Examples of Shewhart Mapping in Kha. An example of building a Shewhart control chart in Excel. Basic provisions of the theory

Algorithm:

1. Process analysis.

First of all, it is necessary to ask about the existing problem, because, in the absence of them, the analysis will not make sense. For greater clarity, you can use the cause-and-effect diagram of Ishikawa (mentioned above, ch. 2). To compile it, it is recommended to involve employees from different departments and use brainstorming. After a thorough analysis of the problem, and finding out the factors influencing it, we proceed to the second stage.

2. Process selection.

Having clarified in the previous stage the factors influencing the process by drawing a detailed skeleton of the “fish”, it is necessary to choose the process that will be subject to further research. This step is very important because choosing the wrong indicators will make the whole control chart less effective due to the examination of insignificant indicators. At this stage, it is worth realizing that the choice of the appropriate process and indicator determines the outcome of the entire study and the costs associated with it.

3. Data collection.

The purpose of this stage is to collect data about the process. To do this, it is necessary to design the most suitable way to collect data, find out who and at what time will take measurements. If the process is not equipped with technical means to automate the entry and processing of data, it is possible to use one of the seven simple ways Ishikawa - checklists. Control sheets, in fact, are forms for registering the parameter under study. Their advantage lies in ease of use and ease of training employees. If there is a computer at the workplace, it is possible to enter data through the appropriate software products.

Depending on the specifics of the indicator, the frequency, time of collection and sample size are determined to ensure representativeness of the data. The collected data is the basis for further operations and calculations.

After collecting information, the researcher must decide on the need to group the data. Grouping often determines the performance of control charts. Here, with the help of the analysis already carried out using the cause-and-effect diagram, it is possible to establish factors by which it will be possible to group the data in the most rational way. It should be noted that data within one group should have little variability, otherwise the data may be misinterpreted. Also, if the process is divided into parts using stratification, each part should be analyzed separately (example: the manufacture of the same parts by different workers).

Changing the way grouping will change the factors that form within-group variation. Therefore, it is necessary to study the factors influencing the change in the indicator in order to be able to apply the correct grouping.

4. Calculation of the values ​​of the control chart.

Shewhart's control charts are divided into quantitative and qualitative (alternative) depending on the measurability of the studied indicator. If the value of the indicator is measurable (temperature, weight, size, etc.), maps of the value of the indicator, ranges and double maps of Shewhart are used. On the contrary, if the indicator does not allow the use of numerical measurements, use card types for an alternative feature. In fact, the indicators studied on this basis are defined as meeting or not meeting the requirements. Hence the use of maps for the proportion (number) of defects and the number of conformances (inconsistencies) per unit of production.

For any type of Shewhart charts, it is assumed to define the central and control lines, where the central line (CL-control limit) actually represents the average value of the indicator, and the control limits (UCL-upper control limit; LCL-lower control limit) are the allowable tolerance values .

At this stage, the researcher must calculate the values ​​of CL, UCL, LCL.

5. Construction of a control chart.

So, we have come to the most interesting process - a graphical reflection of the data obtained. So, if the data was entered into a computer, then using the Statistica or Excel program environment, you can quickly graphically display the data. However, it is possible to build a control chart and, without special programs, then, along the OY axis of the control charts, we plot the values ​​of the quality indicator, and along the OX axis, the time points of registering the values, in the following sequence:

• 1) put on the control card the central line (CL)
• 2) draw borders (UCL; LCL)
• 3) we reflect the data obtained during the study by applying an appropriate marker to the point of intersection of the value of the indicator and the time of its registration. It is recommended to use different types of markers for values ​​that are inside and outside the tolerance limits.
• 6. Checking the stability and controllability of the process.

This stage is designed to show us what the research was conducted for - whether the process is stable. Stability (statistical controllability) is understood as a state in which the repeatability of parameters is guaranteed. Thus, the process will be stable only if the following cases do not occur.

Consider the main criteria for process instability:

• 1) Going beyond the control limits
• 2) A series - a certain number of points, invariably on one side of the center line - (top) bottom.

A series of seven points is considered abnormal. In addition, the situation should be considered abnormal if:

• a) at least 10 out of 11 points are on the same side of the center line;
• b) at least 12 out of 14 points are on the same side of the center line;
• c) at least 16 out of 20 points are on the same side of the center line.
• 3) trend - a continuously rising or falling curve.
• 4) approaching the control boundaries. If 2 or 3 points are very close to the control limits, this indicates an abnormal distribution.
• 5) approaching the center line. If the values ​​are concentrated near the center line, this may indicate an incorrect choice of grouping method, which makes the range too wide and leads to data mixing with different distributions.
• 6) periodicity. When, after certain equal intervals of time, the curve goes either to "decline", or to "rise".
• 7. Analysis of control charts.

Further actions are based on the conclusion about the stability or instability of the process. If the process does not meet the stability criteria, the influence of non-random factors should be reduced and, by collecting new data, a control chart should be built. But, if the process meets the stability criteria, it is necessary to evaluate the capabilities of the process. The smaller the spread of parameters within the tolerance limits, the higher the value of the process capability indicator. The indicator reflects the ratio of the width of the parameter and the degree of its dispersion.

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Introduction

The traditional approach to production, regardless of the type of product, is manufacturing and quality control to check the finished product and reject units that do not meet the established requirements. Such a strategy often leads to losses and is not economical, since it is based on checking after the fact, when defective products have already been created. A more effective loss prevention strategy is to avoid the production of unusable products. Such a strategy involves the collection of information about the processes themselves, its analysis and effective actions in relation to them, and not to products.

The control chart is a graphical tool that uses statistical approaches, the importance of which for the management of industrial processes was first shown by Dr. W. Shewhart in 1924.

The purpose of control charts is to detect unnatural changes in data from repetitive processes and provide criteria for detecting a lack of statistical control. A process is in a statistically controlled state if the variability is caused only by random causes. When determining this acceptable level of variability, any deviation from it is considered the result of special causes that should be identified, eliminated or reduced.

The task of statistical process control is to ensure and maintain processes at an acceptable and stable level, ensuring that products and services meet specified requirements. The main statistical tool used for this is the control chart, a graphical way of presenting and comparing information based on a sequence of samples reflecting the current state of the process, with boundaries set on the basis of inherent process variability. The control chart method helps to determine whether the process has indeed reached the statistically controlled state at the correct level or remains in this state, and then maintain control and a high degree of uniformity. the most important characteristics product or service by continuously recording product quality information during the manufacturing process.

The use of control charts and their careful analysis lead to a better understanding and improvement of processes.

1. Statistical methods of product quality control

1.1 The role of statistical methods of control

The main objective of statistical methods of control is to ensure the production of usable products and the provision of useful services at the lowest cost. For this purpose, analyzes of new operations or other studies aimed at ensuring the production of usable products are carried out.

The introduction of statistical methods of control gives results on the following indicators:

1. improving the quality of purchased raw materials;

2. saving raw materials and labor;

3. improving the quality of products;

4. decrease in the number of marriages;

5. reducing the cost of monitoring;

6. improving the relationship between production and consumer;

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

One of the main principles of quality control using statistical methods is the desire to improve the quality of products, exercising control at various stages of the production process.

Depending on the goals set for product quality management at the enterprise, statistical methods can be used to:

Statistical analysis of the accuracy and stability of products, technological processes, equipment, etc.;

Statistical regulation and management of technological processes;

Statistical acceptance control of product quality and its evaluation.

Statistical analysis of the accuracy and stability of technological processes - the establishment by statistical methods of the values ​​of indicators of accuracy and stability of the technological process and the determination of the patterns of its flow in time.

Determine the actual value of indicators of accuracy and stability of the technological process, equipment or product quality;

To identify the degree of influence of random and systematic factors on the accuracy and stability of the technological process and product quality;

Substantiate technical standards and product tolerances;

Identify the reserves of the production and technological process;

Justify the choice of technological equipment and measuring instruments for the manufacture of products;

Identify the possibility and justify the feasibility of introducing statistical methods into the production process;

Assess the reliability of technological systems;

Justify the need for reconstruction of the technological process or repair of technological equipment and other measures to improve the technical process;

During periodic inspections of the technological accuracy of equipment and tooling in the process of monitoring compliance with the technological discipline of manufacturing products of the main production;

When conducting intra-factory certification of technological processes;

When installing new technological equipment and accepting equipment after repair;

When analyzing and evaluating indicators of the production process and product quality, etc.

In the conditions of serial, small-scale and pilot production, it is first of all recommended to implement statistical analysis for a systematic assessment of the accuracy of process equipment and the rational placement of work on this equipment.

1.2 Shewhart control charts

The control chart is a special form on which a central line and two lines are drawn: above and below the middle, called the upper and lower control limits. Data of measurements and control of parameters and production conditions are plotted on the map with dots.

When examining data changes over time, it is necessary that the points of the graph do not go beyond the control limits. If an outlier of one or more points beyond the control limits is detected, this is perceived as a deviation of the parameters or process conditions from the established norm.

To identify the cause of the deviation, the influence of the quality of the source material or parts, methods, operations, conditions for carrying out technological operations, equipment is examined.

In production practice, the following types of control charts are used:

1. map of arithmetic averages and ranges: -R is used in the case of control on a quantitative basis, such quality indicators as length, weight, tensile strength, etc.

2. arithmetic mean and standard deviation map: The -S map is similar to the -R map, but has a more accurate map of process variability and is more complex to build.

3. median and range map: -R map is used for the same situations as -R maps, the advantage is that there are no complicated calculations, but the median map is less sensitive to changes in the process.

4. Map of individual values: The X-map is used when it is necessary to quickly detect unnoticed factors or when only one observation was made in one day or a week.

5. map of the proportion of defective products: p-map - used in the case of control to determine the proportion of defective products.

6. map of the number of defective units of products: np-map - used in the case of control to determine the number of defective products.

7. Defect number map: The c-map is used when quality control is carried out by determining the total number of defects in a predetermined constant volume of items to be inspected.

8. map of the number of defects per unit of production: u-map - used in the case of quality control by the number of defects per unit of production, when the area, length, or other parameter of the product sample is not a constant value.

The data presented in the control chart is used to build histograms, the graphs obtained on the control charts are compared with the control standards. All this allows you to obtain valuable information for solving problems that have arisen.

2. Initial data, goals and objectives

The purpose of the work is to analyze the technological process by means of Shewhart's control charts and assign appropriate measures and recommendations in case an uncontrolled state of the process is detected.

To achieve this goal, it is necessary to gradually solve certain tasks, which include:

The choice of the type of control charts, taking into account the peculiarities of their application;

Processing of the data array, carrying out the necessary calculations and building control charts;

3. Construction and analysis of control charts

3.1 Selecting the type of control charts

Shewhart's control charts are divided into quantitative and qualitative (alternative) depending on the measurability of the studied indicator. If the value of the indicator is measurable (temperature, weight, size, etc.), maps of the value of the indicator, ranges and double maps of Shewhart are used. On the contrary, if the indicator does not allow the use of numerical measurements, use card types for an alternative feature. In fact, the indicators studied on this basis are defined as meeting or not meeting the requirements. Hence the use of maps for the proportion (number) of defects and the number of conformances (inconsistencies) per unit of production.

To determine the most appropriate control chart for the data set under consideration, we will use the algorithm presented in Figure 3.1.

Figure 3.1 - Algorithm for selecting control charts

Based on the algorithm presented above, it follows that at the first stage it is necessary to determine what type of process data we receive.

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

In this paper, an array of quantitative data of the quality parameter is considered, based on this, at the next stage, the choice of a control chart depends on the sample size, their number and the conditions for constructing a control chart.

Maps for quantitative data reflect the state of the process through dispersion (variability from one to one) and through the location of the center (process average). That's why control cards for quantitative data, it is almost always applied and analyzed in pairs - one map for location and one for scatter. The most commonly used pair - and R - card.

Card type - R is used in mass production, when cards of type X are not applicable due to bulkiness. When using maps of type - R, conclusions about the stability (stability) of the process are made on the basis of data obtained from the analysis of a small number of representatives of all the products under consideration. In this case, all products are combined into batches in the order of manufacture, and small samples are taken from each batch, no more than 9, according to which a control chart is built.

Control chart of individual values ​​(X) - this chart is used if observations are made on a small number of objects, and all of them are controlled. Observations are made over a continuous indicator.

When using individual value maps, rational subgroups are not used to provide an estimate of intra-lot variability and control limits are calculated based on a measure of variation obtained from moving ranges of usually two observations. The sliding range is the absolute value of the difference between measurements in successive pairs, i.e. the difference between the first and second measurements, then the second and third, and so on. Based on the moving ranges, the average moving range is calculated, which is used to build control charts. The overall average is also calculated for all data.

Median maps - an alternative - R maps for process control with measured data. They provide similar conclusions and have certain advantages. Such maps are easy to use and do not require large calculations. This can facilitate their introduction into production. Because median values ​​are mapped along with individual values, a median map provides a spread of process results and a detailed picture of variation.

Control chart of means and standard deviations (-S). This card almost identical to the map (- R), but more accurate and can be recommended when debugging technological processes in the mass production of critical parts. It can be applied in cases where there is a built-in control system with automatic data entry into computers used for automatic process control.

In maps - S, instead of the range R, a more effective statistical characteristic of the dispersion of observed values ​​is used - the standard deviation (S). It shows how closely individual values ​​cluster around the arithmetic mean, or how they scatter around it.

Analyzing the initial data array, we note that the number of samples is 15, the volume of each is 20. Also, when choosing a control chart, we will take into account the need for speed in building control charts, ease of calculation. Based on this, we will conclude on the most appropriate form of control charts for a quantitative trait.

Since we have a sample size greater than 9, there are necessary resources to carry out complex calculations (in this work, Microsoft Excel is used), we will use the most accurate type of control charts of a quantitative trait, namely, S charts.

3.2 Calculation and construction of control charts

The construction procedure - S maps, conditionally, can be divided into several stages:

Calculation of the mean (and standard deviation of each sample (S);

Calculation of midlines for - maps (), and S - maps;

Calculation of control limits for the map (UCLX and LCLX), for map S (UCLS and LCLS);

Mapping of midline, sample means, control limits, and process tolerance limits.

Drawing on the S - map of the middle line, standard deviations of each sample and control limits.

The sample mean (and the standard deviation S is calculated by the formulas:

where: Х - parameter value; n - sample size.

Substituting the sample values ​​into formulas 3.1 and 3.2, we calculate the mean value and standard deviation for each sample (Table 3.1).

Table 3.1 - Results of calculation of mean values ​​and square deviations of samples

To calculate the middle lines and S maps, we will use formulas 3.3 and 3.4.

where, k is the number of subgroups.

Substituting the data from table 3.1 into formulas 3.3 and 3.4, we get:

The obtained values ​​of the middle lines are necessary for the calculation of the control limits, which are calculated by the formulas:

UCLX=+A3 H; (3.5)

LCLX = - A3 H; (3.6)

UCLS= V4 H; (3.7)

LCLS= V3 H; (3.8)

where: A3, B4, B3 - coefficients for calculating the control limits.

The coefficients for calculating the control limits are presented in GOST R 50779.42-99 “Statistical methods. Shewhart's Control Charts. Based on this standard, we select the coefficients necessary for the calculations:

Calculate the numerical values ​​of the control limits by substituting the required values:

UCLX \u003d 8.943833 + 0.68 × 0.912466 \u003d 9.56431;

LCLX \u003d 8.943833 - 0.68 × 0.912466 \u003d 8.323356;

UCLS= 1.49×0.912466= 1.359575;

LCLS= 0.51×0.912466= 0.465358;

All calculations and transformations of the original data array were carried out in Microsoft Excel.

An array of control results values ​​together with calculation results is registered in a special form.

When constructing control charts, it is necessary to pay attention to the choice of scales. For each type of control charts, the difference between the upper and lower values ​​of the scale, the value of the scale division will be different.

In the case of building - S maps, the following features should be noted when choosing scales:

For a map, the difference between the top and bottom values ​​of the scale should be about twice the difference between the highest and lowest values ​​of the mean subgroups;

For the S chart, the scale should have values ​​from 0 to twice the maximum value of S in the initial period (5-6 first subgroups);

Scales and S cards must have the same graduation value.

Thus, guided by the above, we will determine the maximum and minimum values ​​of the scales for control charts.

The maximum and minimum values ​​of the mean subgroups are 9.62 and 8.64 respectively, the doubled difference between these values ​​is ~1.25. Since the difference between the largest and smallest values ​​of the technological tolerance is much greater, we are forced to expand the range of scale values ​​to 7.40 and 11.20, respectively.

The maximum value of the standard deviation in the initial period is 0.98, doubling this number, we get the maximum value of the scale - 1.96. Thus, for the map S, the range of scale values ​​is from 0 to 2. The scale division value for and S maps will be equal to 0.2. The construction of control charts was also performed using Microsoft Excel tools.

3.3 Analysis of control charts

The purpose of the step is to recognize indications that the variability or mean is not at a constant level, that one or both are out of control and appropriate action is required.

The purpose of the process control system is to obtain a statistical signal about the presence of special (non-random) causes of variations. The systematic elimination of special causes of excessive variability brings the process into a state of statistical controllability. If the process is in a statistically controlled state, the product quality is predictable and the process is fit to meet the requirements specified in the regulations.

The Shewhart chart system is based on the following condition: if the unit-to-unit process variability and the process mean remain constant at given levels (estimated by S and X), then the S deviations and X means of individual groups will change only randomly and rarely go beyond the control limits . No obvious trends or data structures are allowed, other than those that occur by chance with some degree of probability.

The exit from the controlled state is determined by the control chart based on the following criteria:

1) Points out of control limits.

2) A series is a manifestation of such a state when the points invariably end up on one side of the midline; the number of such points is called the length of the series.

A series of seven points is considered non-random.

Even if the run length is less than six, in some cases the situation should be considered as non-random, for example, when:

a) at least 10 out of 11 points are on the same side of the center line;

b) at least 12 out of 14 points are on the same side of the center line;

c) at least 16 out of 20 points are on the same side of the center line.

3) Trend (drift). If the dots form a continuously rising or falling curve, they say that there is a trend.

4) Approaching the control "zones" limits. Points that approach the 3-sigma control limits are considered, and if 2 or 3 points are outside the 2-sigma lines, then such a case should be considered as abnormal.

5) Approaching the center line. When most of the points are concentrated inside the middle third, due to an inappropriate way of subgrouping. Approaching the center line does not mean that a controllable state has been reached; on the contrary, it means that data from different distributions are mixed in the subgroups, which makes the range of control limits too wide. In this case, you need to change the method of splitting into subgroups.

The maps S and are analyzed separately, but a comparison of the course of their curves can give Additional information about the special reasons for influencing the process.

On a map of standard deviations, a point above UCLS could mean:

Increased variability from part to part, either at one point or as part of a trend;

The measuring system has lost proper resolution.

A point below the LCLS on the standard deviation map could mean:

Incorrect calculation of the control boundary or incorrect drawing of a point;

Part-to-part variability has been reduced;

The measurement system has changed;

The series of dots above or the ascending series of dots can mean:

Increased spread value that could occur due to an irregular cause;

Changes in the measuring system;

The series of dots below or the descending series of dots may refer to:

Decreased spread of values, which is a positive factor, should be used to improve the process;

A change has occurred in the measurement system.

Non-random behavior of points is also possible, manifested in the form of shifts, trends, and cyclicity.

To analyze the control charts for points approaching the midline, it is necessary to calculate the boundaries of the middle third.

To calculate the middle third, we introduce the coefficient A, which is equal to one third of the difference between the value of the upper control border of the map and the value of its middle line (formula 3.9).

A=(UCL-CL)/3; (3.9)

Where: UCL - upper control limit; CL - the value of the middle line; A is a coefficient.

The calculation of the boundaries of the middle third is carried out according to the formulas:

VGST=CL+A; (3.10)

NGST=CL-A; (3.11)

Where: VGST - the upper limit of the middle third; NGST - the lower boundary of the middle third; Calculate coefficient A for maps and S:

Ax \u003d (9.56-8.94) / 3 \u003d 0.207;

AS \u003d (1.36 - 0.91) / 3 \u003d 0.149.

Substituting the values ​​in formulas 3.10 and 3.11, we get the values ​​of the upper and lower limits of the middle third, respectively:

VGSTx=8.94+0.207= 9.15;

VGSTS=0.91+0.149= 1.06;

NGSTx=8.94-0.207= 8.74;

NHSTS=0.91-0.149=0.76;

The boundaries of the middle third are also included in the calculation results table.

Analyzing the obtained control charts, we will compile a table in which we will describe the state of process controllability based on the above criteria.

Table 3.2 - Analysis of control charts

After identifying the non-standard behavior of points on the maps, it is necessary to find the reason for their appearance, to introduce corrective actions.

A weakly increasing trend on the S map may be caused by changes in the measuring system, incompetent personnel, or equipment failure. Due to the small number of points, it is necessary to continue observations. In case of confirmation of non-standard behavior of points, it is necessary to identify the cause and take corrective actions.

To identify the causes, do the following:

Technical inspection of equipment;

Calibration, verification of measuring instruments;

Checking the qualifications of the worker performing the operation;

Verification of the competence of the controller.

Corrective actions include:

A shift in the points on the average map can be caused by changes in the measurement system, wear, or equipment failure. Due to the small number of points, the analysis should be continued to identify the reasons for such an arrangement of points. In case of confirmation of the assumptions about the occurrence of a shift, it is necessary to identify the cause and assign appropriate corrective actions.

A series of dots on the map may indicate changes in the process related to the equipment, measuring system, workers. There is a series of points 6 to 11 on the mean map. The measuring system should be checked for changes in a given period of time, the competence of the worker performing the operation, the equipment and appropriate corrective actions should be taken:

Adjustment, adjustment, repair or replacement of equipment;

Staff development, improvement of working conditions;

Adjustment, adjustment, repair or replacement of measuring instruments.

Process maps allow you to monitor the process and identify non-standard changes in process parameters even within process tolerances.

Analysis of process maps helps to identify non-random causes affecting the process. Such reasons must be eliminated, the systematic elimination of the special causes of excessive variability brings the process into a state of statistical controllability. If the process is in a statistically controlled state, the product quality is predictable and the process is fit to meet the requirements specified in the regulations.

After bringing the process into a statistically controlled state, it becomes possible to evaluate the technological capabilities of the process. The process is first brought into a statistically controlled state, and then its capabilities are determined. Thus, the determination of process capabilities begins after the control tasks for - and S-maps are solved, i.e. special causes are identified, analyzed, corrected and their recurrence is prevented. Current control charts should show that the process was statistically controlled for at least 25 subgroups.

The procedure outlined in Figure 3.2 can be used as a guide to action.

Figure 3.2 - Process improvement strategy

Conclusion

statistical production rms shewhart

The quality of products (works, services) is decisive in the public assessment of the performance of each work collective. The release of efficient and high-quality products allows the enterprise to receive additional profit, to provide self-financing of production and social development.

Shewhart's control charts as a tool for quality control of processes and products are successfully used in many enterprises, including Russian ones.

Control charts have become widespread due to their ability to prevent the occurrence of marriage. This state of affairs helps to significantly reduce production costs associated with the production of non-conforming products.

This paper provides an example of using Shewhart's control charts to control a process. In the course of the work, the original data array was transformed, and the selection of control charts was carried out, taking into account their features. As a result of the choice, the most preferred map for this task is the -S map.

The work on carrying out the necessary calculations and construction was carried out using Microsoft Excel.

As a result of the analysis of control charts, the following non-standard situations of location of points were identified:

Slightly increasing trend on map S;

Possible process shift on the map;

A series of dots above the midline on the map.

The actions necessary to bring the process into a statistically controlled state have been assigned.

List of sources used

1. GOST R 50779.0-95 Statistical methods. Basic provisions.

2. GOST R 50779.11-2000 Statistical methods of quality management. Terms and Definitions.

3. GOST R 50779.42-99 Statistical methods. Shewhart control charts.

4. Efimov V.V. Means and methods of quality management: textbook / V.V. Efimov.- 2nd ed., erased. - M.: KNORUS, 2010. - 232p.

5. Tsarev Yu.V., Trostin A.N. Statistical methods of quality management. Control cards: Teaching aid / GOU VPO Ivan. state chem. - technol. un-t. - Ivanovo, 2006. - 250p.

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4. Examples of constructing Shewhart control charts using GOST R 50779.42–99

Shewhart control charts come in two main types: for quantitative and alternative data. There are two situations for each control chart:

a) standard values ​​are not set;

b) standard values ​​are set.

Default values ​​are values ​​set according to some specific requirement or purpose.

The purpose of control charts for which standard values ​​are not set is to detect deviations in the values ​​of characteristics (for example, or some other statistics) that are caused by reasons other than those that can only be explained by chance. These control charts are based entirely on the data of the samples themselves and are used to detect variations that are due to non-random causes.

The purpose of control charts, given standard values, is to determine whether the observed values ​​are different, etc. for several subgroups (each with a volume of observations) from the corresponding standard values ​​(or ), etc. more than can be expected from the action of only random causes. A feature of maps with predetermined standard values ​​is an additional requirement related to the position of the center and process variation. The set values ​​may be based on experience gained from using control charts at predetermined standard values, as well as on economic indicators established after considering the need for the service and the cost of production, or specified in technical requirements for products.

4.1 Control charts for quantitative data

Control charts for quantitative data are classic control charts used for process control when the characteristics or results of the process are measurable and the actual values ​​of the controlled parameter measured with the required accuracy are recorded.

Control charts for quantitative data allow you to control both the location of the center (level, average, center of adjustment) of the process, and its spread (range, standard deviation). Therefore, control charts for quantitative data are almost always used and analyzed in pairs, one for location and one for scatter.

The most commonly used are pairs and -cards, as well as -cards. Formulas for calculating the position of the control boundaries of these maps are given in Table. 1. The values ​​of the coefficients included in these formulas and depending on the sample size are given in Table. 2.

It should be emphasized that the coefficients given in this table were obtained on the assumption that the quantitative values ​​of the controlled parameter have a normal or close to normal distribution.

Table 1

Control Limit Formulas for Shewhart Maps Using Quantitative Data

table 2

Coefficients for calculating control chart lines

An alternative to maps are median control maps (– maps), which are less computationally intensive than maps. This can facilitate their introduction into production. The position of the central line on the map is determined by the average value of the medians () for all controlled samples. The positions of the upper and lower control boundaries are determined by the relations

(4.1)

The values ​​of the coefficient depending on the sample size are given in Table. 3.

Table 3

Coefficient values

Usually – map is used together with – map, sample size

In some cases, the cost or duration of the measurement of the controlled parameter is so great that it is necessary to control the process based on the measurement of individual values ​​of the controlled parameter. In this case, the sliding range serves as a measure of process variation, i.e. the absolute value of the difference between the measurements of the controlled parameter in successive pairs: the difference between the first and second measurements, then the second and third, etc. Based on the moving ranges, the average moving range is calculated, which is used to build control charts of individual values ​​and moving ranges (and -maps). Formulas for calculating the position of the control boundaries of these maps are given in Table. four.

Table 4

Control Limit Formulas for Individual Value Maps

The values ​​of the coefficients and can be obtained indirectly from Table 2 at n=2.

4.1.1 and -cards. Standard values ​​are not set

In table. 6 shows the results of measurements of the outer radius of the sleeve. Four measurements were taken every half an hour, for a total of 20 samples. The averages and ranges of subgroups are also given in Table. 5. The maximum permissible values ​​of the outer radius are set: 0.219 and 0.125 dm. The goal is to determine the performance of the process and control it by tuning and spread so that it meets the specified requirements.

Table 5

Production data for bushing outside radius

where is the number of subgroups,

The first step: building a map and determining the state of the process from it.

central line:

The values ​​of the factors and are taken from Table. 2 for n=4. Since the values ​​in Table. 5 are within the control limits, the map indicates a statistically controlled state. The value can now be used to calculate map control boundaries.

center line: g

The multiplier values ​​are taken from Table. 2 for n=4.

and -maps are shown in Fig. 5. Analysis of the map shows that the last three points are out of bounds. This indicates the possibility of some special causes of variation being at work. If limits have been calculated from previous data, then action must be taken at the point corresponding to the 18th subgroup.

Fig.5. Medium and Span Cards

At this point in the process, appropriate corrective action should be taken to eliminate special causes and prevent recurrence. The work with the maps continues after the establishment of the revised control boundaries without excluded points that have gone beyond the old boundaries, i.e. values ​​for samples no. 18, 19 and 20. The values ​​and lines of the control chart are recalculated as follows:

revised value

revised value

the revised map has following options:

center line: g

revised map:

central line:

(because the central line: , then there is no LCL).

For a stable process with revised control limits, the possibilities can be assessed. We calculate the index of opportunities:

where is the upper limit value of the controlled parameter; – lower limit value of the controlled parameter; - estimated by the average variability within subgroups and expressed as . The value of the constant is taken from table 2 for n=4.

Rice. 6. Revised and -maps

Since , the possibilities of the process can be considered acceptable. However, upon close examination, it can be seen that the process is not set up correctly in relation to the tolerance and therefore about 11.8% of the units will be outside the set upper limit value. Therefore, before setting the constant parameters of the control charts, one should try to set up the process correctly, while maintaining it in a statistically controlled state.

The tool is used when processing is carried out with a tool whose design and dimensions are approved by GOST and OST or are available in industry standards. When developing technological processes for manufacturing parts, a normalized tool should be used as the cheapest and easiest. A special cutting tool is used in cases where processing with a normalized ...

Such control is very expensive. Therefore, from continuous control, they pass to selective with the use of statistical methods for processing the results. However, such control is effective only when the technological processes, being in an established state, have the accuracy and stability sufficient to “automatically” guarantee the manufacture of defect-free products. Hence the need...

And the organization of the control process. Status of control In this course project, the terms of reference provide for the development of the stages of the process of acceptance control of the details of the gearbox of a cylindrical coaxial two-stage two-stream - gear wheel and active control in the operation of grinding the hole. The methods of active and acceptance control complement each other and are combined. Active...

I recently posted mine here, where enough plain language, in places abusing foul language, under a 20-minute laughter of listeners, he talked about how to separate systemic variations from variations caused by special reasons.

Now I want to analyze in detail an example of constructing a Shewhart control chart based on real data. As real data, I took historical information about completed personal tasks. I have this information thanks to the adaptation of David Allen's personal effectiveness model Getting Things (I also have an old slidecast about this in three parts: Part 1, Part 2, Part 3 + Excel table with macros for analyzing tasks from Outlook).

The task statement looks like this. I have a distribution of the average number of completed tasks depending on the day of the week (below in the graph) and I need to answer the question: “is there anything special about Mondays or is it just a system error?”

Let's answer this question with the help of the Shewhart control chart, the main tool of statistical process control.

So, Shewhart's criterion for the presence of a special cause of variation is quite simple: if any point goes beyond the control limits, calculated in a special way, then it indicates a special reason. If the point lies within these limits, then the deviation is due to the general properties of the system itself. Roughly speaking, is the measurement error.
The formula for calculating the control limits looks like this:

Where
- the average value of the average values ​​for the subgroup,
- average span,
- some engineering coefficient depending on the size of the subgroup.

All formulas and tabular coefficients can be found, for example, in GOST 50779.42-99, where the approach to statistical management is briefly and clearly stated (honestly, I myself did not expect that there is such a GOST. The topic of statistical management and its place in business optimization is disclosed in more detail in book by D. Wheeler).

In our case, we group the number of completed tasks by day of the week - these will be the subgroups of our sample. I took data on the number of completed tasks for 5 weeks of work, that is, the size of the subgroup is 5. Using table 2 from GOST, we find the value of the engineering coefficient:

Calculating the average value and range (difference between the minimum and maximum values) for a subgroup (in our case, by the day of the week) is a fairly simple task, in my case the results are as follows:

The central line of the control chart will be the mean of the group means, i.e.:

We also calculate the average range:

Now we know that the lower control limit for the number of completed tasks will be equal to:

That is, those days on which I complete fewer tasks on average are special from the point of view of the system.

Similarly, we obtain the upper control limit:

Now plot the center line (red), upper control limit (green), and lower control limit (purple) on the chart:

And, oh, miracle! We see three clearly distinct groups outside the control limits, in which there are clearly non-systemic causes of variation!

I don't work on Saturdays and Sundays. Fact. And Monday was a really special day. And now you can think and look for what is really special on Mondays.

However, if the average number of tasks completed on Monday were within the control limits and even if it stood out strongly against the background of other points, then from the point of view of Shewhart and Deming, it would be pointless to look for any features on Mondays, since such behavior is determined solely by general causes. . For example, I built a control chart for another 5 weeks at the end of last year:

And it seems like there is some kind of feeling that Monday somehow stands out, but according to the Shewhart criterion, this is just a fluctuation or an error in the system itself. According to Shewhart, in this case, you can explore the special causes of Mondays for an arbitrarily long time - they simply do not exist. From the point of view of the statistical office, on these data, Monday is no different from any other working day (even Sundays).

SAINT PETERSBURG STATE UNIVERSITY

FACULTY OF ECONOMICS

Department of Economics and Management at the Enterprise

Shewhart control charts in the quality management system

Course work

2nd year students of the EUP group - 22

day department

specialty 080502 - "Economics and management at the enterprise"

Scientific adviser:

St. Petersburg

Introduction

Chapter 1. The concept of a quality management system

Chapter 2. Importance of statistical methods in quality management

Chapter 2.1. Shewhart control charts as a method of statistical control and quality management

Chapter 3

Conclusion

Literature

Attachment 1

The peak of development of quality management fell on 1980-1990, when the quality management system was widely introduced. Early in its development, the concept helped many companies rethink their manufacturing process and avoid the multi-million dollar costs associated with manufacturing defective products.

In parallel with reducing defects and improving product quality, companies began to pay more attention to consumers and their desires. After all, as you know, attracting a new client can cost 6 times more than a company than retaining an existing one.

In its early stages, quality management was not much different from careful administration or dispatching, but as time went on, the theory developed and the practice of applying the concept expanded. Now, not only industrial, but also service companies practice a quality approach and use modern quality control tools; as a rule, these are automated systems (ERP, MRP, automated process control systems) that have in their arsenal applications for building diagrams, maps, accounting for the number of defects, or simply convenient organization of customer data (CRM).

The purpose of this work is to systematize knowledge in the field of quality management. This is what gave rise to the structure. term paper, to consider the historical aspects of the development of the concept, the first chapter is allotted; a description of the significance of statistical methods - the second chapter; and the construction of control charts, on the example of a random sample of some process - in the third. The consideration of Shewhart's control charts, and not other, later developments, is explained, first of all, by the fact that Shewhart's work gave impetus to the development of the concept in this direction. And for a deeper understanding of the entire quality management, it is necessary to have knowledge about the emergence of significant discoveries.

Quality management has many definitions, depending on the position taken by the author. Some emphasize the special role of the human factor, others emphasize the importance of a systematic approach and quantitative measurements, and others emphasize the evolution of management schools.

So, quality management is, in a broad sense, such enterprise management that allows you to most fully meet the needs of customers and anticipate their expectations. Natural, in my opinion, questions arise: firstly, how is their satisfaction carried out, and secondly, how does the quality management approach in this regard differ from the usual process of planning and manufacturing products?

Answering the question about customer satisfaction, we can say that quality management takes the attitude of the consumer to the quality of the products received as the main condition. In this case, product quality becomes the most significant indicator for the consumer and, as a result, the main competitive advantage.

The second question concerns the differences between conventional production and one where the principles of quality are applied. The position of Japanese authors is interesting, relating the process of product quality management to a special philosophy of the enterprise, a new look at production and inextricably linked with the concept of continuous improvement. Besides this slightly idealized attitude, another difference can be shown; the normal production process involves a series of activities aimed at identifying and meeting the needs of consumers, which is also referred to in the definition of quality management. However, the quality approach emphasizes the inherent importance of manufacturing quality products, at all stages of production, from product development to timely delivery to the consumer. This approach dictates the priority task facing the enterprise - the manufacture of high-quality products from cycle to cycle, which undoubtedly guarantees the stability of the consumer receiving good products. For the enterprise, this, first of all, means gaining the respect of consumers and developing their loyalty, which in modern conditions, is by no means an unimportant feature.

Summing up, we see that consumers receive quality products, and manufacturers receive stable profits. Modern Markets show a rapid pace of development, which sets the condition for firms: "develop to survive." And in this case, a good, high-quality product, but not meeting the requirements of the market, will also not be able to provide significant competition, just like a company whose 30% of its products are defective goods. That is why quality management assigns an important role to anticipating the expectations and needs of the consumer, creating new needs for him and satisfying them, in accordance with the approach of ensuring product quality.

As shown above, quality management is an extensive process that affects all production, all levels of management (from controllers to senior managers) and all production processes. But where and under what conditions did it originate? What contributed to the emergence of a new approach to management? Let's look at quality management in retrospect.

Product quality management is a red line that runs through the entire history of management development. Beginning with Towne's famous 1866 work, "The Engineer as Economist," it is customary to talk about the birth of management.

Inspired by the work of Town, the founder of the scientific school of management was F. Taylor. His approach literally revolutionized production. In addition to introducing the practice of measuring the time spent on performing various operations, Taylor established requirements for the quality of products, in the form of tolerance fields (through and non-through calibers). He also established a system of fines for marriage (up to dismissal), motivation and training of employees. Taylor's revolutionary approach gave impetus to the further development of management.

Another notorious manager of the 20th century was Henry Ford, who founded the car company that still exists today. By developing the Model T, Ford doomed himself to perpetuate. He not only invented a light, durable (at that time) and unpretentious car, but also introduced a system of mass conveyor production. He unified and standardized all operations, included after-sales service in the scope of production. Engaged in labor protection and the creation of normal working conditions. “According to Henry Ford, the main factor in the success of an enterprise is the quality product it produces. Until the quality is proven, the production of the product cannot be started.

Emerson made a major contribution to the development of management, with a book published in 1912, The 12 Principles of Productivity. Emerson noted the importance of goal setting, scheduling, performance rewards, and other principles. He saw efficiency as a key aspect of the organization of production, by increasing which it is possible to achieve high results, avoiding overstrain.

During further development management of the enterprise faced the need to reduce labor costs for quality control, since the old methods of quality control, which involved the control of each unit of output, led to the growth of the staff of controllers. The problem was solved by the methods that replaced them - the methods of statistical quality control. G. Dodge and G. Roming proposed sampling methods that made it possible to check not all products, but a certain amount from the entire batch. Statistical control was carried out by new specialists - quality engineers.

A great contribution to the application of statistical methods belongs to Walter Shewhart, who, while working at Bell's company (Bell Telephone Laboratories, now AT & T) as part of a group of quality specialists, in the mid-1920s. laid the foundation for statistical quality control. Shewhart is ranked among the patriarchs of the modern philosophy of quality. Shewhart devoted much attention to the compilation and analysis of control charts, which will be discussed in subsequent chapters.

The contribution of Edward Deming, an American specialist in the field of quality, is great. During World War II, he trained US engineers in quality control as part of the national defense program. After the war, in 1950, Deming was invited to occupied Japan to present a joint theory with Shewhart. Speaking to the owners and managers of most enterprises, Deming exhorted that if statistical methods were followed, then very soon Japanese manufacturers would be able to enter world markets. Which was vital to post-war Japan.

Deming's teachings set the direction for the development of Japanese companies. Deming, inspired the audience with his ideas, "no nation is obliged to be poor" was his opening phrase. Very soon, Japan entered the world markets, with goods superior in quality to their American and European counterparts.

The next scientist to come to Japan from America was Juran. Juran considered quality issues at the level of the entire company and individual divisions. Juran's lectures were of a practical nature, and the emphasis was placed on the definition of indicators of quality products, the establishment of standards and methods of measurement, the conformity of products to specifications.

The goal of a quality approach is to create a better product that can better meet the needs of customers. And such a complex problem cannot be solved only by carrying out the necessary measurements and analyzing the data obtained. To achieve such a goal, it is sometimes necessary to modernize existing equipment, improve the technological process of production, or completely change it. It is also worth considering the necessary work that lies before (market research, design, procurement) and after (packaging, storage, delivery, sales and after-sales service) the production of products. All this proves the need to consider quality management in a single system and manage it, adhering to a single strategy across the enterprise.

In parallel with Deming and Juran, Dr. Feigenbaum (USA), in the 50s, in the monograph "Total Quality Management" outlines the importance of a systematic (complex) approach to product quality management.

In 1922, an expert group from the United States introduced the concept of Total Quality: “Total quality (TQ) is a management system focused on people, the goal of which is to constantly increase the degree of customer satisfaction while constantly reducing real costs. TQ is a system-wide approach (rather than individual sites or programs) and an integral part of the strategy top level; it works horizontally, spanning functions and departments, engaging all employees from the top down and transcending traditional boundaries to include the overall supply chain and, ultimately, the customer chain. In TQ, great influence is placed on mastering the policy of constant change and its adaptation, since these components are considered powerful levers that significantly affect the success of the organization.

The next step in the development of a quality management system is the development of a process approach and the popularization of reengineering. Reengineering proposes to replace the principle of division of labor in management with a process approach. At the head of the organization are processes that have their own performers. Enterprises were embraced by a new idea, a massive review of the work of processes began, their optimization, change and implementation of new ones. Until it was discovered that reengineering is by no means a universal remedy.

Now, in the 21st century, an adaptive model of organization is taking root in science and the concept of knowledge management is spreading.

But, despite the widespread knowledge of quality management methods and systems, many enterprises do not realize the importance of quality control. In an effort to keep up with world standards, they install software products, build control charts, not understanding how this can help them.

No matter how simple or complex the methods of quality management are, by themselves they will not be able to provide any benefit to the enterprise, because, even after conducting all the necessary research and having received conclusions, it is still necessary to develop and implement changes. A significant part of Russian enterprises, starting to develop a quality management system (QMS), does not set the task of achieving effectiveness, and even more so, the effectiveness of the QMS, which is a prerequisite for quality management. The implementation of the widespread ISO system is more like an expensive certification than a management aimed at satisfying consumers.

The introduction of total quality management in Russia is associated with significant difficulties, and above all, it is the rejection of the concept of quality by managers, the unwillingness to be leaders committed to the implementation of quality and to follow the chosen goal. The specificity of Russia, its people, customs and practices, apparently, will not soon be ready for cardinal changes in the system of views on the management of the organization.

These are the main milestones in the development of product quality management systems.

map shewhart quality management

The value of statistical methods can hardly be overestimated, since without such methods of control, it would be difficult, almost impossible, to identify the dependence of defects on certain factors. At the same time, organizations should strive to reduce the variability of factors, and as a result, the manifestation of greater stability in product quality. For example, during the machining of metal, a cutter is used, which, after processing a new unit of metal, becomes a little dull. In addition, changes in temperature, coolant composition, or other influences can lead to product defects.

Not all factors involved in production are stable, and statistical methods of quality control and management are aimed at reducing their variability. There are, however, other ways to reduce the level of product defects, such as using expert intuition or past experience to eliminate such problems.

The proposed methods can either be very effective or fail to correctly diagnose and solve the problem. And here it is up to the person who manages the control, the conformity of methods to achieve the goals of the study, the objectivity of the selected indicators, the reliability of measurements, etc.

Let's consider statistical methods of quality control. Kaeru Ishikawa, professor emeritus at the University of Tokyo, proposed the division of statistical methods into three groups:

1. elementary methods, these include "seven simple tools quality"

control sheet

æ allows you to conveniently record data on defects that the controller encounters. In the future, it becomes a source of statistical information.

quality histogram

æ It is built on the basis of a control sheet and shows the frequency of the values ​​of the controlled parameter falling within the specified intervals.

causal diagram

æ is also called a fishbone diagram. The diagram is based on one quality indicator, which takes the form of a straight horizontal line (“backbone”), to which the main causes that affect the indicator (“big bones of the ridge”) are joined by lines. Secondary and tertiary causes that influence the older causes are also connected by straight lines (“medium and small bones”). After construction, it is necessary to rank all the reasons according to the degree of influence on the indicator.

Pareto chart

æ The main assumption of the diagram is that in most cases, the vast majority of defects arise from a small number of important causes. The consequence of the sharpened diagram will be the conclusion about which types of defects have a large share among the others and, accordingly, what should be paid special attention to.

·Stratification

æ Data stratification or stratification is carried out when it is necessary to compare the results of similar processes performed by different workers, or on different machines, using different materials and in other cases.

scatter diagram

æ is built on the basis of paired data (for example, the number of defects on the air temperature in the furnace), the dependence of which must be investigated. The diagram can give information about the shape of the distribution of pairs. Based on the diagram, it is possible to carry out correlation and regression analysis.

control card

æ principles and methods of constructing control charts will be discussed in the third chapter of the work.

2. intermediate methods, these are acceptance control methods, distribution theories, statistical estimates and criteria.

3. advanced methods, these are methods based on the use of computer technology:

experiment planning,

multivariate analysis

· methods of research of operations.

Product quality is determined by a set of quantities and features, which in general can be called quality indicators. On their basis, statistical studies are carried out. The indicators characterize the consumer properties of products and may have different meaningful meanings.

Control cards belong to the "seven simple methods» quality management, according to the classification of K. Ishikawa. Like other methods, control charts are aimed at identifying factors that affect the variability of processes. Since, variability can be influenced by random or certain (non-random) reasons. Random causes can be attributed to such causes, whose occurrence cannot be avoided, even using the same raw materials, equipment and workers serving the process (for example, temperature fluctuations environment, material characteristics, etc.). Certain (non-random) reasons imply the presence of some dependence between the change in factors and the variability of the process. Such reasons can be identified and eliminated during process tuning (for example, loosening of fasteners, tool wear, insufficient sharpening of the machine, etc.). In an ideal situation, the variability of certain factors should be reduced to zero, and by improving the technological process, a decrease in the influence and random factors should be achieved.

Control charts are used to adjust already existing processes in which the products meet the technical requirements.

The construction of control charts is mainly aimed at confirming or rejecting the hypothesis about the stability and controllability of the process. Due to the fact that the maps are of a multiple nature, they allow you to determine whether the course of the process under study is random, if so, then the process should tend to a normal, Gaussian distribution. Otherwise, trends, series and other abnormal deviations can be traced on the chart.

The next chapter will deal with the practical side of Shewhart's control charts.

Before proceeding to the direct construction of control charts, let's get acquainted with the main stages of the task. So, in view of the fact that different authors pursue their own goals, describing the construction of control charts, the original vision of the stages of construction of Shewhart's control charts will be presented below.

Algorithm for constructing Shewhart control charts:

I. Process analysis.

First of all, it is necessary to ask a question about the existing problem, because, in the absence of these, the analysis will not make sense. For greater clarity, you can use the cause-and-effect diagram of Ishikawa (mentioned above, ch. 2). To compile it, it is recommended to involve employees from different departments and use brainstorming. After a thorough analysis of the problem, and finding out the factors influencing it, we proceed to the second stage.

II. Process selection.

Having clarified in the previous stage the factors influencing the process, having drawn a detailed skeleton of the “fish”, it is necessary to choose the process that will be subject to further research. This step is very important because choosing the wrong indicators will make the whole control chart less effective due to the examination of insignificant indicators. At this stage, it is worth realizing that the choice of the appropriate process and indicator determines the outcome of the entire study and the costs associated with it.

Here are some examples of possible indicators:

Table 1. The use of control cards in service organizations

Source Evans J. Quality Management: textbook. Allowance/J. Evans.-M.: Unity-Dana, 2007.

At the same time, the indicator should be chosen, guided by the main goal of the company, namely, customer satisfaction. When the process and the indicator that characterizes it are selected, you can proceed to data collection.

III. Data collection.

The purpose of this stage is to collect data about the process. To do this, it is necessary to design the most suitable way to collect data, find out who and at what time will take measurements. If the process is not equipped with technical means to automate the entry and processing of data, it is possible to use one of the seven simple Ishikawa methods - checklists. Control sheets, in fact, are forms for registering the parameter under study. Their advantage lies in ease of use and ease of training employees. If there is a computer at the workplace, it is possible to enter data through the appropriate software products.

Depending on the specifics of the indicator, the frequency, time of collection and sample size are determined to ensure representativeness of the data. The collected data is the basis for further operations and calculations.

After collecting information, the researcher must decide on the need to group the data. Grouping often determines the performance of control charts. Here, with the help of the analysis already carried out using the cause-and-effect diagram, it is possible to establish factors by which it will be possible to group the data in the most rational way. It should be noted that data within one group should have little variability, otherwise the data may be misinterpreted. Also, if the process is divided into parts using stratification, each part should be analyzed separately (example: the manufacture of the same parts by different workers).

Changing the way grouping will change the factors that form within-group variation. Therefore, it is necessary to study the factors influencing the change in the indicator in order to be able to apply the correct grouping.

IV. Calculation of control chart values.

Shewhart's control charts are divided into quantitative and qualitative (alternative) depending on the measurability of the studied indicator. If the value of the indicator is measurable (temperature, weight, size, etc.), maps of the value of the indicator, ranges and double maps of Shewhart are used. On the contrary, if the indicator does not allow the use of numerical measurements, use card types for an alternative feature. In fact, the indicators studied on this basis are defined as meeting or not meeting the requirements. Hence the use of maps for the proportion (number) of defects and the number of conformances (inconsistencies) per unit of production.

For any type of Shewhart maps, the definition of the central and control lines is assumed, where the central line (CL-controllimit) actually represents the average value of the indicator, and the control limits (UCL-uppercontrollimit; LCL-lowercontrollimit) are the allowable tolerance values.

The values ​​of the upper and lower control limits are determined by formulas for different types of charts, as can be seen from the diagram in Appendix 1. To calculate them, in order to replace cumbersome formulas, coefficients from special tables are used to build control charts, where the coefficient value depends on the sample size (Appendix 2). If the sample size is large, then maps are used that provide the most complete information.

At this stage, the researcher must calculate the values ​​of CL, UCL, LCL.

V. Construction of a control chart.

So, we have come to the most interesting process - a graphical representation of the data obtained. So, if the data was entered into a computer, then using the Statistica or Excel program environment, you can quickly graphically display the data. However, it is possible to build a control chart and, without special programs, then, along the OY axis of the control charts, we plot the values ​​of the quality indicator, and along the OX axis, the time points of registering the values, in the following sequence:

1. plot the center line (CL) on the control chart

2. draw borders (UCL; LCL)

3. We reflect the data obtained during the study by applying an appropriate marker to the point of intersection of the value of the indicator and the time of its registration. It is recommended to use different types of markers for values ​​that are inside and outside the tolerance limits.

4. In case of using double cards, repeat steps 1-3 for the second card.

VI. Checking the stability and controllability of the process.

This stage is designed to show us what the research was conducted for - whether the process is stable. Stability (statistical controllability) is understood as a state in which the repeatability of parameters is guaranteed. Thus, the process will be stable only if the following cases do not occur.

Consider the main criteria for process instability:

1. Going beyond the control limits

2. A series is a certain number of points, which invariably turns out to be on one side of the center line - (top) bottom.

A series of seven points is considered abnormal. In addition, the situation should be considered abnormal if:

a) at least 10 out of 11 points are on the same side of the center line;

b) at least 12 out of 14 points are on the same side of the center line;

c) at least 16 out of 20 points are on the same side of the center line.

3. trend - a continuously rising or falling curve.

4. approaching the control limits. If 2 or 3 points are very close to the control limits, this indicates an abnormal distribution.

5. approaching the center line. If the values ​​are concentrated near the center line, this may indicate an incorrect choice of grouping method, which makes the range too wide and leads to data mixing with different distributions.

6. periodicity. When, after certain equal intervals of time, the curve goes either to "decline", or to "rise".

VII. Analysis of control charts.

Further actions are based on the conclusion about the stability or instability of the process. If the process does not meet the stability criteria, the influence of non-random factors should be reduced and, by collecting new data, a control chart should be built. But, if the process meets the stability criteria, it is necessary to evaluate the process capabilities (Cp). The smaller the spread of parameters within the tolerance limits, the higher the value of the process capability indicator. The indicator reflects the ratio of the width of the parameter and the degree of its dispersion. Opportunity index is calculated as , where can be calculated as .

If the calculated index is less than 1, then the researcher needs to improve the process, either stop the production of the product, or change the requirements for the product. With index value:

Wed<1 возможности процесса неприемлемы,

Cр=1 the process is on the verge of the required capabilities,

Cp>1 the process satisfies the criterion of possibility.

If there is no displacement relative to the central line Cp=Cpk, where . These two indicators are always used together to determine the status of the process, for example, in mechanical engineering it is considered the norm , which means that the probability of non-compliance does not exceed 0.00006.

Now, having considered the algorithm for constructing control charts, we will analyze a specific example.

Task: Chromium content in steel castings is controlled. Measurements are carried out in four swimming trunks. Table 2 shows data for 15 subgroups. You need to build a map.

Solution: Since it is already known in advance what type of map needs to be built, we calculate the values

The next step is to calculate , where, according to the above scheme, , and . Now, having the values ​​of the central line, the average value of the indicator and the average deviation, we will find the values ​​of the control borders of the maps.

, where is according to the table of coefficients for calculating the lines of control charts and is equal to 0.729. Then UCL=0.880 , LCL=0.596.

For values, the lower and upper control limits are determined by the formulas:

where and are found according to the table of coefficients for calculating the lines of control charts and are equal to 0.000 and 2.282, respectively. Then UCL=0.19*2.282=0.444 and LCL=0.19*0.000=0.

Let's build control charts for the averages and ranges of this sample using Excel:

As we can verify, the control charts did not reveal non-random values, out-of-control limits, series or trends. However, the graph of average values ​​tends to the central position, which may indicate both incorrectly chosen tolerance limits, and abnormal distribution and process instability. To make sure, we calculate the process capability index. , where can be calculated as , according to the table of coefficients, we find the value equal to ;

Since, the computed index<1, что свидетельствует о неприемлемости возможностей процесса, его статистической неуправляемости и не стабильности. Необходимо провести усовершенствования процесса, установить контроль над его протеканием, с целью уменьшения влияния не случайных факторов.

Studying specialized literature and delving into quality management, I was able to gather a large amount of interesting and useful information. For example, the breadth of use of quality management has affected all areas of production from heavy industry and oil procurement to small organizations providing services (catering places, bookstores, etc.).

In recent years, under the overarching influence of thinking aimed at improving quality and customer satisfaction, systems such as CRM-customer-oriented management are attributed to quality management; ERP enterprise resource management system; TPM - system of general care of the equipment, and many other systems. Based on this, we can conclude that there has been a shift in interests from quality management of a specific process to the use of quality systems and software packages that allow one way or another to contribute to customer satisfaction in the most convenient ways. The contribution of Walter Shewhart to statistical quality management is great, and the control charts he proposed are still used, but more often, in conjunction with other methods, due to the provision of a systematic approach and taking into account many factors that were not taken into account in the 20th century.

In conclusion, I would like to say that the main problem of modern quality systems is that, with all the apparent ease of use, they cannot guarantee their effective use in the enterprise. The reasons lie in the origins! After all, the main advantage of using the "7 simple methods" of quality management is that without the penetration of the philosophy of quality, it is hardly possible to obtain any significant results. Thus, companies that are not yet ready for fundamental changes could save themselves from the introduction of expensive systems and unnecessary spending.

Quality management is the philosophy of success for modern companies!

1. GOST R 50779.42-99 “Statistical methods. Shewhart's Control Charts"

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3. Yosio Kondo. Quality management across the company: formation and stages of development. / Per. from English. E.P. Markova, I.N. Rybakov. - Nizhny Novgorod: SMC "priority", 2002.

4. Prosvetov G.I. Forecasting and planning: tasks and solutions: teaching aid./G.I. Prosveov-M.: RDL Publishing House, 2005.

5. Kane M.M., Ivanov B.V., Koreshkov V.N., Skhirtladze A.G. Systems, methods and tools of quality management / M.M. Canet, B.V. Ivanov, V.N. Koreshkov, A.G. Skhirtladze. - St. Petersburg: Peter, 2009

6. Kachalov V.A. What is “continuous improvement of the effectiveness of the QMS”?// Methods of quality management.-2006.-№10.

7. Klyachkin V.N. Statistical methods in quality management: computer technology: textbook. Allowance / V.N. Klyachkin.-M.: Finance and statistics, 2007.

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9. Kuznetsov L.A. Control and evaluation of multidimensional quality//Methods of quality management.-2008.-№10.-p. 40-45.

10. Sazhin Yu.V., Pletneva N.P. On the question of the effectiveness of QMS in Russia// Methods of quality management.-2008.-№10.-P.20-24.

11. Statistical methods of quality improvement: monograph / trans. from English. Yu.P.Adler, L.A. Konareva; ed. Kume.-M.: Finance and statistics, 1990.

12. Feigenbaum A. Product quality control / A. Feigenbaum. - M.: Economics, 1986.

13. Evans J. Quality management: textbook. Allowance/J. Evans.-M.: Unity-Dana, 2007.

Shewhart's chart of control charts

Coefficients for calculating lines of control charts.

Kane M.M., Ivanov B.V., Koreshkov V.N., Skhirtladze A.G. Systems, methods and tools of quality management / M.M. Canet, B.V. Ivanov, V.N. Koreshkov, A.G. Skhirtladze. - St. Petersburg: Peter, 2009

Kane M.M., Ivanov B.V., Koreshkov V.N., Skhirtladze A.G. Systems, methods and tools of quality management / M.M. Canet, B.V. Ivanov, V.N. Koreshkov, A.G. Skhirtladze. - St. Petersburg: Peter, 2009.