Histogram (bar graph)

It is used to visualize the distribution of specific parameter values ​​by repetition frequency over a certain period of time. It can be used when plotting allowable values ​​on a graph. You can determine how often it falls into or out of the acceptable range. The order of plotting the histogram:

• 1. observe a random variable and determine its numerical values. The number of experimental points must be at least 30
• 2. determine the range of the case value, it determines the width of the histogram R and is equal to Xmax - Xmin
• 3. The resulting range is divided into k intervals, the interval width is h = R/k.
• 4. distribute the received data by intervals - the boundaries of the first interval, - the boundaries of the last interval. Determine the number of points that fall into each interval.
• 5. Based on the data obtained, a histogram is built. Frequencies are plotted along the ordinate axis, interval boundaries are plotted along the abscissa axis.
• 6. according to the form of the resulting histogram, they find out the state of the batch of products, the technological process and make management decisions.

Typical types of histograms:

• 1) Typical or (symmetrical). This histogram indicates the stability of the process.
• 2) Multimodal view or comb. Such a histogram indicates the instability of the process.
• 3) Distribution with a break on the left or right
• 4) Plateau (uniform rectangular distribution, such a histogram is obtained in the case of combining several associations, whose average values ​​differ slightly) analyze such a histogram using the stratification method
• 5) Two-peak (bimodal) - two symmetrical with far-standing averages (crowns) are mixed here. Spend stratification on 2 factors. This histogram indicates the occurrence of a measurement error.
• 6) With an isolated peak - this histogram indicates the occurrence of a measurement error

1. Graph expressed by a broken line

2. Bar graph

3. Pie chart

4. Strip chart

5. Z-plot

6. Radar diagram

The graphical representation of numerical data allows you to identify the patterns that the considered group of data obeys. The graph makes it possible not only to assess the state at the moment, but also to predict a more distant result according to the trend of the process that can be found in it, and therefore, to outline measures that can prevent deterioration of the state or enhance a positive result.

1. Graph expressed by a broken line

Such a graph represents, for example, the change over time of a parameter, such as production volume or the proportion of defective products. On the ordinate axis on such a graph, the value of the corresponding quantity is plotted, and on the abscissa axis, time. The points plotted on the graph are connected by straight lines. The effectiveness of the information received will increase if, during the analysis, the data is stratified by such factors as the seller, product, machine, etc. The effectiveness of the information received will increase if a trend line is plotted on the chart.

An example of a graph of the decline of defective piezo sensors in pressure sensors by months is shown below.

Rice. Reducing the marriage of piezo sensors of pressure sensors: 1 - schedule; 2 - trend line

2. Bar graph

With the help of a bar graph, a quantitative dependence is presented, expressed by the height of the bar, of such factors as the cost of the product from the type of product, the amount of losses as a result of marriage from the process, the amount of revenue from the store, etc. Varieties of the bar chart - Pareto chart and histogram. When constructing a bar graph, the quantity is plotted along the ordinate axis, the factors are plotted along the abscissa axis; each factor corresponds to a column.

As an example, a bar graph of the number of faulty pressure sensors depending on their brand is shown, which was identified during repair work in one of the city's boiler houses. Ensk. It can be seen from the graph that repair or replacement with new ones is necessary for Korund sensors.

Rice. The number of faulty pressure sensors, depending on their brand:
To- Corundum; With– Sapphire ; M– Metran; X– Honeyvel; Y– Yokogawa

3. Pie chart

A circular graph expresses the ratio of the components of some whole parameter and the entire parameter as a whole, for example: the ratio of products by their types, manufacturers, or other factors. The whole is taken as 100% and expressed as a full circle. The components are expressed as sectors of a circle and arranged around the circle in a clockwise direction, starting with the element with the largest percentage contribution to the whole, in order of decreasing contribution percentage. The last element is "other". On a pie chart, it is easy to see all the components and their ratio at once.

As an example, the ratio of time to various stages in the production of the displacement sensor FG-5 is shown.

Rice. The ratio of time in the manufacture of a new displacement sensor FG-5:
1 – development of the electronic circuit of the sensor, 5%; 2 – purchase of necessary materials and components, 10%; 3 – manufacture of the electronic board of the sensor, 15%; 4 – debugging a prototype and putting it into production, 70%

4. Strip chart

A strip chart is used to visualize the ratio of the components of a certain parameter and at the same time to express the change in these components over time, for example: to graphically represent the ratio of the components of the amount of revenue from the sale of products by type of product and their changes by months or years: to present the content of questionnaires during the annual survey and its change from year to year; to present the causes of defects and change them by month, etc.

When constructing a strip chart, the rectangle of the graph is divided into zones in proportion to the components or in accordance with quantitative values, and sections are marked along the length of the tape in accordance with the ratio of the components for each factor. By arranging a strip chart so that the strips are arranged in sequential time order, it is possible to evaluate the change in the components over time.

The order of plotting a strip chart:

1. build the horizontal and vertical axes;

2. on the horizontal axis, apply a scale with divisions from 0 to 100%;

3. Divide the vertical axis into time intervals during which the indicator was measured. It is recommended to postpone time intervals from top to bottom, because it is easier for a person to perceive a change in information in this direction;

4. For each time interval, build a tape that indicates the indicator in question. When building, leave a small space between the ribbons;

5. Recalculate the components of the indicator into percentages of the indicator itself, for which the value of each component of the indicator is divided by the value of the indicator itself and multiplied by 100. The value of the indicator can be calculated as the sum of the values ​​of all components of the indicator;

6. Divide the graph tapes into zones so that the width of the zones corresponds to the size of the percentage of the indicator components;

7. connect the boundaries of the zones of each component of the indicator of all tapes with each other with straight line segments;

8. Put the name of each component of the indicator and its percentage on the chart. Mark the zones with different colors or shading so that they are clearly distinguished from each other.

As an example, the ratio of scores on a five-point scale in the exam for the PCD for the period from 2008 to 2012 is shown.

Rice. The ratio of grades in the exam for the UKP for 2008 - 2012

5. Z-plot

The Z-plot is used to evaluate the overall trend when recording actual data by month, such as sales volume, production volume, number of emergency situations, etc.

The graph is built as follows.

1. Construct the vertical and horizontal axes.

2. The horizontal axis must be divided by 12 months of the year under study.

3. On the y-axis, the values ​​of the studied parameter are plotted by months for the period of one year from January to December and connected by straight line segments, as a result, a graph formed by a broken line is obtained.

5. Also calculate the total values ​​of the parameter, changing from month to month, and is built the corresponding graph formed by a broken line. For the changing total, in this case, the total for the year preceding the given month is taken. The general graph, which includes three graphs constructed in this way, looks like the letter Z, which is why it got its name.

The Z-chart is used, in addition to controlling sales volume or production volume, to reduce the number of defective products and the total number of defects, to reduce costs and reduce absenteeism, etc.

By changing the total, you can determine the trend of change over a long period. Instead of a changing total, you can plot the planned values ​​on the graph and check the conditions for achieving these values.

A Z-shaped plot is shown as an example. depending on the number of failures of the circuit breaker when working with a welding machine during the year by months. Three curves are plotted on the graph: the number of failures, their cumulative curve and the final annual values.

Rice. The number of failures of the circuit breaker when working with a welding machine:
1 – machine failures by months; 2 – cumulative sum of failures; 3 - the total values ​​of failures of the circuit breaker for the year

6. Radar diagram

This type of graph is highly visual, it is used for enterprise management analysis, for personnel assessment, for quality assessment, etc.

This graph is built as follows.

1. From the center of the circle to the circle, straight lines (radii) are drawn according to the number of factors, which resemble rays.

2. Graduation divisions are applied to these radii and the values ​​of the analyzed data are plotted.

3. The points that denote the pending values ​​are connected by straight segments.

Thus, the resulting polyline is a radar chart, which is a combination of a pie chart and a line chart. Numerical values ​​related to each of the factors are compared with standard values ​​and with values ​​built on other features or categories.

Rice. 4 Factor Radar Chart Template

As an example, a petal diagram of emergency situations at an oil refinery during the year by shop is shown. For the analysis of emergency situations, three workshops were selected, the situation in which could negatively affect the work of the enterprise as a whole.

Rice. Extraordinary situations at the refinery by months

It follows from the graph that the most dangerous in terms of emergency situations is workshop No. 1, and the safest workshop No. 3. Thus, knowing about the nature of emergency situations at the enterprise, management can take measures to prevent them and reduce their number.

It is used to visualize the distribution of specific parameter values ​​by repetition frequency over a certain period of time. It can be used when plotting allowable values ​​on a graph. You can determine how often it falls into or out of the acceptable range. The order of plotting the histogram:

1. observe a random variable and determine its numerical values. The number of experimental points should be at least 30

2. determine the range of a random variable, it determines the width of the histogram R and is equal to Xmax - Xmin

3. The resulting range is divided into k intervals, the interval width is h = R/k.

4. distribute the received data by intervals - the boundaries of the first interval, - the boundaries of the last interval. Determine the number of points that fall into each interval.

5. Based on the data obtained, a histogram is built. Frequencies are plotted along the y-axis, and interval boundaries are plotted along the abscissa.

6. according to the form of the resulting histogram, they find out the state of the batch of products, the technological process and make management decisions.

Typical types of histograms:

1) Typical or (symmetrical). This histogram indicates the stability of the process.

2) Multimodal view or comb. Such a histogram indicates the instability of the process.

3) Distribution with a break on the left or right

4) Plateau (uniform rectangular distribution, such a histogram is obtained by combining several distributions in which the average values ​​differ slightly) analyze such a histogram using the stratification method

5) Two-peak (bimodal) - here two symmetrical with far-standing average values ​​\u200b\u200bare mixed (crowns). Spend stratification on 2 factors. This histogram indicates the occurrence of a measurement error.

6) With an isolated peak - this histogram indicates the occurrence of a measurement error

Pareto chart.

(20% of people - 80% of income)

In 1887, V. Pareto derived a formula according to which 20% of people have 80% of the money.

In the 20th century, Joseph Juran used this principle to categorize quality problems into few but essential and many but unimportant. According to this method, the vast majority of defects and associated losses occur due to a relatively small number of causes.

The Pareto chart is a tool that allows you to distribute efforts to resolve emerging problems and identify the main causes that need to be analyzed first. Building a Pareto chart:

1) Definition of the goal. Set the data collection period

2) Organization and conduct of observations. Data entry checklist under development

3) Analysis of the results of observations, identification of the most significant factors. A special table form for the data is being developed. Data are arranged in order of importance for each factor. The last row of the table is always the “other factors” group

4) Building a Pareto chart

Example: Pareto chart for analyzing the types of defects of any product.

To take into account the cumulative percentage of losses from several defects, a cumulative curve is built.

Chart analysis: when constructing a chart, you need to pay attention to:

1) it is more efficient if the number of factors is more than 10

2) if "other" is too large, you should repeat the analysis of its content and re-analyze all

3) if the factor standing first is difficult to analyze, analysis should begin with the following

4) if a factor is found in relation to which it is easy to improve, then this should be used without paying attention to the order of the factors

5) stratification by factors in data processing

Control cards

They allow you to track the progress of the process and influence it with the help of feedback, preventing deviation from the requirements imposed on the process. Every map has 3 lines:

1) central line - shows the required average value of the characteristics of the controlled parameter K

2), 3) lines of the upper and lower control limits - show the maximum allowable limits for changing the value of the controlled parameter

Other names for the method: Shewhart Control Charts.

Any QC, even if initially ineffective, is a necessary tool for restoring order in the process control. For the successful implementation of QC in practice, it is important not only to master the technique of compiling and maintaining them, but, which is much more important, to learn how to “read” the map correctly. Advantages of the method: indicates the presence of potential problems before the production of defective products begins, allows you to improve quality indicators and reduce the cost of its provision.

Disadvantages of the method: competent construction of QC is a difficult task and requires certain knowledge. The expected result is obtaining objective information for making decisions about the effectiveness of the process.

MC tools

K control tools use mainly numerical data for analysis.

Affinity diagram

A tool that allows you to identify the main violations of the process by combining verbal data. It is built when there are a large number of ideas and they need to be grouped to clarify their connections. Stages:

1) definition of the topic of the basis for data collection

2) data collection during brainstorming around the chosen topic; data must be collected randomly

3) each message is registered on the card by each participant

4) grouping related data together

Creation principle

common heading for A and B

↓ affinity ↓

common heading A common heading B for

for (a) and (c) (c) and (d) ↕

↕ affinity ____________

↓ affinity ↓

oral data (a); oral data (c); oral data (s); oral data (d).

It is used to systematize a large number of associative information. The Japanese Union of Scientists and Engineers in 1979 included the affinity diagram as part of the seven quality management methods.

When formulating a topic for discussion, use the "rule of 7 plus or minus 2". The sentence must have at least 5 and no more than 9 words, including a verb and a noun.

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 absolutely obvious to everyone, decision-making requires agreement among team members (and possibly among other stakeholders) to work effectively.

Advantages of the method: reveals the relationship between different pieces of information, the procedure for creating an affinity diagram allows team members to go beyond the usual thinking and promotes the creative potential of the team.

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

The affinity diagram is the first tool among the seven quality management methods that contributes to a more accurate understanding of the problem and allows you to identify the main violations of the process by collecting, summarizing and analyzing a large amount of verbal data based on related (close) relationships between each element.

Link diagram

A tool that allows you to identify logical relationships between the main idea and various data.

The purpose of the study using this diagram is to establish relationships between the main causes of process disturbance identified using the affinity diagram and the problems that need to be addressed.

Construction: in the center is the image of the entire problem / task / area of ​​knowledge, thick main branches with captions emanate from the center - they mean the main sections of the diagram. The main branches branch further into thinner branches. All branches are signed with keywords that make you remember this or that concept. Examples of situations of appropriate use:

1) when the topic is so complex that the links between different ideas cannot be established by normal discussion

2) if the problem can become a prerequisite for a more fundamental new problem

Work on this diagram should be done in teams. The initial definition of the end result is very important. Root causes can be generated from an affinity or Ishikawa diagram.

tree diagram

A tool that provides a systematic determination of the optimal means of solving the problems that have arisen, presented at various levels. Tree diagram structure:

Chart Use Cases:

1) when the requirements of the consumer are not clearly formulated in relation to the product

2) if it is necessary to investigate all possible elements of the problem

3) at the design stage, when short-term goals must be realized before the result of all work.

Matrix chart

A tool that reveals the importance of various relationships. Allows you to process a large amount of data with an illustration of the logical relationships between various elements. The diagram displays the contours of relationships and the correlation between tasks, functions, characteristics, highlighting their relative importance.

BUT	AT
	B1	B2	B3	B4	B5	B6
A1			∆
A2						▄0
A3			▄0
A4		▄				▄

A1,..., A4 = components of the studied objects A, B - =//= B

They are characterized by different connection strength, which is shown using special symbols:

▄0 - strong connection

▄ - average connection

∆ - weak link

If there is no figure in the cell, then there is no connection between the components.

arrow diagram

An arrow diagram is a tool that allows you to plan the timing of all the necessary work for the speedy and successful implementation of your goal. The diagram is widely used in planning and subsequent control over the progress of work. There are 2 types of arrow charts: Gantt chart and network chart. Gantt Chart Example: Building a House in 12 Months.

ROOM

Operation

Months

Foundation

skeleton

Forests

Exterior decoration of the house

Interior

Water pipes

Electro work

Doors and windows

Painting ext. walls

End of ext. finishes

Final inspection and handover

Network Diagram Example

A circle with the number of the operation inside, an arrow to the next circle, below it is the number of months. The dotted arrows show the connection of the operation. The stages are the same, except for 11 - final inspection, and 12 - delivery.

A network graph is a graph whose vertices represent the state of a certain object (for example, construction), and the arcs represent the work being done on this object. Each arc is associated with the time for which the work is carried out and/or the number of workers who carry out the work. Often a network graph is constructed in such a way that the horizontal arrangement of vertices corresponds to the time it takes to reach the state corresponding to a given vertex.

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Graphs make it possible to assess the state of the process at the moment, as well as to predict a more distant result according to the process trends that can be detected on. When reflected on a graph of data changes over time, the graph is also called a time series.

The following types of charts are commonly used: Polylined (line chart), Column and Pie

line graph

Use a line chart to display the nature of the change in the size of the annual revenue from the sale of products, and also predict the trend in revenue changes in the next two years (we will first do this using the Trend function).

Revenue, thousand c.u.

Create a new Excel workbook. We enter the title of the work, as well as the initial data, after which we build a line graph. The resulting diagram is edited using the context menus.

The nature of the change in revenue, as well as the forecast, gives a trend line, which can be built by opening the context menu on a broken line and selecting the command Add trend line .

In the dialog box that opens, on the tab Type the possible types of trend line are shown. To choose the type of line that best approximates the data, you can proceed as follows: place on the chart the trend lines of all acceptable types in turn (i.e. linear, logarithmic, polynomial of the second degree, exponential and exponential), setting for each line on the tab Options forward forecast by 1 unit (year) and placement on the diagram of the value of the approximation reliability. In this case, after constructing the next line, the value of the approximation reliability R 2 (The most reliable trend line, for which the value of R 2 is equal to or close to one).

The highest approximation reliability is given by a polynomial line with a degree of two (R 2 = 0.6738), which we choose as a trend line. To do this, we remove all trend lines from the chart, after which we restore the polynomial line of the second degree.

According to the approximating line, it can be assumed that revenue in the coming year will tend to increase.

bar graph

The bar graph represents the quantitative relationship expressed by the height of the bar. For example, the dependence of the cost on the type of product, the amount of losses as a result of marriage, depending on the process, etc. Typically, the bars are shown on the graph in descending order of height from right to left. If among the factors there is a group "Other", then the corresponding column on the graph is shown on the far right.

The figure shows in the form of a bar graph the results of the above table 1.

Circle chart.

The pie chart expresses the ratio of the components of the whole parameter, for example, the ratio of the amounts of proceeds from the sale separately by type of parts and the total amount of proceeds; the ratio of the elements that make up the cost of the product, etc.

On fig. shown in the form of a circular graph, the ratio of failures of the combine by nodes and assemblies.

	Failure type	Number of failures
	Harvest part
	Hydraulic equipment
	thresher
	electrical equipment
	Hydraulic transmission

Graphs are a simple and convenient method of presenting data about the results of a process or other patterns that they reflect. Depending on your experience and the experience of those to whom they will be shown, you can use graphs of any complexity and any type of data presentation.
Below we will consider several graphs that are most often used and are most convenient for perception and analysis.

bar graph
Serves to represent the quantitative relationship expressed by the height of the column. The histogram and Pareto chart is an example of a bar chart.
Using such a graph, you can analyze the level of influence of the factor on the system. For example, Figure 1 shows a graph of the influence of cost factors on the final price of products. According to the graph, it is convenient to visually assess the percentage of the contribution of each factor to the final cost of the product.

Fig.1
Figure 2 shows a bar graph for the same data as a waterfall chart. With its help, it is more convenient to display the formation of the final result by influencing factors.


Fig.2

line graph
The simplest and most commonly used graph showing the influence of any factor on a changing argument, for example, pressure on viscosity, the appearance of defects on the operator's working hours, sales on the time of day. Figure 3 shows an example of a dependence graph of the average indicator of customer calls to the dealership over the time the car was used during the warranty period.


Fig.3
According to this graph, for example, we can conclude that most of the shortcomings appear in the second year of operation of this car. It can also be said that by the end of the warranty period, customers are more likely to contact the dealership in order to have time to repair the car under warranty if possible. In this case, it will be very interesting to apply the stratification for the second year in order to find out what the client most often encounters and take this into account when manufacturing or designing. At the same time, a sharp increase at the end of the third year during the analysis will show that most of the requests do not end with warranty repairs and only the desire of the client to try to repair the car for free affects the growth in the visit rate.

Pie chart
Serves to display the ratio of the component parameters from the overall indicator as a whole. For example, reasons for refusals to purchase, reasons for returning goods, or reasons for manufacturing defects. The whole circle is taken as 100% of the indicator, and the factors are represented by sectors occupying the corresponding part of the circle equal to the influence on the indicator. Typically, the sectors are arranged clockwise in descending order, starting from the most significant factor.
Figure 4 shows an example of a circular graph for the formation of the cost of a product and the influence of various factors as a percentage.


Fig.4

strip chart
Used to show the ratio of the components of a parameter and at the same time display the change in the ratio of the components of the parameter, for example, over time or with a change in temperature or composition. Figure 5 shows a graph of the ratio of the amount of revenue in percent by type of product.


Fig.5
Thus, from Fig. 5 it follows that over time, the share of revenue from smartphones and computer equipment is growing, while the demand for TVs is falling with approximately the same consumption of kitchen appliances.

Radar chart
This type of chart is a combination of a pie chart and a line chart. The number of factors on the graph is the number of rays emanating from the center of the diagram. The numerical parameters of the factors are displayed as dots on each corresponding ray. The dots are connected to each other in the order of drawing.
Most often, this graph is used to analyze the comparison of the company's performance with the activities of competitors for making strategic decisions. For the convenience of evaluating two competing indicators or companies, the graphs are superimposed on each other.
The graph is also convenient to use for comparing product quality indicators to understand its position in the market. A similar analysis is shown in Fig.6.


Fig.6