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USE OF 7 QC TOOLS AND 7 NEW QC TOOLS FOR ANALYSIS

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Page 1: Tqm-7 Qc Tools

USE OF 7 QC TOOLS

AND 7 NEW QC TOOLS

FOR ANALYSIS

Page 2: Tqm-7 Qc Tools

USE OF 7 QC TOOLS AND 7 NEW QC TOOLS FOR ANALYSIS

1. Stratify data.

2. Pareto diagram

3. Cause and effect diagram

4. Histogram

5. Check Sheets

6. Control Charts

To analyze

Quantitative Data

Page 3: Tqm-7 Qc Tools

QUALITY TOOLS

1. Brain Storming

- For identifying Problem & Solution

2. Process flow chart

- For understanding and defining the problem

Page 4: Tqm-7 Qc Tools

QUALITY TOOLS

3. Check sheets

- For collecting data

4. Stratification

- For grouping data

Page 5: Tqm-7 Qc Tools

QUALITY TOOLS

5. Pareto Chart

- For identifying vital few problems

6. Cause and Effect diagram

- For Analyzing Cause and Effect

Page 6: Tqm-7 Qc Tools

QUALITY TOOLS

7. Charts

- For Analyzing Problem and displaying data

(i) Bar Chart (ii) Pie-Chart

(iii) Bond Chart (iv) Line graph

(v) Radar Chart (vi) Histogram

Page 7: Tqm-7 Qc Tools

8. Scatter diagram

To analyze interrelationship between dependent and independent variables.

9. Control Charts

To monitor control of products and processes.

Page 8: Tqm-7 Qc Tools

BRAIN STORMING

Brain storming is a group technique for generating new, useful and creative ideas at various stages of problem solving.

It uses a few simple rules for discussion on a subject matter that contributes to originality and innovation.

Page 9: Tqm-7 Qc Tools

BRAIN STORMING

HUMAN THINKING

1. Analytical

2. Lateral

3. Creative

4. Logical and

5. Reverse

Page 10: Tqm-7 Qc Tools

BRAIN STORMING METHODS

1. Free wheeling or unstructured.

2. Round Robin or Structured.

3. Slip method.

Page 11: Tqm-7 Qc Tools

FREE WHEELING OR UNSTRUCTURED METHOD

In this method, the brain-storming team members give their ideas without any restrictions, either on number of ideas or on the order of members. One can give even hundred ideas at a time.

Page 12: Tqm-7 Qc Tools

FREE WHEELING OR UNSTRUCTURED METHOD

Advantages :• It is Spontaneous, stimulates creativity of

the individual.

• One can build his ideas on the ideas of others.

• Continuity helps in further thinking process.

Page 13: Tqm-7 Qc Tools

Free wheeling or unstructured method

Disadvantages :

• Slow thinking persons and persons lacking confidence may put shutters to their thinking, seeing the enthusiasm of the strong, dominating persons in the group.

• Many may speak simultaneously and hence confusion may prevail.

Page 14: Tqm-7 Qc Tools

Free wheeling or unstructured method

Disadvantages :

3. People may digress away from main point.

4. One may exhaust all points leaving others with no points. Hence involvement may be lost.

Page 15: Tqm-7 Qc Tools

ROUND ROBIN OR STRUCTURED METHOD

In this method, the team members sit in circle and the first member give only one idea at a time.

Then the chance is given to the next person.

This will go on and on until sufficient number of ideas are generated.

Page 16: Tqm-7 Qc Tools

ROUND ROBIN OR STRUCTURED METHOD

Advantages :

1. There is opportunity for every one in the group to give ideas.

2. Improves involvement and sustain interest.

3. Gives satisfaction to every one

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ROUND ROBIN OR STRUCTURED METHOD

Advantages :

4. Control of group is easy and hence less confusion.

5. Possible to generate maximum number of ideas due to hitch-hiking process.

Page 18: Tqm-7 Qc Tools

ROUND ROBIN OR STRUCTURED METHOD

Disadvantages :

1. An active member may loose interest as he wait for his turn, by which time his ideas have been told by others.

Page 19: Tqm-7 Qc Tools

SLIP METHOD

In this method, the members are giving their ideas on a slip paper.

Page 20: Tqm-7 Qc Tools

SLIP METHOD

Advantage :

1. This helps involve the shy and withdrawn persons.

2. When the group is big and arranging a meeting is difficult.

Page 21: Tqm-7 Qc Tools

SLIP METHOD

Disadvantage :

1. One cannot build ideas on others ideas.

2. Hitch thinking is not possible.

3. Illegible hand writing or improper presentations leads to problems.

4. Difficult to trace the originator and get clarifications, if required.

Page 22: Tqm-7 Qc Tools

SLIP METHOD

Disadvantage :

5. If analyzing is avoided, then ideas may not flow in.

6. It is very slow.

7. Due to these disadvantages it can be done in stages.

i.e. collect ideas and display them.

8. Then again go for more ideas.

Page 23: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

1. Choose a meeting place where there is no disturbance or distraction.

Page 24: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

2. Inform in advance the topic for brain storming.

- Topic is specific and clear

- Broad enough to include useful ideas

- Should not create only biased ideas or opinions in the minds of people

- Allow the required incubation period for people to think

and contribute.

Page 25: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

3. Create a lively and informal atmosphere to enable people to open up, contribute ideas and sustain interest.

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STEPS IN BRAIN STORMING

4. Assign a person in the group the task of recording the ideas as hey emerge.

Use a flip chart or back board or OHP for this purpose.

- They should be in full view of the group so that development of ideas by hitch-hiking is possible.

Page 27: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

5. Guests invitees who are knowledgeable on the subject may be invited.

Page 28: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

6. Encourage for free flow of ideas one at a time each person.

- If one cannot think of an idea at a given point of time, they

may say ‘Pass’.

Page 29: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

7. There should be no criticism or appreciation or laugh during brain storming.

8. No evaluation should be done during brain storming.

Page 30: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

9. Clarify, but do not explain or criticize the ideas.

10. Ensure

(i) ideas are specific

(ii) Broad based

(iii) Not biases

Page 31: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

11. Maximum time for a session could be 20-25 minutes.

12. To bring creativity, use five ‘W’ s and one ‘H’ (When, Where, Why, What, Who and How)

Page 32: Tqm-7 Qc Tools

STEPS IN BRAIN STORMING

13. If possible, allow members to incubate ideas for few days and brain storm again for new and more ideas.

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STEPS IN BRAIN STORMING

14. After the brain storming is over, take ideas one by one and evaluate critically and Objectively.

- While processing the ideas, combine and group similar ideas.

Page 34: Tqm-7 Qc Tools

EXAMPLE :

Problem: How to improve

performance?

1. Teachers should work more problems in class.

2. Teachers should not be very fast in class.

3. Teachers should not be very slow.

4. More home works.

5. More special classes.

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Problem: How to improve academic

performance?

6. Group discussions

7. More assignments

8. Text book should be available

9. More tutorials should be available.

10. Notes handouts should be given.

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Problem: How to improve academic

performance?

11. More industrial visits

12. More seminars

13. College functions should be minimum

14. Holidays should be less.

15. Mini-Project work.

Page 37: Tqm-7 Qc Tools

Problem: How to improve academic

performance?

16. Sufficient number of working days.

17. More class tests.

18. Questions should be clear.

19. Students should be interactive.

20. More tutorials.

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Problem: How to improve academic

performance?

21. More video shown.

22. Teachers should interact with students.

23. A permanent class room with teaching aids.

24. Allow late coming of students

25. Some courses on language.

Page 39: Tqm-7 Qc Tools

Problem: How to improve academic

performance?

26. Teachers should not be very strict.

27. Clear explaining of basics.

28. Teachers should complete problems in full with all steps at least for few typical problems.

29. Teachers should solve more problems.

30. Teachers should come prepared for the class.

Page 40: Tqm-7 Qc Tools

Problem: How to improve academic

performance?

31. More stress on theory.

32. Voice of teacher should be audible.

33. Not able to understand basics

34. Teachers should solve tough problems, not easy problems, in class.

35. Two continuous hours should be avoided.

Page 41: Tqm-7 Qc Tools

Problem: How to improve academic

performance?

36. Teachers should not deviate from subject matters.

37. Combined classes should be avoided.

38. Proper ventilation and lighting in class rooms.

39. Last row of student are unable to see black boards.

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Problem: How to improve academic

performance?

40. Assignment should not be given without teaching the basics.

41. Good teacher.

42. Laboratory with working equipment.

43. Students should be able to comprehend the subject matter.

44. Examination questions should be clear and within the syllabus.

Page 43: Tqm-7 Qc Tools

Problem: How to improve academic

performance?

45. Mistakes in the answer sheet should be pin pointed instead of string whole answer.

46. Re-test can be conducted for those students who got less than 40% marks.

47. Marks should be given for steps also instead of result.

Page 44: Tqm-7 Qc Tools

Problem: How to improve academic

performance?

48. Questions should not be twisted?

49. Problems not taught in class should not be asked?

50. No unexpected questions.

51. Syllabus should be more specific it should not be very wide or very general.

Page 45: Tqm-7 Qc Tools

Problem: How to improve academic

performance?

52. Reference books should be available at affordable cost.

53. Time for test should be sufficient.

54. Questions should be specific.

Page 46: Tqm-7 Qc Tools

PROCESS FLOW CHART

Description :

A process flow chart is a representation of sequences of operation of a process from the beginning to the end through certain symbols. It records the series of events, activities and decisions in a form which can be easily understood and communicated to all. A process flow of a manufacturing process is given in fig.1.

Page 47: Tqm-7 Qc Tools

Fig. 1. Flow chart of a manufacturing process

Page 48: Tqm-7 Qc Tools

By studying this chart and analyzing its details, potential problems in the process can be identified.

- They can identified bottle necks, redunt steps and non-value added activities.

- They can also identify where delays can occur.

- A more detailed flow chart would allow pin pointing of key problem areas.

Page 49: Tqm-7 Qc Tools

Therefore, to solve any problem, the process is drawn first. Then this chart is analyzed and any unwanted or cumbersome processes are eliminated.

Improvements can be accomplished by reducing, combining or eliminating steps.

A flow chart is used to solve problems in administration, manufacturing and service processes.

Page 50: Tqm-7 Qc Tools

Type of flow charts

There are three types of flow charts.They are :

1. High level flow chart.

2. Matrix flow chart.

3. Detailed flow chart.

Page 51: Tqm-7 Qc Tools

A high level flow chart gives the broad out line of the process and avoids the details. For example consider a process where customer sends a request for certain product. The following activities are involved to produce the product and supply it to the customer.

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1. Purchase of the raw material required to produce the product

2. Manufacturing the product.

3. Inspection of the product to ascertain its quality.

4. Sending the products to the customer.

Page 53: Tqm-7 Qc Tools

These activities can be represented in a chart as follows

Customer sends request for product

Purchase of raw material required for product

Manufacturing of product

Inspection of product

Sending the product tosupplier

Page 54: Tqm-7 Qc Tools

MATRIX FLOW CHART

These charts are sufficient to understand the overall picture and where details are not required. However, to understand and solve intricate problems.

These activities can also be represented in a matrix form as follows :

Page 55: Tqm-7 Qc Tools

MATRIX FLOW CHART

Sent

requestPurchase

Manufacture

product

Inspect

productStored

Send to

supplier

Customer

Inspection

Purchase

StoresManufacture

Page 56: Tqm-7 Qc Tools

These charts are sufficient to understand the overall picture and where details are not required. However, to understand and solve intricate problems in the process, more details are required. Therefore each one of the above activities can be split into various smaller activities.

Page 57: Tqm-7 Qc Tools

For example, before purchase of the material required for the product, it has to be verified whether the material required is already available in the stores. Only if the material is not available, it has to be purchased. Otherwise manufacturing of the product can be started immediately avoiding ‘Purchasing’ activity.

Page 58: Tqm-7 Qc Tools

The detailed flowchart for the purchasing activity is given below. Like this, the details of other activities such as manufacturing industries can also be split and represented in a detailed chart.

DETAILED FLOWCHART

Page 59: Tqm-7 Qc Tools

In the detailed flow diagram, certain specific symbols can be used to represent various activities they are :

Page 60: Tqm-7 Qc Tools

Start end symbol

Activity symbol

Decision symbol

Data base symbol

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Page 62: Tqm-7 Qc Tools

These Standardized symbols

are used by industrial Engineering. However they are not necessary for problem.

The detailed flow chart used to understand the possible problems, bottle necks in the process.

Page 63: Tqm-7 Qc Tools

For example, if delay occurs in the purchase activities and it has to be reduced significantly to reduce the lead time, then the existing activities can be studied and eliminate or modify some for the activities.

Page 64: Tqm-7 Qc Tools

In this process, sending enquiry every time can be avoided by selecting a supplier based on his reliability and quality of supplied items (Deming’s Principle). This will avoid activities form sending enquiry to finalizing the purchase the purchase order. Similarly improvement can be made in the other activities also.

Page 65: Tqm-7 Qc Tools

Manufacturing

Inspection

Is it Ok Rework

Inspection

ScrapAssembly

Is it OK

No

No

Yes

Page 66: Tqm-7 Qc Tools

EXAMPLE :

This cycle costs more for given output since it needs more area, more equipment, more personal, more stocks, more raw materials and more time. Moreover inspection is not adding any value to the product.

Page 67: Tqm-7 Qc Tools

This cycle can be simplified by removing the inspection activity based on the concepts of prevention instead of detection as follows and reduce cost.

Manufacturing

Assembly

Page 68: Tqm-7 Qc Tools

PROBLEM SOLVING PROCEDURE

1. Draw the flow chart for the existing process.

2. Analyze this chart and identify any unwanted, Cumbersome process.

3. Identify potential trowel spots, bottle, nicks etc.

Page 69: Tqm-7 Qc Tools

PROBLEM SOLVING PROCEDURE

4. Eliminate the unwanted process.

5. Improve the process by reducing combining or eliminating steps.

6. Re-draw new flow chart and compare.

Page 70: Tqm-7 Qc Tools

REVIEW EXERCISE

Draw a flow chart for the followingprocess.

• Manufacturing of a shaft.• Manufacture of a PCB.• Construction of a building.• Commissioning of a Transform.• Development of a software.

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Analyze the flow chart drawn above and suggest ways of improving in terms of number of activities, time, strain etc. Re-draw flow chart after improvements and compare.

Draw flow charts of processes pertaining to your branch of study

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EXAMINATION QUESTIONS

1. What is a flow chart?2. How flow charts are classified?3. What are the uses of a flow diagram?4. How flow diagrams are used for solving

problems. Explain with examples?5. What symbols are used for drawing a

flow chart? What are its advantage.

Page 73: Tqm-7 Qc Tools

DATA COLLECTION

(i) To evaluate quality.

(ii) To control process products.

(iii)To measure improvements.

(iv)To measure company’s performance

Page 74: Tqm-7 Qc Tools

Types of dataData could be collected from the availablerecords or by member of observations made.

The data are classified as:1. Measured data : The data is obtained by

using an instrument Eg: Dimension, Temperature etc.

2. Attribute data : Data obtained by classification Eg: No. of Students passed failed, No. of products accepted rejected.

Page 75: Tqm-7 Qc Tools

Process control information check sheets

Solder Bath Temperature

Checked by : Date :

Take readings of Temp. weariest to degree

Time Temp Time Temp

0800

0900

1000

1100

1200

60

62

59

58

59

1300

1400

1500

1600

1700

61

58

63

63

59

Page 76: Tqm-7 Qc Tools

Product Quality Assurance check sheet

Actual observation

No Parameter

1.

2.

3.

4.

Cleanliness

Surface finish

Paint finish

....................

Spec. 1 2 3 4 5

Clean

0.4

Glossary

Ok

0.3

ok

Ok

0.55

ok

Not ok

0.3

ok

Ok

0.4

ok

Ok

0.3

ok

Page 77: Tqm-7 Qc Tools

Defective Cause Check Sheet

TallyS.No

Defects

1.

2.

3.

4.

5.

6.

Scratch

Paint full

Bad finish

Bare meta

-

26

35

47

25

-

-

Page 78: Tqm-7 Qc Tools

This type of check sheet is used to generate information on cause and their correspondence to the observed defects.

Page 79: Tqm-7 Qc Tools

No  

 

operations Mon 

 

Tue Wed Thur Fri

AM PM AM PM AM PM AM PM AM PM

 

 

 1                    

 

1                    

 

 

 1                    

 

1                    

 

Surface finish . Blow holes. Poor finish . Distorted . Others

Page 80: Tqm-7 Qc Tools

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

                                   

Process Variation check sheet

Component Operations Nets Speed : 852 0.05

Page 81: Tqm-7 Qc Tools

Benefits of Data Collection

1. Right decision can be made.

2. Error due to subjective feeling or personal bias are avoided.

3. Agreement on decisions necessary rather than different

Page 82: Tqm-7 Qc Tools

Benefits of Data Collection

4. Measurement understandable to all.

5. Assessment of magnitude of improvements.

6. Identification of causes affecting quality and productivity

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Example: Absentness in a class due to various diseases

TallyNature of disease

-

Stomach Disorders & water borne diseases

Viral flu

Minor injuries, Head aches, fever

Others

No %

Total

19

14

5

2

40

47.5

35.0

12.5

5.0

100

Page 84: Tqm-7 Qc Tools

STRATIFICATION

For example, consider the followingproblems.

Two lathes were used to producecylindrical shaft using four operators intwo shifts. In two weeks time 96 shaftswere rejected out of 2400 shaftsproduced.

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STRATIFICATIONPROBLEM : IT REJECTS IN TWO WEEKS OUTOF 2400 PARTS TWO LATHES USED BY FOUROPERATORS IN TWO SHIFTS

0

5

10

15

20

25

30

OP1 OP2 OP3 OP4

BASED ON OPERATORS

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BASED ON MACHINES

46

46.5

47

47.5

48

48.5

49

M/C1 M/C2

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BASED ON SHIFT

0

10

20

30

40

50

60

70

80

90

DAYSHIFT

NIGHTSHIFT

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CHECK SHEETS

1. DEFECTIVE ITEM2. DEFECTIVE CAUSE3. PRODUCTION PROCESS DISTRIBUTION4. INSPECTION

- CHECK UP CONFIRMATION- request item inspection

- to confirm customers request- evaluation item inspection

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METHOD MAN

STORE

TRANSPORT

MATERIAL MACHINE

SCRATCH

BIN

ARRANGMENT

SOFT WORK

HOLDINGMEASURMENT

CARELESSNESS

Page 90: Tqm-7 Qc Tools

CHECK SHEETSDEFECTIVE ITEM

Date

Defect20 / 4 21

Scratch

Stain

Crack

Others

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CHECK SHEETS

OPERATORM C

NO

MONTH

A

B

1

2

3

4

7 8 9

- Assembly miss- Changes its time taken- Control miss- Other

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Applications• Define the scope of the problem

• Define data collection requirements needed to verify a cause and effect relationship

• Define suspected casual conditions when problem occur

• For easy analysis of the problem

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PARETO DIAGRAMDescription

Pareto diagram is a pictorial arrangement of data in decreasing order of importance so as to enable prioritize problems for solution.

This is based on the principle of an Italian

economist Vilfredo Pareto.

He observed during his study on the distribution of wealth that 80% of the wealth is owned by 20% of population.

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PARETO DIAGRAM

DR. Joseph Juran later recognized this concept as universal that could be applied to many fields including industries.

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PARETO DIAGRAMFor example,

- 80% of money is spent on 20% of machines and materials.- 80% of defects one due to 20% of causes (root causes).- 80% of problems in a society come form 20% of people.- 80% of sales due to 20% of customers.- 80% of complaints due to 20% defects.

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PARETO DIAGRAM

Dimensional Error

Geometrical error

Surface scratch

Surface finish

No. %

9

6

42

3

60

15

10

70

5

100

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PARETO DIAGRAM

10

20

30

40

50

60

C A B DBefore Solving the problem

A Dimensional Error 9 9

B Geometrical Error 6 6

C Surface scratch 42 4

D Surface finish 3 3

A B C DAfter Solving the problem

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Elements of a Pareto Diagram

Pareto diagram and tables include three

basic elements. They are :

1. All factors which are responsible for the total effect are arranged in a descending order. This gives clarity regarding the level of contribution of each factor.

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Elements of a Pareto Diagram

2. The levels of contribution of each factor so expressed numerically (in quantity as well as percentage)

3. The cumulative curve shows the total of ranked contributions.

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Construction of a Pareto diagram

1. Determine the methods of classifying the data by problem, cause, non-conformity etc,

2. Decide the factors to be used to rank the characteristics

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Construction of a Pareto diagram

3. Collect data an appropriate time interval

4. Summaries the data and rank order from largest to smallest (descending order)

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Construction of a Pareto diagram5. Construct the diagram and find the vital

few.

6. Compute the cumulative values in number and percentage and plot the cumulative curve.

7. After solving a problem, repeat steps 4 through 6 and compare the diagram and measure the percentage improvements.

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Class Average marks

Xth Standard

+2

I year B.E

II year B.E

III year B.E

IV year B.E

80%

90%

50%

55%

60%

70%

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CAUSE AND EFFECT DIAGRAM

• Developed by Dr. Kaoru Ishikahawa in 1943.

• It is also called Ishikawa Diagram or Fishbone diagram.

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CAUSE AND EFFECT DIAGRAM

It includes• EFFECT ON THE RIGHT HAND

SIDE• MAJOR CAUSES• SUB CAUSES• CAUSE AND EFFECT ARE

CONNECTED BY ARROWS

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CAUSE AND EFFECT DIAGRAM

PROCEDURE1. Identify the causes through brain

storming.

2. Classify the causes under major causes such as MAN, MACHINE, METHOD, MATERIAL

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CAUSE AND EFFECT DIAGRAM

3. Evaluate causes to determine most likely Causes.

4. Develop solutions to correct causes.

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METHOD MAN

STORE

TRANSPORT

MATERIAL MACHINE

SCRATCH

BIN

ARRANGMENT

SOFT WORK

HOLDINGMEASURMENT

CARELESSNESS

CAUSE AND EFFECT DIAGRAM

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Types of chart

The common types of the chart are:

1. Run chart (Line graph)2. Bar chart3. Pie chart4. Radar chart

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Bar Chart

Year Net Profit (in lakhs)

1997

1998

1999

2000

2001

22.75

27.10

48.50

42.83

44.80

Page 111: Tqm-7 Qc Tools

0

10

20

30

40

50

60

70

80

90

X XII I II III IV

BAR CHART

SEM SEM SEM SEM

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Run chart (Line graph)

Instead of Drawing bars, if the performance values are plotted as points and if these points are joined by a line, then this becomes a run chart or line graph. Line graph is used for observing quantity changes over time or changing trends.

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Run Chart

0102030405060708090

100

X XII I SEM II SEM III SEM IV SEM

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Pie chart

The Pie chart shows the parts in a whole this used for showing relative proportion of various components. For example, the expenditure of a government under various heads such as defense, salary, development etc., may be shown as circular segments.

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PIE CHART

CUPS21%

BAGS36%CO VERS

43%

PERCENTAGE CONTRIBUTION OF NON BIO DE CRADABLE SUBSTANCE

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Band Graph

Band graph is another form of a pie-chart instead of dividing a circle according to the parameters a long rectangular strip is divided into various segments as shown in fig.

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BAND GRAPH

CUPS21%

COVERS44%

BAGS36%

PERCENTAGE CONTRIBUTION OF NON BIO DE

GRADABLE SUBSTANCES

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Radar chart

When more than two parameters are used to measure the performance, then a radar chart can be used. A radar chart consists of as many lines as there are parameters starting at a point and extending with equal angular division. Each line is divided into scale values of respective parameter.

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Radar chart

0

50

100Dimension

Surface finish

geometryscratches

Blow holes

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SCATTER DIAGRAM

DescriptionA scatter diagram is graphical representation of relationship between two variables, one variable is called independent variable. For example, wear of a machine tool increases with time of operation. That is wear depends on time. Therefore amount of wear depends on time. Therefore amount of wear is dependent0 variable whereas time is independent variables.

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7.00 8.00 9.00 10.00 11.00 12.00 1.00 2.00 3.00 4.00 5.00 6.00

TEMP

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Time Temperature At Pondicherry At Trichy At Trichy6.00 AM 22 21 23 207.00 AM 23 23 24 218.00 AM 24 22 25 239.00 AM 25 24 26 2410.00 AM 26 25 27 2611.00 AM 27 26 28 2712.00 AM 29 30 29 311.00 AM 31 31 30 312.00 AM 34.00 35 36 333.00 AM 33 32 34 314.00 AM 30 31 32 295.00 AM 29 28 30 276.00 AM 28 27 29 26

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HISTOGRAMDescription

Histogram is a graphical representation of frequency distribution at various levels about the target values. It consists of a set of rectangles that represent the frequency of the observed values in each category. If the heights of students of a class is measured and grouped at various heights, then the result will be as shown in fig below.

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HISTOGRAM

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Heights of persons