Seven new quality management tools. Seven Essential Quality Control Tools

Federal State Autonomous

educational institution

higher professional education

"SIBERIAN FEDERAL UNIVERSITY"

Institute of Business Process Management and Economics

Department of Economics and Business Process Management

ABSTRACT

According to methods for assessing the technical level of machines

Seven tools for quality control and management

Teacher ______________ senior teacher V.V. Kostina

Student UB 11-01 ____________________ V.A. Ivkina

Krasnoyarsk 2014

The method is used both directly in production and at various stages of the product life cycle. 4

The purpose of the method is to identify problems that need to be addressed as a matter of priority, based on monitoring the current process, collecting, processing and analyzing the obtained statistical material for subsequent improvement of the quality of the process. 4

The essence of the method is that quality control is one of the main functions in the quality management process, and the collection, processing and analysis of facts is the most important stage of this process. 4

Seven basic quality control tools (Fig. 1) are a set of tools that make it easier to control ongoing processes and provide various kinds of facts for analysis, adjustment and improvement of process quality. 4

Figure 1 – 7 Quality Control Tools 5

LIST OF SOURCES USED 19

INTRODUCTION

In the modern economy, an important place is occupied by such a concept as the quality of goods and services produced. It depends on it whether the manufacturer will survive the competition or not. High quality products significantly increase the manufacturer’s chance to receive significant profits and regular consumers.

Product quality is established in the process of scientific research, design and technological development, ensured by good organization of production and, finally, it is maintained during operation or consumption. At all these stages, it is important to carry out timely control and obtain a reliable assessment of product quality.

Modern manufacturers try to prevent the occurrence of defects rather than eliminating them in finished products.

In order to make the right decision, that is, a decision based on facts, it is necessary to turn to statistical tools that allow you to organize the process of searching for facts, namely statistical material.

The sequence of application of the seven methods may be different depending on the goal set for the system. Likewise, the system used does not necessarily have to include all seven methods.

1 Seven Quality Control Tools

The method is used both directly in production and at various stages of the product life cycle.

The purpose of the method is to identify problems that need to be addressed as a matter of priority, based on monitoring the current process, collecting, processing and analyzing the obtained statistical material for subsequent improvement of the quality of the process.

The essence of the method is that quality control is one of the main functions in the quality management process, and the collection, processing and analysis of facts is the most important stage of this process.

The scientific basis of modern technical control is mathematical and statistical methods.

Of the many statistical methods, only seven have been selected for widespread use, which are understandable and can be easily used by specialists in various fields. They allow you to identify and display problems in a timely manner, establish the main factors from which you need to start acting, and distribute efforts in order to effectively resolve these problems.

The implementation of the seven methods should begin with training in these methods for all participants in the process.

Seven basic quality control tools (Fig. 1) are a set of tools that make it easier to control ongoing processes and provide various kinds of facts for analysis, adjustment and improvement of process quality.

Figure 1 – 7 Quality Control Tools

    Checklist (Fig. 2) is a tool for collecting data and automatically organizing it to facilitate further use of the collected information. A control sheet is a paper form on which controlled parameters are pre-printed, according to which data can be entered using marks or simple symbols. The purpose of using checklists is to facilitate the data collection process and automatically organize the data for their further use. Regardless of the number of goals a company has, you can create a checklist for each of them.

Figure 2 – Example of a check sheet

    A histogram (Fig. 3) is a tool that allows you to visually evaluate the distribution of statistical data, grouped by the frequency of the data falling into a certain, predetermined interval. 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 stably operating process. This statistical tool can be a good aid for constructing control charts.

Figure 3 – Example of a histogram

    The Pareto diagram (Fig. 4) is a tool that allows you to objectively present and identify the main factors influencing the problem under study, and distribute efforts to effectively resolve it. The Pareto diagram is based on the principle that 80% of defects depend 20% on the reasons that caused them. Dr. D.M. Juran used this postulate to classify quality problems into few but essential ones and many unimportant ones, and called this method Pareto analysis. The Pareto method allows you to identify the main factors causing a problem and prioritize their solutions.

Figure 4 – Example of a Pareto chart

    The method of stratification (data stratification) (Fig. 5) is a tool that allows you to divide data into subgroups according to a certain criterion.

Figure 5 – Example of data layering

    A scatter diagram (Fig. 6) is a tool that allows you to determine the type and strength of the relationship between pairs of corresponding variables.

Figure 6 – Example of a scatter plot

    Ishikawa diagram (cause-and-effect diagram) (Fig. 7) is a tool that allows you to identify the most significant factors (reasons) influencing the final result (effect).

The systematic use of a cause-and-effect diagram allows you to identify all sorts of causes that cause a certain problem and separate the causes from the symptoms.

    Figure 7 – Example of a cause-and-effect diagram

A control chart (Fig. 8) is a tool that allows you to monitor the progress of a process and influence it (with the help of appropriate feedback), preventing its deviations from the requirements presented to the process.

Figure 8 - Example of a control chart

2 Seven quality management tools

Most often, these tools are used to solve problems that arise during the design phase.

The purpose of the method is to solve problems that arise in the process of organizing, planning and managing a business based on the analysis of various types of facts.

Seven quality management tools provide insight into complex situations and help make quality management easier by improving the product or service design process.

Quality management tools enhance the planning process through their ability to:

    understand the tasks;

    eliminate deficiencies;

    facilitate the dissemination and exchange of information among stakeholders;

    use everyday vocabulary.

As a result, quality management tools allow you to develop optimal solutions in the shortest possible time. Affinity diagram and link diagram support overall planning. Tree diagram, matrix diagram and priority matrix provide intermediate planning. The decision process flowchart and arrow diagram provide detailed planning.

The sequence of application of methods may be different depending on the goal.

These methods can be considered both as individual tools and as a system of methods. Each method can find its own independent application depending on what class the task belongs to.

Seven quality management tools - a set of tools to facilitate the task of quality management in the process of organizing, planning and managing a business when analyzing various types of facts.

The affinity diagram (Fig. 9) is a tool that allows you to identify the main violations of the process by summarizing and analyzing close oral data.

Figure 9 - Example of Affinity Diagram

A connection diagram (Fig. 10) is a tool that allows you to identify logical connections between the main idea, problem and various influencing factors.

Figure 10 - example of a communication diagram

The tree diagram (Fig. 11) is a tool for stimulating the creative thinking process, facilitating the systematic search for the most suitable and effective means of solving problems.

Figure 11 - Example of a tree diagram

The matrix diagram (Fig. 12) is a tool that allows you to identify the importance of various non-obvious (hidden) connections. Usually two-dimensional matrices are used in the form of tables with rows and columns a1, a2,., b1, b2. - components of the objects under study.

Figure 12 - example of a matrix diagram

The priority matrix (Fig. 13) is a tool for processing a large amount of numerical data obtained when constructing matrix diagrams in order to identify priority data. This analysis is often considered optional.

Figure 13 - example of a priority matrix

The decision-making process flowchart (Fig. 14) is a tool that helps launch the continuous planning mechanism. Its use helps reduce risk in almost any business. Plans for every conceivable eventuality that might occur, moving from problem statements to possible solutions.

Figure 14 is an example of a decision making process flowchart.

An arrow diagram (Fig. 15) is a tool that allows you to plan the optimal timing for completing all the necessary work to achieve the goal and effectively control it.

Figure 15 - example of an arrow diagram

The seven quality management tools provide the means to understand and plan accordingly in complex situations, build consensus, and lead to success in collaborative problem solving.

Initial data collection is usually carried out during brainstorming sessions.

The advantages of the method are clarity, ease of learning and application.

The disadvantage of the method is its low efficiency when analyzing complex processes.

The use of quality management tools allows you to save resources and thereby improve the company's bottom line.

CONCLUSION

Seven simple statistical methods are tools of knowledge, not management. The ability to view events from a statistical perspective is more important than knowledge of the methods themselves. In leading foreign companies, absolutely all employees are required to master seven simple statistical methods. Data must be collected in a manner that facilitates subsequent processing. You need to understand the purposes for which data is collected and processed.

Typically, the objectives of data collection during the quality control process are as follows:

    control and regulation of the process;

    analysis of deviations from established requirements;

    process output control.

The use of seven quality management tools allows you to:

    identify the main violations in the process by combining related oral data;

    identify, analyze and classify the causes and results of those interactions that exist between the main problems and, based on the identified driving forces and likely outcomes, a more effective solution;

    show connections between the topic and its constituent elements;

    clearly show the interdependence of processes and events;

    identify possible solutions to problems and potential opportunities for quality improvement;

    describe an existing technological process, or design a new one.

LIST OF SOURCES USED

    7 simple quality control tools // about quality management.- Access mode: http://quality.eup.ru/DOCUM4/7_instrum.htm

    7 quality management tools // about quality management. - Access mode: http://www.inventech.ru/pub/methods/metod-0005/

Seven new quality management tools

Tree diagram;

Linear (arrow) diagram;

Matrix diagram;

Brainstorming method;

Process map;

“Seven New Quality Control Tools” refers to methods for processing primarily verbal (descriptive) data. The use of these tools is especially effective when they are used as methods for the most complete implementation of plans based on a systematic approach in conditions of cooperation of the entire enterprise team.

Purpose of the work: to consider the essence and application of seven new quality management tools;

Tasks: consider:

relationship diagram;

relationship diagram;

tree diagram;

line (arrow) diagram;

matrix diagram;

brainstorming method;

process map

Affinity Diagram

Application

Affinity diagram is a method that allows you to identify the main violations of the process by combining related oral data. This method is sometimes called the KJ method (named after its founder, the Japanese scientist Jiro Kawakita). This method is a creative means of organizing large quantities of oral data such as ideas, consumer wishes, or the opinions of groups participating in the problem or topic being discussed. etc.) into groups based on the natural relationships between each idea (topic) to define these thematic groups. This is basically a creative method rather than a logical one.

The biggest barrier to improvement planning is past success or failure. We assume that something that worked or didn't work before will work that way in the future. In doing so, we perpetuate a way of thinking that may or may not be appropriate. Continuous improvement requires new logical models.

Description

Affinity diagram is a very good way to help a group of people to reach a creative level as opposed to an intellectual approach. This method also helps to successfully organize these new creative ideas for subsequent work with them; within 30-45 minutes, the discussion group can “produce” and organize more than 100 ideas or topics. It's easy to imagine how long this would have taken using a traditional discussion process. In addition to being effective, this method ensures true participation from everyone as all ideas find their way into the process. This is in contrast to most other discussions where many ideas get lost and thus not discussed.

The best way to understand the Affinity Diagram is to study its origins. It was created in the 60s as an analytical method by the Japanese anthropologist Jiro Kawakito, who studied a large number of different societies and organizations. He took very detailed notes for later analysis. When this time came, he discovered a huge amount of information that was in no way connected with each other: it also did not fall under the previous theories. Kawakito created the so-called. The KJ method achieves two important goals:

1) Efficient processing of large amounts of information

2) Identification of new information models for subsequent more thorough study.

Some situations for using this method are more natural than others. The most “clean” situations:

Facts or thoughts are in chaos. When topics seem too broad and difficult to understand;

It is necessary to overcome traditional approaches. When the only solutions are old solutions, try the Affinity Diagram.

3) Group support for decisions is necessary for their subsequent implementation.

requires a quick solution.

Procedure

1. Team building.

The group that works most effectively is the one that has the knowledge necessary to uncover the various dimensions of a given issue. It's also good if the team has worked together before. But this is not a necessary condition. Conversely, you might include someone in the group who has never worked together before. In other words, try to include people in the group as needed. The group should have 5-6 participants.

2. Formulation of the topic under discussion

To begin with, the topic is formulated very broadly. For example, "What can help us gain the support of senior management?" There should be no other formulation than this, otherwise the group will slide back to its “usual positions.” Once everyone has agreed on the topic, write it at the top of a large piece of paper/on the board so everyone in the group can see it.

3. Formulating and recording ideas

Ideas should be formulated using traditional brainstorming principles:

don't criticize any ideas

focus on formulating a large number of ideas in a short time

encourage everyone's participation

Ideas should be written down exactly as they were expressed and not paraphrased by the writer.

Answers should be written on small cards (one idea per card).

Notes

1) All ideas should be posted on a large board to ensure constant monitoring of all ideas.

2) It is necessary to insist that all wording be short (no more than 5-7 words). On the other hand, 1-2 word statements should be avoided because they can be easily misinterpreted.

3) Each statement must have a noun and a verb.

4) The size of the written statements should be large enough to be read from a distance of 1-1.5 meters.

4. Moving completed cards

The team must mix the cards and place them in random order.

5. Organizing cards into groups by affinity

At this point, the cards should be organized with the entire team or a designated person involved. This should happen in silence.

Notes

1) Although one person can do this work, in this case the advantage of the interaction of different points of view, opinions and views is lost. Therefore, a group approach is recommended. Look at two cards that seem to be related to each other in some way. Set them aside. Look at other cards that are not related to each other or to the previous two cards. Repeat this process until you have arranged all the cards into 6-10 groups. Don't try to squeeze single cards into groups where they don't fit. These cards (“singles”) may become the beginning of new groups or may never find their “home.”

2) Group members should be encouraged to react to what they see. Many managers strive to structure all the cards like chess and put everything in pre-prepared places. In the Diagram, speed, not intelligence, plays a major role. This is a high energy process, not a mind game.

Disagreement about the position of a card should be resolved simply and not diplomatically: if you don't like where the card is, move it! This not only speeds up the procedure, but also makes it possible to disagree with the boss and simply shift his card.

Participants should avoid unconsciously sorting cards into "safe" known categories. They should try to create new groups from the existing chaos of cards.

6. Highlighting leading cards

Find a card in each group that expresses the main idea that links all the other cards together. This will be the leading card, which is placed above each group. Often such cards do not exist. In such cases, it needs to be created.

Notes

1) Lead cards should be very short. They should express the essence of each group in three to five words.

Imagine that all the detailed cards under the leader will be removed, all that will remain is only the leaders. Would anyone who was not a member of the team be able to understand the nature and details of the topics discussed? This is a good test of your lead cards.

Each lead card should clearly express the overall idea that ties all the cards together.

4) Avoid clichés; creating lead cards is an opportunity to bring out new ideas in old topics. If the lead cards look too familiar, then maybe they deserve a fresh look.

7. Construction of the final Affinity Diagram.

Draw lines around each group that clearly show the connection of all its elements to the leading card. Related groups should be placed next to each other and connected by a line. Often when you do this, you find that you need to create another leading card, let's call it a master card, that shows how the two groups relate to each other. This card is placed above the two groups and is also connected by lines.

This final design can be placed on another sheet of paper. This is usually done because the Affinity Diagram is often shown to other people j discussion and changes. Please remember that this process only reflects the current situation; key factors are subject to change.

General view of the Affinity Diagram

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RELATIONSHIP DIAGRAM

Application

This method allows a group of employees to identify, analyze and classify the causes and results of those interactions that exist between the main problems (ideas, assumptions) and thus base a more effective solution on the basis of the identified driving forces and likely outcomes.

Description

Stimulates the working group to see the problem in several ways, and not just in one plane

Helps to explore the causes and results of the relationships between all problems (ideas, assumptions), including the most controversial ones.

Allows key points to be identified in a democratic way, and not as a result of the dominance of any group member.

Systematically identifies underlying assumptions and causes of disagreement among group members.

Allows the team to identify root causes even when hard data is not available.

Typical cases of using a Relationship Diagram (RD)

The quality service is not satisfied with the level of participation in working groups. Service employees believe that this is caused by ordinary and deeper reasons. The company president decides to identify the main causes of the problem and eliminate them.

The store manager has received twice as many complaints as usual over the past 8 weeks. He decides to analyze the complaints and determine the root causes and thus take appropriate action. For example, conduct training, install new equipment, etc.

Procedure

1. A decision is made about the problem being discussed

For example: What are the causes of large amounts of waste?

Using the initial statement, construct a complete statement that is fully understood and agreed upon by all participants.

If you are using results from other methods, such as affinity diagrams, you must ensure that the purpose of the discussion remains the same and is fully understood.

2. Creation of the most suitable group.

DO requires closer familiarity with the subject than was required in the affinity diagram. It is very important here that the identified results and causes are reliable.

Ideal group size is 4-6 people.

3. Collect all the ideas written on the cards that resulted
other techniques or the result of brainstorming.

Organize 5-25 cards into a large circle, leaving as much space as possible for drawing arrows. Write in capital letters, which will make your work easier in subsequent stages.

4. Identify the causes or impacts of interactions between ideas and draw arrows

Choose any of these ideas as a starting point. If all the cards are numbered, then work with them sequentially.

An arrow emanating from a card means a stronger cause or effect

Solution: B is the cause of A

All combinations between all cards are checked in a similar way.

5. Look and analyze the first BEFORE result.

Show your results to people outside the team for additional advice.

6. Count the number of incoming and outgoing arrows and select key points for further planning.

Count and write the number of outgoing and outgoing arrows for each card.

Determine the card with the most outgoing arrows and the card with the most outgoing arrows.

Outgoing arrows. A large number of arrows coming out indicates this problem as the main cause or leading force. This is usually the topic the team deals with first.

Incoming arrows. A large number of incoming arrows point to this topic as the main result. Thus, it can be a focal point for planning, or a means of measuring progress or changing the topic during discussion.

7. Design of the final version of the DO.

Show on the diagram the main drivers (largest number of arrows coming out) and the key results (largest number of arrows coming in). Topic: What are the causes of large amounts of waste?

Leading force result

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The seven Japanese methods discussed above are designed for analyzing quantitative information. They allow you to solve up to 95% of quality problems. However, when creating, for example, a new product, not all factors are of a numerical nature. There are facts that can only be described verbally. They make up approximately 5% of problems in the field of managing processes and teams, and when solving them, along with statistical methods, it is necessary to use the results of operational analysis, psychology, and others.

Therefore, the Union of Japanese Scientists and Engineers developed 7 Latest Tools, which allow us to solve these problems. These instruments were brought together and proposed by the Japan Union in 1979. These include:

1) Affinity diagram;

2) Dependency diagram;

3) System (tree) diagram;

4) Matrix diagram;

5) Arrow diagram;

6) Process evaluation planning diagram;

7) Analysis of matrix data.

Collection of input data for quality tools is usually carried out using the method brainstorming which is carried out with the help of specialists.

Scope of application of these methods: quality management, office work, education, training, etc.

Application of the "affinity diagram"

Affinity diagram– a tool that allows you to identify the main violations of the process by combining related oral data. It is a method of grouping together many similar or related ideas generated during a brainstorming session. The Japanese Union of Scientists and Engineers included the affinity diagram among the seven quality management methods in 1979.

The purpose of the method is to systematize and organize ideas, consumer requirements or opinions of group members expressed in connection with solving a problem. The affinity diagram provides general planning. It is a creative tool that helps to clarify unresolved problems by revealing previously invisible connections between individual pieces of information or ideas by collecting haphazard oral data from various sources and analyzing them according to the principle of mutual affinity (associative proximity).

Action plan:

1 Form a team of specialists who have knowledge of issues on the topic under discussion.

2 Formulate the question or problem in the form of a detailed sentence.

3 Conduct a brainstorming session related to the main reasons for the existence of the problem or answers to the questions posed.

4 Record all the statements on cards, group related data by area and assign headings to each group. Try to combine any of them under a common heading, creating a hierarchy.

The principles of creating an affinity diagram and identifying the main process violations in order to take measures to eliminate them are shown in Fig. 31. As the figure shows, an affinity diagram is a creative means of organizing large amounts of oral data.


Figure 31 - Principle of constructing an affinity diagram

Additional Information:

The affinity diagram is used not with specific numerical data, but with verbal statements.

The affinity diagram should be used mainly when:

It is necessary to systematize a large amount of information (different ideas, different points of view, etc.);

The answer or solution is not completely obvious to everyone;

Decision making requires consensus among team members (and perhaps other stakeholders) in order to work effectively.

Advantages of the method: p hides the relationship between different pieces of information.

The procedure of creating an affinity diagram allows team members to go beyond their usual thinking and helps to realize the creative potential of the team.

Disadvantages of the method: n In the presence of a large number of objects (starting from several dozen), the tools of creativity, which are based on human associative abilities, are inferior to the tools of logical analysis.

The Affinity Diagram is the first of the seven quality management techniques that helps develop a more precise understanding of a problem and identifies major process problems by collecting, summarizing, and analyzing a large amount of oral data based on the affinity relationships between each element.

9.2 Application of the “Interrelationship Diagram”

The relationship diagram is designed to rank related factors (conditions, causes, indicators, etc.) according to the strength of connection between them.

1) it is necessary to write down each problem on a separate sheet of paper and attach these sheets of paper in a circle;

2) you need to start from the top sheet and move clockwise, wondering if there is a connection between these two problems. If so, what event is the cause;

3) draw arrows between two events, showing the directions of influence;

5) the initial one is the one from which more arrows come out.

Example: Diagram of relationships to identify the causes of an increase in injuries at work In Fig. Figure 32 shows an example of a DV, reflecting the results of an analysis of the relationships between the causes of high injuries at work.



Figure 32 - Example of a relationship diagram

The Ishikawa diagram discussed earlier allows us to identify factors influencing any problem. The relationship diagram makes it possible to structure them based on their importance.

Thus, from this diagram it is clear that the main reasons for the increase in injuries during production are: lack of teamwork and insufficiently trained personnel.

When analyzing large amounts of data, we usually use the average value, less often the standard deviation, and even less often other processing methods. What causes this “self-restraint”? 🙂 Most likely, insufficient knowledge and experience in these matters. Where can a modern manager learn about statistical data processing methods? It is unlikely that he will remember the university statistics course. And was it included in the curriculum!?

My acquaintance with statistics, or more precisely with its use in business, began about 15 years ago, when I first read about quality management methods. Unfortunately, the seven basic tools “didn’t seem to me” the first time... I didn’t perceive them as a “guide to action.” Rather, I treated them as something transcendentally abstruse. And only gradually over the course of several years, repeatedly encountering the use of one or another method in the literature, as well as in connection with the emergence of practical problems, step by step, I began to understand the meaning of these tools and the scope of their application. Gradually, I began to use these methods in my practice, sometimes without even remembering that they are part of a coherent system.

The time has come to pay tribute to the original source - Japanese management, and also to show how seemingly book knowledge becomes a powerful tool for managing a real business.

Download the note in format, examples in format

Seven Basic Quality Control Tools Used to analytical problem solving, that is, in a situation where data is available, and in order to solve the problem, you need to analyze it.

1. Cause and effect diagram. This diagram is used to identify process factors that influence the outcome. There are also names: “Ishikawa diagram” or “fishbone diagram”. In the classic version, factors (reasons) are grouped into categories according to the “5M” principle:

Man (person) - reasons associated with the human factor; Machines (machines, equipment) - reasons related to equipment; Materials – reasons related to materials; Methods (methods, technology) - reasons related to the organization of business processes; Measurements - reasons associated with measurement methods.

Rice. 1. Ishikawa diagram. Sample.

It is clear that another relevant grouping can be used. Here, for example, is the “skeleton” we drew when analyzing the possibilities of reducing customer service time in a warehouse:

Rice. 2. Ishikawa diagram. Customer service time at the warehouse.

– a tool for collecting data and automatically organizing it to facilitate further use of the collected information.

Rice. 3. Check sheet. Example.

The advantage of checklists is that they can be used by employees who do not work with a computer. If the data for subsequent analysis is obtained by measurements directly at the workplace, checklists are very effective. It is clear that if the data for analysis is extracted from databases, checklists are not needed, and the data is immediately converted into a histogram, Pareto or scatter plot (see below).

In my practice, checklists have not found use, since the processes with which I deal are either completely related to the use of a computer, or are started by command from the computer, and the finish is recorded by the PC operator.

These charts rank issues by degree (frequency) of impact on the outcome. They got their name from the economist Vilfredo Pareto, who in one of his scientific works at the turn of the 19th and 20th centuries showed that in Italy 20% of households receive 80% of the income. The term “Pareto principle” was coined by the American quality management specialist Joseph Juran in the 40s of the 20th century. Pareto analysis is usually illustrated by a Pareto diagram, on which the causes of quality problems are plotted along the x-axis in descending order of their influence on the number of nonconformities (volume of defects), and along two ordinate axes: a) the number of nonconformities in pieces; b) the accumulated share (percentage) of the contribution to the total number of nonconformities. For example:

Rice. 4. Pareto diagram. Causes of overdue accounts receivable.

First of all, you should work with the causes that cause the most problems. In our example with the first three.

4. Histogram– a tool that allows you to visually evaluate the distribution of statistical data grouped by the frequency of falling into a certain (predetermined) interval. In the classic version, a histogram is used to identify problems by analyzing the shape of the scatter of values, the central value, its proximity to the nominal value, and the nature of the dispersion:

Rice. 5. Options for the location of the histogram in relation to the technological tolerance

Brief comments: a) everything is good: the average coincides with the nominal value, variability is within tolerances; b) the average should be shifted to match the nominal value; c) dispersion should be reduced; d) the mean should be shifted and the dispersion reduced; e) dispersion should be significantly reduced; f) two batches are mixed; should be divided into two histograms and analyzed; g) similar to the previous paragraph, only the situation is more critical; h) it is necessary to understand the reasons for such distribution; the “steep” left edge indicates some kind of action in relation to batches of parts; i) similar to the previous one.

Here are the histograms we have been building for several years to study customer service times in the warehouse:

Rice. 6. Histogram. Customer service time at the warehouse.

The x-axis shows 15-minute ranges of customer service time in the warehouse; The y-axis is the share of applications serviced in the allocated time range from the total number of applications for the year. The red dotted line shows the average service time throughout the year.

5. Scatter diagram(dispersion) is a tool that allows you to determine the type and strength of connection (correlation) between pairs of corresponding variables. These charts contain two sets of data plotted as dots. The relationship between these points shows the dependency between the corresponding data. In Excel, such a chart is of the “scatter” type. Here's an example of how I previously found the usefulness of scatter plots:

Rice. 7. Identification of correlation dependence based on a scatter diagram.

Here is an interesting example of using correlation analysis to manage the placement of goods in a warehouse:

The modern warehouse has very impressive dimensions. It can reach a depth of 100-150 meters (the distance from the loading gate to the back wall). It is clear that by placing goods with high turnover closer to the gate, you can save time moving around the warehouse. The figures above show the frequency of access to individual cells; on the left – for random placement of goods; on the right – for goods divided into ABC groups. The more intense the color, the more often the cell is accessed. It can be seen that without ABC distribution, access to cells is almost random; with ABC division of the nomenclature, zone boundaries can be observed. The left front of each figure faces the receiving area. Thus, in the situation depicted in Fig. b, the total path of storekeepers/equipment will be less than in Fig. A

6. Charts– a tool that allows you to analyze data across various sections. The form and purpose of the analysis may dictate the use of different types of graphs. You can read more about this in Gene Zelazny's book "". Piece-by-piece comparisons of data are best demonstrated using a pie chart. A bar chart is best used to illustrate positional comparison. If component-wise and positional comparisons show relationships at a certain point in time, then temporal comparisons reflect the dynamics of change; Time comparisons are best illustrated with a histogram or graph.

For example, with these diagrams we analyze three parameters for each client at once: the dynamics of accounts receivable, overdue accounts receivable, and limits on the credit line:

Rice. 8. An example of using a graph to analyze data.

7. Control card– a tool that allows you to monitor the progress of a process and influence it, preventing deviations from the requirements presented to the process (or responding to deviations). There are two types of variations: natural, associated with the spread of values ​​around the nominal value inherent in the process; And special, the appearance of which can be explained by specific reasons. You can read more about this in the book by D. Wheeler and D. Chambers “. Business optimization using Shewhart control charts.” Control charts are used to identify special variations. The points corresponding to individual data, the line of average values ​​(μ), and the upper and lower control limits (μ ± 3σ) are plotted on the graph. If the points lie within the control limits, there is no need to react to deviations from the center line. If at least one point is outside the control limits, an analysis of the possible causes of the deviation is required. See, for example, "", "".

Using control charts to analyze the volume of accounts receivable:

Rice. 9. Control card. Natural causes of variation.

At week 27, the debt increased from $1.4 million to $2.6 million. However, no management action is required since the points were located within the control boundaries.

The following chart shows the average (by week) time for vehicles to take off:

Rice. 10. Control card. Special causes of variations.

It can be seen that, starting from the 19th week, the points go beyond the control limits. Process intervention is required to identify specific causes of variation.

I hope my examples will help you realize that the seven basic quality control tools can be a real aid to business process analysis.

They are presented according to the version given in the book by M. Imai “”. I have arranged these methods in the order that seems most logical to me.

Purpose of the "Seven Basic Quality Control Tools" method is to identify problems that need to be addressed as a matter of priority, based on monitoring the current process, collecting, processing and analyzing the obtained facts (statistical material) for subsequent improvement of the quality of the process.

The essence of the method- quality control (comparing the planned quality indicator with its actual value) is one of the main functions in the quality management process, and the collection, processing and analysis of facts is the most important stage of this process.

Of the many statistical methods, only seven have been selected for widespread use, which are understandable and can be easily used by specialists in various fields. They allow you to identify and display problems in a timely manner, establish the main factors from which you need to start acting, and distribute efforts in order to effectively resolve these problems.

The expected result is a solution to up to 95% of all problems arising in production.

Seven Essential Quality Control Tools– a set of tools that make it easier to control ongoing processes and provide various types of facts for analysis, adjustment and improvement of the quality of processes.

1. Checklist- a tool for collecting data and automatically organizing it to facilitate further use of the collected information.

2. Histogram- a tool that allows you to visually evaluate the distribution of statistical data, grouped by the frequency of the data falling into a certain (predetermined) interval.

3. Pareto chart- a tool that allows you to objectively present and identify the main factors influencing the problem under study, and distribute efforts to effectively resolve it.

4. Stratification method(data stratification) - a tool that allows you to divide data into subgroups according to a certain criterion.

5. Scatter diagram(dispersion) - a tool that allows you to determine the type and closeness of the relationship between pairs of corresponding variables.

6. Ishikawa diagram(cause-and-effect diagram) is a tool that allows you to identify the most significant factors (reasons) influencing the final result (effect).

7. Control card- a tool that allows you to monitor the progress of the process and influence it (with the help of appropriate feedback), preventing its deviations from the requirements presented to the process.

Checklists(or data collection) - special forms for data collection. They facilitate the collection process, contribute to the accuracy of data collection and automatically lead to some conclusions, which is very convenient for quick analysis. The results can be easily converted into a histogram or Pareto chart. Checklists can be used for both qualitative and quantitative control. The form of the check sheet may be different, depending on its purpose.


To find the right way to achieve a goal or solve a problem, the first thing you need to do is collect the necessary information, which will serve as the basis for further analysis. It is desirable that the collected data be presented in a structured and easy-to-process form. For this purpose, as well as to reduce the likelihood of errors occurring during data collection, a checklist is used.

A checklist is a form designed to collect data and automatically organize it, which makes it easier to further use the collected information.

At its core, a control sheet is a paper form on which controlled parameters are printed, according to which, with the help of notes or simple symbols, the necessary and sufficient data are entered into the sheet. That is, a check sheet is a means of recording data.

The form of the checklist depends on the task and can be very varied, but in any case it is recommended to indicate:

Topic, object of research (usually indicated in the title of the control sheet);

Data recording period;

Data source;

The position and surname of the employee registering the data;

Symbols for recording received data;

Data logging table.

When preparing control sheets, you need to ensure that the simplest methods of filling them out are used (numbers, symbols), the number of controlled parameters is as small as possible (but sufficient for analyzing and solving the problem), and the form of the sheet is as clear and convenient as possible for filling even by unqualified personnel.

1. Formulate the purpose and objectives for which the information is being collected.

2. Select quality control methods that will be used to further analyze and process the collected data.

3. Determine the time period during which the research will be conducted.

4. Develop measures (create conditions) for conscientious and timely entry of data into the checklist.

5. Assign responsibility for data collection.

6. Develop a form for the checklist.

7. Prepare instructions for performing data collection.

8. Instruct and train workers in collecting data and entering it into the checklist.

9. Organize periodic data collection reviews.

The most pressing issue that arises when solving a problem is the reliability of the information collected by staff. Finding a solution based on distorted data is very difficult (if not impossible). Taking measures (creating conditions) for employees to register true data is a necessary condition for achieving the goal.

Rice. Checklist examples

It is possible to use electronic forms

At the same time, the disadvantages of the electronic form of the check sheet compared to the paper form include:

- bOgreater complexity to use;

- the need to spend more time entering data.

On the plus side:

- ease of data processing and analysis;

- high speed of obtaining the necessary information;

- the ability to simultaneously access information from many people.

However, most of the data collected has to be duplicated in paper form. The problem is that this leads to a decrease in productivity: the time saved on analyzing, storing and retrieving the necessary information is largely offset by the double work of recording data.

bar chart– a tool that allows you to visually depict and easily identify the structure and nature of changes in the obtained data (assess the distribution), which are difficult to notice when presented in a table.

By analyzing the shape of the resulting histogram and its location relative to the tolerance interval, one can make a conclusion about the quality of the product in question or the state of the process being studied. Based on the conclusion, measures are developed to eliminate deviations in product quality or process state from the norm.

Depending on the method of presentation (collection) of the initial data, the method of constructing a histogram is divided into 2 options:

Option I To collect statistical data, checklists of product or process indicators are developed. When developing a checklist form, you must immediately decide on the number and size of intervals in accordance with which data will be collected, on the basis of which, in turn, a histogram will be constructed. This is necessary due to the fact that after filling out the check sheet it will be almost impossible to recalculate the indicator values ​​for other intervals. The maximum that can be done is to ignore intervals in which no value falls and combine by 2, 3, etc. interval, without fear of distorting the data. As you understand, with such restrictions, for example, it is almost impossible to make 7 out of 11 intervals.

Construction method:

1. Determine the number and width of intervals for the control sheet.

The exact number and width of intervals should be chosen based on ease of use or according to statistical rules. If there are tolerances for the measured indicator, then you should focus on 6-12 intervals within the tolerance and 2-3 intervals outside the tolerance. If there are no tolerances, then we evaluate the possible spread of indicator values ​​and also divide them into 6-12 intervals. In this case, the width of the intervals must be the same.

2. Develop checklists and use them to collect the necessary data.

3. Using the completed checklists, calculate the frequency (i.e., how many times) of the obtained indicator values ​​in each interval.

Typically, a separate column is allocated for this, located at the end of the data registration table.

If the indicator value exactly matches the boundary of the interval, then add half to both intervals on the border of which the indicator value falls.

4. To construct a histogram, use only those intervals that contain at least one indicator value.

If there are empty intervals between the intervals in which the indicator values ​​fall, then they also need to be plotted on a histogram.

5. Calculate the average of the observation results.

The arithmetic mean of the resulting sample must be plotted on the histogram.

The standard formula used for calculations is:

Where x i– obtained values ​​of the indicator,

N –the total number of data obtained in the sample.

How to use it if there are no exact values ​​of the indicator x 1, x 2, etc. It's not explained anywhere. In our case, to roughly estimate the arithmetic mean, I can suggest using my own methodology:

a) determine the average value for each interval using the formula:

where j –intervals selected for constructing the histogram,

x j max –the value of the upper limit of the interval,

x j min –the value of the lower boundary of the interval.

b) determine the arithmetic mean of the sample using the formula:

where n –number of selected intervals for constructing a histogram,

v j –frequency of sample results falling within the interval.

6. Construct the horizontal and vertical axes.

7. Draw the boundaries of the selected intervals on the horizontal axis.

If in the future you plan to compare histograms that describe similar factors or characteristics, then when drawing a scale on the abscissa axis, you should be guided not by intervals, but by data units.

8. Place a value scale on the vertical axis in accordance with the selected scale and range.

9. For each selected interval, construct a column whose width is equal to the interval, and whose height is equal to the frequency of observation results falling into the corresponding interval (the frequency has already been calculated earlier).

Draw a line on the graph corresponding to the arithmetic mean value of the indicator under study. If there is a tolerance zone, draw lines corresponding to the boundaries and center of the tolerance interval.

Option II Statistics have already been collected (for example, recorded in log books) or are intended to be collected in the form of accurately measured values. In this regard, we are not limited by any initial conditions, so we can choose and at any time change the number and width of intervals in accordance with current needs.

Construction method:

1. Compile the received data into one document in a form convenient for further processing (for example, in the form of a table).

2. Calculate the range of indicator values ​​(sample range) using the formula:

Where xmax– the highest value obtained,

xmin– the smallest value obtained.

3. Determine the number of histogram bins.

To do this, you can use a table calculated based on the Sturgess formula:

You can also use a table calculated based on the formula:

4. Determine the width (size) of the intervals using the formula:

5. Round the result up to a convenient value.

Please note that the entire sample must be divided into equally sized intervals.

6. Determine the boundaries of the intervals. First define the lower bound of the first interval so that it is less than xmin. Add the width of the interval to it to get the border between the first and second intervals. Next, continue adding the width of the interval ( N) to the previous value to get the second boundary, then the third, etc.

After performing these actions, you should make sure that the upper limit of the last interval is greater than xmax.

7. For the selected intervals, calculate the frequency of occurrence of the values ​​of the indicator under study in each interval.

If the indicator value exactly matches the interval boundary, then add half to both intervals whose border the indicator value falls on.

8. Calculate the average value of the indicator under study using the formula:

Follow the order of constructing a histogram, starting from step 5, of the above method for Option I.

Histogram Analysis is also divided into 2 options, depending on the availability of technological approval.

Option I Tolerances for the indicator are not specified. In this case, we analyze the shape of the histogram:

Regular (symmetrical, bell-shaped) shape. The mean value of the histogram corresponds to the middle of the data range. The maximum frequency also occurs in the middle and gradually decreases towards both ends. The shape is symmetrical.

This form of histogram is the most common. It indicates the stability of the process.

Negatively skewed distribution (positively skewed distribution). The mean value of the histogram is located to the right (left) of the middle of the data range. The frequencies decrease sharply when moving from the center of the histogram to the right (left) and slowly to the left (right). The shape is asymmetrical.

This shape is formed either if the upper (lower) limit is adjusted theoretically or by a tolerance value, or if the right (left) value cannot be achieved.

Distribution with a cliff on the right (distribution with a cliff on the left). The mean value of the histogram is located far to the right (left) of the middle of the data range. The frequencies decrease very sharply when moving from the center of the histogram to the right (left) and slowly to the left (right). The shape is asymmetrical.

This form is often found in situations of 100% product control due to poor process reproducibility.

Comb (multimodal type). Intervals of one or two have lower (higher) frequencies.

This form is formed either if the number of individual observations included in the interval fluctuates from interval to interval or if a certain data rounding rule is applied.

A histogram that does not have a high central part (plateau). The frequencies in the middle of the histogram are approximately the same (for the plateau, all frequencies are approximately equal).

This form occurs when several distributions with means close to each other are combined. For further analysis, it is recommended to use the stratification method.

Double peak type (bimodal type). Around the middle of the histogram, the frequency is low, but there is a frequency peak on each side.

This form occurs when two distributions with means that are far apart are combined. For further analysis, it is recommended to use the stratification method.

A histogram with a dip (with a “pulled out tooth”). The shape of the histogram is close to the usual type distribution, but there is an interval with a frequency lower than both adjacent intervals.

This form occurs if the width of the interval is not a multiple of the unit of measurement, if the scale readings are incorrectly read, etc.

Distribution with an isolated peak. Along with the normal histogram shape, a small isolated peak appears.

This form is formed when a small amount of data is included from another distribution, for example, if the controllability of the process is impaired, errors occurred during measurement, or data from another process was included.

Option II. There is a technological tolerance for the indicator under study. In this case, both the shape of the histogram and its location in relation to the tolerance zone are analyzed. Possible options:

The histogram looks like a normal distribution. The average value of the histogram coincides with the center of the tolerance zone. The width of the histogram is less than the width of the tolerance field with a margin.

In this situation, the process does not need to be adjusted.

The histogram looks like a normal distribution. The average value of the histogram coincides with the center of the tolerance field. The width of the histogram is equal to the width of the tolerance interval, and therefore there is concern about the appearance of substandard parts from both the upper and lower tolerance margins.

In this case, it is necessary either to consider the possibility of changing the technological process in order to reduce the width of the histogram (for example, increasing the accuracy of equipment, using better materials, changing the processing conditions of products, etc.) or expanding the tolerance range, because The requirements for the quality of parts in this case are difficult to meet.

The histogram looks like a normal distribution. The average value of the histogram coincides with the center of the tolerance field. The width of the histogram is greater than the width of the tolerance interval, and therefore substandard parts are detected from both the upper and lower tolerance margins.

In this case, it is necessary to implement the measures described in paragraph 2.

The histogram looks like a normal distribution. The width of the histogram is less than the width of the tolerance field with a margin. The average value of the histogram is shifted to the left (right) relative to the center of the tolerance interval, and therefore there are concerns that substandard parts may be located on the side of the lower (upper) limit of the tolerance zone.

In this situation, it is necessary to check whether the measurement tools used are introducing a systematic error. If the measuring instruments are working properly, the process should be adjusted so that the center of the histogram coincides with the center of the tolerance field.

The histogram looks like a normal distribution. The width of the histogram is approximately equal to the width of the tolerance field. The average value of the histogram is shifted to the left (right) relative to the center of the tolerance interval, with one or more intervals outside the tolerance zone, which indicates the presence of defective parts.

In this case, it is initially necessary to adjust the technological operations so that the center of the histogram coincides with the center of the tolerance field. After this, measures must be taken to reduce the histogram span or increase the size of the tolerance interval.

The center of the histogram is shifted to the upper (lower) tolerance limit, and the right (left) side of the histogram near the upper (lower) tolerance limit has a sharp break.

In this case, we can conclude that products with an indicator value outside the tolerance range were excluded from the batch or were deliberately distributed as suitable for inclusion within the tolerance limits. Therefore, it is necessary to identify the reason that led to the occurrence of this phenomenon.

The center of the histogram is shifted to the upper (lower) tolerance limit, and the right (left) side of the histogram near the upper (lower) tolerance limit has a sharp break. In addition, one or more intervals are outside the tolerance range.

The case is similar to 6., but the histogram intervals outside the tolerance range indicate that the measuring instrument was faulty. In connection with this, it is necessary to verify the measuring instruments, as well as re-instruct workers on the rules for performing measurements.

The histogram has two peaks, although the values ​​of the indicator were measured for products from the same batch.

In this case, we can conclude that the products were obtained under different conditions (for example, materials of different grades were used, equipment settings were changed, products were produced on different machines, etc.). In this regard, it is recommended to use the stratification method for further analysis.

The main characteristics of the histogram are in order (corresponding to case 1.), while there are defective products with indicator values ​​outside the tolerance range, which form a separate “island” (isolated peak).

This situation may have arisen as a result of negligence in which defective parts were mixed with good ones. In this case, it is necessary to identify the causes and circumstances leading to the occurrence of this situation, and also take measures to eliminate them.