Types of statistical methods of quality control. Methods of statistical quality control of products. Elementary statistical methods

05.04.2021

Surzhanskaya I.Yu.

Balakovo 2010

Introduction…………………………………………………………………………….3

1 Statistical quality control of products…………………………….4

2 Methods of total quality management………………………………………………………………………………………………………………………………………………………………………………………

Conclusion……………………………………………………………….…….20

List of used literature……………………………………..…….21

Introduction

The problem of quality is relevant for absolutely all goods and services. This is especially true when moving to market economy. Russian entrepreneurs need to be ready to work in a highly competitive environment today. Enterprises of any form of ownership that do not pay attention to quality issues will simply be ruined; no protectionist measures of the state will help them.

The most important source of growth in production efficiency is the constant improvement of the technical level and quality of products. For technical systems characterized by a rigid functional integration of all elements, so they do not have secondary elements that can be poorly designed and manufactured. Thus, the current level of development of scientific and technological progress has significantly tightened the requirements for technical level and the quality of products in general and their individual elements.

In industries, statistical methods are used to analyze product and process quality. Quality analysis is an analysis by which, using data and statistical methods, the relationship between the exact and replaced quality characteristics is determined. Process analysis is an analysis that makes it possible to understand the relationship between causal factors and outcomes such as quality, cost, productivity, etc. Process control involves the identification of causal factors that affect the smooth functioning of the production process. Quality, cost and productivity are the results of the control process.

Statistical quality control of products

Process analysis is an analysis that makes it possible to understand the relationship between causal factors and outcomes such as quality, cost, productivity, etc.

Process control involves the identification of causal factors affecting the smooth functioning of the production process 1 . Quality, cost and productivity are the results of the control process.

Statistical quality control of products is now gaining more recognition and distribution in the industry. Scientific methods of statistical quality control of products are used in the following industries: in mechanical engineering, in light industry, in the field of public services.

The main task of statistical control is to ensure the production of usable products and the provision of useful services at the lowest cost.

Statistical quality control of products gives significant results in the following indicators:

Improving the quality of purchased raw materials;

Saving raw materials and labor;

_________________________________________

1 Aristov O.V. Quality management: Proc. for university students. 2004 Page 65

Improving the quality of manufactured products;

Reducing the cost of monitoring;

Decreased number of marriages

Improving the relationship between production and consumer;

facilitating the transition of production from one type of product to another.

The main task is not just to increase the quality of products, but to increase the quantity of such products that would be suitable for consumption.

The two main concepts in quality control are the measurement of controlled parameters and their distribution. In order to be able to judge the quality of products, it is not necessary to measure such parameters as the strength of the material, paper, weight of the object, color quality, etc.

The second concept - the distribution of the values of the controlled parameter - is based on the fact that there are no two completely identical parameters for the same products; as measurements become more accurate, small discrepancies are found in the measurement results of a parameter.

The variability of the "behavior" of the controlled parameter can be of 2 types. The first case is when its values constitute a set of random variables formed under normal conditions; the second - when the totality of its random variables is formed under conditions that are different from normal under the influence of certain reasons.

The personnel who manages the process in which the controlled parameter is formed must, by its values, establish: firstly, under what conditions they were obtained (normal or different from them); and if they are obtained under conditions other than normal, then what are the reasons for the violation of the normal conditions of the process. Then a control action is taken to eliminate these causes.

Statistical control of production and product quality has a number of advantages:

1) are preventive;

2) allows in many cases to reasonably switch to selective control and thereby reduce the complexity of control operations;

3) create conditions for a visual representation of the dynamics of changes in product quality and the mood of the production process, which allows timely measures to prevent defects not only for supervisors, but also for shop workers - workers, foremen, technologists, adjusters, foremen.

Statistical control of product quality management involves:

1) analysis technological process in order to bring it to the required tuning, accuracy and statistically stable state;

2) current control in order to regulate and maintain the process in a state that provides the specified quality parameters;

3) selective statistical acceptance control of quality finished products.

Statistical Process Control is a process of analysis and problem solving based on statistical thinking, using both statistical (probabilistic) and non-statistical methods, with the aim of taking the actions necessary to achieve and maintain a state of statistical controllability of processes, and continuously improve their stability and reproducibility

Statistical thinking is a method for diagnosing the state of processes and / or systems, based on theory of variability, and aimed at making optimal management decisions.

Under quality object (product, process, service) understand the totality of its characteristics that provide the necessary degree of satisfaction of the expected needs of the user of this object. For example, the quality of a car is characterized by the number of passengers, speed (these are indicators of destination), service life (one of the indicators of reliability), gasoline consumption (an indicator of efficiency), appearance (an indicator of aesthetics), etc.

The result of each of these stages is influenced by many different factors, and this leads to variability(variability) of object properties. For example, the production stage of a product is characterized by variations (fluctuations) in the properties of the material, instability of the equipment, different qualifications and individual characteristics employee, environmental changes (temperature, humidity, vibration, etc.) and other factors.

The variability of the properties of an object at different stages has a significant impact on its quality. Statistical methods make it possible to measure and analyze variations in order to reduce them, and in this way ensure that product defects are reduced to an acceptable level.

The reasons for variations in any processes can be divided into two groups. The first one is common reasons related to the production system (equipment, buildings, raw materials, personnel); the corresponding variability cannot be changed without changing the system. Any actions of ordinary employees - performers in this situation will most likely only worsen the situation. Intervention in the system almost always requires action from the top management.

The second group - special reasons, associated with operator errors, configuration failures, violation of the regime. The elimination of these causes is carried out by the personnel directly involved in the process. These are non-random reasons - tool wear, loosening of fasteners, changes in coolant temperature, violation of the technological regime. Such reasons should be studied and can be eliminated during process tuning, which will ensure its stability.

For the first time, a systematic approach to the issues of quality control of industrial products was proposed in 1905 by F. Taylor (1856-1915), who is sometimes called the "father of scientific management."

Taylor system establishes requirements for the quality of products in the form of tolerance fields (upper and lower limits of the controlled indicator), introduces measuring tools - templates, two types of gauges (through and through).

Statistical quality control(Statistical Quality Control - SQC) - a concept based on the systematic application of mathematical statistics methods. Its foundations were laid in 1924 at the American firm Bell Telephone Laboratories.

One direction of the use of statistical methods was the selective control of finished products (the first control plans were developed by G. Dodge and G. Romig). Another direction - ensuring the stability of processes based on control charts (and practically implementing the theory of variability) - was proposed by W. Shewhart (1891-1967).

G. Taguchi proposed to take into account the loss of quality associated not only with the output of the value of the controlled indicator beyond the tolerance, but also with the deviation of this indicator from nominal value, even if this deviation is within tolerance.

Modern tendencies quality management are reflected in the latest version of the ISO 9000 series of standards, one of the eight principles of quality management: “Decision-making based on facts. Effective decisions are based on the analysis of data and information.” Collection necessary information, its processing and analysis in order to make effective decisions are possible only with the use of statistical methods.

A special place in the group of quality control methods is occupied by statistical methods. Their application is based on the results of measurements, analysis, tests, operating data, expert assessments. These tools are designed for analysis and quality control directly at the workplace and are aimed primarily at workers without special education: all these tools are drawn up manually, often on special forms.

tasks, At the same time, the tasks to be solved are planning, obtaining, processing and unification of information, its use in the analysis and management, decision-making based on the results of the analysis, forecasting, etc.

A set of modern statistical methods of quality control subdivided according to the degree of difficulty into three categories.

1. Elementary statistical methods, including Pareto chart, cause and effect diagram, control sheet, histogram, scatter chart, stratification method, control chart. This category of methods is used in Japanese enterprises by everyone from high school graduates to senior managers.

2. Intermediate statistical methods, which include: the theory of sample studies; statistical sampling control; various methods conducting statistical assessments and defining criteria; method for calculating experiments. This group of methods is used by engineers and specialists in the field of quality management.

3. Advanced statistical methods, including methods for calculating experiments, multivariate analysis, various methods of operations research. A limited number of engineers and specialists are trained in their application.

Elementary statistical methods:

Control sheet is a form on which the controlled parameters of a part or product are applied so that measurement data can be easily and accurately entered into it. The form of the sheet depends on its purpose.

On fig. 2.1 shown control sheet for recording the distribution of the controlled parameter.

Checklist for registration of types of defects - for example, for acceptance control of stamped parts, shown in fig. 2.2. When a defect is found, a mark is placed in the line corresponding to the detected defect.

Process Stability Analysis Checklist(the deviation of the shaft diameter from the nominal value is controlled in µm) shown in fig. 2.3. Every thirty minutes, a sample of 5 parts is taken. In addition to the measurement results, the arithmetic mean value of the deviation is calculated on the sheet and its range R(as the difference between the maximum and minimum values) in each sample.

Rice. 2.1. Checklist for recording parameter distribution

Rice. 2.2. Checklist for registration of types of defects

Rice. 2.3. Checklist for Process Stability Analysis

Often the control sheet is a source of information for the application of other quality tools: quality histograms, Pareto charts, control charts, etc.

In large-scale and mass production, methods of statistical quality control (statistical quality control (English), SQC) have become widespread. The most famous among them were the “seven tools of quality control”, which were first widely used in quality circles in Japan, and then in other countries, due to their effectiveness and accessibility to ordinary employees of enterprises.

These "seven tools" include: Pareto Chart, Cause and Effect Diagram, Control Charts, Histograms, Stratification Method, Graphs, Scatter Plot. A summary of these methods in relation to quality management is as follows:

Layering method(layered analysis, zoned sampling-stratification (English)) is used to find out the reasons for the spread of product characteristics. The essence of the method is to separate (stratify) the obtained characteristics depending on various factors: the qualifications of workers, the quality of raw materials, working methods, equipment characteristics, etc. In this case, the influence of one or another factor on the characteristics of the product is determined, which allows you to take the necessary measures to eliminate their unacceptable spread.

Graphs(diagrams) are used to visualize and facilitate understanding of the interdependence of quantities or their changes over time. The most commonly used are line, pie, column and strip charts.

Pareto chart(Pareto diagram), named after its author, the Italian economist Pareto (1848-1923), allows you to visualize the amount of loss depending on various defects. (see Pareto curve). This allows you to first focus on eliminating those defects that lead to the greatest losses. To clarify the causes of these defects, it is advisable to additionally use a cause-and-effect diagram. After clarification of the causes and elimination of defects, the Pareto diagram is again built in order to check the effectiveness of the measures taken.

cause and effect diagram(cause and effect diagram) is used, as a rule, in the analysis of defects that lead to the greatest losses. It allows you to identify the causes of such defects and focus on eliminating these causes. In this case, four main causal factors are analyzed: man, machine (equipment), material and method of work. The analysis of these factors reveals secondary, and perhaps tertiary causes that lead to defects and must be eliminated. Therefore, in order to analyze defects and build a diagram, it is necessary to determine the maximum number of causes that may be related to the admitted defects.

Such a diagram in the form of a fish skeleton was proposed by the Japanese scientist Kaoru Ishikawa. His diagram is also called the "branching scheme of characteristic factors." Sometimes it is also called the “four M” diagram - according to the composition of the main factors: Man (person), Method (method), Material (material), Machine (machine). Ishikawa diagram:

The histogram is a bar graph and is used to visualize the distribution of specific parameter values by repetition frequency for a certain period of time (week, month, year).

When plotting the allowable values of a parameter on a graph, you can determine how often this parameter falls within the allowable range, shifts within the tolerance, or goes beyond it.

The data obtained is analyzed using other methods:

losses from rejects depending on various defects are examined using the Pareto diagram;

the causes of defects are determined using a cause-and-effect diagram, a layering method and a scatter diagram;

change in characteristics over time is determined by control charts.

Scatterplot(Scatter diagram - correlation diagram) is built as a graph of the relationship between two parameters. This allows you to determine if there is a relationship between these parameters. And if such a relationship exists, it is possible to eliminate the deviation of one parameter by influencing the other.

Control card(Control chart) is a type of chart that is distinguished by the presence of control boundaries that indicate the permissible range of variation in characteristics under normal process conditions. (See Shewhart Control Chart). The output of characteristics outside the control limits means a violation of the stability of the process and requires an analysis of the causes and the adoption of appropriate measures.

These "seven tools" help to solve most of the quality problems that arise. For more complex problems, "seven new quality control tools" can additionally be applied: Affinity Diagram, Dependency Diagram, Tree Diagram, Matrix Diagram, Arrow Diagram, Process Evaluation Planning Diagram, Matrix Data Analysis.

For a detailed study of statistical methods, one should refer to the specialized literature, as well as to the international standard ISO 10017 on statistical methods.

Standardization in the field of statistical methods at the international level is carried out by the technical committee of the International Organization for Standardization ISO / TC 69 "Application of statistical methods". The materials of this committee may be of interest to those who, by the nature of their work, are associated with the use of statistical methods.

In addition to the above statistical methods, the Six Sigma method and the Taguchi methods are used for quality control and management.

Six Sigma is used for statistical process control to reduce the likelihood of product failures. The lowest probability of failures is achieved under the condition of a stable hit of six standard deviations from the nominal (plus - minus three sigma) in a given tolerance field with a certain margin. This requires high precision in the manufacture of parts, ensuring minimum sigma values.

Traditionally, statistical process control in manufacturing is a random selection of a part of the product and its testing. Deviations are continuously checked for tolerance and where necessary corrected before the production of defective parts.

INTRODUCTION

The most important source of growth in production efficiency is the constant improvement of the technical level and quality of products. Technical systems are characterized by strict functional integration of all elements, so they do not have secondary elements that can be poorly designed and manufactured. Thus, the current level of development of scientific and technical progress has significantly tightened the requirements for the technical level and quality of products in general and their individual elements. Systems approach allows you to objectively choose the scale and direction of quality management, types of products, forms and methods of production, providing the greatest effect of the efforts and funds spent on improving product quality. A systematic approach to improving the quality of products allows you to lay the scientific foundations industrial enterprises, associations, planning bodies.

Statistical methods for quality control of products today are gaining more recognition and distribution in the industry. Scientific methods of statistical quality control of products are used in the following industries: in mechanical engineering, in light industry, in the field of public services.

The main objective of statistical methods of control is to ensure the production of usable products and the provision of useful services at the lowest cost.

Statistical methods of product quality control give significant results for the following indicators:

improving the quality of purchased raw materials;

saving raw materials and labor;

improving the quality of manufactured products;

reducing the cost of monitoring;

decrease in the number of marriages;

improving the relationship between production and consumer;

facilitating the transition of production from one type of product to another.

The main task is not just to increase the quality of products, but to increase the quantity of such products that would be suitable for consumption.

1. Statistical acceptance control by attribute

The consumer, as a rule, does not have the ability to control the quality of the product during its manufacture. However, he must be sure that the products he receives from the manufacturer meet the established requirements, and if this is not confirmed, he has the right to require the manufacturer to replace the defect or eliminate defects.

The main method of control incoming to the consumer of raw materials, materials and finished products is statistical acceptance control of product quality.

Statistical acceptance control of product quality- selective quality control of products, based on the use of mathematical statistics methods to check the quality of products to established requirements.

If, with all this, the sample size becomes equal to the volume of the entire controlled population, then such control is called continuous. Solid control is possible only in those cases when the quality of the product does not deteriorate during the control process, otherwise selective control, i.e. control of a certain small part of the totality of products becomes forced.

Continuous control is carried out if there are no special obstacles to this, in the case of the possibility of a critical defect, i.e. defect, the presence of which completely precludes the use of the product for its intended purpose.

All products can also be tested under the following conditions:

the batch of products or material is small;

the quality of the input material is poor or unknown.

You can limit yourself to checking a part of the material or products if:

the defect will not cause a serious malfunction of the equipment and does not endanger life;

products are used by groups;

defective products can be found at a later stage of assembly.

In the practice of statistical control, the general share q is unknown and should be estimated from the results of control of a random sample of n items, of which m are defective.

A statistical control plan is a system of rules that specifies the methods for selecting items for testing and the conditions under which a lot should be accepted, rejected, or continued to be tested.

Distinguish the following types plans for statistical control of a batch of products on an alternative basis:

one-stage plans, according to which, if among n randomly selected products the number of defective m is not more than the acceptance number C (mC), then the lot is accepted; otherwise, the batch is rejected;

two-stage plans, according to which, if among n1 randomly selected products the number of defective m1 is not more than the acceptance number C1 (m1C1), then the lot is accepted; if m11, where d1 is the rejection number, then the lot is rejected. If C1 m1 d1, then a decision is made to take the second sample of size n2. Then, if the total number of products in two samples is (m1 + m2) C2, then the lot is accepted, otherwise the lot is rejected according to the data of two samples;

multi-stage plans are a logical continuation of two-stage ones. Initially, a batch of n1 is taken and the number of defective products m1 is determined. If m1?C1, then the batch is accepted. If C1p m1 d1 (D1C1+1), then the lot is rejected. If C1m1d1, then a decision is made to take the second sample of size n2. Let there be m2 defective ones among n1 + n2. Then if m2c2, where c2 is the second acceptance number, the lot is accepted; if m2d2 (d2 c2 + 1), then the lot is rejected. For c2 m2 d2, a decision is made to take the third sample. Further control is carried out according to a similar scheme, except for the last k-th step. On the k-th step, if there are mk defective and mkck among the checked items of the sample, then the batch is accepted; if m k ck, then the batch is rejected. In multistage plans, the number of steps k is assumed to be n1 =n2=…= nk;

sequential control, in which the decision on the inspected batch is made after assessing the quality of samples, the total number of which is not predetermined and is determined in the process, which is based on the results of previous samples.

Single-stage plans are simpler in terms of organizing production control. Two-stage, multi-stage and sequential control plans provide, with the same sample size, greater accuracy of the decisions made, but they are more complex in organizational terms.

The task of selective acceptance control is actually reduced to a statistical verification of the hypothesis that the proportion of defective products q in the batch is equal to the allowable value qo, i.e. H0:q = q0.

A task right choice The plan of statistical control is to make Type I and Type II errors unlikely. Recall that errors of the first kind are associated with the possibility of erroneously rejecting a batch of products; errors of the second kind are associated with the possibility of erroneously skipping a defective batch.

2. Statistical Acceptance Control Standards

For the successful application of statistical methods of product quality control, the availability of relevant guidelines and standards, which should be available to a wide range of engineering and technical workers, is of great importance. Standards for statistical acceptance control provide an opportunity to objectively compare the quality levels of batches of the same type of product both over time and across different enterprises.

Let us dwell on the basic requirements for standards for statistical acceptance control.

First of all, the standard should contain a sufficiently large number of plans with different operational characteristics. This is important, as it will allow you to choose control plans, taking into account the characteristics of production and customer requirements for product quality. It is desirable that different types of plans be specified in the standard: single-stage, two-stage, multi-stage, sequential control plans, etc.

The main elements of acceptance control standards are:

1. Tables of sampling plans used in the normal course of production, as well as plans for enhanced control in conditions of disorder and to facilitate control when achieving high quality.

2. Rules for choosing plans, taking into account the features of control.

3. Rules for the transition from normal control to enhanced or light control and the reverse transition during the normal course of production.

4. Methods for calculating subsequent estimates of the quality indicators of the controlled process.

Depending on the guarantees provided by acceptance control plans, the following methods for constructing plans are distinguished:

set the values of the risk of the supplier and the risk of the consumer and put forward the requirement that the operational characteristic P(q) pass approximately through two points: q0, ? and qm, where q0 and qm are, respectively, acceptable and rejection quality levels. This plan is called a compromise plan, since it protects the interests of both the consumer and the supplier. For small values? And? the sample size should be large;

selecting one point on the operating characteristic curve and accepting one or more additional independent conditions.

The first system of statistical acceptance control plans, which found wide application in industry, was developed by Dodge and Rohlig. The plans of this system provide for the complete control of products from rejected lots and the replacement of defective products with good ones.

In many countries, the American standard MIL-STD-LO5D has become widespread. The domestic standard GOST-18242-72 is close in construction to the American one and contains plans for one-stage and two-stage acceptance control. The standard is based on the concept of an acceptable quality level (ARQ) q0, which is considered as the maximum allowable by the consumer proportion of defective products in a batch manufactured during the normal course of production. The probability of rejecting a lot with a proportion of defective products equal to q0 is small for the plans of the standard and decreases as the sample size increases. For most plans, it does not exceed 0.05.

When testing products on several grounds, the standard recommends classifying defects into three classes: critical, major, and minor.

3. Control cards

One of the main tools in the vast arsenal of statistical quality control methods are control charts. It is generally accepted that the idea of the control chart belongs to the famous American statistician Walter L. Shewhart. It was stated in 1924 and described in detail in 1931. Initially, they were used to record the results of measurements of the required properties of products. The parameter going beyond the tolerance field indicated the need to stop production and adjust the process in accordance with the knowledge of the specialist managing production.

This gave information about when someone, on what equipment, received marriage in the past.

At the same time, in this case, the decision to adjust was made when the marriage had already been received. Therefore, it was important to find a procedure that would accumulate information not only for a retrospective study, but also for use in decision making. This proposal was published by the American statistician I. Page in 1954. Maps that are used in decision making are called cumulative.

A control chart consists of a center line, two control limits (above and below the center line), and characteristic (quality score) values plotted on the map to represent the state of the process.

In certain periods of time, n manufactured products are selected (all in a row; selectively; periodically from a continuous flow, etc.) and the controlled parameter is measured.

The measurement results are applied to the control chart, and depending on this value, a decision is made to correct the process or to continue the process without adjustments.

A signal about a possible adjustment of the technological process can be:

point going beyond the control limits (point 6); (the process is out of control);

the location of a group of successive points near one control boundary, but not going beyond it (11, 12, 13, 14), which indicates a violation of the equipment setting level;

strong scattering of points (15, 16, 17, 18, 19, 20) on the control map relative to the midline, which indicates a decrease in the accuracy of the technological process.

Upper limit

central line

lower limit

6 11 12 13 14 15 16 17 18 19 20 Sample number

Conclusion

Increasing development of the economic environment of reproduction, new for our country, i.e. market relations, dictates the need for continuous improvement of quality using for this all the possibilities, all the achievements of progress in the field of technology and organization of production.

The most complete and comprehensive assessment of quality is ensured when all the properties of the analyzed object are taken into account, which manifest themselves at all stages of its life cycle: during manufacture, transportation, storage, use, repair, maintenance. service.

Thus, the manufacturer must control the quality of products and, based on the results of sampling, judge the state of the corresponding technological process. Due to this, he timely detects the disorder of the process and corrects it.

Bibliography

1. GembrisS. Herrmann J., Quality Management, Omega-L SmartBook, 2008

2. Shevchuk D.A., “Quality control”, Gross-Media., M., 2009

3. Electronic textbook "Quality Control"

Statistical process control originated in 1931. It was proposed by the scientist Walter Shewhart in the book "Economic Quality Control of Manufactured Products". At the time, Shewhart was working as a statistician for Bell Laboratories. He noticed that in production processes there are such data that, after statistical processing, can signal whether the process is under control or any deviations have occurred in it (caused by reasons that are not an integral characteristic of the process). The checklists and checklists currently in use are based on Shewhart's work. Statistical process control may require the use of any of the statistical methods discussed in Section 3.4 Quality Analysis Methods.

Although SPC was originally used only for manufacturing processes, it can be applied to almost any process. Everything that is done by employees can be considered as processes. Each process is influenced by many factors (equipment used, materials, methods and work instructions, measurements, and people involved in the process). If, apart from this, nothing affects the process, and all these factors work flawlessly and as they should, then the process is statistically controlled. This means that no side causes affect the process. All crashes have been fixed. According to Shewhart's position, this does not mean that all 100% of manufactured products will be flawless, that there are no variations in the process. Every process has natural variations and deviations that affect the yield. They are 3 units of defective products per 1000 (by defective here we mean products that go beyond the acceptable limits - ± 3s).

That every process has natural variations can be illustrated in the following way: for example, the diameters of cylinders machined on a machine will rarely be exactly 17 mm. Their value will vary around 17 mm, at least within the accuracy of the measuring instrument and control equipment. In fact, there will be many more process-inherent causes for this variation.

In statistical process control, using statistical methods (and only!) It is determined which deviations from the ideal are normal for a given process (these “normal” deviations should not be confused with the technical characteristics of the equipment, of course, specifications affect the process, but these “normal” deviations are determined statistically).

Statistical process control does not completely exclude variations and deviations of products from the ideal in processes. But it allows you to control the process and distinguish between natural variations that are present in all processes, and failures caused by some additional reasons. It is the basis for process improvement and defect-free production. After all causes of failures are identified and eliminated and only natural variation remains, the process is considered to be in a state of statistical control. When this condition is reached, the process is stable and 99.73% of the production is within the statistical control limits (upper and lower control limits, they have already been mentioned in paragraph 3.4.8. “Control chart”). Only then can the process be improved. So:

Statistical process controlis a statistical method for separating the variations caused by failures in a process from the “natural” variations that are an integral part of the process. The purpose of statistical process control is to identify and eliminate failures and establish and maintain process stability, allowing further improvements to be made.

Statistical process control, as part of total quality management, improves product quality and reduces costs. Statistical process control makes the following processes much more efficient:

control of variations.

· Continuous improvement.

· Predictability of processes.

Elimination of losses.

· Selective control of production.

Let us consider what statistical control of processes gives in these processes.

Variation control

As already mentioned, the process is affected by two types of factors - failures and natural causes. Statistical process control makes it possible to distinguish one from the other. Process improvement is only the elimination or minimization of natural causes. It is possible after the failures are eliminated, otherwise the failures do not allow us to evaluate the effect of the improvement.

In the absence of failures, the distribution of the amount of production by the value of any characteristic relative to its required value is a bell-shaped curve. How such a distribution is constructed is described in detail in paragraph 3.4.9. "Bar graph". The values of this characteristic for 99.73% of product units do not go beyond ±3s (Fig. 3.9 a). If a failure occurs in the process, then more products go beyond the border ± 3s (Fig. 3.9 b). In general, in a failing process, the distribution does not necessarily have the form of a bell curve.

Continuous Improvement

To improve the quality of products, it is necessary to improve the processes of its creation. Process improvement is about improving its natural characteristics. It can only be carried out after all failures have been eliminated. At the same time, the improvement itself will be controlled and it will be possible to create checklists and control charts to evaluate the effects of the improvement. The results of process improvement can be graphically represented as in Fig. 3.9 in.

Rice. 3.9 Distribution of the diameter values of the cylinders to be machined in relation to the required value

Process Predictability

Statistical process control makes processes stable, repeatable and predictable. When the process is under control, the enterprise knows exactly its characteristics. This allows you to accurately assess the possibility of fulfilling a particular order and take the lowest possible risk assessments (which, accordingly, reduces the cost of the contract and increases competitiveness). If the process is uncontrolled, then there is a risk of either not fulfilling the terms of the contract, or not getting the contract due to the high price (if we take the maximum possible risks). In any case, the manager will spend a lot of nerves getting a contract and fulfilling its conditions.

Loss Elimination

If the process is under statistical control, then it allows to detect failures immediately after they occur, which reduces the production of low-quality products. It was considered that it is cheaper to organize statistical control of processes than to correct the produced defects.

Product control

Statistical process control allows you to optimally organize the control of finished products (so that the cost of it is minimal with acceptable reliability). Product control requires expensive equipment and highly skilled (and highly paid) personnel, so the reduction in control costs is significant. In addition, even a 100% control of finished products reveals only 80% of defects. If the process is under statistical control, then the required amount of sampling can be determined and the most convenient forms of control sheets and control charts can be developed. As already mentioned, all this is done on the basis of statistics and was developed in detail by Shewhart.

Operator powers

Operators performing statistical process control and monitoring the process must be specially trained. They should be given the appropriate authority to influence the process. There is no consensus in the world about the level of authority. There are two options:

The operator must stop the manufacturing process to detect failure.

· The operator has no right to stop the process. He must report the failure to his superiors. If the failure still requires a stop, then it is necessary to start the process again as soon as possible, perhaps with the help of temporary measures. The causes of the failure and how to eliminate it, as well as its elimination itself, will be carried out later, without delaying the process.

Which method is better depends on many reasons and can only be said in each specific case. However, most enterprises are of the opinion that it is necessary to immediately stop the process and eliminate the failure. In their opinion, it is more economically profitable, because. no defective products are produced. In addition, if you do not immediately stop the process, then the symptoms of the failure may disappear, it will not be possible to identify it when maintenance equipment and it can manifest itself in the future, causing more damage.

Types of statistical methods of quality control. Methods of statistical quality control of products. Elementary statistical methods

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