slides topic 6 op

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Planificación Agregada

Topic 6Quality Control

Operations Management

Economy and Business Organization Department

Quality Control 2

Index

Quality control Seven Ishikawa´s tools

Pareto chart / Cause-and-effect diagram / Check sheets / Histogram / Scatter diagram / Control chart / Stratification

Statistical Process Control (SPC) Analysis of the process capacity Acceptance sample Sampling by attributes Sampling plan. Characteristic curve. Bibliography

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Quality Control 3

Quality control

Evaluates the results of the process by comparing to the ideal results. If there is any difference between them, then the objective is to minimise it.

Apart from separating correct products (the ones that comply specifications) from defective products that must be redone, includes the prevention concept (actions to guarantee the expected results).

All the efforts dedicated to obtain products or services that comply design specifications at minimum cost.

Quality Control 4

Pareto chart Cause-and-effect diagrams Check sheets Histograms Scatter diagram Stratification Control chart

Ishikawa’s basic tools

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Quality Control 5

Pareto chart

Based on the idea that, in general, most defects in an article can be attributed to a reduced number of causes (Pareto Law 20-80)

Classifies few vital causes from the rest of trivial causes.

Pareto diagrams identify the causes of a quality problem rapidly and easily.

Quality Control 6

Pareto chart. Example

A company produces an article which presents several manufacturing defects. The objective is to remove them. Management wishes to know which are the causes of most defective items.

Defect type

Quantity of defective

articles

Accumulated quantities

% defective products

%

accumulated

Grated surface 198 198 66,00 66,00 Arm rupture 53 251 17,67 83,67 Spots 28 279 9,33 93,00 Adjustment 11 290 3,67 96,67 Tension 2 292 0,67 97,33 Others 8 300 2,67 100,00 Total 300 100,00

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Quality Control 7

Pareto chart. Example

0

50

100

150

200

250

300

Ral

lado

supe

rfici

al

Rup

tura

sbr

azo

Man

chas

Ajus

te

Tens

ión

Otro

s

Causes

Qua

ntity

of d

efec

tive

prod

.

0,00

20,00

40,00

60,00

80,00

100,00

% a

ccum

ulat

ed

If the two main causes of the problem are removed (grated surface and arm rupture), 84% of defective articles are avoided.

Quality Control 8

Cause-and-effect diagram

Cause-and-effect diagram, also known as Ishikawa diagramor fishbone, is used to classify and clear the causes that originate an effect.

It is necessary to identify and face the causes (and NOT the effects) to solve a problem.

The basic structure of these diagrams is a central arrow and thestudied effect is placed on the right. Consequently, firstly thequality problem must be defined and the effect that measures it.Then the causes are classified.

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Quality Control 9

Cause-and-effect diagram

The causes are placed tidily in the main branches:

Effect

Machines Personnel

Methods Materials

Inside these main branches, causes are placed in little branches. A brainstorming session can be performed previously to identify

the causes.

Quality Control 10

Variable dimension

Machines Personnel

Methods Materials

Stability

Operation

Inspection

Tools

Abrasion

Deformation

Motivation

Concentration

Abilities

Training

Experience Tiredness

Health

Illness

Orden

PositionAdjustm.

AngleWork

Variety

Procedure

Materials quality

Raw material

Storage

ShapeDiameter

Components

Final comment: the identified and classified causes are potential causes. This diagram is the starting point to verify and confirm the real causes.

Cause-and-effect diagram. Example

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Quality Control 11

Check sheets

Check sheets are printed sheets that allow data collection in a simple and precise way so that collection tasks are easier for the operators.

The fundamental objectives are: To ease data collection and organize data for further analysis.

There are different type of templates according to its application.

Quality Control 12

Check sheets for defective articles

They’re used to detect the type of defects and their frequency percentages in defective products in order to reduce them.

Código del Producto: 25312-A

Proceso: inspección final

Plantilla de inspección

Defectos: rallado, incompleto, deformado

Fecha: 12-marzo-97Operario:Lote:

I I I I

Tipo

Rallado

Fisuras

Deformado

Incompleto

Otros

Total

I I I I I I I I

I I I II I I I

I I I II I I I

I I I I

I I I I

I I I I

I I I II I I I

I I I

I I I I

I I I

I I I I

I I I I I I I I

I I 37

23

5

8

14

Total 87Observaciones:

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Quality Control 13

Sheets for defects location

Sketches of the manufactured piece where defects are located. They allow to detect if defects are always placed in the same place.

Quality Control 14

Check sheets to control the distribution of the production process

They’re used to collect data of continuous variables such as weight, diameter, volume,… Then, it is possible to draw an histogram to study the distribution of the production process, and calculate the average and dispersion.

Código del Producto: Proceso: Lote:

Plantilla de inspecciónFecha:Medidor:Observaciones:

I I I I

Dimensión

310-319320-329330-339340-349350-359

Total

I I I II I I II I I II I I I I I I I

I I I II I I II I I I

I I I I

I I I I

I I I I

I

I I I I I I I

I I I I

I I I I

I I I I

I I 2

211723

7

I I I I360-369370-379380-389390-399400-410

I I I I I I I I

I I I II I I I

I I I II I I I

I I I II I I I

I I I II I I II I I I

I I I

I I I I

I I I I I

I I I I I I I I

I I

I I I I

I I I I

I I I

I I

I I I I

I I

I

38

31178

34

420-429430-439

I I I II I I I

I I I 31

Frecuencias10 30 35 405 15 20 25 45

300-309

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Quality Control 15

Histogram

An histogram is a graphical representation of the distribution of data. Data is organised to study frequency of ocurrence.

Example: Consider 100 measurements of the diameter of a cylindrical

piece. The number of measurements n should be (at least) between 50 and 100 to study a certain characteristic.

Firstly, data is divided in 10 groups of 10 measurements. For each set of data, we determine the maximum and minimum values.

Quality Control 16

Histogram. Example

Data Max Min

7,38 7,39 7,41 7,19 7,26 7,52 7,39 7,20 7,41 7,40 7,52 7,19 7,31 7,42 7,43 7,39 7,28 7,33 7,32 7,37 7,36 7,26 7,43 7,26 7,35 7,33 7,23 7,58 7,39 7,45 7,35 7,29 7,42 7,35 7,58 7,23 7,40 7,36 7,36 7,38 7,48 7,39 7,44 7,36 7,42 7,28 7,48 7,28 7,35 7,35 7,38 7,46 7,36 7,39 7,19 7,28 7,41 7,38 7,46 7,19 7,29 7,29 7,42 7,53 7,38 7,35 7,39 7,39 7,28 7,41 7,53 7,28 7,53 7,26 7,36 7,42 7,39 7,34 7,34 7,27 7,39 7,20 7,53 7,2 7,38 7,34 7,42 7,45 7,35 7,38 7,38 7,44 7,29 7,38 7,45 7,29 7,51 7,52 7,45 7,36 7,38 7,37 7,39 7,46 7,42 7,30 7,52 7,3 7,33 7,44 7,34 7,34 7,33 7,33 7,37 7,36 7,37 7,41 7,44 7,33

Secondly, the amplitude of all data is determined: Maximum value – Minimum value = 7,58 – 7,19 = 0,39 This value is divided by k = 10 to obtain the number of classes (number of

groups or bars) of the graphic:

0,050,040,03910

0,39

kMinMaxh

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Quality Control 17

Histogram. Example.

The interval h is the unit to adjust the horizontal axis (bar width). In this case we consider 0,05.

The number of classes k depends on data collection:

The value that limits the first bar is fixed taking into account the extreme of the amplitude + half of the accuracy of collected data. In this case, the minimum value is 7,19 accuracy of real data is 0,01. Consequently, the limits of first bar is : 7,19 - 0,01/2 = 7,185

Rest of limits of bars will be: 7,185 - 7,235; 7,235 – 7,285; 7,285 –7,335; ...

Data collection n Number of classes k < 50 5 – 7

50 - 100 6 – 10 100 - 250 7 – 12

> 250 10 – 20

Quality Control 18

Histogram. Example

Then, the frequencies table must be calculated accounting data that belongs to each interval:

Frequency table Class Limits Aver.

nº Classes value

Frequencies Frequency 1 7,185 7,235 7,21 I I I I 4 2 7,235 7,285 7,26 I I I I 5 3 7,285 7,335 7,31 I I I I I I I I I 11 4 7,335 7,385 7,36 I I I I I I I I I I I I I I I I I I I I I I I I 29 5 7,385 7,435 7,41 I I I I I I I I I I I I I I I I I I I I I I I I I I I I 35 6 7,435 7,485 7,46 I I I I I I I I 9 7 7,485 7,535 7,51 I I I I 4 8 7,535 7,585 7,56 I I 2 9 7,585 7,635 7,61 I 1

N = 100 These data allows to draw the histogram. In Cartesian axis, horizontal axis

represents a quality characteristic and the vertical axis represents the frequency (number of data inside one bar).

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Quality Control 19

Histogram. Example

Consider that the diameter tolerances are between 7,15 cm and 7,55 cm

In this case the process is off-centre. A certain number of pieces are produced outside specifications limits.

0

5

10

15

20

25

30

35

40

7,15 7,21 7,26 7,31 7,36 7,41 7,46 7,51 7,56 7,61 7,70

Freq

uenc

yas

Lower specification limit Upper specification limitEach bar limit is a class. Bar width is a class interval. The central value is the average value.

Quality Control 20

Histograms. Examples

These two cases show the same frequency distribution BUT case 1is centered inside the tolerance limits. Nevertheless, case 2 is an off-centre distribution and shows that some articles are produced outside specifications (grey bars).

LTI LTS LTI LTS

Case 1 Case 2

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Quality Control 21


Case 3 is a bell-shaped distribution that represents a variability due to random causes. Ideal distribution.

Case 4 shows a right-skewed histogram. The right tail is longer and mass of distribution is concentrated on the left. This indicates that data does NOT follow normal law.

Case 3 Case 4

Quality Control 22


Case 5 is a bimodal histogram because it presents two peaks. In some cases indicates that data can be divided in two subsets of data that differ from each other in some way.

Case 6 is distribution that shows a small peak on the right. This indicates defects or errors because these data does not follow the general behaviour. Probably an assignable cause can be determined.

Case 5 Case 6

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Quality Control 23

Histograms. Functions

It’s a tool used to:

1) Verify if production is inside specifications. 2) Determine the behaviour of the distribution of data by

observing the histogram shape. 3) Analyse if stratification is necessary due to interference

of different factors that can affect variability. In this case, data are separated is subsets to differentiate causes of dispersion and to identify the origin of the problem easily.

Quality Control 24

Scatter diagram

These diagrams are useful to analyse whether a quality characteristic and a factor are related. Also they’re called correlation diagrams.

Steps to make a scatter plot: Identify the factors that seem to be correlated. Take 50 pairs of data approximately. Draw Cartesian axis to place the pairs of data. The quality characteristic is located in Y-axis.

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Quality Control 25

Scatter diagram. Example

Nº X Y Nº X Y

1 60,8 25,0 26 61,5 25,12 61,2 26,0 27 64,0 29,33 60,3 24,8 28 63,1 29,14 62,5 27,3 29 63,5 28,55 61,3 27,8 30 64,8 29,96 60,8 25,9 31 62,0 27,57 63,0 27,4 32 62,9 26,18 61,5 26,8 33 62,5 26,09 63,4 29,5 34 64,0 28,0

10 64,1 29,8 35 62,8 27,911 63,2 26,9 36 63,5 29,912 61,9 28,3 37 64,3 29,513 61,7 27,4 38 62,6 26,814 62,6 28,6 39 62,2 25,815 63,9 27,3 40 63,1 28,516 61,8 26,7 41 62,8 27,317 61,8 26,0 42 62,4 28,418 60,5 25,3 43 63,5 27,619 60,9 27,5 44 63,7 28,520 63,8 29,4 45 62,2 27,021 64,5 30,6 46 62,0 26,822 65,0 30,4 47 61,9 25,123 62,8 29,3 48 63,4 28,224 63,8 30,1 49 61,0 25,025 60,9 26,6 50 64,3 28,0

Variable X is a possible cause and Yis the quality characteristic that seems correlated.

Quality Control 26

Scatter diagram

Both variables present certain positive correlation. In other words, the quality characteristic is related to the cause as suspected.

24,0

25,0

26,0

27,0

28,0

29,0

30,0

31,0

60,0 61,0 62,0 63,0 64,0 65,0 66,0

Cause

Qua

lity

char

acte

ristic

14

Quality Control 27

Scatter diagram

It is possible to calculate the correlation coefficient quantitively:

In the example: SXX = 71,56; SYY = 122,53; SXY = 74,46; r = 0,7952 (positive correlation)

The correlation coefficient takes values between -1 and 1. If the resulting value is close to 1, this indicates there is a strong positive correlation. If the value is close to -1, then the correlation is negative and if the value is close to 0, then the correlation is weak.

n

1i

n

1i

n

1ii

n

1ii

iiiiXYn

1i

n

1i

2n

1ii

2i

2iYY

n

1i

n

1i

2n

1i

i2i

2iXX

YYXX

XY

n

)Y).(X(.YX)Y).(YX(XS;

n

)Y(Y)Y(YS

n

)X(X)X(XS;

.SSSr

Quality Control 28

Stratification

It’s a method to identify the origins of variability of collected data.

For example, when an article is manufactured by different machines, by different operators or using different materials, then it’s advisable to classify the data by machinery, operators or materials. This way, it’s possible to identify the origin of the problem. Maybe this could not be detected if all data is mixed.

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Quality Control 29

Stratification. Example

Stratification is one of the seven basic Ishikawa tools. Normally complements the rest of methodologies.

Diagrama bivariant

0

100

200

300

400

500

600

700

10,0 10,1 10,2 10,3 10,4 10,5 10,6 10,7 10,8 10,9 11,0Variable x

Vari

able

y

Quality Control 30

Statistical Process Control

Statistical Process Control (SPC) is the application of statistical techniques to measure and analyse the variations of a production process.

Causes of these variations can be: random and assignable.

Random causes: They cannot be controlled and they appear at random. They affect all production processes and always they

can be considered.

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Quality Control 31

Random and assignable causes

Assignable causes: They can be studied and are the ones that contribute

most to the variability of the process. Usually, they’re due to tiredness of workers, different

grade of experience/training, different behaviour of materials,… so that it’s NOT possible to obtain identical products.

The same happens in service industries: a cook CANNOT obtain two identical dishes or a lecturer CANNOT repeat two identical classes,…

Quality Control 32

Process capacity

Process capacity is defined as the variability amplitude of a process when this is under control; in other words, when variability is not due to assignable causes.

When a product is designed, the nominal value and a tolerance margin is defined. The tolerances interval defines the limits inside which the product is considered correct. This interval of tolerances is limited by an upper tolerance limit (LTS) and lower tolerance limit (LTI).

For example:

10 0,05 mm

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Quality Control 33

Control graphics

The objective of a control graphic is to differentiate variations due to random causes or due to assignable causes.

The vertical axis represents the range of the studied quality characteristic. Also, the lower tolerance limit, the upper tolerance limit and the average are placed on the graphic.

The horizontal axis represents time. This way, the evolution of the quality characteristic can

be observed vs. time. Also, it can be compared with respect to established control limits.

Quality Control 34

Control graphics

Types: Control graphic by variables. Control graphic by attributes.

VC

LCS

LCI

Tiempo

Normal variation due to random causes

Variation due to assignable causes.

Variation due to assignable causes

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Quality Control 35

Control graphic by variables

Control graphic by variables: This means that measurements belong to a continuous quality characteristic such as weigth, length, speed, density, volume,…

In this case, the control graphics for the average and range will be plotted. To start with, at least 100-150 elements must

be measured (and grouped in samples of 4-5 units) to guarantee that the sample is significant.

Quality Control 36

Control graphic by variables. Example

Sample Value1 Value 2 Value 3 Value 4 Value 5 Average Range

1 15 14 13 14 14 14,0 2 2 16 14 12 13 15 14,0 4 3 13 15 15 11 12 13,2 4 4 15 15 14 15 18 15,4 4 5 14 13 16 14 14 14,2 3 6 16 15 15 15 16 15,4 1 7 15 14 15 16 15 15,0 2 8 15 14 15 15 16 15,0 2 9 14 16 14 14 13 14,2 3 10 14 18 14 14 13 14,6 5 11 12 13 12 12 15 12,8 3 12 15 15 12 15 11 13,6 4 13 15 18 15 14 14 15,2 4 14 16 15 15 13 15 14,8 3 15 13 16 16 15 16 15,2 3 16 18 17 15 13 14 15,4 5 17 14 12 14 14 17 14,2 5 18 15 13 14 14 15 14,2 2 19 16 14 14 12 15 14,2 4 20 14 16 18 14 19 16,2 5 21 14 18 13 13 18 15,2 5 22 13 19 15 14 14 15,0 6 23 13 14 15 14 18 14,8 5 24 14 12 11 16 12 13,0 5 25 17 14 15 13 17 15,2 4 TOTALS 14,56 3,72

25 samples of 5 measurements.

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Quality Control 37

Sample average:

For the first sample:

Sample range: R = Maximum Value – Minimum value For the first sample: R = 15 – 13 = 2 Global average for X and R:

In the example:

n

X

nX ...XXX

n

1i

in 2 1

14,05

14 14 13 14 15X1

k

R

kR...RRR;

k

X

kX...XXX

k

1i

ik21

k

1i

ik21

3,7225

455...442R;14,5625

15,213,014,8...13,214,014,0X


Quality Control 38

072,3*0.

:lim868,772,3*115,2.

:lim72,3:_

:

414,1272,3*577,056,14.

:lim70644,1672,3*577,056,14.

:lim56,14:

3

4

2

2

RDLCI

itcontrolLowerRDLCS

itcontrolUpperRVCvalueCentral

RGraphic

RAXLCI

itcontrolLowerRAXLCS

itcontrolUpperXVCvalueCentral

xGraphic

n A2 D3 D4

2 1,880 0,000 3,2673 1,023 0,000 2,5754 0,729 0,000 2,2825 0,577 0,000 2,1156 0,483 0,000 2,0047 0,419 0,076 1,9248 0,373 0,136 1,8649 0,337 0,184 1,81610 0,308 0,223 1,777

A2, D3 y D4parameters dependon n, the number ofelements of thesample:


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Quality Control 39

Graphic X

10,0

12,0

14,0

16,0

18,0

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

Samples

Ave

rage

s

LCS = 16,71

VC = 14,56

LCI = 12,41

Graphic R

0

2468

10

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

Samples

Ave

rage

s LCS = 7,89

VC = 3,72

LCI = 0


Quality Control 40

Graphic X: shows variation of the average of the process. Graphic R: shows variations of the process dispersion.

Consequently, control graphics are very interesting because they show variations of the average and dispersion at the same time and indicate process anomalies.

In this example, both average and range graphics show that the process is under control because:1. All the points are inside the control limits. 2. Points do not follow any particular tendency.


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Quality Control 41

Control graphic by attributes

An attribute is a quality characteristic that cannot be measured.

Control graphics by attributes classify the product as Acceptable or Defective.

For example, if a piece presents spots, we wish to know if the product shows this characteristic to determine if it is acceptable or defective.

Quality Control 42

Control graphics by attributes

Sample type Type of control Constant Variable

Umber of defective products Graphic np Graphic p

Number of defects Graphic c Graphic u

Since a defective products can have several defects, these graphics monitor the number of detected defects or the number of defects.According to this criteria and the sample, there are several types of graphics.

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Quality Control 43

Acceptance sampling

The acceptance sampling determines the percentage of products that verify specifications.

It is used to inspect elements that the company purchase to suppliers (raw material, components,…) or also pieces that have been processed in one step of the process and are evaluated before going into the next step.

This technique involves taking random lots of products, measuring a certain characteristic and then comparing it with a established standard. This is much cheaper than 100% inspection.

The quality of the sample is used to judge the quality of the complete production lot.

Sampling can be defined by variables or by attributes.

Quality Control 44

Simple sampling by attributes

The acceptance sampling is performed through a sampling plan.

A simple sampling plan is defined by the sample size, n, and by the acceptance number, c, ( maximum number of defects that can be found in the sample before rejecting the lot),...

If the inspected sample has a number of defects < c , the lot isaccepted.

If the number of detected defects is higher, then the lot is rejected or then it’s performed a 100% inspection.

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Quality Control 45

Simple sampling by attributes. Example

Consider that we wish to accept all production lots whose number of defective products < 2,5% and reject the rest.

Imagine a lot of 1.000 pieces that has a 4% of defective products.

The inspection has taken a sample of 20 pieces and none is defective Lot is accepted.

In this case, the sampling plan gives a wrong result. The 20 pieces sample could have showed at random, one, two, three,…defective pieces.

This fact is fundamental in sampling plans. It’s possible to reject good production lots or accept defective lots.

Quality Control 46

Simple sampling plan by attributes. Characteristic curve.

Each sampling plan has associated a characteristic curvethat describes the ability of the plan to distinguish between correct lots and defective lots.

Indicates the probability that the plan accepts lots of different qualities.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

Defects percentage w

Acc

epta

nce

prob

abili

tyPa

(w) 0,05 =Producer risk for AQL

AQL LTPD

0,10 = Consumer risk for LTPD

Correct lots Indifference zone Defective lots

Pa (AQL)

Pa (LTPD)

24

Quality Control 47

Characteristic curve. Concepts.

AOQ, Average Output Quality: AOQ = w . Pa (w)

AQL, Acceptable Quality Level:

Maximum number of defective articles inside a lot so that it is considered acceptable.

Lowest level of quality that the company accepts. Lots with this level of quality will be accepted.

LTPD, Lot Tolerance Percent Defective:

Level of quality of a defective lot. Lots with this quality level will be rejected.

Quality Control 48

Characteristic curve. Concepts.

From the producer perspective, a good sampling plan is one that has a low probability to reject correct lots.

Producer risk (): Probability that the lot is rejected even though the number of defective products is lower than AQL.

From customers or consumers perspective, the sampling plan, should have a low probability to accept defective lots:

Consumer risk ():Probability that the lot is accepted although the number of defective products ≥ LTPD

25

Quality Control 49

Sampling plan. Considerations.

Normally, the sampling plans are designed considering a producerrisk of 5% ( = 0,05) and a consumer risk of 10% ( = 0,10).

The selection of specific values AQL, LTPD, and is an economic decision based on costs, company policies or contract requirements.

Quality Control 50

Valores de LTD / NAC para: Valores de LTD / NAC para:

c = 0,05

= 0,10

= 0,05

= 0,05

= 0,05

= 0,01 n . NAC c = 0,01

= 0,10

= 0,01

= 0,05

= 0,01

= 0,01 n . NAC0 44,890 58,404 89,781 0,052 0 229,105 298,073 458,210 0,0101 10,946 13,349 18,681 0,355 1 26,184 31,933 44,686 0,1492 6,509 7,699 10,280 0,818 2 12,206 14,439 19,278 0,4363 4,890 5,675 7,352 1,366 3 8,115 9,418 12,202 0,8234 4,057 4,646 5,890 1,970 4 6,249 7,156 9,072 1,2795 3,549 4,023 5,017 2,613 5 5,192 5,889 7,343 1,7856 3,206 3,604 4,435 3,286 6 4,520 5,082 6,253 2,3307 2,957 3,303 4,019 3,981 7 4,050 4,524 5,506 2,9068 2,768 3,074 3,707 4,695 8 3,705 4,115 4,962 3,5079 2,618 2,895 3,462 5,426 9 3,440 3,803 4,548 4,130

10 2,497 2,750 3,265 6,169 10 3,229 3,555 4,222 4,77111 2,397 2,630 3,104 6,924 11 3,058 3,354 3,959 5,42812 2,312 2,528 2,968 7,690 12 2,915 3,188 3,742 6,09913 2,240 2,442 2,852 8,464 13 2,795 3,047 3,559 6,78214 2,177 2,367 2,752 9,246 14 2,692 2,927 3,403 7,47715 2,122 2,302 2,665 10,035 15 2,603 2,823 3,269 8,18116 2,073 2,244 2,588 10,831 16 2,524 2,732 3,151 8,89517 2,029 2,192 2,520 11,633 17 2,455 2,652 3,048 9,61618 1,990 2,145 2,458 12,442 18 2,393 2,580 2,956 10,34619 1,954 2,103 2,403 13,254 19 2,337 2,516 2,874 11,08220 1,922 2,065 2,352 14,072 20 2,287 2,458 2,799 11,82521 1,892 2,030 2,307 14,894 21 2,241 2,405 2,733 12,57422 1,865 1,999 2,265 15,719 22 2,200 2,357 2,671 13,32923 1,840 1,969 2,226 16,548 23 2,162 2,313 2,615 14,08824 1,817 1,942 2,191 17,382 24 2,126 2,272 2,564 14,85325 1,795 1,917 2,158 18,218 25 2,094 2,235 2,516 15,623

Tables

26

Quality Control 51

Bibliography:

Castán, J.M.; Guitart, L. y Núñez, A. (1999): Direcció de la ProduccióII. Barcelona: Edicions de la UOC.

Chase & Aquilano. (1992): Dirección y Administración de la Producción y de las Operaciones. U.S.A.: Addison-Wesley Iberoamericana.

Domínguez Machuca, J.A. et al. (1994): Dirección de Operaciones. Aspectos tácticos y operativos en la producción y los servicios. Madrid:McGraw-Hill.

Fernández Sánchez, E. y Vázquez Ordás, C.J. (1994): Dirección de la Producción. II. Métodos Operativos. Madrid: Editorial Civitas.

Heizer, J. y Render, B. (2001): Dirección de la Producción. Decisiones estratégicas (Sexta edición). Madrid: Prentice-Hall.

Ishikawa, K. (1985): Guía de control de calidad. Nueva York: UNIPUB. Juran, J.M. y Gryna, F.M. (1993): Manual de Control de Calidad. Madrid:

McGraw-Hill.

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