A role of statistical methods in management of productions

One by one preparations arrive on the conveyor. At the end of the conveyor the packing machine continuously packs products and sends them to finished goods warehouse. The attentive look finds the person standing between the conveyor and a packing machine. He strictly watches a stream of products and from time to time takes some products and throws them into the basket standing at it behind the back. It is a defective product.

How there are defective products and what it is necessary to make to reduce their number?

For reduction of number of defective products it is necessary to believe resolutely that it is possible. Each concrete defective product appeared as a result of the special reasons and only their identification and elimination can help of them will get rid.

Many think that defective products are inevitable as production has to meet strict requirements of standards on quality, and factors conducting to emergence of defects are numerous. However despite distinction in types of production and types of technological processes, the reasons of emergence of defective products are universal. The reasons of changes of quality are uncountable also their influence variously. Some of them strongly influence quality change while others, theoretically considered important, actually do not make essential impact if are properly controlled.

All uncountable possible reasons share on two groups. Treat the first a small number of the reasons which makes essential impact (them call "numerous significantly important"). The second group is made by a large number of the reasons making nevertheless insignificant impact (them call "numerous insignificant"). Usually the factors causing defects, not so much. It is the principle called by Pareto principle, we will apply in many case.

Using the specified principle of variability together with Pareto principle, it is possible to solve much more simply a problem of reduction of number of defective products. First of all it is necessary to find su4shchestvenno the important reasons causing emergence of defective products, and after they are accurately revealed to eliminate them.

To reduce number of substandard products, it is necessary to make first of all correct "diagnosis" - the true reasons of defects. If diagnostics is incorrect, it is impossible to reduce number of defective products.

How to make the correct diagnosis? There are many methods. Some rely on intuition, others rely on last experience, the third resort to the statistical analysis of data. It is possible to conduct pilot studies also. The method of intuition is used very often because, in this case the decision can be made quickly enough. Really, to intuition of experiment it is necessary is respectful as in it something is shown, beyond abilities of the ordinary person. However complexity of a problem of destruction of number of defects that is not always clear who - true experiment. The problems conducting to emergence of defective products often arises where there is no previous experience. The saved-up experience, how many strong will to their decrease and desire objectively to analyze a real situation is important for elimination of defective products not so much for years. View of things through a prism of statistics and statistical methods - most, an effective remedy of objective supervision.

Application of statistical methods - very effective way of development of new technology and quality control of productions. Many leading firms seek for their active use, and some of them spend more than hundred hours annually for the training in these methods which is carried out within the firm. Though the knowledge of statistical methods - part normal education of the engineer, knowledge does not mean yet ability to apply it. Ability to consider events from the point of view of statistics is more important, than knowledge of methods. Besides, it is necessary to be able to recognize honestly shortcomings and the arisen changes and to collect the relevant information. In the conclusion it is necessary to emphasize that the knowledge of statistical methods, how many conscious desire to use them is important not so.

Statistics methods - that means which is necessary will study to introduce quality management. They - the most important component of complex system of general quality management in firm. In Japanese corporations everything, beginning from the chairman of the board of directors and to the ordinary worker in shop, are obliged to know bases of statistical methods. Each employee of Japanese corporation, using statistical methods for the analysis and control of processes, thereby promotes improvement of quality, production efficiency and decrease in expenses.

Control leaves

Control leaf - the paper form on which in advance printed controlled parameters was it is possible it was possible to write down easily and precisely data of measurements. Its main appointment is double:

1) to facilitate data collection process;

2) automatically to order data for simplification of their further use.

Collecting and data recording at first sight seem easy business, actually it is quite difficult. Usually than more people process data, that a high probability of emergence of mistakes in the course of record. Therefore the control leaf on which it is possible to bring data with the help of marks or simple symbols and kotoryy1 allows to order automatically data without their subsequent copying by hand, - good means of data recording. It is given examples below.


Control leaf for registration of distribution of the measured parameter during production. Let's assume that we want to reveal change in razmakha of some detail which is exposed to machining, and the size specified in the drawing - 8,300±0,008. For receiving distribution of values of this indicator during process histograms are usually used. On the basis of the histogram average value and dispersion is calculated, it is investigated as well a distribution curve form. To construct the histogram, it is necessary to spend a lot of work for collecting a large number of data and for representation of frequency distribution in a graphic form. It is simpler to classify data at the time of collecting. In fig. 2.1 the form which can be prepared for this purpose in advance is shown. Every time when is made measurement, in the corresponding cage the cross is put, so hundred the histogram is ready to the end of measurements. If it is necessary to make stratification with use of one control leaf, it is better to take pencils of different color that a difference it was shown visually for marks.

  Deviation Measurements frequency
5 10 15 20
· -8                                          

- access field Border (according to the drawing)

Figure 2.1 the Control leaf for registration of distribution of parameter during production


Control leaf for registration of types of defects. In fig. 2.2 the control leaf used in the course of acceptance control of one stamped plastic detail is shown. Every time when the controller finds defect, it does in it a mark. At the end of the working day it can quickly count number and a kind of the found defects.

Simply the knowledge number of defects does not allow to make the decision on the correcting measures but if the leaf similar to it is used, it can give important information for process improvement as shows, what types of defects meet often, and what - no.

Using a similar control leaf, it is impossible to make then stratification of data, having broken them, for example, into morning and evening changes as it was possible in a case with the leaf presented in fig. 2.1. Therefore if stratification is necessary, when developing the form it needs to be provided in advance.

It is also necessary to provide how to register data in case the product contains two defects, and it is necessary to give instructions to people who mark products. In the case presented in fig. 2.2 defective were 42 products from 1525, but total number of the found defects - 62 as contained in some products on two or several defects.

Product name
Производственная операция, приемочный контроль
Тип дефекта: царапина, пропуск операции, трещина , неправильная обработка
Общее число проконтролированных изделий: 1525
Применения по всем проконтролированным изделиям
Фамилия контролера
Номер партии
Номер заказа

Тип дефекта Результат контроля Итоги по типам дефектов
Поверхностные царапины //// //// //// //
Трещины //// //// /
Пропуск операции //// //// //// //// //// /
Неправильное исполнение операции ///
Другие ////
Общее число забракованных деталей  

Figure 2.2 control leaf of types of defects

Pareto's analysis

Problems of quality are wrapped in losses (the defective products and expenses connected with their production). It is extremely important to explain a picture of distribution of losses. The majority of them will be caused by insignificant number of types of the defects caused by a small amount of the reasons. Thus, to find out the reasons of emergence not numerous it is essential important defects, it is possible to eliminate almost all losses, having concentrated conditions on elimination of these reasons and having postponed consideration of the reasons bringing to other numerous defects so far. The such problem is successfully solved with the help of the chart of Pareto.

In 1897 the Italian economist V. Pareto invented the form showing that the distribution benefits unevenly. The same theory is illustrated on the chart by the American economist M. S. Lorentz in 1907 both scientists proved that in most cases the greatest share of the income or the benefits belongs to a small number of people. Doctor D. M. Dzhuran applied the chart and M. Lorentz's formula in the sphere of quality control to classification of problems of quality on not numerous significantly important and numerous insignificant and called this method Pareto's analysis. He specified that in most cases the overwhelming number of defects and the related losses arises because of rather small number of the reasons.

How to construct Pareto's chart?

Stage 1.

Solve, what problems should be investigated and how to collect data.

1) What like a problem you want to investigate?

Example: defective products, losses in money, accidents.

2) What data should be collected and how to classify them?

Example: by types working, on technological processes.

Note. It is summarized other infrequently meeting signs under the general headings "other".

3) Establish a method and the period of data collection.

Note. If it is recommended, use special forms.

Stage 2.

Develop a control leaf for data recording with the list of types of the collected information. It is necessary to provide a place for graphic data recording of checks in it (table 2.1).

Table 2.1

Control leaf of data recording

Тип дефектов Группы данных Итого
Трещины Царапины Пятна Деформация Разрыв Раковины Прочие //// //// //// //// //// … //// // //// / //// /// //// … //// //// //// //// ///// /// //// //// //// ////

Stage 3.

Fill a leaf of data recording and count results.

Stage 4.

For creation of the chart of Pareto develop the form of the table for verifications of data, having provided in it columns for results on each checked sign separately, the saved-up sum of number of defects, percent to the general result and the saved-up percent (table 2.2).

Table 2.2

Tables of data for creation of the chart of Pareto

Types of defects Number of defects The saved-up sum of number of defects Percent of number of defects on each sign in total amount The saved-up percent
Deformation Scratch Sink Crack Spot Gap Other
Total - -

Stage 5.

Arrange the data obtained on each checked sign as the importance and fill in the table.

Note. It is necessary to place prochiye group the last line regardless of that, the number as it is made by set of signs turned out how big, the numerical result on each of which is less, than the smallest value received for the sign allocated in a separate line.

Stage 6.

Draw one horizontal and two vertical axes.

1) Vertical axes:

(a) left axis. Apply on this axis a scale with intervals from 0 to the number corresponding to the general result;

(b) right axis. Apply on this axis a scale with intervals from 0 to 100%.

2) Horizontal axis. Divide this axis into intervals according to numbers of controlled signs.

Stage 7.

Construct the stylar chart.

Stage 8.

Draw a cumulative curve (Curve Pareto).

On the verticals corresponding to the right ends of each interval on a horizontal axis put points of the saved-up sums (results and percent) and connect them among themselves pieces of straight lines.

Stage 9.

Apply all designations and inscriptions on the chart:

1) inscriptions the concerning charts (the name, a marking of numerical values on axes, the name of a controlled product, a name of the author of the chart);

2) the inscriptions concerning data (the period of collection of information, object of research and a place of its carrying out, total number of objects of control (figure 2.1)).

1 апреля – 30 июня
Число проконтролированных изделий: 5,000
А: трещины Г: деформация Б: царапины Д: разрыв В: пятна Е: раковины
A role of statistical methods in management of productions - student2.ru A role of statistical methods in management of productions - student2.ru

Picture-2.3 Diagramma Paretog on types of defects

Digaramma Pareto on result of activity and on the reasons

As already was it is told, creation of the chart of Pareto - a method of definition of not numerous significantly important factors. Distinguish two look such dshchiagramm.

1. Pareto's chart on result of activity.

This chart is intended for identification of the main problem and reflects the following undesirable results of activity:

- quality: defects, breakages, mistakes, refusals, claims, repairs, returns of production;

- prime cost: volume of losses, expense;

- terms of deliveries: shortage of apas, mistakes in billing, failure terms of deliveries;

- safety: accidents, tragic mistakes, accidents.

2. Pareto's chart for the reasons

This chart otraat the reasons proby, arising during production, and is used for a vyyavleiya main of them:

- worker: change, crew, age, experience, qualification, individual characteristics;

- equipment: machines, units, tools, equipment, organization uses, models, shtampyts;

- raw materials: the manufacturer, a type of raw materials, plant - the supplier, party;

- work method: conditions of production, zakuaza - dresses, receptions works, sequence of operations.

Some reasons about Pareto's charts (councils for productive/effective construction)

Councils for creation of charts of Pareto:

1. Use different classifications and make many charts of Pareto. The essence of a problem can be captured, observing the phenomena from the different points of view therefore it is important to test various ways of classification of data, will not come to light important factors not numerous significantly yet, as serves as the purpose of the analysis of Pareto.

2. It is undesirable that the prochiye group factors made big percent. If such occurs, means objects of supervision are classified incorrectly and too many objects in one group. In this case it is necessary to use other principle of classification.

3. If data can be submitted in terms of money, it is best of all to show it on vertical axes of the chart of Pareto. If it is impossible to estimate the existing problem in terms of money, research can be not effective. Expenses - important criterion of measurements in management.

Councils for use of the chart:

1. If are not desirable a factor it is possible to eliminate by means of the simple decision, it should be made immediately irrespective of the fact which insignificant it was. As Pareto's chart is regarded as an effective remedy of the solution of problems, so it is necessary to consider only the important reasons not numerous significantly. However, if relatively the reason is eliminated in the simple way, it will serve an example of an effective solution, and the gained experience, information and moral satisfaction will make big impact on further procedure of the solution of problems.

2. Do not miss opportunity to make Pareto's chart for the reasons.

After identification of a problem by drawing up the chart of Pareto on result, it is important to define the reasons of emergence of a problem to solve it. Therefore if we want improvements, it is important to make Pareto's chart for the reasons.

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