the general system of psychological knowledge and outline ways to improve it. Studying works in the field of mathematical psychology, we can identify one general principle for the use of general systems, which we will call the principle of superposition. Let us try to indicate in general terms the features of the functioning of the game-theoretic scheme in human activity. Let us assume that we have three objects or three scientific fields in which we will try to trace the basic principles of their relationships. One of these fields is the subject of psychology, i.e. her special approach to studying the world. The second theory of games, as a special theoretical construction with its own concept, mathematical apparatus and rules of use. And finally, the third synthetic area of application of game theory in psychology. As for game theory, it studies the following scheme. Let's imagine several players, each of whom has the ability to choose one of several actions. As a result of the sequence of choices and a series of actions taken, players sum up the results: receive income or pay a fine. If the players’ task is to find the best moves, then the task of game theory is to find the principle of finding these moves. The application of this theory in psychology is to impose this scheme on objective psychological reality. If the game, as a special form of reflecting human activity, arose in ancient times, then the first sketches of game theory appeared only three centuries ago in the works of Bernoulli. At the present stage of development of this theory, a fact of extreme importance has been discovered: cybernetic theory, alien at first glance to psychology, is inextricably linked with human activity. The game scheme, as a form of activity itself, reflects other forms of activity in a social form. That is why the game, in theoretical terms, is not an integral part of psychology. At the same time, we must, of course, remember that in order to be fully included in psychological theory, the game scheme must be changed, since when applied to activity, a game is never a functional formation. Among the various research methods: methods for analyzing the products of psychological activity, modeling, questioning, observation, testing, etc. One of the most effective methods for studying the psychological properties of a person can be identified - testing. In contrast to traditional means of control, tests under certain conditions make it possible to identify not only the level of mental development, but also the degree of its deviation from the ideal structure. The use of testing in real psychological and pedagogical activities can significantly increase the objectivity and accuracy of assessing performance results. An elementary idea of the degree of deviation allows us to analyze the response profile of the subjects to various test tasks.

Testing is associated with an objective assessment, because here, a set of methods works on the idea of objectifying the results of those being studied, starting from the moment the test is conceived until the moment the work on it is completed and its use, ending with the scaling of test scores. The problem of objectification is solved especially effectively in modern test theory, where special mathematical methods and measurement models provide a transition to more plausible estimates that provide an optimal approximation to the true components of the measurement. The term “testing” itself goes back to the English test-exam and is used, according to the French encyclopedic dictionary Larousse, to measure or evaluate natural or acquired abilities in order to predict the behavior or achievements of a person in certain circumstances. Important work in the field of testing is the work of the Danish mathematician G Rocha (1960), it gave impetus to the active development of the theoretical basis of testing. The result of this is a modern theory, which in the English literature is called Item Response Theory (IRT). The main goal of IRT is to develop a mathematical model of the testing process, the parameters of which are various characteristics of the test participants and the testing itself. test. The Soviet encyclopedic dictionary focuses our attention on its application only in the field of psychology and pedagogy, because a test is a standardized task, the results of which are used to judge the psychophysiological and personal characteristics, as well as the knowledge, skills and abilities of the subject. Classic definitions in psychology emphasize: a) the empirical nature of the assessment; b) determination of personal characteristics and qualities through the use of quantitative indicators.

The testing method must comply as much as possible with the principles of comparison, objectivity, reliability, validity and discriminativeness of measurements. It must undergo processing and interpretation and be acceptable for use in psychological practice. Test indicators are, as a rule, reduced to a normal distribution, which makes it possible to carry out a full and accurate statistical analysis of them, since for the normal distribution there is a rich set of statistical research tools. Methods for statistical processing of experimental results are mathematical techniques, methods of quantitative calculations, with the help of which quantitative indicators obtained during the experiment can be generalized, brought into the system, revealing hidden patterns in them. Some of the methods of statistical analysis make it possible to calculate the so-called elementary mathematical statistics that characterize the sample distribution of data. Other mathematical statistics make it possible to judge the dynamics of changes in individual sample statistics.  Primary method of statistical data processing. Primary is a method that can be used to obtain indicators that reflect the results of changes made in an experiment. Accordingly, by primary statistical indicators we mean those that are used in the psychological methods themselves and are the result of the initial statistical processing of the results of psychodiagnostics. Primary methods of statistical processing include determining the sample mean, sample variance, sample mode and sample median.  Secondary method of statistical processing of data. Using the secondary method of statistical processing of data, hypotheses associated with the experiment are directly tested, proven or disproved. These methods are more complex than the methods of primary statistical processing, and require the researcher to have good training in the field of elementary mathematics and statistics. The group of methods under discussion can be divided into several subgroups: 1) Regression calculus. 2) Methods for comparing several elementary statistics with each other. 3) Methods establishing statistical relationships between variables. 4) Methods for identifying the internal statistical structure of empirical data.  Methods for tabular and graphical presentation of experimental results. Tables are horizontally and vertically ordered sets of quantitative and qualitative data, framed or without them. Tables may or may not have titles and subtitles. Tables, if there are more than two or three of them in the text, are numbered. Directly below them is the table name. Sometimes this is done by making a note regarding the material contained in the table. Tables have headings that indicate what is presented in individual columns, as well as headings by rows, which indicate the features of the material presented. Graphs on a plane represent a certain line that depicts the relationship between two variables, and a graph in space is a plane representing the dependence between three variables. When using a two-dimensional graph, an independent variable is placed along a horizontal line on the plane, which is considered as a possible cause being sought. The dependent variable that is considered as the presumed cause is placed vertically. Rice. 1. Conclusions Our work has shown a close connection between mathematics and psychology. An analysis of the scientific literature was carried out, which revealed the shortcomings of the existing system for testing the psychological qualities of a developing personality. The work identifies the psychological problems of modern society, conducted an experiment to select the most effective methods for studying personality, and justified the feasibility of using mathematical methods for processing experimental data from psychological research and using these results to select methods that have the most effective impact on solving psychological problems of personality in modern society. Three main forms of studying mathematics in psychology are named, a classification of psychological problems solved using statistical methods is given. The work shows that a set of test tasks, which is one of the effective diagnostic methods, is advisable to build on the basis of creating tests of different levels of complexity that have been tested for reliability , validity, accuracy, discriminativity. The appendices provide examples of practical research in game theory, reveal the “paradox of pictures”, and provide formulas from mathematical statistics that were used to determine testing criteria. The research hypothesis is confirmed, consisting in the assumption that the processing of the results of psychological research using methods of mathematical statistics allows us to determine the effectiveness of a particular technique. The results of this study have a beneficial effect on the formation of positive motivation in high school students, both when studying mathematics and psychology.

Links to sources 1. Avanesov, V.S. Tests in sociological research/V.S. Avanesov // – M.: Nauka, 1982. – 200 p. 2. Ananyev, B. G. About the problems of human knowledge / B. G. Ananyev // – M.: Nauka, 1997. 3. Basova, N.V. Pedagogy and practical psychology / N.V. Basova // – Rostov-on-Don: Phoenix, 2000. – 412 pp. 4. Beshelev, S.D. Mathematical and statistical methods of expert assessments / S.D. Beshelev, F.G. Gurvich // – M.: Statistics, 1980.263 p. 5. Burlachu, L.F. Dictionary reference book on psychological diagnostics / L.F. Burlachuk, S.M. Morozov // –Kiev.: Naukova Duma, 1989. –198 pp. 6. Vitulak, G. Fundamentals of psychodiagnostics / G. Vitulak // Trans. with him. – M.: Progress, 1986. –123 p. 7. Vitulak, G. Principles of development and application of psychodiagnostic methods in school practice / G. Vitulak // Psychodiagnostics: theory and practice / Trans. with him. – M.: Progress, 1986. – 142 p. 8. Kovalev, A.G. General psychology / A.G. Kovalev // – M.: Education, 1981. – 361 p. 9. Lyubimova, E.S. Using methods of mathematical statistics in solving psychological problems of the modern world / E.S. Lyubimova, D.N. Nesterenko // Materials of the VΙΙ International Scientific and Practical Conference of Young Researchers “Science and Youth: New Ideas and Solutions”. Part 3. Volgograd, 2013.–288 p. 10. Spasennikov, V.V. Construction and use of psychological and didactic tests / V.V. Spasennikov // Textbook. allowance. –Kaluga: KSU, 1991. –116 p.

Solving practical problems using mathematical methods is consistently carried out by mathematically formulating the problem (developing a mathematical model), choosing a method for conducting research on the resulting mathematical model, and analyzing the results obtained.

The mathematical formulation of the problem is usually presented in the form of numbers, geometric images, functions, systems of equations, etc.

Mathematical model is a system of mathematical relationships - formulas, functions, equations, systems of equations that describe certain aspects of the object, phenomenon, process being studied.

At the stage of choosing the type of mathematical model, using the analysis of data from a search experiment, the following are established: linearity or nonlinearity, dynamism or staticity, stationarity or nonstationarity, as well as the degree of determinism of the object or process under study.

Establishing the general characteristics of an object allows you to select a mathematical apparatus on the basis of which a mathematical model is built. The choice of mathematical apparatus can be carried out in accordance with the diagram presented on rice. 1.2 .

Rice. 2. Mathematical apparatus for constructing a mathematical model

As can be seen from this diagram, the choice of mathematical apparatus is not unambiguous and rigid.

To describe complex objects with a large number of parameters, it is possible to split the object into elements (subsystems), establish a hierarchy of elements and describe the relationships between them at various levels of the hierarchy.

A special place at the stage of choosing the type of mathematical model is occupied by the description of the transformation of input signals into output characteristics of the object.

If at the previous stage it was established that the object is static, then the construction of a functional model is carried out using algebraic equations. In addition to the simplest algebraic dependencies, regression models and systems of algebraic equations are used.

If the nature of the change in the indicator under study is known in advance, then the number of possible structures of algebraic models is sharply reduced and preference is given to the structure that expresses the most general pattern or well-known law.

If the nature of the change in the indicator under study is unknown in advance, then a search experiment is carried out. Preference is given to the mathematical formula that gives the best match with the data of the search experiment.

Search experiment results and an a priori information array make it possible to establish a scheme for the interaction of an object with the external environment based on the ratio of input and output quantities.

In principle, it is possible to establish four interaction schemes:

one-dimensional-one-dimensional scheme ( rice. 1.3, a ) - the object is affected by only one factor, and its behavior is considered according to one indicator (one output signal);

one-dimensional-multidimensional scheme ( rice. 1.3 b ) - an object is influenced by one factor, and its behavior is assessed by several indicators;

multidimensional-unidimensional scheme ( rice. 1.3, in ) - an object is influenced by several factors, and its behavior is assessed by one indicator;

multidimensional-multidimensional scheme ( rice. 1.3, g ) - an object is influenced by many factors and its behavior is assessed by many indicators.

mathematical model synthesis

Rice. 3. Schemes of interaction of an object with the external environment

The process of selecting a mathematical model of an object ends with its preliminary control.

In this case, the following types of control are carried out : dimensions; orders; nature of dependencies; extreme situations; boundary conditions; mathematical isolation; physical meaning; stability of the model.

Dimensional control comes down to checking the fulfillment of the rule according to which only quantities of the same dimension can be equated and added.

Order control aimed at simplifying the model. In this case, the orders of the added quantities are determined and clearly insignificant terms are discarded.

Controlling the nature of dependencies comes down to checking the direction and rate of change of some quantities when others change. The directions and speeds resulting from the mathematical model must correspond to the physical meaning of the problem.

Control of extreme situations comes down to checking the visual meaning of the solution when the model parameters approach zero or infinity.

Boundary Condition Control consists in checking the compliance of the mathematical model with the boundary conditions arising from the meaning of the problem. At the same time, it is checked whether the boundary conditions are really set and taken into account when constructing the desired function and that this function actually satisfies such conditions.

Control of mathematical closedness comes down to checking that the mathematical model gives a unique solution.

Physical sense control comes down to checking the physical content of the intermediate relationships used in constructing the mathematical model.

Stability control model consists of checking that varying the initial data within the framework of the available data about the real object will not lead to a significant change in the solution.

Several years ago, when the author of this book worked as a consultant on mathematical statistics in a small medical research group, talk about the possibility of cutting a mathematical path through the dense jungle of environmental factors often ended with a rather skeptical shake of the head and the assertion that “medicine is, after all, art". This is partly true, of course, in the sense that intuition and imagination are indeed necessary for a doctor. At the same time, most patients and potential patients undoubtedly hope for the continuous development and expansion of the scientific aspects of medicine. And science means the application of mathematics.

An essential question is in what areas mathematical methods are applicable. In Sect. 1.1 we have already noted that the need for mathematical description appears in any attempt to conduct a discussion in precise terms and that this applies even to such complex areas as art and ethics. In this section we will look somewhat more specifically at the areas of application of mathematics in biology and medicine.

It is well known that one of the approaches to describing the picture of nature is to build a hierarchy of levels of organization studied by various sciences; According to the level of abstraction inherent in each of them, these sciences can be arranged in the following sequence: physics, chemistry, biochemistry, physiology, psychology, sociology. We begin with the basic material elements of the real world, that is, at the subatomic level, and end with the extraordinarily diverse manifestations of the spiritual life of human society. In this sequence of levels, organization and complexity continually increase. Each level has its own laws and can therefore be studied to some extent independently of each other. However, any of them is inextricably linked with the laws operating at lower levels. Thus, the laws of physics and chemistry partly apply to psychology, although the concepts and laws of the latter go beyond the limits of physical and chemical laws.

Problems concerning the organization and operation of hospitals should be classified at a higher level of abstraction than, say, human physiology and pathology. But although to a certain extent the logical content of this higher level is independent of the lower, questions of physiology and pathology must inevitably be taken into account in solving any problem concerning the organization of hospital services. We do not intend to delve into these philosophical considerations here or discuss their individual details, but only want to emphasize that the described sequence of levels approximately corresponds to the order of increasing difficulties in using scientific methods and conducting mathematical research.

As we have already noted, applied mathematics has made major and undeniable advances in the field of physics and chemistry, but we will not touch on these issues in this book. In Sect. 1.2 it was shown that mathematical descriptions associated with biological forms cover a wide range of issues and can be carried out quite accurately. In Sect. 1.3 we became acquainted with dynamic models of development and touched upon the problems associated with random fluctuations in population sizes. The presentation of these questions required a fair degree of abstraction, but it was the use of simplifying assumptions that allowed us to gain some insight into the laws governing the growth of populations. It was noted that when considering problems of this kind one inevitably has to deal with the factor of statistical variability, a detailed discussion of which is transferred to Chap. 2.

As we move to higher levels of abstraction, we are faced not only with more complex issues, but also with an increasing degree of variability, much of it unpredictable. For example, the full picture of competition between several species living in a given environment involves a huge variety of factors. Significant progress has been made in the field of scientific environmental descriptions, carried out mainly in verbal form, but the development of mathematical models is still at the most elementary level. Another example is the field of medical diagnostics. To make a diagnosis, the doctor, together with other specialists, is often forced to take into account a wide variety of facts, relying partly on his own personal experience, and partly on materials given in numerous medical manuals and journals. The total amount of information is increasing with ever-increasing intensity, and there are diseases about which so much has already been written that one person is not able to accurately study, evaluate, explain and use all the available information when making a diagnosis in each specific case.

Of course, a good diagnostician, using his extensive experience and intuition, can select the necessary part of the important data and give a fairly accurate conclusion. However, as paradoxical as it may sound, as knowledge accumulates, the situation worsens.

It is in these kinds of situations, when the mind of one person is not able to cope with the complexity of the problems facing him and to describe their solution even in general verbal form, specialists in the field of the so-called soft sciences (including, of course, biology and medicine) often argue that mathematical the analysis is imperfect, inappropriate, leads to erroneous conclusions, or is impossible, and is therefore best avoided. This objection contains a rational grain in the sense that modern mathematics may not yet be perfect enough; However, as time passes, we will see that just the opposite is true. In cases where the problem contains a large number of significant interdependent factors, each of which is significantly subject to natural variability, only with the help of a properly selected statistical method can the entire set of interrelated measurement results be accurately described, explained and explored in depth. If the number of factors or important results is so large that the human mind is not able to process them even with the introduction of some statistical simplifications, then the data processing can be carried out on an electronic computer. The use of statistical methods and computer technology is discussed in Chap. 2 and 5 respectively.

The main reason for the mistrust of mathematical and computational methods seems to be the following. A mathematical model of some biological phenomenon will be acceptable to a biologist only if the information expressed in verbal form about this phenomenon, which he has, is sufficiently complete so that one can judge the adequacy of the model. It is clear that the acquisition of such information represents the first and most important stage of biological research and that at this stage mathematics plays a secondary role. Naturally, the thought arises that as questions become more difficult and complex, mathematics becomes less and less important. However, what is not always taken into account is the fact that, having reached a sufficient degree of complexity, mathematics develops further according to its own laws and gives the biologist concepts and a way of thinking that he did not have before. Let us hope that this book will at least to some extent illustrate the truth of this statement.

So far we have had in mind mainly those biological and medical studies which require a higher level of abstraction than physics and chemistry, but are closely related to the latter. Next we will move on to problems related to animal behavior and human psychology, that is, to the use of applied sciences to achieve some more general goals. This area is rather loosely called operations research and is discussed in more detail in Chap. 4. For now, we will only note that we will talk about the application of scientific methods in solving administrative and organizational problems, especially those that are directly or indirectly related to biology and medicine. Forestry, animal husbandry, general agricultural production, hospital design and medical care are just a few of the issues that fall into this category.

Of course, not all administrative management problems can be solved scientifically using operations research methods. However, the use of these methods where possible (and they are applicable to many problems of this kind) has great advantages, since it allows one to expand the area of precise research and reduce the area of vague verbal reasoning. Thanks to this, a person’s intuition and common sense can be directed to solving those issues where the use of template methods is impossible. Issues that involve any ethical considerations are even more complex. But sometimes mathematical analysis can help even in these cases. For example, in medicine there are often complex problems associated with the use of drugs that are still in the testing phase. The doctor is morally obliged to offer his patient the best available drug, but in fact he cannot make a choice until the trial is completed. In these cases, the use of properly designed sequential statistical tests can reduce the time required to obtain definitive results. This does not eliminate ethical problems, but this mathematical approach makes their solution somewhat easier. Sequential methods are discussed in more detail in Section. 2.3.

The main point of this section is that mathematical methods are applicable to a wide range of issues - from particle physics to moral problems. It is convenient (although not at all necessary) to consider a certain hierarchy of levels. As we move to more abstract levels, mathematical methods become less developed and more difficult to apply.

However, when properly applied, the mathematical approach does not differ significantly from the approach based simply on common sense. Mathematical methods are simply more precise and use clearer formulations and a wider range of concepts, but ultimately they must be compatible with, although probably going beyond, ordinary verbal reasoning.