Seven Simple Japanese Methods. "seven tools" of quality management

Any manufacturing process necessarily includes product quality control, important goals which is to determine the marriage and check the process. There are different techniques for doing this, such as tests, trials, comparisons, and so on.

Quality control - what is it?

This term refers to the verification of quality indicators for compliance with existing requirements, which are defined by regulatory documents: standards, norms, rules, and so on. The organization of quality control implies the process of obtaining information about the object in order to determine the parameters that must be within specified limits. It consists of input, production and systematic control, as well as accounting for models, prototypes and finished products.

Quality control methods

In order to determine the quality of products are used different techniques, which, when applied, ensure the achievement of the desired quality indicators. There are different types of quality control, for example, related to the identification of characteristics software, stimulation of his work, identification of violations and so on. In most cases, several methods are used in production at once, which is important for obtaining a high-quality result.

Statistical quality control methods

In order to obtain high-quality products as a result, statistical methods are often used, the purpose of which is to eliminate the causes that cause random changes in quality indicators. Statistical quality control is divided into several groups, which have their own advantages and disadvantages:

• selective control by changing characteristics during reception;
• quality control on an alternative sign at the time of admission;
• regulation techniques technological process;
• acceptance control standards;
• continuous sampling plans.

Technical quality control of products

To understand whether a product or process meets existing requirements, technical control is carried out. Different types product quality control are used on different stages production, for example, during development, they check whether the prototype fits the terms of reference or documentation. Technical control includes three main stages:

1. Collection of primary information about the object and its specific indicators.
2. Secondary information shows possible deviations from the required parameters specified when compiling primary information, taking into account the planned criteria, norms and requirements.
3. Drawing up a report that includes the conclusions necessary for the development of control actions on the object that was under control.

Intralaboratory quality control

This controlling method is understood as a set of measures aimed at conducting high-quality clinical trials in the laboratory and improving their characteristics. Product quality control is done in order to evaluate whether the result of the experiment meets the existing criteria. It applies to all types of research.

The presented methodology is aimed at identifying problems that are solved first. To do this, the process is controlled, the collection, processing and analysis of the information received. The selected seven quality control tools are self-explanatory and can be used by a variety of professionals. Thanks to them, you can quickly identify the problem and think about ways to fix it. Statistics show that up to 95% of failures are solved with their help. Quality control is carried out with the following seven tools:

1. The checklist is used to collect data and organize it for ease of further use.
2. The histogram helps to visually evaluate the distribution of statistical data that has been distributed according to the frequency of falling into a specific interval.
3. The Pareto diagram objectively represents and identifies the main factor influencing the problem under study, and distributes efforts to eradicate it.
4. The stratification method divides data into subgroups according to a specific attribute.
5. A scatterplot defines the type and relationship between variables.
6. The Ishikawa diagram reveals the most important causes that affect the final result.
7. The control chart helps to track the progress of the process and the impact on it. Thanks to this, it can be prevented from deviating from the requirements put forward.

Organization of quality control at the enterprise

In order for the production of products to fully comply with the requirements specified in the documents, the enterprise uses a system of technical and administrative measures. The quality control system at the enterprise is based on the following conditions:

1. Careful processing and modification technical documentation which is important for the production of high quality products.
2. Development and mastering of technical processes that are important for the production of products that will fully comply with the design documentation.
3. The quality control system includes the development and inclusion in the work of accompanying documentation. It must contain data on the conduct of control measurements.
4. Periodic accuracy check measuring instruments and other devices used in the work.
5. Purchase quality materials and components specified in the technical documentation.
6. For quality control, it is important that the qualifications of the working personnel correspond to the requirements put forward for the position held.

Quality control department

The organization that coordinates the quality control work in the enterprise is called the quality control department (QC). The structure and staff of this organization is developed taking into account the nature and volume of production. The quality control service in most cases includes laboratories that carry out analytical, microbiological and pharmacological control. The OCC performs the following functions:

• conducts control operations provided for by the technical process;
• carries out input control the quality of materials coming from outside;
• draws up documents confirming the compliance of the finished product with the requirements;
• takes part in product testing;
• analyzes and records marriage;
• participates in the preparation of products for certification;
• contributes to the development of the system technical control etc.

Quality Control Engineer

One of the key positions in the enterprise is a product quality control engineer, since from his correct operation depends on whether the product will be accepted by the consumer. The quality control specialist must have a professional technical or higher education in this industry. His main responsibilities are: control of the work of the company's divisions, compliance with safety regulations, ensuring the compliance of products / services with existing requirements. In addition, he analyzes claims to quality coming from the side.

These include 7 methods:

1. Stratification (stratification) is a tool that allows you to select data that reflect the required information about the process in accordance with various factors. Data divided into groups according to their features are called layers (strata). The stratification is carried out by performers (qualification, experience, gender), by material, by batch, by production, by equipment and machines (new, old, brand, service life).

2. Graphs - make it possible not only to assess the state of this moment, but also to predict the long-term result according to trends in the process that can be predicted. Distinguish:

broken line;

A bar graph is a relationship expressed by the height of the bar. When constructing a bar graph, the y-axis plots the quantity ( numerical value), and the factors along the abscissa. Each factor corresponds to a column;

Pie chart - shows the ratio of the parameter as a whole and its constituent parts;

A strip chart is used to visually represent the ratio of the components of a parameter and at the same time to express the change in these components over time. To build this graph, a rectangle is drawn, divided into identical horizontal sections (analysis time, month), at the top is the scale of the measured parameter, at the bottom of the shift;

Z - shaped chart is used to assess general trends when recording actual data by month (sales volume, production volume, etc.). The graph is under construction in the following way:

1) the value of the parameter is set aside by months from January to December (abscissa - time, ordinate - quantity) and connected by straight line segments, a graph formed by a broken line is obtained;

2) the cumulative amount for each month is calculated and the corresponding schedule is built;

3) the total values ​​are calculated, changing from month to month.

3. A histogram is a tool that allows you to visually evaluate the distribution of statistical data, grouped by the frequency of data entry into given interval. A histogram is a bar graph that shows a statistical picture of the behavior of a process. Applicable:

To demonstrate the nature of variability;

Obtaining visual information about the progress of the process;

Making decisions about the focus of improvement efforts.

Building order:

1) data collection;

2) definition of max., min., value and scope;

3) division into intervals;

4) determining the width of the interval (the data obtained are distributed over intervals, we count the number of values ​​that fall into the interval;

5) construction of a histogram.

Information about the nature of the distribution can be obtained:

By shape (bell-shaped, comb, distribution with a cliff on the right, plateau, etc.);

If the center of dispersion is displaced: along with random equally probable factors, the dispersion of quality parameters is affected by constant factors. Reasons: not random deviations from the methods, but inherent in the standard method, process, recipe, inconsistency in the design and development of products.

4. Control chart - a tool for collecting data and automatically organizing them in order to further use collected information. It is used in the form of graphs obtained during the technological process. Graphs determine the dynamics of the process.

5. Scatterplot - a tool that allows you to determine the type and closeness of the relationship between the two considered process parameters. It is used to identify cause-and-effect relationships of quality indicators and influencing factors. A scatterplot is constructed as a graph of the relationship between two parameters (direct, inverse, absent, curvilinear).

6. The Ishikawa Cause and Effect Diagram is a tool that allows you to identify the most significant factors or causes that affect the final result.

Building order:

Target selection;

Compile a list of factors that affect this problem(brainstorming method);

Grouping factors by kinship into groups, subgroups with varying degrees of detail;

Chart construction;

Establishing the significance of each factor.

7. The Pareto diagram is a tool that allows you to present and identify the main factors influencing the problem under study and distribute the conditions for its solution. 2 types: by results and by causes.

Pareto analysis steps:

Choice of purpose (object of study, method of classification);

Organization of observations, development of a checklist;

Analysis of observations of the most significant factors, a blank table for each feature;

Chart construction;

Construction of the Pareto curve;

Corrective actions;

Building a Pareto chart.

When studying the Pareto chart, the method of analyzing the causes is ABC - analysis. The Pareto curve is divided into 3 parts:

A small number of factors, but which have a strong influence (group A - 80% of defects or costs);

Group B is intermediate - 10-20%

Minor factors - group C 5-10%.

FEDERAL AGENCY FOR EDUCATION

State educational institution

higher professional education

"VOLGOGRAD STATE TECHNICAL UNIVERSITY"

KAMYSHINSKY TECHNOLOGICAL INSTITUTE (branch)

VOLGOGRAD STATE TECHNICAL UNIVERSITY

SEMESTER ASSIGNMENT

in the academic discipline "Quality Management"

"Seven tools of quality control"

Performed:

student Prytkova E.S.

Kmen-041 group (c)

Checked:

teacher

Smelova N.Yu.

KAMYSHIN 2009

Introduction________________________________________________ 3

1. checklist ____________________________________ 5

2. histogram ____________________________________________________ 7

3. scatterplot ____________________________________ 8

4. Pareto chart ______________________________________ 9

5. stratification (stratification) ____________________________ 10

6. Ishikawa cause-and-effect diagram________________ 11

7. control card ___________________________________________ 12

Conclusion ____________________________________________ 14

List of used literature ________________________________ 15

Introduction.

In the modern world, the problem of product quality is extremely important. The well-being of any company, any supplier largely depends on its successful solution. Products more High Quality significantly increases the chances of the supplier in the competition for sales markets and, most importantly, better meets the needs of consumers. Product quality is the most important indicator of the company's competitiveness.

Product quality is built into the process scientific research, design and technological developments, is provided by a good organization of production and, finally, it is supported in the process of operation or consumption. At all these stages, it is important to carry out timely control and obtain a reliable assessment of product quality.

To reduce costs and achieve a quality level that satisfies the consumer, methods are needed that are not aimed at eliminating defects (inconsistencies) in the finished product, but at preventing the causes of their occurrence in the production process.

Statistical methods are inextricably linked with the development of quality management, so it is not possible to ignore the seven most simple and common quality control tools.

In order to accept the right decision, that is, a decision based on facts, it is necessary to turn to statistical tools that allow organizing the process of finding facts, namely, statistical material.

Some of the easiest statistical tools to use include:

control sheet

bar graph

scatterplot

Pareto chart

stratification (stratification)

Ishikawa causal diagram

control card.

The sequence of applying the seven methods may be different depending on the goal that is set for the system. Similarly, the applied system does not need to include all seven methods. However, we can say with full confidence that the seven quality control tools are necessary and sufficient statistical methods, the use of which helps to solve 95% of all problems that arise in production.

1.Control sheet

Control sheet (or sheet) - a tool for collecting data and automatically organizing them to facilitate further use of the information collected.

Regardless of the type of statistical tools used to solve the problem facing the company, the first thing to do is to collect the initial data on the basis of which this or that tool is used. It is known that the number of people involved in data processing has a direct impact on the reliability of these data. A checklist is used to eliminate the possibility of errors in data processing.

Control sheet - a paper form on which controlled parameters are pre-printed, according to which data can be entered using notes or simple symbols. The purpose of using checklists is to facilitate the data collection process and to automatically organize the data for further use. Regardless of the number of goals a company has, you can create a checklist for each of them.

When compiling checklists, it should be ensured that the sheet should indicate who, at what stage of the process and for how long, collected data, and also that the form of the sheet should be simple and understandable without additional explanations. It is also important that all data be recorded in good faith so that the information collected can be used to analyze the process.

Fig.2 Example of a checklist

In addition, any control sheet must contain the address part, which indicates its name, measured parameter, name and part number, workshop, section, machine, shift, operator, material being processed, processing modes and other data of interest for analysis. ways to improve product quality or labor productivity. The date of filling is set, the sheet is signed by the person who directly filled it out, and in cases where the results of calculations are given on it, by the person who performed these calculations.

2.Histogram

A histogram (bar chart) shows the distribution of data across groups of values. Bar charts help you compare data values ​​in a visual way. Histograms are useful when describing a process or system. It must be remembered that a histogram will be effective if the data for its construction were obtained on the basis of a stable process. This statistical tool can be a good aid for building control charts.

Fig.3 Histogram example

3.Pareto chart

The Pareto chart is a graphical tool that allows you to identify the most important causes of a particular problem.

The Pareto chart is based on the principle that 80% of defects are 20% dependent on the causes that caused them. Dr. D.M. Juran used this postulate to classify quality problems into a few but essential and many non-essential, and called this method Pareto analysis. The Pareto method allows you to identify the main factors of the problem and prioritize their solution.

Rice. 4 Pareto Chart Example

4. Cause and effect diagram.

A cause and effect diagram helps to identify and visualize the causes of a particular problem or outcome (Figure 5). The idea of ​​the method is to identify and then consistently eliminate or minimize the impact of the identified causes, which will lead to quality improvement.

Rice. 5 Causal Diagram for Exam

The systematic use of a cause-and-effect diagram allows you to:

Identify all possible causes that cause a particular problem.

Separate causes from symptoms.

Analyze the relative importance of the relevant causes.

5. Scatter plot.

A scatterplot is a means of showing relationships between two variables (for example, speed and gas mileage, or hours worked and output).

Fig.6 Scatterplot example: there is a direct relationship between quality indicators

This chart clearly shows if there is a relationship between two variables:

Positive relationship - if X increases, then Y also increases. Negative relationship - if X increases, then Y decreases. There is no connection - one quantity does not correlate with another in any way.

The scatterplot can be used in the Analysis phase to further explore the elements identified in the cause-and-effect analysis; for example, a scatterplot can confirm a cause identified by an Ishikawa plot. When plotting a scatterplot, you must be very careful to ensure that there is a valid relationship.

6. Stratification (stratification).

Basically, stratification is the process of sorting data according to some criteria or variables, the results of which are often shown in charts and graphs.

Stratification is the basis for other tools such as Pareto analysis or scatterplots. This combination of tools makes them more powerful.

The figure shows an example of analysis of the source of defects. All defects (100%) were classified into four categories - by suppliers, by operators, by shift and by equipment. From the analysis of the presented bottom data, it is clearly seen that the largest contribution to the presence of defects is made in this case by "supplier 1".

Rice. 7 Data layering example

7. Control card.

Control card - special kind diagrams for a visual representation of the results of the process.

To present the results of a process, it is important to use the set of control charts that most closely matches the collected process data.

The use of control charts is:

Reducing process deviations,

Process results control,

Establishing a common language for discussing process indicators

Fig.8. General form control chart

Quantitative control charts are, as a rule, double charts, one of which depicts the change in the average value of the process, and the 2nd - the scatter of the process.

The spread can be calculated either on the basis of the range of the process R (the difference between the largest and the smallest value), or based on the process standard deviation S.

Currently, x - S cards are commonly used, x - R cards are used less frequently.

Qualitative control charts:

Map for the proportion of defective products (pmap)

The p-map calculates the proportion of defective products in the sample. It is used when the sample size is variable.

Map for the number of defective items (npmap)

The np-map counts the number of defective items in the sample. It is used when the sample size is constant.

Map for the number of defects in a sample (scart)

The scart counts the number of defects in the sample.

Map for the number of defects per product (umap)

The u-map counts the number of defects per item in the sample

Conclusion.

Statistical methods of quality management is a philosophy, policy, system, methodology, and also technical means quality management based on the results of measurements, analysis, testing, control, operation data, expert assessments and any other information that allows you to make reliable, reasonable, evidence-based decisions.

The use of statistical methods is a very effective way to develop new technology and control the quality of production processes. Many leading firms seek to actively use them, and some of them spend more than a hundred hours annually on in-house training in these methods. Although knowledge of statistical methods is part of the normal education of an engineer, knowledge itself does not mean the ability to apply it. The ability to consider events in terms of statistics is more important than knowledge of the methods themselves. In addition, one must be able to honestly recognize shortcomings and changes that have occurred and collect objective information. indicators quality. They are the most important part integrated system control General Management quality. Implementation seven tools control quality... say that seven tools control quality are essential and...

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The simple quality control tools discussed above (“The Seven Quality Control Tools”) are designed to analyze quantitative quality data. They allow quite simple, but scientifically sound methods to solve 95% of the problems of analysis and quality management in different areas. They use techniques mainly of mathematical statistics, but are available to all participants in the production process and are used at almost all stages. life cycle products.

However, when creating a new product, not all facts are of a numerical nature. There are factors that can only be verbal description. Accounting for these factors accounts for approximately 5% of quality problems. These problems arise mainly in the field of managing processes, systems, teams, and when solving them, along with statistical methods, it is necessary to use the results of operational analysis, optimization theory, psychology, etc.

Therefore, JUSE (Union of Japanese Scientists and Engineers - Union of Japanese Scientists and Engineers) in 1979, based on these sciences, developed a very powerful and useful set tools to facilitate the task of quality management in the analysis of these factors.

The "Seven Instruments of Management" include:

1) affinity diagram;

2) diagram (graph) of relationships (dependencies) (interrelationship diagram);

3) tree (system) diagram (decision tree) (tree diagram);

4) matrix diagram or quality table (matrix diagram or quality table);

5) arrow diagram (arrow diagram);

6) a diagram of the process of implementing the program (planning the implementation of the process) (Process Decision Program Chart - PDPC);

7) matrix of priorities (analysis of matrix data) (matrix data analysis).

The collection of initial data is usually carried out during the period of "brainstorming" of specialists in the field under study and non-specialists, but able to generate productive ideas in new questions.

Each participant can speak freely on the topic under discussion. His proposals are fixed. The results of the discussion are processed, and means are proposed to solve the problem.

The scope of the Seven New Quality Control Tools is rapidly expanding. These methods are applied in such areas as office work and management, education and training, etc.

The most effective way to apply the "Seven New Tools" at the stage

development of new products and preparation of the project;

To develop measures to reduce marriage and reduce claims;

To improve reliability and safety;

To ensure the release of ecological products;

To improve standardization, etc.

Let's take a quick look at these tools.

1. Affinity Diagram (AD)- allows you to identify the main violations of the process by combining homogeneous oral data.

§ defining the topic for data collection;

§ creation of a group to collect data from consumers;

§ Entering the received data on cards (self-adhesive sheets) that can be freely moved;

§ grouping (systematization) of homogeneous data in areas of different levels;

§ Formation of a common opinion among the members of the group on the distribution of data;

§ creation of a hierarchy of selected areas.

2. Relationship Diagram (DV)- helps to determine the relationship of the root causes of process disruption with problems existing in the organization.

The procedure for creating a DS consists of the following steps:

a group of specialists is formed who establish and group data on the problem;

Identified causes are placed on the cards, and a link is established between them. When comparing causes (events), it is necessary to ask the question: “Is there a connection between these two events?” If there is, then ask: "Which event causes another or is the cause of the occurrence of another event?";

draw an arrow between two events, showing the direction of influence;

After identifying the relationships between all events, the number of arrows emanating from each and entering each event is counted.

The event with the largest number of outgoing arrows is the initial one.

3. Tree diagram (DD). After identifying the most important problems, characteristics, etc. with the help of a relationship diagram (DR), using DD, they look for methods to solve these problems. DD indicates the ways and tasks at various levels that need to be addressed in order to achieve a given goal.

DD is used:

1. when the wishes of consumers are converted into performance indicators of the organization;

2. it is required to establish a sequence of solving problems to achieve the goal;

3. secondary tasks must be completed before the main task;

4. The facts that define the underlying problem must be revealed.

Creating a DD includes the following steps:

§ a group is organized, which, on the basis of DS and DV, determines the research problem;

§ determine the possible root causes of the identified problem;

§ allocate main reason;

§ develop measures for its full or partial elimination.

4. Matrix chart (MD) - allows you to visualize the relationship between various factors and the degree of their tightness. This improves the efficiency of the solution. various tasks taking into account such relationships. The following factors can be analyzed using MD:

§ problems in the field of quality and the reasons for their occurrence;

§ Problems and ways to solve them;

§ consumer properties of products, their engineering characteristics;

§ properties of the product and its components;

§ characteristics of the quality of the process and its elements;

§ performance characteristics of the organization;

§ elements of the quality management system, etc.

Matrix diagrams, like other new quality tools, are usually implemented by a team that is assigned a quality improvement task. The degree of closeness of the relationship between factors is assessed either with the help of expert assessments or with the help of correlation analysis.

5.Arrow diagram (SD). After a preliminary analysis of the problem and ways to solve it, performed using the methods of DS, DV, DD, MD, a work plan is drawn up to solve the problem, for example, to create a product. The plan should contain all stages of work and information about their duration. To facilitate the development and control of the work plan by increasing its visibility, the SD is used. An arrow chart can take the form of either a Gantt chart or a network graph. The network graph using arrows clearly shows the sequence of actions and the impact of a particular operation on the progress of subsequent operations, so the network graph is more convenient for monitoring the progress of work than the Gantt chart.

6.Process Implementation Planning Chart - PDPC (Process Decision Program Chart) it is applied for:

§ planning and estimating deadlines complex processes in the field of scientific research,

§ production of new products,

§ solving management problems with many unknowns, when it is necessary to provide various options decisions, the possibility of adjusting the program of work.

Using the PDPC diagram, reflect the process to which the Deming cycle (PDCA) is applicable. As a result of using the Deming cycle to a specific process, if necessary, the improvement of this process is carried out simultaneously.

7.Matrix data analysis (priority matrix).

This method, along with the relationship diagram (DV) and, to a certain extent, the matrix diagram (MD) is designed to highlight the factors that have a priority impact on the problem under study. A feature of this method is that the task is solved by multivariate analysis a large number experimental data, often indirectly characterizing the relationships being studied. An analysis of the relationship between these data and the factors under study makes it possible to identify the most important factors, for which relationships are then established with the output indicators of the phenomenon (process) being studied.

SELF-CHECK QUESTIONS

1. List seven simple quality control tools. What are they used for?;

2. What is a checklist and a Pareto chart used for?;

3. What factors influencing quality are presented in the Ishikawa diagram?;

4. What is determined using a histogram, scatter plot and stratification?;

5. With what a simple tool judge the manageability of the process?;

6. What is the purpose of the Seven New Quality Control Tools? List them.

7. At what stages is it most effective to apply the Seven New Tools of Quality?

Seven simple tools for product quality control

Figure 8 shows seven of the simplest statistical quality control methods.

Figure 8 - Seven simple statistical methods

2.1.1 Control sheet

Whatever the task facing the system, they always begin with the collection of initial quantitative data, on the basis of which this or that tool is then used.

A checklist is a tool for collecting data, a means of recording and automatically organizing them to facilitate further use of information.

Control sheet - a paper form on which controlled parameters are pre-printed, according to which data can be entered using notes or simple symbols, designed to register emerging events, i.e. to collect data for further analysis. Externally, the control sheet is a table, the filling of which is reduced to simply adding a vertical stroke to the corresponding cell when an event occurs. The first four events are marked with vertical strokes, and every fifth event is marked with a horizontal stroke crossing the first four strokes. Thus, each dash represents 5 events.

Filling out a control sheet is the simplest of quality tools - there is nothing easier than putting a stroke in the right cell. Calculating the results is also quite easy.

The following is an example of a data collection sheet that recorded customer complaints about certain types discrepancies on different days of the week (Figure 9).

Figure 9 - Data Collection Sheet

A statistical process control chart, or control chart, is a graphical representation of sampled data that is periodically taken from a process and plotted over time. In addition, "control limits" are marked on the control charts, which describe the inherent variability of a sustainable process. The purpose of a control chart is to help evaluate process stability by examining and plotting data against control limits. Any variable (measured data) or attribute (calculated data) representing the characteristic of the product or process under study can be plotted.

An example is the control sheet used to fix the marriage in detail (Figure 10).

Figure 10 - Checklist

When compiling checklists, care should be taken to indicate at what stage of the process and for how long the data were collected, and that the form of the sheet is simple and understandable without additional explanations.

2.1.2 bar graph

For a visual representation of the trend in the quality of parts, a graphical representation of the statistical material is used. The most common graph used when analyzing the distribution of a random variable is a histogram.

bar graph– a tool that allows you to visually evaluate the law of distribution of statistical data.

Histograms are one of the options for a bar chart that displays the dependence of the frequency of hitting the quality parameters of a product or process in a certain range of these values. In Figure 11, hit intervals are plotted on the x-axis, and hit rates on the y-axis.

Figure 11 - Histogram of frequencies of the interval series of location

The histogram is constructed as follows.

1) Determined highest value quality indicator.

2) The lowest value of the quality indicator is determined.

3) The range of the histogram is defined as the difference between the largest and smallest value.

4) The number of intervals of the histogram (the number of intervals) = C (the number of values ​​of quality indicators) is determined.

5) The length of the histogram interval is determined = (histogram range) / (number of intervals).

6) The range of the histogram is divided into intervals.

7) The number of hits of the results in each interval is counted.

8) The frequency of hits in the interval is determined = (number of hits) / (total number of quality indicators).

9) A bar chart is being built.

As the number of measurements increases, the width of the columns decreases and the polygon turns into a probability density curve, which is a theoretical distribution curve.

In order to assess the adequacy of the process to the requirements of the consumer, we must compare the quality of the process with the tolerance field set by the user. If there is a tolerance, then the upper ( S u) and lower ( S L) its boundaries perpendicular to the abscissa axis (Figure 12). Then you can see if the histogram is well located within these boundaries.

Figure 12 - To the concept of suitability for sampling
three-sigma limits

If the histogram has a symmetrical (bell-shaped) form, when the average value falls in the middle of the data range, then this is a normal (Gaussian) distribution law of a random variable. For the normal distribution law, it becomes possible to investigate the reproducibility of the process, the invariance of the main process parameters: the average value x or mathematical expectation M( x) and standard deviation over time. In this case, it is possible to determine the output of the distribution of the general population for given values ​​of M( x), based on a comparison of the corresponding three-sigma limits and tolerance limits.

Figure 12 shows that if we take three-sigma limits as tolerance limits (σ - standard deviation), then 99.73% of all data in the general population will be considered valid and only 0.27% of the data will be considered inappropriate (non-conformity - NC) the requirements of the consumer (user), as they are located outside the specified tolerance field.

2.1.3 Scatterplots

Scatterplots are graphs that show the correlation between two different factors.(picture 13) .

Figure 13 - Scatterplot

A scatterplot, also called a correlation field, is a tool that allows you to determine the type and strength of the relationship between pairs of relevant variables.

These two variables may refer to:

to the quality characteristic and the factor influencing it;

to two different quality characteristics;

to two factors that affect one quality characteristic. For example, the temperature and pressure in the furnace.

A scatter diagram is used to identify the relationship between them.

The construction of a scatter diagram is performed in the following sequence.

1) Paired data is collected ( x, y), between which they want to investigate the dependence, and are arranged in a table. If one variable is a factor, and the second is a quality characteristic, then the horizontal axis is chosen for the factor x, and for the quality characteristic - the vertical axis y. At least 25–30 data pairs are desirable.

2) Find the maximum and minimum value for x and y.

3) On a separate sheet of paper, a graph is drawn and data is applied. If in different observations one obtains same values, they are denoted by concentric circles.

4) Designated:

chart title;

time interval;

number of data pairs;

names and units for each axis.

The use of a scatter diagram is not limited to identifying the type and closeness of the relationship between pairs of variables. The scatterplot is also used to identify cause-and-effect relationships of quality indicators and influencing factors in the analysis
cause-and-effect diagram, which will be discussed below.

The scatter diagram allows you to visually show the nature of the change in the quality parameter over time. To do this, we draw a bisector from the origin of coordinates. If all points lie on the bisector, this means that the value of this parameter has not changed during the experiment. Therefore, the factor (or factors) under consideration does not affect the quality parameter. If the bulk of the points lies under the bisector, then this means that the values ​​of the quality parameter have decreased over the past time. If the points lie above the bisector, then the values ​​of the parameter have increased over the considered time.

Having drawn rays from the origin of coordinates corresponding to a decrease and an increase in the parameter by 10, 14, 30, 50%, it is possible, by counting the points between the straight lines, to find out the frequency of the parameter values ​​in the intervals of 0...10%, 10...20%.

The most widespread use of scatterplots to determine the type of connections, the overall distribution of pairs. To do this, you first need to find out if there are any far-off points (outliers) on the diagram, which are due to some changes in operating conditions. attention should be paid to the causes of such irregularities, since by looking for their cause, we often obtain information about the quality.

2.1.4 Stratification method (data stratification)

In accordance with the data stratification method (Figure 14), statistical data are stratified, i.e. group data depending on the conditions of their receipt and process each group of data separately.

Data divided into groups according to their characteristics is called layers (strata), and the process of division into layers (strata) is called stratification (stratification).

Exist various methods delamination, the use of which depends on specific tasks. For example, data related
to a product manufactured in a workshop at the workplace may vary to some extent depending on the contractor, the equipment used, the methods of carrying out work operations, temperature
conditions, etc. All of these differences can be delamination factors. In manufacturing processes, the 5M method is often used, taking into account factors depending on the person (man), machine (machine), material (material), method (method), measurement (measurement).

Figure 14 - Data stratification

The delamination is carried out as follows:

stratification by performers - by qualification, gender, work experience;

stratification by material - by place of production, manufacturing company, batch, quality of raw materials, etc.;

stratification by machines and equipment - by new and old equipment, brand, design, manufacturing company, etc.;

stratification according to the method of production - according to temperature, technological method, place of production, etc.;

stratification by measurement - by the place of measurement, the type of measuring instruments or their accuracy, etc.

As a result of delamination, the following two conditions must be observed.

1) Differences between the values ​​of a random variable within a layer (dispersion) should be as small as possible compared to the difference in its values ​​in a non-stratified initial population.

2) The difference between the layers (differences between the average values ​​of the random variables of the layers) should be as large as possible.

When controlling the quality of manufacturing products, the task often arises in practice of identifying the alleged source of deterioration in the quality of products; such information can be obtained by stratifying the dispersion using dispersion analysis.

2.1.5 Ishikawa diagram

The Ishikawa diagram (cause-and-effect diagram) allows you to formalize and structure the causes of the occurrence of an event, for example, the appearance of a discrepancy, as well as establish cause-and-effect relationships.

All possible causes are classified according to the 5M principle:

1.Man(Man) - causes associated with the human factor;

2.Machines(Machinery, equipment) - causes related to equipment;

3.materials(Materials) - causes related to materials;

4.methods(Methods) - reasons associated with the technology of work, with the organization of processes;

5.Measurements(Measurements) - Causes associated with measurement methods.

The event under study is displayed on the right side of the diagram, symbolizing the root of the tree diagram, which is built to the right of the event designation. Horizontally, from the root of the diagram to the left edge of the sheet, the central axis of the diagram is plotted, similar to a tree trunk.

Five branches adjoin the central axis of the Ishikawa diagram, each of which corresponds to its own class of causes, or its own M.

Further, on each branch separately, as on an axis, additional branches are built, each of which represents a separate reason in its class. To each such branch, in turn, shoots are brought up - the reasons for more high level detailing it. Continuing in this way, we get a branched tree that connects the causes of the occurrence of an event located on different levels detail. Thus, we can establish a causal relationship between particular deviations from the norm (primary causes) and their influence on the likelihood of a particular event.

For the effectiveness of the application of this method and the reliability of the results obtained, the construction of the Ishikawa diagram should be performed by professionals.

Because of its structure, the Ishikawa diagram is also called the fishbone diagram (Figure 15).

Figure 15 - Ishikawa Diagrams

2.1.6 Pareto chart

The Pareto chart, or ABC analysis, allows you to identify the main causes that have greatest influence to the emergence of
or other situation. The Pareto Principle states that 20% of the causes produce 80% of the effects. In other words, out of all possible causes only 20% are particularly significant, as they affect the results, which are 80% of the total.

The Pareto Principle is also known as the 20-80 Rule. This principle is named after the Italian economist Vilfredo Pareto, who late XIX century drew attention to the fact that 80% of Italian capital is concentrated in the hands of 20% of the population of Italy. Later, the validity of this rule was confirmed by observations and subsequent calculations of results in various branches of life. So, removing 20% ​​of total number emerging inconsistencies diverts 80% of the total cost of eliminating all possible inconsistencies; for the supplier company, 20% of the total number of customers form 80% of the profit, etc. Thus, by focusing our influence on 20% of the causes, we influence 80% of the consequences. The next 30% of causes generate, oddly enough, only 15% of the effects and, finally, the remaining 50% affect only 5% of the effects. So we can
allocate their attention and impact based on the significance and effectiveness of the results.

For example, if you take an arbitrary text and count how many times each letter occurs in it, then with a high degree of probability it turns out that the letters that make up 20% of the alphabet form about
80% of the entire text.

An example of a Pareto chart is shown in Figure 16.

Figure 16 - Pareto Chart

2.1.7 Correlation diagram

Correlation diagram (scatter diagram) - a graphical display of the relationship between variables related to each other. This diagram is designed to reveal the principle by which the conditionally dependent variable changes when the value of the independent variable changes.

For example, Figure 17 shows how the sales volume of carbonated drinks changes when weather conditions. There is a strong positive correlation.

drinks, pcs.

Figure 17 - Scatterplot

2.1.8 Control charts

The use of control charts is used in planning, designing, determining process changes, as well as measuring the effect of a certain external intervention or action (Figure 18).

In addition, time series analysis against control charts is useful for comparing the results obtained in the case of improvements and changes.

Figure 18 - Control cards

A control chart is a graph with limit lines showing the acceptable limit of quality production. It is very helpful for detecting abnormal situations in standard manufacturing processes.

Control charts are a special kind of chart, first proposed by Shewhart in 1925. They have the form shown in Figure 18. Control charts are used to show over time (from left to right) an observed result or state of a process relative to an average level or between an upper and lower limit.

Types of control charts

There are two types of control charts: one is designed to control quality parameters, the values ​​of which are quantitative quality parameter data (dimension values, mass, electrical and mechanical parameters, etc.), and the second - to control quality parameters, which are discrete random variables and values ​​that are quality data (good - not good, corresponds - does not correspond, defective - defect-free product, etc.) (Figure 19).

Figure 19 - The procedure for selecting the type of control chart

(n– sample size)

Qualitative Control Charts

In the map for the proportion of defective products ( p-map), the proportion of defective products in the sample is calculated. It is used when the sample size is variable.

In the map for the number of defective products ( np-map) counts the number of defective items in the sample. It is used when the sample size is constant.

In the map for the number of defects in the sample ( with-map), the number of defects in the sample is counted.

In the map for the number of defects per product ( u-map) counts the number of defects per item in the sample.

Control charts by quantitative characteristics

Quantitative control charts are, as a rule, dual charts, one of which depicts the change in the average value of the process, and the second one depicts the scatter of the process. Scatter can be calculated based on process range R(difference between the largest and smallest value), control charts, namely, control charts:

– arithmetic mean and ranges ( X – R);

– medians and ranges (Me – R);

– individual values ​​( X);

– share of defective products ( R);

– the number of defective units of production ( pn);

– number of defects ( c);

– the number of defects per unit of production ( u).

In any production process, there are always changes, or variations, manifested in the deviation from the nominal values ​​of some parameters that characterize this process. Stability in the statistical sense is understood as a process when the average value of the observed parameter does not deviate from the nominal value over time, and the value of the parameter scatter falls within a given interval. However, variations can also be caused by non-random reasons. Such reasons include, for example, incorrect setting of the machine, wear and tear, incorrect execution of work instructions by the operator due to fatigue or illness, computer errors, etc. In the presence of such reasons, the production process goes out of statistical control.

The main purpose of the control charts is to quickly detect non-random changes in the production process in order to identify the cause of the change and make the necessary adjustments to the process before a large number of poor quality products are released. In addition, control charts allow you to evaluate the parameters that characterize the quality and potential of the process.

Thus, if the process is statistically controlled, then almost all values ​​of the observed parameter (P) fit into a limited zone. However, no corrective action is required. If the values ​​of the observed parameter fall outside the allowable zone, it indicates that the process has become statistically uncontrollable. It should be noted that situations are possible when the values ​​of the controlled parameter fall within the allowable zone, but all ten last points hit the area below the center line (Figure 20). In this case, the “randomness” factor was violated and the “regularity” factor appeared, i.e. the process became statistically uncontrollable.

Figure 20 - Examples of the appearance of the regularity factor
on the control chart

In the manufacturing process, the product is subject to the complex influence of these reasons.

To assess the quality of the product, i.e. the degree of compliance of its parameters (characteristics) with the required values, the permissible areas of change of these characteristics are assigned, while taking into account the reasons listed above, possible deviations are combined into two groups: random and systematic.

Random deviations are caused by the production process itself and are largely unavoidable. They arise as a result of a complex interaction of various causes, such as vibration, bearing runout, and, as a rule, affect the spread of controlled
characteristics.

Figure 21a shows two graphs of the distribution density of the quality attribute X for two methods of manufacturing the same product. The distribution is normal and has the same mathematical expectation for both manufacturing methods m X, that is, the values ​​of the quality attribute in both cases coincide on average. Both methods differ only in the degree of scattering. If it is required that the values ​​of quality attributes lie within allowable area with an average value m X in the range [ a, b], then with the second manufacturing method, a larger percentage of defects is possible (in the figure, the probability of its occurrence is shown by shading).

Systematic deviations due to such reasons as tool wear, a change in the batch of raw materials, a new work shift. Systematic reasons lead to a shift in the center of dispersion of the controlled characteristic, as shown in
figure 21b. The appearance of systematic deviations also leads to an increase in marriage, however, the causes of such deviations can be identified and eliminated.

a- random; b– systematic

Figure 21 - Types of deviations

The functional purpose of production quality control is to assess the conformity of manufactured products with the required characteristics by comparing the characteristics of manufactured products with the tolerances for these characteristics specified in the documentation for the manufacture of these products, and identifying the causes of deviations.

There are three types of production quality control: input control of materials, raw materials and components, control of the production process and control of manufactured products.

Input control ensures the quality of raw materials and materials.

Production process control- this is a set of all control operations carried out during the manufacturing process and allowing, based on information about the state of the process, to control it so that the quality sign of the manufactured products remains within the specified tolerances.

Finished product control is an acceptance control, which should ensure the proportion of good products in the supplied products is not lower than the level specified by the customer.

Thus, production control ensures the quality of manufactured products, and acceptance control - the quality of products delivered to the customer.

Since any control requires certain cost costs, the manufacturer, when developing a quality management system, must correctly correlate the volumes of these two types of control, optimizing the function of the total control costs, taking into account the cost of risks of both the supplier and the customer.

Quality control can be carried out both quantitatively and qualitatively.

Quantitative features

Many characteristics that determine the quality of a product can be measured. These characteristics include, for example, the diameter of the projectile, the tensile strength of the thread, chemical composition steel, etc. Usually, the quantitative characteristics of the product are continuous random variables. Often this distribution is normal or log-normal. Sometimes quantitative signs are discrete random variables. Examples are the number of threads in a piece of cloth or the number of defects on the surface of a metal disk. If the production process is controlled,
then the distribution of defective disks can obey the law
Poisson.

Qualitative features

Typically, a product is classified as either good (good) or bad (defective, defective). For example, a lighter that does not ignite is defective. Sometimes defects are divided into major and minor. So the lack of a screw in outboard motor is a major defect and will result in the rejection of the motor, while scratches on the motor paint will be classified as minor defects.

Control of products by quantitative characteristics also allows you to classify products and qualitatively: "good - not good". In the case of acceptance control of products based on the results of a sample assessment to describe the distribution qualitative features often used are such types of distributions as binomial, geometric, hypergeometric.