Can a process be absolutely controllable. Managed and unmanaged processes of anti-crisis development

The bankruptcy or collapse of such firms can lead to severe, and not only economic, consequences both in the region where the company is located and on the scale of global economic relations. Therefore, it is necessary to regulate the development of such firms both at the regional and state levels. They especially need anti-crisis management, which should take into account both national interests and global economic development trends.
The violet crisis not only upsets the balance in the market, but also causes serious complications in the social sphere. In most countries, bankruptcy laws tend to focus specifically on these types of firms.
In Russia the legislative framework and the experience of solving bankruptcy problems is just beginning to take shape. And these processes are contradictory. It is necessary to take into account a wide range of factors - social, economic, environmental, scientific and technical.
Fourth transitional period the fall: decrease in most important indicators of the company's vital activity.
In general, a drop in the main indicators is no longer a danger of a crisis, but a sign of it, but the rate of decline can show whether this should be assessed as the onset of an irreversible crisis or is this a stage of development that is most dangerous for the emergence of a destructive crisis, i.e., an extreme aggravation of contradictions, gradually increasing the risk of destruction, decay. In the exit from the fall big role plays the system of state regulation, which should be aimed at maintaining a normal general socio-economic situation. This is especially important for countries with large manufacturing industries, in particular for Russia. Today in Russia one can observe the processes of disintegration of many enterprises (former violets) into small switching firms. Very often they become a threat to environmental safety. Therefore, a federal program for anti-crisis management is needed, the main task of which is to minimize damage in the event of an enterprise's bankruptcy or its division.
Fifth transitional period - Exodus: the final destruction of the firm, its liquidation in one way or another.
Each of the transitional periods, as well as the stages, has its own time limits and qualitative features. The former are determined by the effectiveness of management, more precisely, by the system crisis management, the second - by a regular sequence of the emergence of new properties in the development of the company, which can be considered by internal and external features.
Internal features - financial position, manageability, socio-psychological atmosphere of activity, intellectual and innovative potential, resource conservation, strategy, Information Technology, the quality of the staff.
External signs- competitiveness, competitive advantages, company image, regional structure, socio-political position, international relations, public relations ( public relations), natural conditions.
It is the combination of all these properties, expressed in the performance indicators of the company, that characterizes the qualitative certainty of the stage of its development, and the transition period reflects successive changes in a certain direction from stage to stage.
But not all changes reflect a transitional period. Some changes characterize simple instability, fluctuations (fluctuations) of indicators under the influence of natural or social conditions, ups and downs of competition, market conditions, etc.
Therefore, in the practice of anti-crisis management, it is very important to be able to recognize the nature of changes in managed and unmanaged processes, to separate changes in the transition period from changes in the normal functioning of the company.

Questions

1. What factors in the development of the organization characterize the danger of a crisis?
2. How are these factors interrelated?
3. What are possible reasons and symptoms crisis development firms?
4. What are the trends in the cyclical development of the organization? Rate each step in the cycle.
5. When do the likelihood and danger of a crisis increase?
6. Is bankruptcy always a nuisance for a company? Give an example of a situation.
7. What type of management prevails in the anti-crisis recovery of the debtor enterprise?

Part II
Formation and manifestation of anti-crisis management

Chapter 6
The main features of anti-crisis management

Issues. What is crisis management? When is it needed? What character does it have - temporary or permanent? What are the main features and features of anti-crisis management? What determines the effectiveness of crisis management?

6.1. Managed and unmanaged processes of anti-crisis development

All processes that occur in an organization can be divided into managed and unmanaged. Managed processes are amenable to change in a certain direction with a conscious impact on them. Orientation and character unmanaged processes cannot be changed, for one reason or another, they proceed according to their own laws; as a result of these processes, what should happen will happen anyway.
Managed and unmanaged processes are in a certain ratio, which reflects the excellence and art of management. Managed processes under certain conditions can become unmanaged, and vice versa. The predominance of unmanaged processes leads to anarchy and crises, while the prevalence of managed processes depends on the effectiveness of management and, under certain conditions, also leads to crisis situations. Thus, excessive bureaucracy gives rise to social tension, conflict situations. Previously, the term “overorganization” was often used, which characterizes the desire to manage everything and in every possible way, even in cases where there is no real need for this. Often this arises as a result of unfounded fears, lack of trust in the staff, lack of professionalism, as well as on the basis of the ambitiousness of the manager.
In addition to the fact that managed processes reflect only a part of all the processes of functioning and development of the organization, they have a measure of control, that is, they are manageable to a certain extent. So, a good and clear performer will not carry out orders that go against common sense or legal law.
Therefore, we can conclude that not all processes can be (and are) manageable, and managed processes cannot be absolutely manageable. This provision is directly related to anti-crisis development and management.
A crisis can be caused by “lack of vision” of those processes that can be managed and that must be skillfully directed. If this is not done, they can turn into elemental ones. A crisis can also arise in the case of a desire to manage unmanaged processes, when there are no control mechanisms. This leads to a waste of resources.
Anti-crisis development is a controlled process of preventing or overcoming a crisis that meets the goals of the organization and corresponds to the objective trends of its development.
It is known that many development processes are characterized by the increasing complexity of the organization. This is what happens with production, the economy, social sphere. The increasingly complex manufacturing technology of a product, its diversity and functional purpose lead to the complication of economic relations, an ever greater diversity of human interests. This is determined by education, the urbanization of life, the sociodynamics of culture, and other factors.
Development processes are cyclical, and the increase in complexity occurs along a logistic curve. It characterizes the stages of the emergence of prerequisites, the manifestation of processes of complication, the exhaustion of the existing foundation and the accumulation of the potential for further changes.
The logistic curve reflects four stages of development (Figure 6.1). Not only an organization, production or firm develops in this way, management develops in the same way. After all, management is part of the socio-economic system and has all its features.

Rice. 6.1. Development of management in the processes of production development
1 - simple control;
2 - management in conditions of increasing complexity of production;
3 - control adapted to the corresponding complexity of production;
4 - management that does not correspond to the complexity of production (crisis, management).

However, the development of management occurs along a “shifted” logistic curve. This reflects its status, its correlation with the development trends of the socio-economic system, its ability and limitations to respond to the processes of change in the socio-economic system as a whole.
The firststage development is simple management. This is management, visible in all its characteristics and relationships, does not require large expenditures to ensure its effectiveness, does not differ in the diversity of its functional content, and involves elementary organizational forms.
Secondstage - management in the conditions of increasing complexity of production, which in its development should outstrip the development of production. Only in this case it can be effective. This will require the reconstruction of management, which, of course, will entail complication in functional, organizational, motivational, informational terms, as well as the professionalization of management.
Thirdstage – management adapted to the respective complexity of production. It can stimulate the accelerated development of production and contribute to a further increase in its complexity. This is a management of a pronounced innovative type, but quickly exhausting its innovative potential.
Fourthstage - slowdown in the development of management at sufficiently high rates of development of production. Here, a new discrepancy between the complexity of production and management, a violation of the correlation between the control and controlled systems, is possible. This is already a danger of a management crisis, and after it - the entire managed system.
Anti-crisis management in this perspective of its analysis looks like the maximum convergence of the branches of logistic curves at the initial and final stages of the production and management development cycle and as the maximum advance of the management development trend relative to the production development trend at the middle stages of these trends.

6.2. Possibility, necessity and problems of anti-crisis management

As already mentioned, the danger of a crisis always exists: in management there is always the risk of a cyclical development of the socio-economic system, a change in the ratio of managed and unmanaged processes.
The management of the socio-economic system must always be anti-crisis to a certain extent.
Crisis management - this is management that in a certain way foresees the danger of a crisis, providing for an analysis of its symptoms, measures to reduce the negative consequences of the crisis and the use of its factors for subsequent development.
The possibility of anti-crisis management is determined primarily by the human factor, the potential for active and decisive human behavior in a crisis, his interest in overcoming crises, understanding the origins and nature of the crisis, the patterns of its course. Conscious human activity allows one to seek and find ways out of critical situations, to concentrate efforts on solving the most difficult problems, to use the accumulated experience in overcoming crises, and to adapt to emerging situations.
In addition, the possibility of anti-crisis management is also determined by the knowledge of the cyclical nature of the development of socio-economic systems. This allows you to anticipate situations of crisis and prepare for them. The most dangerous are unexpected crises.
The need for anti-crisis management reflects the needs of overcoming and resolving the crisis, and possible mitigation of its consequences. This is a natural human and organizational need. It can only be realized through special arrangements crisis management, which should be created and improved.
The need for anti-crisis management is also due to development goals. For example, the emergence of crisis situations in the environment that threaten the existence of a person, his health, make him look for and find new means of anti-crisis management, which includes making decisions about changing technology. So, nuclear power is an area of ​​activity with an increased risk of crisis situations. And here the main thing in anti-crisis management is the need to improve the professionalism of technical personnel, strengthen discipline, and organize the development of new and safer technologies. These are all management issues. Solving technical problems also starts with management.
In economic anti-crisis management, there is also a need to search - types of production diversification, conversion.
The problem of anti-crisis management is extensive and varied; it can be divided into four groups (Figure 6.2).
First group– problems of recognition of pre-crisis situations. It is not an easy task to see the onset of a crisis in time, to detect its first signs, to understand its nature. The possible prevention of the crisis depends on this. But not only from this. Crisis prevention mechanisms need to be built and put into action. And this is also a management problem.
But not all crises can be prevented; many of them must be experienced and overcome. And this is achieved through management. It solves the problems of the life of the organization during the crisis, contributes to the exit from the crisis and the elimination of its consequences.
Second group problems of anti-crisis management is associated with key areas of the organization's life. These are, first of all, the methodological problems of its life activity.

In the processes of their solution, the mission and purpose of management are formulated, the ways, means and methods of management in a crisis situation are determined. This group includes a complex of financial and economic problems. For example, in economic anti-crisis management, it becomes necessary to determine the types of production diversification or conversion, which requires additional resources, search for sources of financing. There are also problems of organizational and legal content, socio-psychological problems.
The problems of anti-crisis management can also be represented in the diversification of management technologies (the third group of problems). It includes in general view problems of forecasting crises and options for the behavior of the socio-economic system in a crisis state, problems of searching necessary information and development management decisions. Problems of analysis and assessment of crisis situations also have great importance. There are many time constraints, staff qualifications, lack of information, etc. This group also includes the problems of developing innovative strategies that help to bring the organization out of the crisis.
Fourth group problems include conflictology and staff selection, which always accompany crisis situations, investment in anti-crisis measures, problems of bankruptcy and reorganization of enterprises.
The composition of typical problems of anti-crisis management emphasizes that it is a special type of management that has both common management features and specific characteristics.

6.3. Signs and features of anti-crisis management

Management is carried out in the socio-economic system, which is the object of management. One of the characteristics of management is its subject. In a generalized view, the subject of control is always human activity. But this activity consists of a multitude of problems that are resolved in one way or another by this activity itself or in the course of it. Therefore, the subject of management can be differentiated by the totality of its problems. This is how strategic management, environmental management, etc.
Anti-crisis management has a subject of influence - crisis factors, i.e. all manifestations of an immoderate cumulative exacerbation of contradictions that cause the danger of its extreme manifestation, the onset of a crisis. Crisis factors can be perceived and real.
Any management to a certain extent must be anti-crisis or becomes anti-crisis as the organization enters a period of crisis development. Ignoring this provision is negative consequences, and its accounting contributes to the painless passage of crisis situations.
The essence of anti-crisis management is expressed in the following provisions:
a) crises can be foreseen, expected and caused;
b) crises to a certain extent can be accelerated, anticipated, postponed;
c) it is possible and necessary to prepare for crises;
d) crises can be mitigated;
e) crisis management requires special approaches, special knowledge, experience and art;
f) crisis processes can be controlled to a certain extent;
g) managing the processes of overcoming the crisis can accelerate these processes and minimize their consequences.
Crises are different, and their management can also be different. This diversity is manifested in the management system and processes (algorithms for developing management decisions) and especially in the management mechanism (Fig. 6.3). Not all means of influence give the necessary effect in a pre-crisis or crisis situation.
The anti-crisis management system should have special properties:
flexibility and adaptability, which are most often inherent in matrix control systems;
propensity to increase informal management, motivation enthusiasm, patience, confidence;
management diversification, search for the most appropriate typological features effective management in difficult situations;
reducing centralism to ensure timely situational response to emerging problems;
strengthening of integration processes, allowing to concentrate efforts and more effectively use the potential of competence.
Anti-crisis management has features in terms of its technologies:
mobility and dynamism in the use of resources, the implementation of changes and transformations, the implementation of innovative programs;
implementation of program-targeted approaches in technologies for the development and implementation of management decisions;
increased sensitivity to the time factor in management processes, the implementation of timely actions on the dynamics of situations;

Increased attention to preliminary and subsequent assessments of management decisions and the choice of alternatives for behavior and activities;
use of an anti-crisis criterion for the quality of management decisions in their development and implementation.
The control mechanism that characterizes the means of influence also has its own characteristics. Not always the usual means of influence give the desired effect in a pre-crisis or crisis situation.
In the mechanism of anti-crisis management, priorities should be given to:
motivation focused on anti-crisis measures, saving resources, avoiding mistakes (“measure seven times ...”), caution, in-depth analysis of situations, professionalism, etc.;
attitudes towards optimism and confidence, socio-psychological stability of activity;
integration on the values ​​of professionalism and competence;
initiative in solving problems and finding the best options development;
corporatism, mutual acceptability, search and support of innovations.
All this together should be reflected in the style of management, which must be understood not only as a characteristic of the manager's activities, but also as a generalized characteristic of the entire management. The style of anti-crisis management should be characterized by professional trust, purposefulness, anti-bureaucracy, research approach, self-organization, acceptance of responsibility.
Some of the characteristics of crisis management require more detailed consideration.
1. Crisis Management Functions- these are activities that reflect the subject of management and determine its result. They answer a simple question: what should be done to manage successfully in anticipation of a crisis, in the process of a crisis and in the presence of its consequences? In this regard, six functions can be distinguished: pre-crisis management, crisis management, management of crisis recovery processes, stabilization of unstable situations (ensuring controllability), minimization of losses and missed opportunities, regulation of the time for making and executing decisions (Fig. 6.4).
Causes of crises:
1) financial and economic situation in the country;
2) intense competition;
3) unprofessional management (wrong decisions);
4) risky development (strategy);
5) crisis management (creating conflicts, crises);
6) difficult socio-political situation;
7) natural disasters.
Functions and factors of anti-crisis management

Rice. 6.4. The reasonscrisis and the need for crisis management

Each of the management functions has its own characteristics, but in general they characterize the main features of anti-crisis management.
2. In the development of any management, two of its opposites coexist - integration and differentiation, which are in a dialectical relationship. Strengthening integration always leads to weakening differentiation, and vice versa. These processes reflect the trend of the logistic curve (Fig. 6.5). The connection between integration and differentiation at the turning points of the change in the curve characterizes the emergence of new organizational forms of management or organizations of a new type. In this interaction there are points of crisis in the organization. As a rule, these are points that reflect the danger of "disintegration", the destruction of organizational foundations. The way out of the crisis is to change the ratio of integration and differentiation of management on a new organizational basis.

3. Office has restrictions - internal and external, which are in a certain, but changing ratio. Depending on this ratio, the probability of crisis phenomena also changes (Fig. 6.6).

Restrictions - unmanaged processes, complex problems, resolved either naturally or indirectly.
There are always external and internal limits. Their detection and accounting is the task of anti-crisis management.
In management, constraints exist as factors in the development and effectiveness of management.
But restrictions can be adjusted, and this is also the essence of anti-crisis management. Internal restrictions are removed through either the selection of personnel, its rotation, training, or the improvement of the motivation system. Information Support management also contributes to the removal of internal restrictions on effective management.
External restrictions are regulated by the development of marketing, public relations.
4. One of the most important characteristics crisis management - combination of formal and informal management. Various types of such a combination determine the zone of rational organization of anti-crisis management (Fig. 6.7), which can narrow or expand. Its narrowing reflects the increased danger of a crisis or the danger of its most acute manifestation.

2 Generalized statistical model technological process

2.1 Manageability of the process.

Any manufacturing process is characterized by the technological possibility of production. Under technological possibility of production understood not only and not so much familiar and understandable to everyone quantitative side - performance, but and its qualitative side, most often represented as the average value of the group quality indicator and its variance. Moreover, the mean and variance fully characterize both measurable signs of quality and non-measurable ones - qualitative (alternative).

Indeed, if the group quality indicator is the level of nonconformities of the final population (batch) of products, expressed as the absolute value of nonconforming products in it or the proportion of nonconforming products in the batch (or the number of nonconformities per 100 units of production), then for any quality indicator of its group the analog can always be represented as a distribution corresponding (at least asymptotically, as n ® ¥) to the normal law. To show this, suppose that as a result of testing a technological process (or a single operation), m trial batches are obtained. Then, as a result of the sampling of these lots, it is possible to obtain an estimate of the average value of nonconforming items in each lot (see, for example, / /):

where d i is the number of non-conformities in the i-th batch;

N i and n i , respectively, the volume of the trial lot and the volume of the sample from it, used to estimate .

The unbiased estimate of the variance will be / /:

(2.2)

According to the Central Limit Theorem, asymptotically normal as N ® ¥ and (or) m ® ¥ (where N = ) approximation for the generalized group quality indicator can be obtained by taking the following values ​​as distribution parameters of this indicator:

(or as a share: q cp = m/N, where N = ); (2.3)

, (or, respectively, D[q]=), (2.4)

calculated based on the results of sampling control of m trial lots.

Naturally, similar estimates can be obtained not only for trial lots, but also for lots of products intended for consumers. In addition, getting these estimates in different periods time, it is possible to study the dynamics of their change.

Let y be a generalized indicator of product quality (size, weight, electrical capacity, impregnation depth, number of chips, etc.). Each value of i for the i-th product is a consequence of perturbations from l operations that make up the manufacturing process, and t external influences (temperature, humidity, vibration, etc.). The mean value m and the variance s 2 of the group quality index of N products, i.e. batches are also the result of l technological operations and t influencing factors. It is known from probability theory and statistics that dispersion is a strictly additive quantity:

(2.5)

(sometimes the sum (2.5) is more convenient to write in the form:

implying that each external influence affects different operations in its own way).

The technological process is absolutely controllable if three conditions are met:

1) process explored, i.e. all perturbations are identified (identified) and minimized at least to such an extent that there are no one, two or maximum three operations and (or) external influencing factors that make a predominant contribution to the sum (2.5) or (2.6). From a mathematical point of view, this means the fulfillment of the conditions of the Central Limit Theorem, moreover, at the "physical" level, i.e. the contribution to the overall dispersion of the process of each technological operation and each external influencing factor is estimated and verified experimentally;

2) technological process is regulated, i.e. organized in such a way that home Feedback in the form of a lever, valve, electrical impulse, etc., with which you can adjust the entire process without stopping it (if the process consists of separate operations that have independent significance, then, naturally, each such operation must be controlled in the above sense, or should include at the output a complete control with sorting out nonconforming products - blanks, at least - a selective control with a more stringent plan than the control plan at the output of the entire process);

3) process as an object of regulation stable, i.e. the range of quality features R = y max – y min at the output of the process for any set of finite volume does not exceed the value z g s/ with a one-sided limitation of the quality feature or 2×z 1+ g /2 s/ for the case of a two-sided limitation of the quality feature (where y max and y min are the maximum and minimum values ​​of the generalized quality attribute, respectively; z g is the quantile of the standard normal distribution function of the level g; g ³ 0.9 is the confidence level, most often taken equal to 0.95; n is the sample size).

If the process is absolutely controllable , i.e. all three conditions are met, then in this case it is not advisable to introduce acceptance control as a mandatory operation, in particular, selective control. In this case, control can only be carried out periodically (control with skipped batches, control at the request of the customer or certification body, etc.). Sampling of each lot is appropriate if either or both of the last two conditions are not met. If all three conditions are not met, complete control is necessary. If the first condition is not met, then sampling according to the relevant standards is possible only on an alternative basis, since all standard sampling systems are developed exclusively for normally distributed quantitative quality attributes.

2.2 Mathematical interpretation of discrepancies in the form of distributions.

We will consider a technological process for which at least the first controllability condition is satisfied, i.e. performed physical conditions Central limit theorem. Then the generalized quality attribute will have an asymptotically normal distribution with parameters (m;s). Let a and b be the maximum allowable values ​​of the quantitative (measurable) quality attribute y (the product is good if a< y i < b). Уровень несоответствий будет равен (см. рисунок 2.1):

where Ф 1 = - the level of inconsistencies, equal to the area the left "tail" of the distribution, i.e. the proportion of products whose quality attribute values ​​are less than a (y i< a);

- the level of inconsistencies, Figure 2.1 is equal to the area of ​​the right "tail" of the distribution, i.e. share of products with values ​​(y i > b);

Ф(…) is a standard normal distribution function.

In this case, the minimum level of inconsistencies will be if expected value quality features at the output of the process will coincide with the middle of the tolerance ( show why?):

(2.8)

On fig. 2.1 presents the ideal case. In fact, even in the case of absolute controllability of the technological process (fulfillment of all three controllability conditions listed in the previous subsection), three cases of deviation from ideality are possible:

m=var; s=const (see figure 2.2);

m=const; s p >s (see figure 2.3);

m=var; s=var (see figure 2.4).

In Figure 2.5, for clarity, all three cases are shown in the form of the development of deviations from ideality over time. In practice, the first case of deviation of the flow of the technological process from the ideal is most often implemented. dispersion is more stable in statistical sense characteristic than the average value.

Figure 2.2 Figure 2.3

Indeed, suppose that random characteristic y from some point in time, the trend d(t) is superimposed in the form of a non-random function of time t. Then it is obvious that the average value of the characteristic m y will begin to change:

Figure 2.4 m y = y cp + d(t).

The variance as the sum of the variance s y 2 and the variance of the non-random variable d(t) will remain unchanged, since s d 2 = 0. Although the third case (m=var; s=var) cannot be ruled out and, generally speaking, the stability of the variance, as well as the stability of the mean, should be tracked. (For example, the trend d(t) may be of a random nature and, therefore, contribute to the overall variance of the process).

Obviously, in all three cases, the level of inconsistencies will be greater than q min and vary from batch to batch. Therefore, in order to assess the level of inconsistencies in each particular batch (for example, during acceptance control by sampling methods), it is necessary to obtain estimates of the mean value and dispersion of quality attributes and calculate q, for example, according to (2.7). In this case, estimates can be point and interval, but in any case, the value of the level of inconsistencies q must be determined with a guarantee, i.e. a given level of trust must be maintained. In practice, the sampling procedure is formulated as a test of a statistical hypothesis, which automatically

involves setting one of the risks (type I or II) while minimizing the other and obtaining the power function of the criterion or operational characteristic.

2.3 Distributions used in statistical quality control.

In the course "Probability Theory and mathematical statistics» are considered in sufficient detail different kinds distributions, both discrete and continuous random variables. Discrete distributions simulate the so-called binary events, i.e. events about which it can be concluded that it took place or it did not take place. Such events are also called alternative. For example, in quality control in the form of the presence of shells or tempering colors on the surface, the dimensions of which do not matter, the random binary event is only the very fact of their presence or absence. Continuous distributions describe measurable characteristics of quality media, which are called " quantitative features» and can accept any numerical value in some limited or unlimited range of acceptable values.

When using mathematical statistics in process control and management systems, one should distinguish between the problems associated with the distribution of control characteristics at the output of the process and the problem of modeling control methods. When it comes to the distribution of quality features and inconsistencies in batches, they mean result analysis the work of the technological process of production as random number generator – product quality indicators. When modeling (statistical description) of control procedures, we are talking about a mathematical representation of methods for obtaining and processing information about the characteristics of already manufactured products, about the adequacy and accuracy of control as an independent process, at the output of which reliable control decisions should be formed. Therefore, it is not entirely correct to speak, for example, about the distribution of some quality attribute according to the hypergeometric law. Hypergeometric distribution law determines the number of nonconforming products that fall into the sample, generally speaking, under any law of distribution of nonconformities in the batch, but subject to the formation of the sample according to the “no return” rule and analysis during the control of only the binary relation: “good - bad”. Hypergeometric distribution initially involves the process of sampling, i.e. execution of the control procedure.

More difficult with the binomial distribution. Binomial law distribution can describe the output of the technological process of production, when each product with the same probability can be both suitable and unsuitable. In addition, the sampling procedure itself, when the sample is taken "with a return" and the binary relation "good - bad" is analyzed, is also described using the binomial distribution.

Poisson distribution can only describe the distribution of inconsistencies at the output of the manufacturing process. The use of this distribution for processing the results of sampling control is done solely for the purpose of simplifying the mathematically complex formulas of the hypergeometric and binomial models of control procedures.

normal law distribution can be used to simplify the processing of the results of the control of alternative quality attributes and describe the distribution law quantitative indicators quality at the output of the production process as a generator of continuous random variables.

2.3.1 Hypergeometric distribution.

The most complete and accurate model that reflects the quality control methodology for any binary distributions is the following:

Suppose there is a box with a finite number N of balls, D of which are white and the remaining N - D are black. Obviously, if we remove n balls from the box, i.e. make a sample of size n and calculate the number of white balls in the sample, then this number of white balls will depend on total number balls in box N, the number of white balls in box D, and the sample size. To express this mathematically, we define the probability that in a sample of size n there will be d =1, 2, 3, ..., k white balls. It is known from combinatorics that out of all possible samples of size n from the total set of size N, it is possible to compose only C N n combinations:

, (2.9)

where C N n is the number of possible sets of n elements from a set of N elements, in which the sequence of elements is not taken into account. On the other hand, each such sample can contain C D n times k white balls and each time be combined with cases when the remaining balls in each sample are black. Therefore, based on classical definition probability, we obtain a conditional distribution of the form:

H(k | N; D; n)=hy(i|N; D; n), (2.10)

where = hy(i | N; D; n)

where is the sign | " means "subject to". (Formula (2.10) automatically takes into account that the sample cannot contain more than n or more than D, white balls).

It is important to note that formula (2.10) simultaneously describes the probability that if k white balls are found in a sample of n balls, then the box with N balls contains D white balls, i.e. P(D | N; n; k) is equivalent to the probability Р(k | N; D; n).

Distribution (2.10) is called hypergeometric. The function of this distribution is written as:

Hy(k | N; D; n)=P(d | N; D; n)= (2.11)

It can be shown that for the hypergeometric distribution, the mathematical expectation is:

M = nP, (2.12)

where P = D/N is the proportion of white balls in the box.

The variance of the hypergeometric distribution is:

where Q = 1 – P is the proportion of black balls in the box.

Thus, the hypergeometric distribution is a four-parameter one and, in addition to the value of k, is determined by the parameters N; D and n. Distribution (2.11), taking into account the fact that the volume of a batch can reach several thousand units of production, is quite difficult to calculate even with the use of modern computer technology.

2.3.2 Binomial distribution

The hypergeometric distribution describes the case of sampling without replacement. In this case, the probability of drawing a white ball in the first attempt is D/N, the probability of the second white ball will be equal to (D-1)/(N-1) if the first ball was white, and equal to D/(N-1) if the first the ball was black.

Thus, the probability that the second ball will be white according to the total probability formula is:

Similarly, it can be shown that at any step the probability of drawing a white ball is equal to D/N, despite the fact that this probability, in general, depends on which balls were drawn at the previous steps.

If after each step of removing a ball randomly, it will return back to the box, it is obvious that the probability of drawing a white ball at the i-th step will always be equal to D / N, regardless of what color the balls were drawn at the previous steps.

Assume that a selection of n balls is made, as in the case of considering the hypergeometric distribution, but each time after the extraction and determination of the color of the ball taken out, this ball is returned to the box. Find the probability that out of n drawn and returned balls, the number of white balls will be equal to d. Those. find the distribution of white balls in fetch with return. Since in this case, at each i - th step, the probability of a white or black ball appearing is independent, then the probability of taking out a white ball k times will be equal to:

P(k=d) = P d (1-P) n - d = P d Q n - d.

The total number of such events can be equal to the number of combinations from n to k. So the required probability is:

P(k=d) = be(k=d | N; D; n) = (2.14)

The distribution (2.14) is called the Bernoulli distribution and, generally speaking, connects only three parameters: d; n and P = D/N (the values ​​D and N are included in this distribution, in contrast to the hypergeometric distribution in the form relations, i.e. one parameter P). Accordingly, the Bernoulli distribution function will be equal to:

Be(d< k| P; n) = (2.15)

Naturally, this probability is equivalent to the probability that the proportion of white balls in the box is equal to P, if there are d white balls in the sample with a return of size n. The mathematical expectation and variance for this distribution will be equal to:

M = nP (2.16)

σ B 2 = n P Q (2.17)

Therefore, when using the test scheme with return, a simpler expression for estimating the proportion of white balls in the box is obtained than in the model without return, which is described by the hypergeometric distribution law, but it should be borne in mind that in the case of the Bernoulli distribution, the accuracy of the model will be less than for the hypergeometric distribution , since σ H 2 is less than σ B 2 in (N-n)/(N-1) times.

2.3.3 Poisson distribution

Consider the flow of events, i.e. a sequence of events that occur at random times. Any production process can, in principle, be considered as a flow. For example, a stream of products “flows” along the conveyor, in which non-conforming products come across at random times. In the production of fabrics, it is convenient to consider many stretched parallel threads under the flow. In this case, a random event is a break in one of the threads. Then the independent variable of the thread is the geometric variable associated with the thread number.

A stream of events is called simple or Poisson if it obeys three conditions simultaneously:

1) condition stationarity: the probability of an event occurring in a small time interval Δt is proportional to the value of this interval up to an infinitesimal higher order:

P(d=1) ≈ c Δt + O(Δt),

where O(Δt) is an infinitesimal value of order (Δt) 2 ;

c is some constant.

2) condition ordinary: the probability of occurrence in the interval Δt of more than one event tends to zero faster than Δt:

;

3) condition lack of aftereffect: the frequencies of occurrence of events in non-overlapping time intervals are independent, i.e. the appearance of k events in the I-th interval Δt i does not depend on the frequency with which events appeared in the previous moments of time.

These conditions are quite stringent and it is rarely possible to strictly show that they are satisfied for a real process. It is usually easier to show which condition is not met, and when modeling the process under consideration with a Poisson flow, it is necessary to specify the non-fulfillment of this condition or change the model conditions in order to smooth out the deviation from the strict fulfillment of all the above conditions. For example, for one machine, the appearance of an inappropriate part size depends on the wear of the tool and, therefore, the frequency of occurrence of this event will not be proportional to the time interval (it will increase with increasing tool wear). However, if we consider several machines with random (uniform) tool change moments, then the applicability of the simplest flow to describe the appearance of inconsistencies will be fully justified. This model is also applicable, if we assume the intervals between tool changes under the moments of time Δt. Most often, the distribution associated with the simplest flow is used as a simplification of more accurate models described by the hypergeometric or binomial distribution.

The distribution that models the simplest flow obeys the Poisson distribution:

P(d=k) = p 0 (d=k | λ)= (2.18)

This distribution has a distribution function:

P 0 (d | λ) = (2.19)

The only parameter of this distribution is:

The mathematical expectation and variance of this distribution are equal to the parameter λ:

M[d] = λ = n P (2.20)

σ р 2 = λ = n P (2.21)

2.3.4 Approximation of the hypergeometric distribution.

Comparing the scatter of the above discrete distributions of binary random variables, it is easy to establish:

Therefore, the simplification of the batch sampling model, i.e. the transition from the hypergeometric model to the model of the Bernoulli or Poisson distribution inevitably leads to an increase in the scatter, i.e. dispersion growth. In other words, the simplification of the model is accompanied by a decrease in the accuracy of the simulation results. The most accurate hypergeometric distribution, due to the need to take into account four parameters, is the most difficult to calculate and tabulate, i.e. representations in tabular form. The Bernoulli distribution, which is easier to tabulate, is quite often found in the form of tables in various reference books. The Poisson distribution is presented in tabular form in almost every reference book. At present, with the development of programmable computing tools, the issue of tabulation ceases to be relevant.

In some books on the theory of probability and mathematical statistics, various sometimes not quite correct conditions are given for approximating the hypergeometric distribution by the Bernoulli and Poisson distributions. Below are the most correct conditions for the transition from the hypergeometric distribution to simpler ones, without significant loss in accuracy:

1) hy(k | N; D; n) ≈ be(k | p; n) (2.23)

at 0.1 10 and n/N<0,1;

(Literature sources often give only one condition: n/N<0,1, однако, основываясь только на этом условии, не принимая другие два условия можно допустить ошибку более 10 %);

2) hy(k | N; D; n) ≈ P 0 (k | λ=np) (2.24)

at P< 0,1 или P >0.9; n > 30; n/n< 0,1.

3) for n > 30, for P< D/N < 0,9 гипергеометрическое распределение можно аппроксимировать нормальным законом распределения с параметрами (np; nPQ(N‑n)/(N-1)) и с коррекцией на непрерывность:

hy(k | N; D; n) ≈
(2.25)

Hy(k | N; D; n) ≈ (2.26)

where, as before, P = D/N;

f(..) is the density function of the normal distribution.

2.3.5 Normal distribution

Almost all quality control systems by statistical methods are built on the assumption that quantitative indicators of quality are subordinate to the normal distribution law. The normal distribution law, its properties and existence conditions are considered in almost all textbooks and books on probability theory and mathematical statistics.

As noted above (see Section 2.1), the uniformly small contribution of each external influence and each operation to the total dispersion of the process is a necessary and sufficient condition (according to the Central Limit Theorem) for compliance with the normal distribution law of the quality index at the output of the process. But the converse statement is also true, i.e., if any attribute of quality does not correspond to the normal distribution law, then this means that the conditions of the Central Limit Theorem are not met. Thus, the very fact that the distribution of the indicator deviates from the normal law “suggests” that there are one or two (maximum three) factors that are decisive in terms of their contribution to the overall dispersion of the process. These factors must be found and eliminated, at least to reduce their influence as much as possible, so that the considered quality indicator is distributed according to the normal law and the well-known system of statistical quality control can be used.

Pay attention to 4 points:

1) the probability of getting into the sample of any unsuitable product is equal toD/ Nand does not depend on the control model, i.e. whether the sample is taken with or without replacement;

2) simplification of the control model due to the use for calculations instead of hypergeometric more “simple” distributions leads to an increase in the dispersion in the control results (see (2.22) and, ultimately, to an increase in the probability of making wrong decisions;

3) ratiosn/ N < 0,1 не достаточно для сохранения точности анализа при переходе от более сложных распределений к более простым (see text for details) ;

4) the normality of the distribution of a quantitative characteristic at the output of the production process can serve as one of the signs of the stability of the process or the controllability of this process (in the terminologySPC / /).

Any statistical analysis must ultimately be represented as two numbers: a preference figure and a risk figure. The preference digit determines the decision to be made, and the risk digit determines the probability of the error of the decision made on the basis of the preference digit.

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1. Model is
hierarchical system of principles of system analysis
inconsistent with other choices
research method
conditional image of the system under study
requirement that the values ​​of the utility function indicator must satisfy

2. Observation is




no correct answer

3. Scientific research is
study of cause-and-effect relationships that arise in reality
system of regulative principles of practical or theoretical human activity
set of principles of system analysis
cognitive activity of a scientist, during which objective knowledge is developed about the phenomenon or process being studied
cognitive activity of a scientist, during which subjective knowledge is developed about the phenomenon or process being studied

4. Abstraction is
no correct answer
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
derivation from general provisions of certain consequences, particular conclusions (from general to particular)
a set of techniques and patterns of connecting individual parts of an object into a single whole
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
inference from particular to general (to some hypothesis)
study of any processes, phenomena, systems by building and studying models

5. Political process




expresses the struggle of various social forces for state power, using it to realize their own economic and political interests

6. Ashby's law of "necessary variety":
for effective management, it is necessary that the information potential of the subject of management be below the level of diversity of manifestations of the management object
for effective management, it is necessary that the total power of connections between the elements of the system be higher than the power of connections of the elements of the system with the external environment
for effective management, it is necessary that the information potential of the subject of management be higher than the level of diversity of manifestations of the management object
for effective management, it is necessary that the total power of connections between the elements of the system be lower than the power of connections of the elements of the system with the external environment

7. Process is
structure
phenomenon
no correct answer
change from one state to another
time-ordered sequence of elementary events

8. Social process
reflects the process of development of material production, its inherent productive forces and production relations

in a broad sense means "public", i.e. belonging not to nature, but to society; in the narrow sense - it is used to characterize only those processes that occur in the social sphere
no correct answer

9. Synthesis is
inference from particular to general (to some hypothesis)
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
a set of techniques and patterns of connecting individual parts of an object into a single whole
study of any processes, phenomena, systems by building and studying models
derivation from general provisions of certain consequences, particular conclusions (from general to particular)
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features

10. An unmanaged process is
process, the nature of which is not amenable to change in the desired direction
no correct answer

a process that can be changed in the right direction with a conscious impact on them

11. The methods of theoretical research include:
formalization; idealization; the ascent from the abstract to the concrete; axiomatic method
analysis and synthesis; deduction and induction; abstraction; modeling;

axiomatic method; experiment; measurement; observation; comparison

formalization; idealization; observation; abstraction; modeling

12. Can a process be absolutely controllable?
Yes
No

13. Signs of a systemic revolution:
equifinality, variety of manifestations, historicity
globalization, intensity of processes and catastrophic
integrativity, equifinality; spherocenosis
globalization, complication, intensification of processes
globality, instability, integrability of processes
interactivity, isomorphism, structuredness
integrity, predictability, openness
irreversibility, lack of spirituality, lack of resources

14. Induction is
a set of techniques and patterns of connecting individual parts of an object into a single whole
derivation from general provisions of certain consequences, particular conclusions (from general to particular)
inference from particular to general (to some hypothesis)
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
study of any processes, phenomena, systems by building and studying models

15. Analysis is
a set of techniques and patterns of connecting individual parts of an object into a single whole
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
inference from particular to general (to some hypothesis)
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
study of any processes, phenomena, systems by building and studying models
derivation from general provisions of certain consequences, particular conclusions (from general to particular)

16. Research method is
conditional image of the system under consideration
epistemological model
system of regulative principles of practical or theoretical human activity
way to achieve some goal, solution, task
partial image of the system under study
no correct answer

17. Deduction is
a set of techniques and patterns of connecting individual parts of an object into a single whole
study of any processes, phenomena, systems by building and studying models
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
derivation from general provisions of certain consequences, particular conclusions (from general to particular)
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
inference from particular to general (to some hypothesis)

18. Managed process is
a process that cannot be changed in the right direction
no correct answer
a process that is spontaneous
a process that can be changed in the right direction with a conscious impact on them

19. Causes of the systemic (managerial) crisis:
dual control
the level of complexity and diversity of economic and socio-political objects far exceeded the level of complexity of living organisms
subject-monopoly management
the systemic revolution that engulfed society as an object of management, practically did not affect the subject of management

20. Formalization is
a set of cognitive operations that provides a distraction from the meaning of concepts and the meaning of the expression of a scientific theory
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
study of any processes, phenomena, systems by building and studying models
a set of techniques and patterns of connecting individual parts of an object into a single whole
inference from particular to general (to some hypothesis)
no correct answer
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts

21. Comparison is
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
study of any processes, phenomena, systems by building and studying models
inference from particular to general (to some hypothesis)
establishment of similarities and differences of objects, phenomena, objects
adequacy
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
derivation from general provisions of certain consequences, particular conclusions (from general to particular)

22. The axiomatic method is
a method when a number of statements are accepted without proof, and all other knowledge is derived according to certain logical rules
no correct answer
a set of techniques and patterns of connecting individual parts of an object into a single whole
inference from particular to general (to some hypothesis)
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
derivation from general provisions of certain consequences, particular conclusions (from general to particular)
study of any processes, phenomena, systems by building and studying models

23. Measurement is
a set of techniques and patterns of connecting individual parts of an object into a single whole
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
derivation from general provisions of certain consequences, particular conclusions (from general to particular)
inference from particular to general (to some hypothesis)
a set of actions performed using measuring instruments in order to find the numerical value of the measured quantity
no correct answer

24. The methods of empirical research include:
fact; observation; abstraction; modeling
experiment; measurement; observation; comparison
comparison; abstraction; observation; idealization
analysis and synthesis; deduction and induction; abstraction; modeling
experiment; analysis and synthesis; comparison; primitivization

no correct answer

25. Modeling is
a set of techniques and patterns of connecting individual parts of an object into a single whole
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts
mental distraction from non-essential private properties and relationships of an object in order to highlight essential features
derivation from general provisions of certain consequences, particular conclusions (from general to particular)
inference from particular to general (to some hypothesis)
study of any processes, phenomena, systems by building and studying models
no correct answer

26. The methods of empirical and theoretical research include:
fact; observation; abstraction; modeling; idealization
experiment; measurement; observation; comparison
comparison; abstraction; observation; idealization
analysis and synthesis; deduction and induction; abstraction; modeling;
experiment; analysis and synthesis; comparison; primitivization
formalization; idealization; the ascent from the abstract to the concrete; axiomatic method

27. Economic process
expresses the struggle of various social forces for state power, using it to realize their own economic and political interests
reflects the process of development of material production, its inherent productive forces and production relations
in a broad sense means "public", i.e. belonging not to nature but to society
reflects those relationships that occur in the spiritual realm
in a narrow sense reflects the social process taking place in the social sphere

28. Experiment is
a set of techniques and patterns of connecting individual parts of an object into a single whole
a set of techniques and patterns of dismemberment (mental or real) of the subject of research into its constituent parts

All processes occurring in the organization can be divided into two groups: managed and unmanaged.
Managed Processes amenable to change in a certain direction with a conscious impact on them.
Unmanaged Processes- when it is impossible to change their direction and nature for one reason or another, they proceed according to their own laws. As a result of these processes, what should happen will happen anyway.
Managed processes reflect only a part of all the processes of functioning and development of the organization, they themselves have a measure of control, are manageable to a certain extent. For example, a subordinate who is a conscientious and competent performer will not carry out orders that are inconsistent with the goals of the company, contrary to common sense or current legislation.
In the practice of development management, it is important to be able to recognize the nature of changes in managed and unmanaged processes, to separate changes in the transition period from changes in the normal functioning of the organization.
Not all processes are controllable, moreover, controllable processes cannot be absolutely controllable. This provision is directly related to organizational development and management: for example, the human factor is often the cause of organizational problems.
Anti-crisis development is a controlled process of preventing or overcoming a crisis that meets the goals of the organization and corresponds to the objective trends of its development. The management of the socio-economic system must always be anti-crisis.
Anti-crisis management is management in which the prediction of the danger of a crisis is set in a certain way, the analysis of its symptoms, measures to reduce the negative consequences of the crisis and the use of its factors for subsequent development.
The problems of anti-crisis management are extensive and varied. The whole set of problems can be represented by four groups (Fig. 3.5).
The first group includes the problems of recognizing pre-crisis situations: to see the onset of a crisis in a timely manner, to detect its first signs, to understand its nature. The possibility of preventing a crisis depends on this. In addition, crisis prevention mechanisms need to be built and put into action. And this is also a management problem.


Rice. 3.5. The set of problems of anti-crisis management
The second group of problems of anti-crisis management is associated with key areas of the organization's life, primarily with methodological problems. In the process of their solution, the mission and goal of management are formulated, ways, means and methods of management in a crisis situation are determined. This group includes a complex of financial and economic problems. For example, in economic anti-crisis management, it becomes necessary to determine the types of production diversification or conversion. This requires additional resources, the search for sources of funding. There are also problems of organizational and legal content, a lot of socio-psychological problems.
The problems of anti-crisis management can also be represented in the differentiation of management technologies (the third group of problems). In the most general form, these are the problems of predicting crises and behavioral patterns of the socio-economic system in a crisis state, the problems of finding the necessary information and developing managerial decisions.
The fourth group of problems includes conflict management and staff selection, which always accompanies crisis situations.
During the transition period from the state "as is" to the position "as it should" it is important to preserve the basic properties of the organizational system, expressed in terms of the functioning of the organization and characterizing the qualitative certainty of the transitional stage of its development. The transition period reflects successive changes in the chosen direction from stage to stage. Not all changes reflect a transitional period - some characterize simple instability, fluctuations in indicators under the influence of natural, social or economic conditions, competition, market conditions.