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.

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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25	47 19 19 29 28 40 15 35 27 23 28 31 22 37 25 7 38 35 31 12 52 20 29 28 42	32 37 11 29 12 35 30 44 37 45 44 25 37 32 40 31 0 12 20 27 42 31 47 27 34	44 31 16 423 45 11 12 32 26 26 40 24 19 12 24 23 41 29 35 38 52 15 41 22 15	35 25 11 59 36 38 33 11 20 37 31 32 47 38 50 18 40 48 24 40 24 3 32 32 29	20 34 44 38 25 33 26 38 35 32 18 22 14 30 19 32 37 20 47 31 25 28 22 54 21	178 146 101 197 146 157 116 160 145 163 161 134 139 149 158 111 156 144 157 148 195 97 171 163 141		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	27 18 33 30 33 29 21 33 17 22 26 10 33 26 31 25 41 36 27 28 28 28 258 32 27
							Итого	746,6		686
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
2 3 4 5 6	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
2 3 4 5 6 7 8 9 10	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).

to collect the relevant information metodov.mka of the firama. to decrease and desire objektivn

3blitsa 3.13diagramme what - =, () ykh products also collect 03 subgroups 20 - 25 in each subgroup popordplo

собирать соответствующую информацию методов.мках самой фирамы. снижению и желание объективн

3блица 3.13диаграмме какие – ни________________________________________________________________________________________________= ,03 подгрупп ()ых изделий и соберите 20 - 25 в каждую подгруппу попордпло ___________________________________________________

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.

3) Trend (drift). If points form the continuous raising or lowering curve, say that the trend takes place.

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.

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.

6 Frequency. When the curve repeats structure "that rise, recession" with approximately identical intervals of time, it too is abnormal.

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"

6 Vida of control

7 Methodology of statistical quality control

8 Statistical methods applied in technological process

9 A role of statistical methods in management of productions

10 Basic purpose of control sheets. Give an example of filling of control sheets

11 What issues when conducting technological process are resolved on the basis of Pareto's chart. Stages of creation of the chart of Pareto.

12 Main objective of use of DPR and structure of the chart of the reasons and results. Give a concrete example.

13 Appointment and types of control cards. Give an example of drawing up control cards.

Literature:

1 Лапидус В.А. Система статистического управления процессами. Система Шухарта // Методы менеджмента качества. Надежность и контроль качества, № 3, № 5, № 7, 2002.

2 Каплан Р., Нортон Д. Сбалансированная система показателей: от стратегии к действиям. — М.: ЗАО "Олимп-Бизнес", 2003.

3 Мазур И.И., Шапиро В.Д. Управление качеством: учебное пособие. - М.: Высшая школа, 2003. - С. 75-77.

4 Современное управление качеством на предприятиях: методы, инструменты, рекомендации. А.Ю. Афонин, В.А. Васильев, С.В. Васильева, П.В. Москалев, С.А. Одиноков, В.С. Родионов, М.А. Скворцов. - М.: ИТЦ «МАТИ» - РГТУ им. К.Э. Циолковского, 2002.

5 Аристов О.В. Управление качеством: Учеб. пособие для вузов.- М., 2007

Lecture 14

Theme: External and internal audit of the quality system: Audit conditions. Plan of audit. Documentation of audit.

Lecture plan:

1 Basic concepts about internal audit

2 Main stages of carrying out internal audit

3 Requirements to resources

4 Requirements to auditors - the principles, competence

5 Criteria of productivity of process

6 Working procedures

7 Documentation of internal audit (Appendix)

8 Certification of quality systems

8.1 Purposes and conditions of carrying out certification of quality systems

8.2 Carrying out certification of quality systems

8.3 Final meeting

8.4 Inspection control of the certified quality system

1 At introduction and functioning of quality management system at the enterprise (organization) procedure of planning and the organization of carrying out objective and independent internal audits of QMS, assessment of compliance to the carried-out activity to requirements of the RK ISO 9001:2001 ST standard, policy of the enterprise in the field of the quality, the Quality manual and other documents QMS used by the checked organization (division, department, the top management and the director), documentary registration of the conclusion by results of audit, use of these results for maintenance of procedures and processes of QMS in working order and for improvement of procedures, processes of QMS and Quality management system in general is developed.

Procedure serves as the management for auditors (internal), the booking internal audits, to heads of divisions of the enterprise, owners of procedures and processes of QMS. Carrying out internal audits requires knowledge of such concepts as:

Criteria of audit - set of policy, procedures or requirements

Audit area - volume and borders of audit

The plan of audit - the description of activity and actions for audit

The checked organization - the organization subjecting to audit (division of the organization).

"Internal audit" is the process purpose:

- planning of internal audits; carrying out objective and independent internal audits of QMS;

- an assessment of compliance to the carried-out activity to requirements of the RK ISO 9001:2001 ST standard, Policy of the enterprise in the field of quality, Quality manuals, other processes and procedures, and also the standard documentation used by the checked organization (division, department, group, the top management);

- an assessment of compliance to the carried-out activity to requirements of the Consumer;

- documentary registration of the conclusion by results of audit;

- use of results of audit for maintenance of procedures and processes of QMS in working order and for improvement of procedures, processes of QMS and Quality management system in general;

- improvement of methods and procedures of carrying out internal audits;

- continuous increase of competence of internal auditors.

Constantly carried out internal checks and works on identification and elimination of discrepancies provide confidence of the consumer as production of the enterprise.

- internal audits (checks) can be planned and unplanned.

- planned audits are booked according to the schedule of carrying out the internal audits made and approved till December 20 of the current year the next year.

- unplanned audits are booked out of the annual schedule of carrying out internal audits according to the indication of the top management and the representative of the management in the following cases:

a) on request of consumers;

b) changes of organizational structure of the organization;

c) modification of QMS;

d) preparation for certification of QMS;

e) possibility of emergence of problems with quality;

- by inquiries of the organization additional internal audits can be booked.

The representative of a quality manual is responsible for carrying out internal checks. Belongs to its duties:

- definition of the checked organization, areas and the purpose of audit;

- development and the statement at the top management of the annual schedule of carrying out internal audits;

- development and the statement at the top management of the schedule of unplanned internal audits;

- organization of planning and carrying out internal audits;

- operating control and assessment of results of internal audits;

- control of timely registration of reports on audit;

- control of works on development and performance of the correcting and/or precautionary measures for elimination of the discrepancies revealed during audit;

- control of registration and storage of documents on internal audits;

- methodical help to auditors;

- organization of discussions of results of audits;

- permission of the possible conflict situations arising during internal audits;

- preparation of data on results of audits for the analysis from the top management and for process of continuous improvement.

The service of quality of the enterprise annually forms structure of the experts capable to carry out internal quality checks. The structure of these experts is approved by the order on the enterprise and made out in a matrix of distribution of responsibility.

3 of a stage of carrying out internal audits treat the main:

Name of stages of process	The responsible	Records (output)
1	2	3
1 Planning of internal audit	Representative of a quality manual	The schedule of carrying out internal audits (the approved form)
2 Choice of group on audit	Representative of a quality manual	The list of internal auditors the appendix Zh, the Personal leaf of the accounting of the auditor (the approved form)
3 Scheduling of audit and the notification of the checked division	Head of group on audit	Plan of audit appendix L
4 Preparation for carrying out audit	Auditors	The auditor questionnaire the appendix K of the Task to internal auditors (the approved form)
5 Representation of auditors and appointment of attendants	Unit manager
6 Carrying out introduction meeting and an explanation is more whole than audit	Head of group on audit
7 Direct carrying out audit	Auditors
8 discrepancy Is revealed? If yes, that transition to a stage 9, differently to a stage 10	Auditors
9 Registration of a leaf of the revealed discrepancies	Auditors	Leaf of the revealed discrepancies (the approved form)
10 The volume of check is finished? If yes, that transition to a stage 11, differently to a stage 7	Auditors
11 Meeting of auditors and decision-making	Auditors	The report on audit (the approved form)
12 Final meeting	Auditors
13 Preparation of the report	Auditors
14 Elimination of discrepancies	Unit manager	Protocol of meeting
15 the Correcting measures are necessary? If yes, that transition to a stage 16, differently transition to a stage 20	Auditors
16 Development of the correcting measures	Division	Leaf of the revealed discrepancies (the approved form)
17 Realization of the correcting measures	Division	Oral message
18 Check (verification) of realization of the correcting measures
19 Objectives are achieved? If yes, that transition to a stage 20, differently to a stage 16	Auditors	Mark in Liszt of the revealed discrepancies (the approved form)
20 Preparation of the report on audit	Auditors	The report on audit (the approved form)
21 Mailing of the report on audit		List of mailing appendix P, PR-02
22 Preparation of data for the analysis from the management and for process of continuous improvement	Representative of a quality manual	Condition of carrying out internal audit of QMS of the enterprise (the approved form)
23 Storage of records on internal audit	Service of quality
Destruction of records on internal audit after a period of storage	Service of quality	The act of destruction of records (the approved form), PR-03