Начиная с начала 2000 года осуществляется внедрение GHIS в здравоохранении, в рамках принятого проекта о реформирование информ Mathematical Problems of Computer Science 48, 89--97, 2017. Modeling of Compliance Processes with Specified Criteria in Complex Dynamic Systems Ruben B. Aghajanyan Yerevan State University e-mail: ruboo1993@gmail.com Abstract The urgency of research and modeling of complex systems lies in the fact that it is necessary to effectively manage such systems, to predict their development, to use corrective and preventive actions, to eliminate undesirable phenomena. It is necessary to ensure that the system parameters meet the specified requirements and criteria [1],[2],[3],[4]. The complexity of research and modeling of such systems is as follows: - Increase in the number of components and links in the system - Complication of internal random relationships - Existence of stochastic processes - Changes in the requirements for compliance of key indicators with specified criteria. The considered class of complex systems is encountered in practice in a number of industries in which strict requirements are imposed on the parameters of the system, to their estimates. For example, to indicators of the quality of products (aircraft construction, management of complex equipment, production of food and drugs, health). For such systems, the problem of identifying deviations, estimating the indices of individual parameters for the objects of the system and methods of applying corrective actions for their elimination is urgent. Topical for the class of systems under consideration are the problems of self-regulation and self-development. Keywords: Dynamic network systems, Deviations and inconsistencies, Dynamic evaluation criteria, Weight coefficients of groups of criteria, Corrective and preventive actions (CAPA, Corrective and Preventive Action). 1. Introduction The main problem in the development and implementation of various methods for estimating parameters when deviations and inconsistencies are detected in complex systems is the duration and laboriousness of the corresponding processes. Without developed technological 89 mailto:ruboo1993@gmail.com Modeling of Compliance Processes with Specified Criteria in Complex Dynamic Systems 90 tools, it is not always possible to quickly analyze a large number of dynamic estimates and make the right timely decision. In Fig. 1, for the considered class of complex systems, a diagram of interacting processes for estimating parameters and monitoring their compliance with the established criteria is shown. Fig. 1. Sequence of control and analysis of key parameters. The main topic of this article is the study of the automation of the procedure for performing parameter estimation in dynamic complex systems when nonconformities are detected for making decisions about carrying out the necessary studies, obtaining estimates and performing corrective and preventive actions (CAPA) in order to eliminate the detected inconsistencies. 2. Mathematical Model for Estimating Parameters in Complex Systems First, we introduce the following notation in the language of set theory: 𝑆𝑆 = {𝑠𝑠1, 𝑠𝑠2 … , 𝑠𝑠𝑛𝑛} - a finite set of components of the system to be evaluated, 𝐺𝐺 = {𝐺𝐺1, 𝐺𝐺2 … , 𝐺𝐺𝑚𝑚} - a finite set of groups of criteria in which each element 𝐺𝐺𝑖𝑖 is in turn a set the elements of which are a collection of certain similar (with the same characteristic parameters) criteria , i.e., 𝐺𝐺1 = �𝑔𝑔11, 𝑔𝑔12, … �, 𝐺𝐺1 = �𝑔𝑔21, 𝑔𝑔22, … �, … 𝐺𝐺𝑖𝑖 = �𝑔𝑔𝑖𝑖1, 𝑔𝑔𝑖𝑖2, … �- there are sets of different groups of criteria. To each 𝐺𝐺𝑖𝑖 we assign a certain weighting coefficient 𝜆𝜆(𝐺𝐺𝑖𝑖) ∈ 𝜆𝜆, where 𝜆𝜆(𝐺𝐺𝑖𝑖) = (0 ÷ 1). We define a binary function 𝐹𝐹 that can take the value 0 or 1 and is defined on the set 𝐺𝐺𝑖𝑖, 𝐹𝐹(𝐺𝐺𝑖𝑖) = 𝑁𝑁′ ∈ 𝑁𝑁 , where 𝑁𝑁′𝑖𝑖 = {0,1}. (1) We also introduce a set of standard estimates in the form of ordered subsets of natural numbers 𝐾𝐾 = {𝐾𝐾1,𝐾𝐾2,… 𝐾𝐾𝑧𝑧}, (2) where 𝐾𝐾𝑧𝑧 ⊂ N & (𝐾𝐾1 ∩ 𝐾𝐾2 ∩ … ∩ 𝐾𝐾𝑧𝑧 = {∅}&(𝐾𝐾1 ∪ 𝐾𝐾2 ∪ … ∪ 𝐾𝐾𝑧𝑧! = {∅}. The elements of each subset 𝐾𝐾𝑧𝑧 is the ordered sequence of natural numbers {𝑚𝑚1, 𝑚𝑚2 … , 𝑚𝑚𝑛𝑛} from the set of 𝑁𝑁, where 𝑚𝑚𝑗𝑗 = 𝑚𝑚𝑖𝑖 + 1, 𝑗𝑗 = 𝑖𝑖 + 1 . 𝐾𝐾𝑖𝑖 will be called the i-th correspondence class. For each element s we have a chain of averaged values for each group 𝐺𝐺𝑖𝑖: 𝐹𝐹(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖) = (𝑓𝑓(𝑔𝑔𝑖𝑖1, 𝑠𝑠𝑚𝑚) + (𝑓𝑓(𝑔𝑔𝑖𝑖2, 𝑠𝑠𝑚𝑚) … + (𝑓𝑓(𝑔𝑔𝑖𝑖𝑖𝑖, 𝑠𝑠𝑚𝑚) ), (3) • Definition of the correspondence class. • Expert opinion • Calculation of new values of weight coefficients and evaluation criteria • Calculation of estimates according to given criteria • Calculation of estimates • System state analysis • Selection of the sequence of criteria • Defining assessment classes Selection of evaluation criteria Calculation of estimated values Comparison with given values Formation of new indicators R. Aghajanyan 91 We define for sm an integral estimate with allowance for the weight coefficients 𝜆𝜆, 𝐼𝐼(𝑠𝑠𝑚𝑚) = � (𝐹𝐹(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖)𝜆𝜆𝑖𝑖) 𝑘𝑘 𝑖𝑖=1 , (4) where 𝑚𝑚 = {0, 1, … 𝑛𝑛} – the number of components in the system, 𝑘𝑘 = {0, 1, … 𝑧𝑧} – the number of set elements 𝐾𝐾 (2). Finally, we get a couple of expressions that describe the procedure for obtaining a quantitative assessment and monitoring compliance with specified criteria։ 𝐼𝐼(𝑠𝑠𝑚𝑚) = � (𝐹𝐹(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖)𝜆𝜆𝑖𝑖) 𝑘𝑘 𝑖𝑖=1 𝑄𝑄(𝐼𝐼(𝑠𝑠𝑚𝑚)) = 𝐾𝐾′ ⊂ 𝐾𝐾𝑖𝑖 The problem is to determine for the integral estimate 𝐼𝐼(𝑠𝑠𝑚𝑚) belonging to one of the classes of correspondences 𝐾𝐾𝑖𝑖 . For each 𝑠𝑠𝑛𝑛 element, it is necessary to execute the sequence of the following 5 procedures: 1) Generating a value chain 𝐹𝐹(𝐺𝐺𝑖𝑖1), 𝐹𝐹(𝐺𝐺2), … 𝐹𝐹(𝐺𝐺𝑖𝑖), (1) where 𝑖𝑖 – the number of criteria groups 2) Calculation of the average values for each group, taking into account the weighting factors: 𝐹𝐹(𝑠𝑠𝑚𝑚, 𝐺𝐺1)𝜆𝜆1, (𝑠𝑠𝑚𝑚, 𝐺𝐺2)𝜆𝜆2,… 𝐹𝐹(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖)𝜆𝜆𝑖𝑖 , where 𝐹𝐹(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖) – the mean value according to expression (3) 3) Calculation of the integral sum 𝐼𝐼(𝑠𝑠𝑚𝑚), according to expression (4) 4) The definition of 𝐾𝐾𝑖𝑖 (i=1,2…z) for which 𝐼𝐼(𝑠𝑠𝑚𝑚) ∈ 𝐾𝐾𝑖𝑖, i.e., the definition of the group that includes the given integral sum 𝐼𝐼(𝑠𝑠𝑚𝑚) (5) 5) Generation of actions (expert opinion) according to the estimation of 𝐼𝐼(𝑠𝑠𝑚𝑚) and the corresponding group 𝐾𝐾𝑖𝑖 A practical example (pharmaceutical production) Consider the foregoing with the example of evaluating and selecting a supplier of ingredients and packaging materials in a pharmaceutical company. The task is to obtain in a timely manner a possible objective integral evaluation with subsequent periodic reassessment that would help to make the right decision when choosing a supplier. The production of pharmaceuticals by pharmaceutical enterprises is a chain of interrelated processes - from the choice of the supplier and the organization of the supply of ingredients to the production, packaging and supply of medicines to the consumer. All these processes must meet the quality requirements, according to the GMP standard. Ingredients and packaging materials are the most important components of modern medicines and their manufacturers have to be cautious in choosing suppliers. Among the most important aspects of supplier selection for manufacturers are the following: - information about the supplier, its reputation and position in the market, the availability of quality certificates, financial statements, customer references and other available information, negative processes related to quality violations, deviations from specified parameters, etc. - Conditions for providing a guarantee for the delivered products, responsibility for the quality of the products supplied, readiness to assist in eliminating inconsistencies and compensating losses that arose, for example, during transportation - Terms of payment, product cost, cost and delivery time, quality and timeliness of registration of documentation for product registration and customs operations - Estimating the total cost of the cost of purchasing the ingredients, taking into account transportation costs, tax duties, the cost of excise taxes, registration certificates, insurance premiums and other payments (5) Modeling of Compliance Processes with Specified Criteria in Complex Dynamic Systems 92 - Types of packages of supplied ingredients and materials in terms of ease of transportation, storage and packaging - Compliance of the declared quality indicators with their actual estimated values during the period of interaction between the customer and the supplier - Estimation of profitability of production taking into account expenses for ingredients and packaging materials. The task is to obtain in a timely manner a possible objective integral evaluation with subsequent periodic reassessment that would help to make the right decision when choosing a supplier [5]. There are many vendor classification systems. Such systems depend entirely on the competence and qualifications of relevant specialists in the pharmaceutical, food and other industries. Each company needs to create its own acceptable classification system. One of the classification options for the pharmaceutical industry is presented in Table 1. [5]. Consider the application of the proposed algorithm for this classification option. Table 1: Vendor classification method. N Topic (group of criteria) Criteria (gij) Values F(Gi) (0,1) Values 𝜆𝜆𝑖𝑖 (0-1) 1. Quality level (𝐺𝐺1) • Compliance with the specification parameters (𝑔𝑔11) • Compliance with quality system requirements (𝑔𝑔12) • Availability of certificates of conformity (𝑔𝑔13) • Access to the product dossier (𝑔𝑔14) • Product Stability (𝑔𝑔15) • Quality index by product series (𝑔𝑔16) 𝑓𝑓(𝑔𝑔11) 𝑓𝑓(𝑔𝑔12) 𝑓𝑓(𝑔𝑔13) 𝑓𝑓(𝑔𝑔14) 𝑓𝑓(𝑔𝑔15) 𝑓𝑓(𝑔𝑔16) 1 2. Production level (𝐺𝐺2) • Availability of full production cycle (𝑔𝑔21) • Competence of the staff (𝑔𝑔22) • Level and potential of development (𝑔𝑔23) 𝑓𝑓(𝑔𝑔21) 𝑓𝑓(𝑔𝑔22) 𝑓𝑓(𝑔𝑔23) 0.8 3. Logistics (𝐺𝐺3) • Types and dimensions of packaging (𝑔𝑔31) • Offered service (𝑔𝑔32) • Periodicity of delivery (𝑔𝑔33) • Transport condition (𝑔𝑔34) • Geographical location (𝑔𝑔35) • Reliability of delivery (𝑔𝑔36) 𝑓𝑓(𝑔𝑔31) 𝑓𝑓(𝑔𝑔32) 𝑓𝑓(𝑔𝑔33) 𝑓𝑓(𝑔𝑔34) 𝑓𝑓(𝑔𝑔35) 𝑓𝑓(𝑔𝑔36) 0.7 4. Marketing (𝐺𝐺4) • Contract pric (𝑔𝑔41) • Terms of payment (𝑔𝑔42) • Proposed assortment today (𝑔𝑔43) • The claimed asortment of tomorrow (𝑔𝑔44) • Image and reputation (𝑔𝑔45) • Customer Orientation (𝑔𝑔46) 𝑓𝑓(𝑔𝑔41) 𝑓𝑓(𝑔𝑔42) 𝑓𝑓(𝑔𝑔43) 𝑓𝑓(𝑔𝑔44) 𝑓𝑓(𝑔𝑔45) 𝑓𝑓(𝑔𝑔46) 0.3 R. Aghajanyan 93 It is also necessary to specify several characteristic groups with given ranges of numbers that define the group to which the supplier in question can enter. For example, Table 2: Characteristic groups and their metrics. Group Metric (Value Range) Characteristic 𝐾𝐾1 <5 Does not meet the specified criteria 𝐾𝐾2 5-8 Requires revision 𝐾𝐾3 8-10 Partially matched 𝐾𝐾4 10-14.4 Totally coincides Then it is necessary to calculate the average value for all four groups of criteria: 1. 𝐴𝐴𝐴𝐴. (𝐺𝐺1) = (f(𝑔𝑔11) + f(𝑔𝑔12) + f(𝑔𝑔13) + f(𝑔𝑔14) + f(𝑔𝑔15) + f(𝑔𝑔16)) /6 2. 𝐴𝐴𝐴𝐴. (𝐺𝐺2) = (f(𝑔𝑔21) + f(𝑔𝑔22) + f(𝑔𝑔23))/3 3. 𝐴𝐴𝐴𝐴. (𝐺𝐺3) = (f(𝑔𝑔31) + f(𝑔𝑔32) + f(𝑔𝑔33) + f(𝑔𝑔34) + f(𝑔𝑔35) + f(𝑔𝑔36))/6 4. 𝐴𝐴𝐴𝐴. (𝐺𝐺4) = (f(𝑔𝑔41) + f(𝑔𝑔42) + f(𝑔𝑔43) + f(𝑔𝑔44) + f(𝑔𝑔45) + f(𝑔𝑔46))/6 Further taking into account the given weight coefficients for each group of criteria, it is necessary to calculate the integral estimate according to a pair of expressions (5) : 𝐼𝐼𝑛𝑛𝐼𝐼. = 𝐴𝐴𝐴𝐴. (𝐺𝐺1) ∗ 1 + 𝐴𝐴𝐴𝐴. (𝐺𝐺2) ∗ 0.8 + 𝐴𝐴𝐴𝐴. (𝐺𝐺3) ∗ 0.7 + 𝐴𝐴𝐴𝐴. (𝐺𝐺4) ∗ 0.3 Now it is necessary to check which group from the given set 𝐾𝐾 = {𝐾𝐾1, 𝐾𝐾2, 𝐾𝐾3,𝐾𝐾4 contains the obtained estimate to take appropriate action: - 𝐼𝐼𝑛𝑛𝐼𝐼. ∈ 𝐾𝐾1 -> the supplier does not meet the specified criteria - 𝐼𝐼𝑛𝑛𝐼𝐼. ∈ 𝐾𝐾2 -> data on the supplier need to be revised, it may be required to request additional materials - 𝐼𝐼𝑛𝑛𝐼𝐼. ∈ 𝐾𝐾3 -> the supplier partially meets the specified criteria - 𝐼𝐼𝑛𝑛𝐼𝐼. ∈ 𝐾𝐾4 -> the supplier fully meets the specified criteria Let's pay attention to two basic singularities of similar systems of estimations: a. The risk of obtaining inaccurate data due to subjectivity in the development of a system of criteria and the designation of weighting factors. As noted above, you often have to rely on the professionalism of the staff involved in developing the criteria and the vendor evaluation system. b. When certain events occur, verification is required not at all but at certain criteria, i.е., the choice of the evaluation criteria system is dynamic. 3. Model with Dynamic Definition of Control Criteria In order to take into account the above-mentioned peculiarities of the class of systems under consideration, we introduce an additional set of states 𝐶𝐶{𝑐𝑐1, 𝑐𝑐2 … } and the set of mappings 𝑊𝑊 = {𝑤𝑤1, 𝑤𝑤2 … , 𝑤𝑤𝑛𝑛} , where 𝑤𝑤𝑖𝑖(𝐶𝐶 → 𝐺𝐺1, 𝑖𝑖 = (1,2, … 𝑛𝑛) ), (6) Modeling of Compliance Processes with Specified Criteria in Complex Dynamic Systems 94 for which to a certain ci there corresponds a chain of the following subsets (𝐺𝐺1′ ⊂ 𝐺𝐺1) ∩ (𝐺𝐺2′ ⊂ 𝐺𝐺2) ∩ (𝐺𝐺3′ ⊂ 𝐺𝐺3) ∩ … ∩ (𝐺𝐺𝑖𝑖 ′ ⊂ 𝐺𝐺𝑖𝑖) , it is possible 𝐺𝐺𝑖𝑖 = {∅} for anyone (𝑖𝑖 = 1,2, … 𝑛𝑛). By the states ci we mean the appearance in the system of some deviations (inconsistencies), in the result of which it is required to test by groups of criteria according to (expressions 3,4,5). In practice, this may be, for example - the inconsistency of the equipment's indicators with the specified permissible values or the breakdown of individual components, which may suspend some stages of the production process, etc. In this case, the problem (item "a") can be formulated as follows: determine the state of the system ci, choose the corresponding subsets of the criteria 𝐺𝐺1′, 𝐺𝐺2′ … and apply the above algorithm for a given chain of criteria. To determine the weighting coefficients (subsection "b"), we present the following procedure. Suppose for a certain period N production processes were performed, during which, 𝑀𝑀(𝑐𝑐𝑖𝑖) times the deviation of 𝑐𝑐𝑖𝑖 from the set values was observed. At the same time, testing with the given criterion showed k times the discrepancy, i.e., 𝑓𝑓�𝑔𝑔𝑖𝑖𝑗𝑗� takes the value "0" (see expression 1), then 𝑀𝑀(𝑐𝑐𝑖𝑖)/𝑁𝑁 - will be the probability of occurrence of the event 𝑐𝑐𝑚𝑚. And 𝑘𝑘(𝑐𝑐𝑖𝑖, 𝑔𝑔𝑖𝑖𝑗𝑗)/𝑀𝑀(𝑐𝑐𝑖𝑖) is the probability of occurrence of the discrepancy by the criterion 𝑔𝑔𝑖𝑖𝑗𝑗 at the occurrence of the event 𝑐𝑐𝑖𝑖. The total probability of non-compliance with the 𝑔𝑔𝑖𝑖𝑗𝑗 criterion during the N production processes will be: 𝑃𝑃(𝑐𝑐𝑖𝑖, 𝑔𝑔𝑖𝑖𝑗𝑗) = 𝑀𝑀(𝑐𝑐𝑖𝑖) 𝑁𝑁 ∗ 𝐾𝐾�𝑐𝑐𝑖𝑖,𝑔𝑔𝑖𝑖𝑖𝑖� 𝑀𝑀(𝑐𝑐𝑖𝑖) . (6) In this case, the value of the weighting coefficient for the given criteria 𝑔𝑔𝑖𝑖𝑗𝑗 from 𝐺𝐺𝑖𝑖 ′ at occurrence of the events ci can be calculated as follows: 𝜆𝜆′𝑖𝑖(𝑐𝑐𝑖𝑖) = � 𝑃𝑃�𝑔𝑔𝑖𝑖𝑖𝑖,𝑐𝑐𝑖𝑖� 𝑚𝑚 𝑚𝑚 𝑗𝑗=1 , (7) where 𝑗𝑗 = (1 ÷ 𝑚𝑚) , m- the number of criteria in a group 𝐺𝐺𝑖𝑖. Similarly, calculating for the criteria of the group 𝐺𝐺𝑖𝑖 when other events 𝑐𝑐𝑗𝑗 ∈ 𝐶𝐶 occur, for which the condition 𝑤𝑤𝑖𝑖(𝐶𝐶 → 𝐺𝐺𝑖𝑖) is satisfied, we obtain the final value of the weight coefficient for the group 𝐺𝐺𝑖𝑖: 𝜆𝜆𝑖𝑖 = 𝑠𝑠𝑠𝑠𝑚𝑚(𝜆𝜆′𝑖𝑖(𝑐𝑐1𝑖𝑖) + 𝜆𝜆′𝑖𝑖(𝑐𝑐2𝑖𝑖) + ⋯ + 𝜆𝜆′𝑖𝑖(𝑐𝑐𝑚𝑚𝑖𝑖). (8) In this case, the expressions (5) describing the model of quantitative estimation and control of compliance with the given criteria for 𝑠𝑠𝑚𝑚 will take the following form: 𝐼𝐼(𝑠𝑠𝑚𝑚) = �(𝐹𝐹(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖)𝜆𝜆𝑖𝑖), 𝑘𝑘 𝑖𝑖=1 𝑄𝑄(𝐼𝐼(𝑠𝑠𝑚𝑚)) = 𝐾𝐾′ ⊂ 𝐾𝐾𝑖𝑖, 𝜆𝜆𝑖𝑖 = 𝑠𝑠𝑠𝑠𝑚𝑚(𝜆𝜆′𝑖𝑖(𝑐𝑐1𝑖𝑖) + 𝜆𝜆′𝑖𝑖(𝑐𝑐2𝑖𝑖) + ⋯ + 𝜆𝜆′𝑖𝑖(𝑐𝑐𝑚𝑚𝑖𝑖), 𝜆𝜆′𝑖𝑖(𝑐𝑐𝑖𝑖) = � 𝑃𝑃�𝑔𝑔𝑖𝑖𝑗𝑗, 𝑐𝑐𝑖𝑖� 𝑚𝑚 𝑚𝑚 𝑗𝑗=1 . The corresponding procedure can be specified in the form of the following 6 steps: R. Aghajanyan 95 1. Analysis of the state of the system and dynamic generation of the chain of criteria (𝐺𝐺1′ ⊂ 𝐺𝐺1) ∩ (𝐺𝐺2′ ⊂ 𝐺𝐺2) ∩ (𝐺𝐺3′ ⊂ 𝐺𝐺3) ∩ … ∩ (𝐺𝐺𝑖𝑖 ′ ⊂ 𝐺𝐺𝑖𝑖) , where “i” is the number of groups of evaluation criteria defined for a given state. 2. Calculation of the average values for each group, taking into account the weighting factors: 𝐹𝐹1(𝑠𝑠𝑚𝑚, 𝐺𝐺1) ∗ 𝜆𝜆1, 𝐹𝐹2(𝑠𝑠𝑚𝑚, 𝐺𝐺2) ∗ 𝜆𝜆2 … 𝐹𝐹𝑖𝑖(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖) ∗ 𝜆𝜆𝑖𝑖 , where 𝐹𝐹𝑖𝑖(𝑠𝑠𝑚𝑚, 𝐺𝐺𝑖𝑖) – the mean value according to expression (1). 3. Calculation of the sum 𝐼𝐼(𝑠𝑠𝑚𝑚) according to expression (2). 4. Definition 𝐾𝐾𝑖𝑖, for which 𝐼𝐼(𝑠𝑠𝑚𝑚) ∈ 𝐾𝐾𝑖𝑖, where 𝑖𝑖 =1,2,3,4,5, 6, ie., the definition of the group that includes this integral sum 𝐼𝐼(𝑠𝑠𝑛𝑛). 5. Generation of actions (expert opinion) according to the estimation of 𝐼𝐼(𝑠𝑠𝑚𝑚) and the corresponding group 𝐾𝐾𝑖𝑖. 6. Formation of new probabilistic values for determining the chain of evaluation criteria and their weight coefficients. Below is a structural and functional diagram of an information system (software) that implements interrelated processes of evaluation and control of the parameters of the class of complex systems under consideration. Fig. 2. Functional Components of the Information System. Objects and evaluation criteria Estimated values of parameters Decision management Generation of weighting coefficients Registration of the onset of events Creating lists of control objects Generating lists of criteria and their classification by topic Creating of weight coefficients for groups of criteria Log Valuation Values Calculating average values of object parameters Calculation of the amount taking into account the average values and weights Formation of evaluation groups for monitoring parameter values Selection of the object of control Selecting a list of criteria The definition of an evaluation group for each sum of values Generation of corrective actions according to the evaluation group Logging the results of the functioning of the system Calculation of probabilistic values for the chain of criteria and weighting coefficients Modeling of Compliance Processes with Specified Criteria in Complex Dynamic Systems 96 4. Conclusion In this paper we propose a model for estimating the parameters of complex systems and detecting nonconformities (deviations) to a given set of dynamically generated criteria. Based on the described model, a method is proposed for determining corrective and preventive actions to eliminate the detected discrepancies. During the operation of the system, experimental data were obtained, which make it possible to calculate the probabilistic values of the interrelated evaluation criteria and their weight coefficients. The software that implements this method was introduced in pharmaceutical manufacturing companies. The main result obtained in the course of operation is the prompt elimination of inconsistencies and the reduction of current expenses by 45-50% due to 1) reducing the time for calculating the monitored parameters of the nonconformity detection system and taking decisions on the implementation of CAPA actions 2) reducing the risk of inconsistencies and deviations of the main parameters from the specified criteria. References [1] V. A. Ostrejkovsky, Theory of Systems, M .: High School, 1997. [2] B.Ya. Sovetov, Modeling of Systems, Moscow: Higher School, 2001. [3] M. Mesarovic, D. Mako and I. Tahakara, The Theory of Hierarchical Multi-level Systems, Moscow: Mir, 1978. [4] J. Peterson, Petri Nets Theory and Systems Modeling, Moscow: Mir, 1984. . [5] A. V. Aleksandrov, “GMP: evaluation and audit of a pharmaceutical company supplier”, "Industrial Review", vol. 6, no. 11, pp. 42--45, 2008. Submitted 08.10.2017, accepted 05. 12.2017. Բարդ դինամիկ համակարգերում համապատասխանության վերահսկման պրոցեսների մոդելավորման մեթոդներ Ռ. Աղաջանյան Ամփոփում Բարդ համակարգերի հետազոտման և մոդելավորման կարևորությունը պայմանավորված է այդ համակարգերի արդյունավետ կառավարման անհրաժեշտությամբ, դրանց զարգացման կանխատեսման և գործունեության մեջ շեղումների վերացման ուղղությամբ։ Համակարգի հիմնական խնդիրն է ապահովել համապատասխանությունը հիմնական ցուցանիշների և տրված չափորոշիչների միջև։ Նման համակարգերի R. Aghajanyan 97 հետազոտման և մոդելավորման բարդությունը պայմանավորված է մի շարք պատճառներով, որոնց թվում` - Համակարգում կոմպոնենտների քանակի ավելացումը - Մեծ թվով բարդ ներքին ստոխաստիկ կապերի առկայությունը - Պատահական պրոցեսների առկայությունը - Հիմնական ցուցանիշների համապատասխանության պահանջների փոփոխություն Դիտարկվող բարդ համակարգերը հանդիպում են մի շարք ոլորտներում (բարդ տեխնիկայի կառավարում, սննդամթերքի և դեղերի արտադրություն, առողջապահություն), որոնց պարամետրերի նկատմամբ դրված են խիստ պահանջներ, օրինակ՝ արտադրանքի որակի չափանիշների նկատմամբ։ Շեղումների հայտնաբերումը, համակարգի պարամետրերի ցուցանիշների գնահատումը և կանխարգելիչ մեթոդների կիրառումը համարվում են արդի նման համակարգերի ուսումնասիրման և մոդելավորման համար։ Метод моделирования процессов контроля соответствия заданным критериям в сложных динамических системах Р. Агаджанян Аннотация Актуальность исследования и моделирования сложных систем обусловлена прежде всего необходимостью эффективного управления подобными системами, прогнозированием их развитием и использованием корректирующих и превентивных действий для устранения нежелательных явлений в их функционировании, обеспечении соответствия параметров системы заданным требованиям и критериям. Сложность исследования и моделирования подобных систем обусловлена рядом причин, среди которых можно выделить следующие: - увеличение числа компонент и звеньев системы - наличие большого количества сложных внутренних случайных взаимосвязей - наличие стохастических процессов - изменения в требованиях на соответствие ключевых показателей заданным критериям. Рассматриваемый класс сложных систем встречается на практике в ряде отраслях, в которых предъявляются строгие требования к параметрам системы, их оценкам, например к показателям качества выпускаемой продукции (авиастроение, управление сложным оборудованием, производство пищевых продуктов и медикаментов, здравоохранение). Для подобных систем является актуальной задача выявления отклонений, оценка показателей отдельных параметров для объектов (звеньев) системы и методы применения корректирующих действий для их устранения.