Chart of the reasons and results
The result of process depends on numerous factors between which there are relations like reason - result. It is possible to define structure or character of these multiple-factor relations thanks to systematic supervision. It is difficult to solve complex problems, without knowing this structure which represents the purpose of the reasons and results. The chart of the reasons and results - the means allowing to express these relations in a simple and available form.
In 1953 professor of the Tokyo university to Cahors Isikava, Discussing a quality problem at one plant, summarized opinion of engineers in the form of the chart of the reasons and results. It is considered that then this approach was applied in the first, but even earlier employees professors of Isikava used this method for streamlining of factors in the scientifically - research work. When the chart started being used in practice, it was very useful and was widely adopted in many companies of Japan soon. It was included in the Japanese industrial standard (JIS) on terminology in the field of quality control and is defined in it as follows: the chart of the reasons and results - the chart which shows the attitude between an indicator of quality and the factors influencing it.
Now this chart is used around the world not only in relation to indicators of quality of production, but also in other areas.
How to construct the chart of the reasons and results?
To construct the chart of the reasons and results - difficult business. Rightfully it is possible to declare that those who succeeded in the solution of problems of quality control, is just those who mastered creation of the present charts. There are many ways of their construction, but two most typical will be considered here. Before starting the description of procedure of their construction on an example, we will explain their structure.
Structure of the chart of the reasons and results and concrete example
The chart of the reasons and results differently call "a fish skeleton" as it reminds a skeleton of fish that is visible in figure 3.2. Sometimes it is also called "tree" or the chart of "river inflows". Let's use the name "fish skeleton". The concrete example is given on figure 2.3.
| Показатель качества |
| «Большая кость» |
| «Хребет» |
| Средняя кость» |
| «Мелкая кость» |
| Показатель (результат) |
| Факторы (причины) |
Figure 2.4 Structure of the Chart of the Reasons and result
| Поражение в спортивных матчах |
| Здоровье |
| Отдых |
| Расслабление |
| Развлечения |
| Сон |
| Время сна |
| Глубина сна |
| Питательность |
| Количество калорий |
| Количество |
| Пища |
| Дух |
| Внимательность |
| Терпение |
| Сосредоточенность |
| Поощрение |
| Гордость |
| Спортивный дух |
| Привязанность |
| Спокойствие |
| Самообладание |
| Уверенность |
| Стратегия |
| Планирование |
| Теория |
| Правила |
| Здоровый смысл |
| Информация |
| Изучение противника |
| Анализ |
| Оценка ситуации |
| Наблюдение |
| Опыт проведения матчей |
| Техника |
| Сила |
| Подвижность |
| Скорость |
| Совместные действия в команде |
| Кооперация |
| Функция |
| Тренировка |
| График |
| Объем |
| Качество |
| Форма |
| Совет |
| Образец |
| Повторяемость результатов |
Figure 2.5 Example of the Chart of the Reasons and Results
Method of creation of charts of the reasons and results for definition of the reasons
1. Procedure
Stage 1
Define a quality indicator
Stage 2
Choose one indicator of quality and write it in the middle of the right edge of a clean sheet of paper. From left to right draw a straight line ("ridge"), and conclude the written-down indicator in a rectangle. Further write the main reasons which influence a quality indicator, conclude them in a rectangle and connect to "spine" shooters (in a look) "big bones of ridge".
Stage 3
Write the reasons (secondary) influencing the main reasons ("big bones"), and arrange them in the form of the "average bones" adjoining to "big". Write the reasons of a tertiary order which influence the secondary reasons, and arrange them in the form of the "small bones" adjoining "averages".
Stage 4
Range factors on their importance and allocate especially important which allegedly have the greatest impact on a quality indicator.
Stage 5
Write down all necessary information.
2. Procedure explanations
Putting this procedure into practice, it is possible will meet difficulties. The best way in this case - to consider a problem from the point of view of "variability". For example, when you think of "big bones", argue about changes in a quality indicator. If data show that changes exist, think why so occurs. Change of result can be caused by changes in factors. Such turn in thoughts is very effective.
When build the chart of the reasons and results in relation to concrete defect, for example, it is possible to find out that number of the defects allowed different days of week, variously. If it is found out that defects meet on Monday, than in other days of week more often, it is possible to ask a question: "And why defects on Monday are allowed more often than in other days of week", "Why they arise?". It will force to pay attention to consideration of factors which distinguish Monday of other days of week that as a result will lead to detection of the reason of defect.
Having resorted to such way of a reasoning at each stage of research of the relations between an indicator of quality and "big bones", between "big" and "average", and also between the last and "small bones", perhaps logical way to construct the useful chart of the reasons and results.
After creation of the chart, the following step - distribution of factors on degree of their importance. Not necessarily all factors included in the chart will have strong impact on a quality indicator. Designate what make the greatest impact.
And at last, on the chart all necessary information: its name, name of a product, process or group of processes, names of participants of process, date, etc.
Procedure of creation of the chart of the reasons and results for systematization of the list of the reasons
1. Procedure
Stage 1
Solve, what indicator of quality will be investigated.
Stage 2
Find as much as possible number of the reasons which, perhaps, influence this indicator.
Stage 3
Consider the relations between the reasons and construct the chart, jointing its elements on the basis of the relations the reason - result with a quality indicator.
Stage 4
Establish importance of each factor and note major factors which, make the greatest impact on a quality indicator.
Stage 5
Write down all necessary information.
2. Procedure explanation
Such approach is characterized by a combination of two different types of activity: search of the greatest possible number of the reasons and their systematization.
For search of the reasons carry out, in case of need, active discussion. The "brain storm" which is thought up in the USA by A.F. Osborn will be the effective method applied in that case.
At creation of the chart of the reasons and results it is better to systematize, considering their sequences: from "small bones" to "averages" and from "averages" to "big".
Control cards
For the first time control cards were offered in 1924 by U. Shukhart working in Bell Telephone Laboratories with intention to exclude an unusual variation, separating variations which are caused by certain reasons, that are caused by the casual reasons. Any control card consists of the central line, a time of control limits, on one over and under the central line, and the values of the characteristic (a quality indicator) plotted for representation of a condition of process. If all these values appear in control limits, without showing any tendencies, process is considered as being in a controlled state. If, on the contrary, they get out of control limits or will take any unusual form, process is considered got out of hand. Examples are given in fig. 2.14. quality of an industrial output in the course of production is inevitably subject to a variation. For such variation there are various reasons which can be divided into the following two look.
Casual reason. The variation caused by the casual reasons is necessary; it inevitably meets in any process even if technological operation is performed with use of standard raw materials and methods. Now the exception of the casual reasons is impractical technically and economically.
Certain reason. The variation caused by a certain reason means that there are factors, the allowing studying. These influences can be avoided and it is impossible to miss such opportunity: there are cases when changes are caused by non-compliance with standards or application not of those standards.
When points do not get out of control limits or show a certain tendency, we say that process came out from - under control. In other words, it is possible to tell: "there are certain reasons of a variation, and process came out from - under control". To operate process, to this process it is necessary to return though the variations connected with the casual reasons are allowed.
For creation of the control card it is necessary to estimate the variation caused by the casual reasons. For this purpose we divide data on under groups in which remain invariable party of raw materials, the machine, the operator and other general factors so the variation in subgroups can consider approximately as well as the variations caused by the casual reasons.
| Верхний контрольный предел |
| Центральная линия |
| Нижний контрольный предел |
| Контрольная карта для управляемого состояния |
 |
| Верхний контрольный предел |
| Центральная линия |
| Нижний контрольный предел |
| Контрольная карта для неуправляемого состояния |
 |
Рисунок 2.14 Пр
Figure 2.14 Examples of control cards
Dependences on a type of an indicator and on the purpose exist various types of control cards. In one of types the control limit is calculated on such formula:
(average value) ±3´(standard deviation),
where the standard deviation is also the variation caused by the casual reasons. This type of control cards is called as the control card with 3 - sigmovy limits.
Types of control cards
There are two types of control cards: one for continuous values, and the second - for discrete. Types of the control are regulated by the Japanese Industrial Standard (JIS), as shown in table 2.10, and formulas for calculation of control lines are given in tab. 2.11.
Table 2.10
Types of control cards
| Values of the characteristic (quality indicator) | Name |
| Continuous values Discrete values Дискретные значения | (  ) - card (average value and scope) x - the card (the measured value) pn - the card (number of defective products) p - card (share of defects) c - card (number of defects) u - the card (number of defects on unit) |
Table 2.11
The list of formulas for control lines
| Type of the control card | Top control limit (UCL), central line (CL), lower control limit (LCL) |
 |    |
| R |    |
| x |    |
| pn |    |
| p |   |
| c |    |
| u |    |
( 
) –card
This card is used for the analysis and management of processes which indicators of quality represent continuous sizes (length, the weight or concentration) and bears the greatest number of information on process. Size 
is average value for subgroup, and R - selective scope for the same subgroup. Usually R - the card use together with 
- the card for management of dispersion in subgroups.
x - card
If data on process arrive through big intervals of time or if grouping of data is not effective, they are applied on the schedule with separate points in process of receipt, and they too can be used for creation of the control card. As subgroups are not present, it is impossible to calculate value R, and for definition of control limits x it is necessary to use the current values of scope of RS according to consistently arriving data.
pn - the card, p - the card
These cards are used when the indicator of quality is presented by number of defective products or their shares. For selections of the constant fixed volume pn - the card of number of defective products whereas r - the card of shares of defects it is necessary at selections of the changing volume is used.
c - carat, u - carat
Happens that the analysis and management of process are kept on defects in production, such, number of scratches on a leaf threw, number of defects of the soldering in the TV or number rough in a woven matter. Cards of type with are used to number of defects in products of the lonely size, and u - cards are intended for products of the different size.
How to construct control cards?
( ) - card
Method
Stage 1. Data collection.
Collect about 100 data. Divide them into 20 or 25 uniform subgroups of 4 or 5 in everyone. Fill in with data the prepared table (see tab. 2.12). When practically there is no reason for division of data into subgroups, divide them on first come. In most cases the volume of group undertakes in the range from 2 to 10.
Table 2.12
The table of data for ( ) - cards
| Номер подгруппы | х1 | х2 | х3 | х4 | х5 |  |  | R |
| 35,6 29,2 20,2 39,4 29,2 31,4 23,2 32,0 29,0 32,6 32,2 26,8 27,8 29,8 31,6 22,2 31,2 28,8 31,4 29,6 39,0 19,4 34,2 32,6 28,2 | ||||||||
| Итого | 746,6 | |||||||
Среднее  = 29,86  = 27,44 |
Stage 2. Calculation of averages 
Calculate a value average 
for each subgroup:
(h1 + h2 + h3 + h4 + … + xn) / n,
where n - the volume of subgroup.
This result is usually counted with one excess sign in comparison with initial data.
Stage 3. Calculation 
Calculate the general average meaning , dividing a column result 
for each of subgroups into their number 
:
= ( 
1 + 2 + … + to) / to,
and it is necessary to calculate with two excess signs in comparison with the measured values.
Stage 4. Calculation of R.
Calculate scope of R in each subgroup, subtracting the minimum value in subgroup from the maximum:
R = (the maximum value in subgroup) - (the minimum value in subgroup).
Stage 5. Calculation 
Calculate average value 
for scope of R, dividing a result of a column of razmakh for all subgroups into their number k:
(R1 + R2 + … + Rk) / k.
Value 
should be calculated with two excess signs in comparison with the measured values, i.e. with the same number of signs, as .
Stage 6. Calculation control lines
Calculate each control line for 
- cards and for R - the card on the following formulas.
- cards. Central line:
CL = 
Top control limit:
UCL = 
A2 
Lower control limit:
LCL = 
A2
R - card. Central line:
CL = 
Top control limit:
UCL=D4 
Lower control limit:
LCL = D3
The lower limit is not considered, when n less than 6.
The constants A2, D4 and D3 - the coefficients determined by the volume of subgroups (n). They are brought in tab. 2.13, and also in table 2.14
Table 2.13
The list of coefficients for ( ) – cards
| Объем подгруппы, n |  - карта |  - карта | ||
| А2 | D3 | D4 | d2 | |
| 1,880 1,023 0,729 0,577 0,483 | - - - - - | 3,267 2,575 2,282 2,115 2,004 | 1,128 1,693 2,059 2,326 2,534 |
Table 2.14
Coefficient for - cards
| Объем выборки, n |  - карта | R - карта | ||||
| А2 | d2 | 1/d2 | d3 | D3 | D2 | |
| 1,880 1,023 0,729 0,577 0,483 0,419 0,373 0,337 0,308 | 1,128 1,693 2,059 2,326 2,534 2,704 2,847 2,970 3,078 | 0,8862 0,5908 0,4857 0,4299 0,3946 0,3648 0,3512 0,3367 0,3249 | 0,853 0,888 0,880 0,864 0,848 0,833 0,820 0,808 0,797 | - - - - - 0,076 0,136 0,184 0,223 | 3,267 2,575 2,282 2,115 2,004 1,924 1,864 1,816 1,777 |
Note. The - symbol in the D3 column means that in these cases the lower control limit is not calculated.
Stage 7. Drawing control lines
Prepare a sheet of paper in a section, then put a vertical axis with value 
and 
horizontal axes with numbers of subgroups at the left . Place the top and lower limits so that between them there were 20 - 30 mm. The central line needs to be made continuous, and control limits - dashed lines.
Stage 8. Drawing points.
Place 
and 
for each subgroup on the same vertical axis opposite to the corresponding number of subgroup. Apply numbers of subgroups on a horizontal axis with an interval of 2 - 5 mm. That it was easier to distinguish and , we will take for a sign - (point), for - (rombik), and for those values which go beyond - circles.
Stage 9. Record of necessary information.
It is necessary to write out the volume of subgroup (n) in the top left corner - cards. Write down as well other necessary data concerning the studied process such as the name of process and a product, time period, a method of measurement, a working condition, change, etc.
Example
Stage 2
So for the first group:
= (47+32+44+35+20)/5=35,6
Stage 3
= (35,6+29,2+ … + 28,2)/25=29,86
Stage 4.
For the first group:
R = 47-20=27
Stage 5
=27+18+ … + 27/25=27,41
Stage 6 (see fig. 2.13)
- card
CL = 
= 29,86
UCL = 
+ 
A2=29,86 + 0,577 × 27,44 = 45,69
LCL = - A2=29,86 - 0,577 × 27,44 = 14,03
R-card
CL = 
= 27,44
UCL = D4R=2,115 27,44 = 58,04
LCL = - (is not considered).
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| UCL =45,69 |
| CL = 29,86 |
| LCL =14,03 |
| |
| n=5 |
| UCL =58,04 |
| CL = 27,44 |
| LCL =14,03 |
 |
| Рисунок 2.15 - карты |
Pn – карта
pn - the card
How to read control maps?
That this exact understanding of provision of object of management by means of reading the control card and fast implementation of suitable actions as soon as in object something is found unusual is most important in management process, so. The controlled condition of object is such state when process is stable, and its average and dispersion does not change. Whether there is a process in this state or not, is determined by the control card on the basis of the following criteria.
1) An exit out of control limits. Points which lie out of control limits.
2) A series is a manifestation of such state when points steadily appear on one party from average lines; the number of such points is called as series length.
A series of 7 points is considered as abnormal.
Even if length of a series appears less than 6, in some cases the situation should be considered as abnormal, for example, when:
a) not less than 10 of 11 points appears on one party from the central line;
b) not less than 12 of 14 points appear on one party from the central line;
c) not less than 16 of 20 points appear on one party from the central line.
| Рисунок 2.17 Серия |
| Серия длиной семь точек - ненормальность |
| Десять из 11 последовательных точек оказались по одну сторону от центра – это ненормально |
3) Trend (drift). If points form the continuous raising or lowering curve, say that the trend takes place.
| Рисунок 2.18. Тренд (дрейф) |
| Семь поднимающихся точек |
| Круто падающий тренд |
4) Approach to a control limit. Points which come nearer to 3 - a sigmovy control limit and if 2 or 3 points are for 2 - sigmovy lines are considered, such case should be considered as abnormal.
| Рисунок 2.19 Приближение контрольным пределам (две из трех точек) |
| 3 – сигмовая линия |
| 2 – сигмовая линия |
| 2 – сигмовая линия |
| 3 – сигмовая линия |
5) Approach to the central line. When the majority of points concentrates in the central one and a half sigmovy lines halving distance between the central line and each of control lines it is caused not by a suitable way of splitting into subgroups. Approach to the central line does not mean at all that the controlled state is reached, on the contrary, it means that in subgroups data from various distributions that does scope of control limits too wide mix up. In that case it is necessary to change a way splitting on under groups.
| Рисунок 2.20 Приближение к центральной линии |
| 3 – сигмовая линия |
| 1,5 – сигмовая линия |
6 Frequency. When the curve repeats structure "that rise, recession" with approximately identical intervals of time, it too is abnormal.
| Рисунок 2.21 Периодичность |
Thus the knowledge and use of statistical methods allows to operate competently any technological process and to reveal discrepancies at an early stage that allows to reduce time of correction of defects.
Control questions:
1 Give definition to the term "quality of production"
2 the quality pyramid consists Of what elements
3 Main categories of management and providing production with quality
4 On what ensuring quality of production in the course of conducting technological process is based
5 Give definition to the concept "control"
Vida of control