SUGGESTED STEPS FOR PROBLEM SOLVING · PDF fileFOLLOW UP/REVIEW METHOD Implement evaluation procedure, use Control Chart, have ... Boiler House Pare Mill Pulp Mill Finish Area Other

QCFI Publication Chart-1

STEP 1

IDENTIFICATION OF WORK RELATED PROBLEM

METHOD

a) Generate a list of problems using ‘BRAINSTORMING’

b) Prioritize Problems using ‘A’ ‘B’ ‘C’ analysis given

below.

‘A’ Category Problem

Minimum involvement of other departments in

solving them

‘B’ Category Problem

Involvement of other departments is a necessity

‘C’ Category Problem

Management sanction may be needed in

implementing the solution.

STEP 2

SELECTION OF PROBLEM

(First from ‘A’ Category list)

METHOD

a) ‘PARETO ANALYSIS’ or ‘RATING ’ based on past data

or system.

b) Register the selected problem with coordinating

agency.

c) Make a Milestone Chart indicating the time needed

for solving the selected problem.

STEP 3

DEFINE THE PROBLEM

METHOD

By using ‘FLOW DIAGRAM’

Note down the actual time taken.

STEP 4

ANALYSE THE PROBLEM

METHOD

‘DATA COLLECTION’ on the problem on all possible aspects


STEP 5

IDENTIFICATION OF CAUSES

METHOD

BRAIN STORMING and make CAUSE and EFFECT DIAGRAM


STEP 6

FINDING OUT THE ROOT CAUSES

METHOD

Identifying the main causes in ‘CAUSE and EFFECT

DIAGRAM’ by DATA COLLECTION and discussion


A SYSTEMATIC APPROACH NOT ONLY HELPS IN STUDYING THE PROBLEM INTHE PROPER PERSPECTIVE BUT ALSO TO MAKE USE OF PROBLEM SOLVING

TECHNIQUE AT THE APPROPRIATE PLACE

SUGGESTED STEPS FOR PROBLEM SOLVING

STEP 7

DATA ANALYSIS

METHOD

Using techniques LINE GRAPH, BAR GRAPH, PIE GRAPH,

AREA GRAPH, HISTOGRAM, STRATIFICATION, SCATTER

DIAGRAM etc.


STEP 8

DEVELOPING SOLUTION

METHOD

‘BRAIN STORMING’


STEP 9

FORESEEING PROBABLE RESISTANCE

METHOD

BRAIN STORMING

Identifying the probable constraints and finding ways to

overcome them.

Make a presentation to all involved with the solution i.e.,

Dept. Head, Facilitator, other officials and non-members

involved with the implementation. Discuss and evaluate

a system for implementation.


STEP 10

TRIAL IMPLEMENTATION AND CHECK PERFORMANCE

METHOD

Data collection after implementation compared with the

data collected before solving the problem. Collect fresh

data using control chart and watch process trends. Analyse

the result, discuss and incorporate the changes needed.


STEP 11

REGULAR IMPLEMENTATION

METHOD

Once validity is checked and improvement observed with

data, regular implementation can be effected.

Make the final Milestone Chart showing estimated and

actual time.

STEP 12

FOLLOW UP/REVIEW

METHOD

Implement evaluation procedure, use Control Chart, have

six monthly report for evaluation.

Make modifications if necessary.

All presentation should include up to date information.

MILESTONE CHART - QUALITY CIRCLE ACTIVITY PLANNING

Project study planning is an effective method by which Quality Circle members

attain the skill to plan their activities and effective time management


Quality Circle Name

Project

Project No.

Meeting Day

Time

Department Manager Facilitator Members' Name

Reason for selection

Date of beginning Date of completion

No. of projects completed

No. Activity Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1. Defining the problem

2. Analyzing the problem

3. Identifying the causes

4. Finding out the rootcauses

5. Data analysis

7. Foreseeing possibleresistance

6. Developing solution

8. Trial implmn. andchecking performance

9. Regular Implmn.

10. Follow-up/Review

Target Actual


GUIDELINES FOR CONSTRUCTING FLOW DIAGRAM

HIGH LEVEL FLOW DIAGRAM MATRIX FLOW DIAGRAM

DETAILED FLOW

DIAGRAM

WHEN TO DRAW FLOWDIAGRAMS?

1. For defining the

process flow.

2. For defining the

problem.

3. For identifying the

root causes.

4. For devising the

solution.

5. For implementing the

solution.

6. At the time of review/

follow up.

HOW TO DRAW A FLOWDIAGRAM?

Discuss the purpose of it.

Decide on your expectation.

Decide the boundaries.

Put each process in writingfrom the beginning.

When you come to adecision area follow one tillyou complete.

For unknown areas, checkup later on and complete.

Ensure every branch iscompleted.

Review it and ask othermembers also to review.

HOW TO ENSURE ACCURACY?

Ensure that it is about

actual process and not what

is intended.

Ensure rework loops are not

omitted.

Be honest about what you

do

Observe actual process

before drawing a Flow

diagram

Elicit support of other

members for accuracy and

completeness and allow

them to review it.

SYMBOLS USED IN

FLOW DIAGRAM?

Activity symbol Decision

symbol

Flow Lines Document

symbol

Data Base Connector

Start & End

USER SENDSINDENT

QUOTATIONOBTAINED

MATERIALORDERED

MATERIALRECEIVED

MATERIALMADE

INSPECTED USEROBTAINS

USER PURCHASE MANUFAC STORES INSPEC -TURER -TION

USER SENDSINDENT

QUOTATIONOBTAINED

MATERIALORDERED

MATERIALRECEIVED

MATERIALMADE

INSPECTED

USEROBTAINS

Flow Diagram is graphical or a pictorial way to depict a process. With the help of a flowdiagram we can show process sequence. It can be used to dissect a process for betterunderstanding and analysing. It can also be used for replanning or making a change.

The process may be a manufacturing process of a product (entire or segment), a serviceprovided, to convey some information or a combination of any of them.

START

Mtrl. needed

Mtrl. database

Is

it

there

Send Reqsn .

Mtrl.

Obtained

STOP

Raise Indent

Indent Recd.

Is it OK

Send Enqrs .

Qtn. OK

Return for correction

Place order

Mtrl. made

Mtrl. recd.

Inspection

Is it

OK

Take as stock

Put in

database

Return to supplier

Yes

Yes

No

No

YesNo

Yes

No

START

Mtrl. needed

Mtrl. database

Is

it

there

Send Reqsn .

Mtrl.

Obtained

STOP

Raise Indent

Indent Recd.

Is it OK

Send Enqrs .

Qtn. OK

Return for correction

Place order

Mtrl. made

Mtrl. recd.

Inspection

Is it

OK

Take as stock

Put in

database

Return to supplier

Yes

Yes

No

No

YesNo

Yes

No


GUIDELINES FOR CONDUCTING BRAINSTORMING

Brainstorming is a group technique for generating new and usefulideas. It uses a few simple rules for discussion on a subject matter

that contributes to originality and innovation.

TYPES OF BRAINSTORMING

a. Free Wheeling or Unstructured

No hold, no bar system. No limit on

number of ideas at a time. It is

spontaneous and stimulates the

creativity of the individual.

b. Slip Method

When you need the involvement of

a large groups such method is used.

c. Round Robin or Structured

Quality Circle uses this system.

KEY ELEMENTS CONCERNING HUMANCREATIVE ABILITY

(JP GUILFORD’S RESEARCH FINDINGS)

FLUENCY

Capability of producing maximum ideas within

a given time.

FLEXIBILITY

Ability for the mind to move from one aspect

to another.

ORIGINALITY

Innovative or new ideas one can think of.

AWARENESS

Ability to look ahead into future.

DRIVE

Willingness to participate and contribute

without any hesitation.

GUIDELINES FORCONDUCTING BRAINSTORMINGIN A STRUCTURED MANNER

1. Keep the participants, preferably,

between six to ten.

2. Make it very clear to all the

participants on what subject the

Brainstorming is done.

3. Give required time for incubation.

4. Enter the points on a Black Board,

Flip Chart or in a Transparency for

all to see.

5. Explain the guidelines.

6. One idea only at a time.

7. Contribution in turn.

8. You may pass.

9. Clarify the point but don’t explain

the ideas.

10. No criticism. Encourage them to

do ‘hitch hiking’.

11. If session looses grip, have a break

or change.

12. To bring creativity use five Ws and

one H (When, Where, What, Who,

Why and How) appropriately.

13. Get maximum number of ideas.

14. Guests are welcome but will abide

by the rules.

15. Clarify each contribution.

16. Agree on a evaluation criteria.


GUIDELINES FOR DATA COLLECTION

Data collection is nothing but collection of the required 'information' infigures for statistical analysis of a problem. This provides a sound basis

for decision making and corrective action.

SOLDER BATH TEMPERATURE

CHECKED BY : DATE:

TAKE READING OF TEMPERATURE NEAREST TO DEGREE.

TIME TEMP (deg. cen.) TIME TEMP (deg. cen.)

0800 60 1300 610900 62 1400 581000 59 1500 631100 58 1600 631200 59 . 1700 59

FUNCTIONALREJECT

PARAMETRICREJECT

CHECK SHEET (IN PICTURE) DEFECT IN CHIPS

USEFUL POINTS FOR DATACOLLECTION

� Be clear in mind about the

objective.

� Prepare the question which will

make it clear and precise.

� Collect data relevant to that

� Use data sheet, check sheet and/

or check list as per the

requirement.

� Keep them simple and easy.

� Reduce opportunities for error.

� Capture data for analysis,

reference and traceability.

� Form should be self explanatory.

� Analyse the collected data for its

credibility and relevance (for

whom, when or who collected the

data are important.)

� Present data in a way that clearly

answers the questions.

DATA SHEET

CHECK SHEET

CHECK SHEET (IN PICTURE)

M/L No.: Shop manager :Location: Supervisor:

Component Check PointsMonths

J F M A M J J A S O N D

Drive NoiseGear Box VibrationBearing TemperatureTransmitter Operation

ELECTRICMotorControl OperationWiring AgeInstrumentation

CHECK LIST TYPE CHECKSHEET

5

10

15

20

25

30

35

40

45

50

-20

and

bel

ow

-20 -15 -10 -5 0 +5 +10 +15 +20 +20

and

abo

ve

�Spec. Limit�

5

10

15

20

25

30

35

40

45

50

-20

and

bel

ow

-20 -15 -10 -5 0 +5 +10 +15 +20 +20

and

abo

ve

�Spec. Limit�


GUIDELINES FOR STRATIFICATIONS

Stratification is the process of separation of data into categories.It is normally done for identifying the categories contributing to the

problem tackled.

� Try to have the clarity of the problem. This will

normally help to identify the Stratification variables

to be selected.

� If we have ready information and if they are reliable

they can be straightaway used, otherwise, start

collecting data needed.

� Make sure that all Stratification variables are

identified for data collection.

� Data collected may be enormous, which will call

for establishing categories for each Stratification

variable.

� The categories may be discrete values or range of

values.

� Sort out the data into the categories of

Stratification variables.

� Now summarize the number in each category.

� If they are simple numbers then total them.

� If it is a range of values and needs further

classification provide it.

� Present the result in graphic form to enable

effective communication.

� Study the display.

� If you feel that Stratification has to be done in a

different way, go ahead and do it on the same

lines as stated above.

� Sometimes stratified information may need to be

further stratified.

� Once you are satisfied with the Stratification,

collect additional information, if needed to ensure

that the interpretation is right.

� Always present the total information of the work

done in an orderly manner to satisfy the concerned

that all aspects connected to the problem are

covered.

0

5

10

15

20

25

30

Supplier

ABC

Def

ectiv

e %

DEFECTIVE QUALITY - SUPPLIER WISE

0

5

10

15

20

25

30

35

40

45

50

Nar BeadKinked BeadPulled BeadPinched BeadOther

Type of defect

Def

ecti

ve %

DEFECTIVE DATA IN A SHIFT

0

5

10

15

20

25

ABC

WORKER

DE

FE

CT

IVE

%DEFECTIVE ASSEMBLIES

0

10

20

30

40

50

60

Machine AMachine B

Pro

duct

ion

%

Production machine wise

0

5

10

15

20

25

30

35

Boiler HousePare MillPulp MillFinish AreaOther

Process area

Pow

er c

onsu

mpt

ion

%

Power consumption process area wise

Material Based

Quality Based

Worker Based

Machine Based

Processing Based


USEFUL POINTS FORMAKING GRAPH

� Be clear on the purpose of

making a graph

� Arrange the information in order

� Decide on the type of graph

� Decide on the title

� Show the data

� Substance is more important

than method. Good graphs are

those which draw attention to

data

� Avoid distorting the information

� Make it easier for eyes to

compare

� Large amount of data should be

depicted in summary form and

then into finer details

� Let graph serve a clear purpose

of exploration, tabulation or

decoration

� Should be closely integrated

with statistical and verbal

descriptions of a data set.

GUIDELINES FOR MAKING GRAPH

Graph is a pictorial representation of data which, when presented, iseasily understandable. It helps to represent large amount of information

comprehensively and in a compact manner.

0

2

4

6

8

10

12

23 24 25 26 27 28 1 2 3 4 5 6 7 8

FOUNDRY REJECTIONS (FEB-MAR 1996)

%

0

50

100

150

200

250

Cause & effect diagram

Pareto chart

Check sheet

Graphs

Histogram

Control chart

ScatterDiagram

Stratification100

80

60

40

20

After Training

Before Training

8

7

6

5

4

3

2

1

0

87 88 89 90 91 92 93

Failure

Appraisal

Preventive

%

MA

TU

RE

WIS

E

PR

OH

IND

U

PR

OM

US

LIM

STR

ON

GW

EA

K

NO N

O

NO N

O NO

IND

EC

ISIV

E

68%78%

36% 34%

46%

28%

32%22%

36% 34%

46%

72%

J F M A M J J A S O N D

800

700

600

500

400

300

200

100MONTHLY

LAST 12 MONTHS CUMULATIVE

LINE GRAPH BAR GRAPH

PIE GRAPH PICTORIAL GRAPH

RADAR GRAPH STRATA GRAPH

FLOAT GRAPH ZEE GRAPH


GUIDELINES FOR MAKING PARETO DIAGRAM

Pareto Diagram is a technique of arranging data according to priority or importanceand using it into a problem solving frame work.

This helps to find out the “VITAL FEW” from the “USEFUL MANY” for problem selection.

These are the data of 150

defectives out of 100 fans

inspected.

Type of Defect Quantity

Motor winding 20

Bend in fan blades 15

Cracks on central rod 14

Capacitor 10

Scratches on surfaces 12

Regulator 40

Bend in screws 25

Others 14____

Total 150____

To make a Pareto Diagram

rearrange data table

Type of Defect Number ofDefects

Regulator 40

Bend in screws 25

Motor winding 20

Bend in blades 15

Cracks on central rod 14

Scratches 12

Capacitor 10

Others 14

___

Total 150___

Now arrange them in a table

showing.

a) Type of defect

b) Number or quantum of

defect.

c) Cumulative

d) Percentage of defect to

total and

e) Cumulative percentage

TYPE NUMBER CUM %TO CUM OF OF TOTAL %DEFECT FANS

F. Regulator 40 40 27% 27%G. Bend in Screws 25 65 17% 44%A. Motor winding 20 85 13% 57%B. Bend in wings 15 100 10% 67%C. Cracks in Central rod 14 114 9% 76%E. Scratches 12 126 8% 84%D. Capacitor 10 136 7% 91%H. Others 14 150 9% 100%

Total 150 100%0

102030405060708090

100110120130140150

100

90

80

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60

50

40

30

20

10

0

%

Qu

anti

ty (

No

s)

Draw a Graph as shown below:

Construct a bar diagram to

represent the data as per

tally sheet

Draw cumulative curve and

write down all valuesPareto Diagram before and after

solving a problem

0102030405060708090

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90

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%

Qu

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114126

136 100

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%

Qu

anti

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os )

0102030405060708090

100110120130140150

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114126

136 100

9080

7060

5040

3020

100

%

Qu

anti

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os )

Worker F

Worker EWorker C

Worker B

Worker A

Worker D

Worker G

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Worker G

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AFTER

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Worker B

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Worker C

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Worker G

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Worker F

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Worker D

Worker G

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AFTER

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Worker F

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Worker B

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Worker EWorker C

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Worker A

Worker D

Worker G

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Worker C

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Worker G

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Worker G

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Any defect in a component, a product or service could be due to one ormore causes. To find out the relationship between the causes and effect,a diagram is drawn systematically by mapping out all the probable causesinfluencing the effect. This is called a Cause and Effect Diagram.

TYPES OF C & E DIAGRAM

a. Dispersion analysis type

A diagram drawn asking ‘why

does this dispersion occur?’

This helps to organise and

relate the factors for

dispersion.

b. Production process classifica-tion type

This system follows the process

and all things that may affect

at various stages of processing.

c. Cause enumeration type

In this all possible causes are

simply listed. Causes must by

organised subsequently in

accordance with the product

quality.

HOW TO USE C & E DIAGRAM

i. Preparing itself is an

educational process.

ii. It can be used as a guide for

discussion.

iii. You can use it to find out

reasons behind the causes in a

systematic manner.

iv. It can be used to post data for

future reference.

v. A detailed C & E diagram

making exercise helps to have

an in depth knowledge about

the process.

vi. It can be used for any kind of

a problem.

DISPERSION ANALYSIS TYPE C&E DIAGRAM

d. For each sub cause sub sub causes identifed

c. For each main cause sub causes identifed

Defeat in acricketmatch

Batting Bowling

FieldingOthers

b. Four Main causes identified

a. An arrow with the box made and the defect iswritten

GUIDELINES FOR MAKING CAUSE AND EFFECT DIAGRAM (PART - 1)

DEFEAT IN TEST MATCH

Bowling

Inadequate pace attack

Spinners unable to

exploit conditions

Bowling lacked punch

Not enough Experience


Bowling

Inadequate pace attack

Spinners unable to

exploit conditions

Bowling lacked punch

Not enough

Experience

Not enough seamers in India

Fitness problem to few seamers




GUIDELINES FOR MAKING CAUSE AND EFFECT DIAGRAM (PART - 2)


Batting

Lack of Tech.To face Pacers

Not enough practice infast wickets

Batsmen lack goodbackfoot tech.

Differentwicketsbackhome

No time to practice

Bad teamSelection

Lack of foresight byselectors

Politics atregional level

Few batsmen havingfitness problems

Irresponsibleshots

Lack of concentration

No proper instructionsfrom Captain

Unsure of hisplace in team

Infighing inthe team

Main batsmenexposed to

new ball

Opening batters could not seethe new ball through

No specialistopeners

g. Complete analysis for the other subcause


Bowling

Inadequatepace attack


Indian pitch donot helpseamers

Very few Paceacademies

Fitness problem to few seamers

Bowling in netwithout properwarm up.

Spinners unableto exploit

conditions

Bowlinglacked punch

Not enoughExperience

e. For each sub sub cause sub sub sub causesidentifed


Batting


Bad teamSelection

Irresponsibleshots


new ball

f. Similar analysis for another sub cause

Def eatDef eatDef eatDef eat i ni ni ni n Mat chMat chMat chMat ch

Batting


Not enough practice infast wickets

Batsmen lack goodbackfoot tech.

Differentwicketsbackhome

No time to practice

Bad teamSelection

Lack of foresight byselectors

Politics atregional level

Few batsmen havingfitness problems

Irresponsibleshots

Lack of concentration

No proper instructionsfrom Captain

Unsure of hisplace in team

Infighing inthe team


new ball

Opening batters could not seethe new ball through

No specialistopeners

FINAL DIAGRAM

h. Similar analysis for another sub cause

Strategy

Improper fieldplacement

Improperbatting order

Captain cannotmotivate

Notrespected

byteammates Lot of new

batsmenLack of

foresight

Immaturity

Egoproblems

Lack ofstrategy

No basic strategy

Players do notcontribute

ego hassles

No time toprepare

No professionalstrategist consulted

No game plan to playfast bowling

Batsmen notstudied

Inability

No batsmentakes lead Lack of

proff . helpLack of

Videos

Badcaptaincy

Others

Strategy

Improper fieldplacement

Improperbatting order

Captain cannotmotivate

Notrespected

byteammates Lot of new

batsmenLack of

foresight

Immaturity

Egoproblems

Lack ofstrategy

No basic strategy

Players do notcontribute

ego hassles

No time toprepare

No professionalstrategist consulted

No game plan to playfast bowling

Batsmen notstudied

Inability

No batsmentakes lead Lack of

proff . helpLack of

Videos

Badcaptaincy

Others

Mis-fielding

Lack of practice

No specialistfielders

Bad field Placement

No Sp. Fielders atSp. positions

Wrong fielders at wrongpositionsNo game plan

Droppedcatches

No specialistslip fielders

Lack of catchingpractice

Bowlers not consulted

ego hassles

Bad fieldplacement

No fielders where batsmenplays his favorite shots

Lack of

strategy

Batsmen not

studied properly

Fielding

Mis-fielding

Lack of practice

No specialistfielders

Bad field Placement

No Sp. Fielders atSp. positions

Wrong fielders at wrongpositionsNo game plan

Droppedcatches

No specialistslip fielders

Lack of catchingpractice

Bowlers not consulted

ego hassles

Bad fieldplacement

No fielders where batsmenplays his favorite shots

Lack of

strategy

Batsmen not

studied properly

Fielding

Bowling

Inadequatepace attack

Spinners unableto exploitconditions

Kumble not a bigspinner of the ball

Wicket wasflat & grassy

Not enough spinners in team

Bowlinglacked punch

Main bowlers sick

Bad teamselectionNot motivated enough

Few bowlers lacked commitment


Fitness problem to fewseamers

Most sp in nersin a bad patch

Had to sacr ificespinner for extrabatsmen

Not enoughExperience

Regoina l po liticsHighlymotivatedoppos itio n

Flat track Frustatedspinners

Ind ian pitch d onot he lpseamers

Very few Paceacademies

Bowling in netwithot properwarm up.


GUIDELINES FOR MAKING SCATTER DIAGRAM (PART - 1)

Scatter Diagram is a graphical representation ofrelationship between two variables. It can be between a

Cause and Effect and between two causes

ANGLE BEFORE LAPPING

AN

GLE

AF

TE

R L

AP

PIN

G


AN

GLE

AF

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R L

AP

PIN

G

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. ....


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PIN

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. ....

.


AN

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( a )

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Positive correlation

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( a )

( b )

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Negative correlation

AN

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Possibility of a positivecorrelation

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Orientation angle (minutes)

before and after lapping in

quartz crystal unit

Same diagram in the form of a table

BEFORE

AFTER

10 20 30 40 50 60 70 80

80

60

70

60

50

40

30

20

10

No correlation

( b )

Possibility of a negative correlationDiagram with peak and trough

No After Before No After Before No After Before No After Before

1 37 36

2 41 39

3 41 45

4 42 46

5 44 44

6 47 48

7 48 51

8 51 57

9 53 42

10 55 47

11 46 48

12 47 48

13 58 55

14 58 58

15 53 49

16 54 46

17 46 48

18 67 69

19 71 68

20 70 72

21 71 73

22 76 77

23 80 70

24 71 73

No After Before No After Before No After Before No After Before

1 37 36

2 41 39

3 41 45

4 42 46

5 44 44

6 47 48

7 48 51

8 51 57

9 53 42

10 55 47

11 46 48

12 47 48

13 58 55

14 58 58

15 53 49

16 54 46

17 46 48

18 67 69

19 71 68

20 70 72

21 71 73

22 76 77

23 80 70

24 71 73

80

70

60

50

40

30

30 40 50 60 70

I

II

IIIIII

III

IIIIIII

IIII

2 6 8 3 5

1

5

4

7

6

1

80

70

60

50

40

30

30 40 50 60 70

I

II

IIIIII

III

IIIIIII

IIII

2 6 8 3 5

1

5

4

7

6

1


GUIDELINES FOR MAKING SCATTER DIAGRAM (PART - 2)

It also reveals the nature of relationship betweentwo variables and their approximate strength.

Σ Σ Σ Σ n = 25

Σ Σ Σ Σ x = 2147

Σ Σ Σ Σ Y = 899.7

Σ Σ Σ Σ X2 = 185597

Σ Σ Σ Σ Y2 = 32715.29

Σ Σ Σ Σ XY = 77749.2

DATA ON HARDNESS ANDTENSILE STRENGTH OFCOPPER ALLOY CASTING

STEP: 1

OBTAIN PAIRS OF OBSERVATION FOR

THE TWO VARIABLES UNDER STUDY

VALUE CALCULATION

STEP: 2

FIND OUT VALUES OF X2 ,Y2 AND XY OF

OBSERVATIONS

STEP: 3

FIND OUT ‘N’ AND OBTAIN

TOTAL OF X, Y, X2 ,Y2 AND XY

STEP: 4

SIMPLIFIED FORMULA FOR COEFFICIENT OF

CORRELATION

STEP: 5

SUBSITITUTE THE VALUES IN’STEP THREE’ IN THE

FORMULA

STEP: 6

FIND OUT THE VALUE OF ‘r’ IF THE ‘r2’ VALUE IS ABOVE 0.7

THEN THE CORRELATION IS USEFUL

r2 = 0.5710

and

100 r2 = 57.10

STEP: 7

FIND OUT 100 r2. THIS GIVES PERCENTAGE OF VARIATIN IN

‘Y’ INFLUENCED BY ‘X’ I.E., THE INDEPENDENT VARIABLE. IN

THIS CASE 100 r2 = 57.1. THEREFORE CORRELATION BETWEEN

THESE TWO VARIABLES IS USEFUL

483= 0.7557

639.15r =r =

ΣΣΣΣ xy -(ΣΣΣΣx) (ΣΣΣΣ y)

n

2

{ Σ { Σ { Σ { Σ X -ΣΣΣΣ x) ΣΣΣΣ y)

n n2

2( { Σ { Σ { Σ { Σ Y -

2}

(}

r =

(2147) (899.7)(2147) (899.7)(2147) (899.7)(2147) (899.7)25

( 2147) ( 2147) ( 2147) ( 2147) } (899.7 ) (899.7 ) (899.7 ) (899.7 )

}25 25

2 2

77749.2 −77749.2 −77749.2 −77749.2 −

{185597 −{185597 −{185597 −{185597 − {32715.29 −{32715.29 −{32715.29 −{32715.29 −

TestPiece

No.

Hardness(BHN)

X

Textile Strength(kg/mm 2 )

Y1. 84 38.02. 93 40.73. 89 35.34. 86 37.65. 87 36.26. 93 37.67. 88 33.18. 80 24.99. 68 28.3

10. 92 39.911. 69 31.812. 85 36.213. 93 39.114. 89 36.115. 91 39.516. 85 36.017. 90 37.918. 92 38.619. 76 32.320. 88 34.621. 87 39.822. 76 33.123. 92 38.824. 91 37.425. 83 36.9

2147 899.7

TestPiece

No.

Hardness(BHN)

X

Textile Strength(kg/mm 2 )

Y1. 84 38.02. 93 40.73. 89 35.34. 86 37.65. 87 36.26. 93 37.67. 88 33.18. 80 24.99. 68 28.3

10. 92 39.911. 69 31.812. 85 36.213. 93 39.114. 89 36.115. 91 39.516. 85 36.017. 90 37.918. 92 38.619. 76 32.320. 88 34.621. 87 39.822. 76 33.123. 92 38.824. 91 37.425. 83 36.9

2147 899.7

No. X2 Y2

1. 7056 1444.00 3192.02. 8649 1656.49 3785.13. 7921 1246.09 3142.74. 7396 1413.76 3233.65. 7569 1310.44 3149.46. 8649 1413.76 3496.87. 7744 1095.61 2912.88. 6400 620.01 1992.09. 4624 800.89 1924.4

10. 8464 1592.01 3670.811. 4761 1011.24 2194.212. 7225 1310.44 3077.013. 8649 1528.81 3636.314. 7921 1303.21 3212.915. 8281 1560.25 3594.516. 7225 1296.00 3060.017. 8100 1436.41 3411.018. 8464 1489.96 3551.219. 5776 1043.29 2454.820. 7744 1197.16 3044.821. 7569 1584.04 3462.622. 5776 1095.61 2515.623. 8464 1505.44 3569.624. 8281 1398.76 3403.425. 6889 1361.61 3062.7

185597 32715.29 77749.2

XYNo. X2 Y2

1. 7056 1444.00 3192.02. 8649 1656.49 3785.13. 7921 1246.09 3142.74. 7396 1413.76 3233.65. 7569 1310.44 3149.46. 8649 1413.76 3496.87. 7744 1095.61 2912.88. 6400 620.01 1992.09. 4624 800.89 1924.4

10. 8464 1592.01 3670.811. 4761 1011.24 2194.212. 7225 1310.44 3077.013. 8649 1528.81 3636.314. 7921 1303.21 3212.915. 8281 1560.25 3594.516. 7225 1296.00 3060.017. 8100 1436.41 3411.018. 8464 1489.96 3551.219. 5776 1043.29 2454.820. 7744 1197.16 3044.821. 7569 1584.04 3462.622. 5776 1095.61 2515.623. 8464 1505.44 3569.624. 8281 1398.76 3403.425. 6889 1361.61 3062.7

185597 32715.29 77749.2

XY


GUIDELINES FOR MAKING HISTOGRAM

Histogram is a graphical representation of a frequency distributionwhich is a summary of variation in a product or process.

1.97 2.49 2.29 2.24 2.42 2.16 2.89 1.75 2.24 2.07

2.20 2.52 2.32 2.10 1.98 1.96 2.16 1.94 2.13 2.43

2.45 1.76 1.91 2.06 2.04 2.52 2.02 1.95 2.31 2.16

2.00 1.96 2.00 2.29 2.33 2.08 2.23 2.05 1.92 2.25

2.36 1.87 1.95 1.92 2.14 2.08 2.17 2.13 2.08 1.92

2.04 2.00 2.08 1.86 2.34 2.05 2.04 2.16 1.74 1.96

1.83 1.95 2.17 2.02 2.23 2.07 2.08 2.64 2.17 2.02

2.45 1.76 1.91 2.06 2.04 2.52 2.02 1.95 2.31 2.16

2.00 1.96 2.00 2.29 2.33 2.08 2.23 2.05 1.92 2.25

2.36 1.87 1.95 1.92 2.14 2.08 2.17 2.13 2.08 1.92

POWER CONSUMPTION (kWh) OF REFRIGERATOR

1.97 2.49 2.29 2.24 2.42 2.16 2.89 1.75 2.24 2.07

2.20 2.52 2.32 2.10 1.98 1.96 2.16 1.94 2.13 2.43

2.45 1.76 1.91 2.06 2.04 2.52 2.02 1.95 2.31 2.16

2.00 1.96 2.00 2.29 2.33 2.08 2.23 2.05 1.92 2.25

2.36 1.87 1.95 1.92 2.14 2.08 2.17 2.13 2.08 1.92

2.04 2.00 2.08 1.86 2.34 2.05 2.04 2.16 1.74 1.96

1.83 1.95 2.17 2.02 2.23 2.07 2.08 2.64 2.17 2.02

2.45 1.76 1.91 2.06 2.04 2.52 2.02 1.95 2.31 2.16

2.00 1.96 2.00 2.29 2.33 2.08 2.23 2.05 1.92 2.25

2.36 1.87 1.95 1.92 2.14 2.08 2.17 2.13 2.08 1.92

POWER CONSUMPTION (kWh) OF REFRIGERATOR

Mark the lowest among Xs and highest valueamong XL

RowRow XsXs XXLL

1. 1.75 2.312. 1.84 2.493. 1.89 2.23

4. 1.74 2.295. 1.94 2.246. 1.91 2.287. 1.83 2.648. 1.93 2.549. 1.95 2.4610. 1.87 2.45

Calculate the approximate width ofclass intervals based on the formula(R+W) /K where

'R' = range = 0.90'W' = accuracy in observation = 0.01and'K' = No.of classes = 7

C = R + W = 0.90 + 0.01

K 7

= 0.13

Now specify the class boundaries.

The lower limit of the first class is

=X min - 0.5 W= 1.74 - 0.005 = 1.735

The Upper limit of the first class is

= 1.735 + C= 1.735 + 0.13= 1.865

Based on that we get

1.735 - 1.8651.865 - 1.9951.995 - 2.1252.125 - 2.2552.255 - 2.3852.385 - 2.5152.515 - 2.645

Class Tally Frequency

1.735 - 1.865 //// / = 61.865 - 1.995 //// //// //// //// //// / = 261.995 - 2.125 //// //// //// //// //// = 252.125 - 2.225 //// //// //// //// //// = 252.225 - 2.255 //// /// = 82.385 - 2.515 //// / = 62.515 - 2.645 //// = 4

Have 80-100 observations. Put them ina data sheet like above

Find the minimum (XS) and maximum (XL)in each line and circle them

Write them as follows

RowRow XsXs XXLL

1. 1.75 2.312. 1.84 2.493. 1.89 2.234. 1.74 2.295. 1.94 2.246. 1.91 2.287. 1.83 2.648. 1.93 2.549. 1.95 2.4610. 1.87 2.56

Number of RecommendedObservations No of classes or

groups (K)< 50 6

51 - 100 7 101 - 200 8 201 - 500 9 501 - 1000 10

Here N = 100therefore K = 7

Compute the range

R = X max - X minR = 2.64 - 1.74 = 0.90

0

4

8

12

16

20

24

28

1.54 1.67 1.80 1.93 2.06 2.19 2.32 2.45 2.58 2.71

Lower

spec.Limit

Upper

spec.Limit

FINAL DIAGRAMTYPES OF HISTOGRAM

Skewed Type Double Peaked Type

Comb Type

Isolated Peak Type Plateau Type


GUIDELINES FOR CONSTRUCTING CONTROL CHART (PART - 1)

Control Chart is a graphical device to aid in process control. It consistof a graph with a central line denoting the target value or standard andtwo limit lines on either side of the central line called 'Upper ControlLimit' and 'Lower Control Limit'. Quality measured periodically is plottedon the chart and status of control assessed.

498 502 500 498 500 500 494 500 492 502 502 502 500 500 504 498 500 496 502 508

8.00 8.15 8.30 8.45 9.00 9.15 9.30 9.45 10.00 10.15 10.30 10.45 11.00 11.15 11.30 11.45 12.00 12.15 12.30 12.45

502 492 500 506 492 500 502 502 500 496 498 510 504 502 502 500 498 500 496 502

502 504 492 490 502 502 506 506 496 498 498 496 504 508 496 498 500 498 500 508

496 496 500 508 498 502 500 498 500 498 502 494 498 502 504 502 500 502 500 494

500 500 502 498 500 502 498 496 502 500 504 498 502 502 502 504 500 502 504 502

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

A) Collect samples at fixed interval and record the measurements

B) Total the value for each subgroup. Calculatethe average for each subgroup

We call each measurement as 'X' and the average of

the subgroup as XXFirst subgroup Second subgroup

498 502

502 492

502 504

496 496

500 500

______ ______2498 2494

Average = Total/Number of values

i.e. X1X1 = 2498

= 499.6

_____

5

X2X2 = 2494 = 498.8 and so on.

____

5

C) Calculate the overall average. This is called XX

Averages XX s = 499.6, 498.8, 498.8, 500 498.4, 501.2,

500, 500.4, 498, 498.8, 500.8, 500,

501.6, 502.8, 501.6, 500.4, 499.6,

499.6, 500.4 and 502.8.

Total of XX s = 10003.6

Number of XX s = 20

X = 10003.6 = 500.18 20

=

D) Determine the range for each subgroup

Range is equal to largest value minus smallest value.

Range for the first subgroup is 6, for second 12 and

so on.

First subgroup is = 498, 502, 502, 496, 500

Range (R) = 502-496 = 6

Second subgroup is = 502, 492, 504, 496, 500

Range (R) = 504-492 = 12

E) Calculate the average range

Ranges are =

6, 12, 10, 18, 10, 2, 12, 10, 10,

6, 6, 16, 6, 8, 8, 6, 2, 6, 8 & 14.

Total = 176

Average = R = 176 = 8.8 20

F) Calculate the control limit for XX

Read A2 from standard factor table to determine 3 σ

limits. For subgroup size 5, A2 = 0.577

* Used for estimating the standard deviation fromthe knowledge of R

2 1.880 --- 3.267 1.128 2.6593 1.023 --- 2.575 1.693 1.772

4 0.729 --- 2.282 2.059 1.457

5 0.577 --- 2.115 2.326 1.290

6 0.483 --- 2.004 2.534 1.184

D3

D4A2 d*2

3/d2

Size of SubGroup (n)

* Used for estimating the standard deviation fromthe knowledge of R

2 1.880 --- 3.267 1.128 2.6593 1.023 --- 2.575 1.693 1.772

4 0.729 --- 2.282 2.059 1.457

5 0.577 --- 2.115 2.326 1.290

6 0.483 --- 2.004 2.534 1.184

D3

D4A2 d*2

3/d2

Size of SubGroup (n)



G) Calculate the control limits for XX as

UCL–x = XX + A

2

RR = 500.18 + (0.577 x 8.8)

= 500.18 + 5.08 = 505.26

LCL–x = XX - A

2

RR = 500.18 - 5.08 = 495.10

H) Similarly Calculate the UCLR & LCL

R using

the factor D3 and D

4

For ‘D’ value use the standard table given above.

UCLR = D

4 RR

2.115 x 8.8 = 18.6

LCLR = D

3 RR = 0 x 8.8 = 0

I) DETERMINE THE SCALE FOR THE GRAPH AND PLOT THE GRAPH

Variable Control Chart ( X-R ) Part No. Chart No.1

Specification Limits5 0 0 m m + mm

CharacteristicPly width

ProcessBias Cutter

Part NameTruck Tyre Band Ply

OperatorK. Sunder

SUB GROUP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time 8.00 8.15 8.30 8.45 9.00 9.15 9.30 9.45 10.00 10.15 10.30 10.45 11.00 11.15 11.30 11.45 12.00 12.15 12.30 12.45

1. 498 502 500 498 500 500 494 500 492 502 502 502 500 500 504 498 500 496 502 508

2. 502 492 500 506 492 500 502 502 500 496 498 510 504 502 502 500 498 500 496 502

3. 502 504 492 490 502 502 506 506 496 498 498 496 504 508 496 498 500 498 500 508

4. 496 496 500 508 598 502 500 498 500 498 502 494 498 502 504 502 500 502 500 494

5. 500 500 502 498 500 502 498 496 502 500 504 498 502 502 502 504 500 502 504 502

SUM 2498 2494 2494 2500 2492 2506 2500 2502 2490 2494 2504 2500 2508 2514 2508 2502 2498 2498 2502 2514

AVERAGE X 499.6 498.8 498.8 500 498.4 501.2 500 500.4 498 498.8 500.8 500 501.6 502.8 501.6 500.4 499.6 499.6 500.4 502.8

AVERAGE X 6 12 10 18 10 2 12 10 10 6 6 16 6 8 8 6 2 6 8 1

MachineBias Cutter - 1

Measuring InstrumentSteel Tape

Unit of Measuremm

X = 500.18R = 88

505.26

500.18

495.10

18.6

6

x

R

LCL

LCL

X

X-R CHART

Time - Hours

8.8 R

R

UCL R

X

UCLX

505.26

500.18

495.10

18.6

6

x

R

LCL

LCL

X

X-R CHART

Time - Hours

8.8 R

R

UCL R

X

UCLX



While X - R and X Control Charts are used for continuous value(measurement) we have other control charts for discrete variables(Attribute Data)

1. 3/8 185 17 9.19

2. 4/8 210 22 10.48

3. 5/8 196 16 8.16

4. 6/8 214 26 12.15

5. 7/8 225 22 9.78

6. 8/8 176 18 10.23

7. 9/8 182 16 8.79

8. 10/8 203 25 12.32

9. 11/8 176 18 10.23

10. 12/8 95 10 10.53

11. 13/8 115 13 11.30

12. 14/8 202 19 9.41

13. 15/8 65 6 9.23

14. 16/8 160 14 8.75

15. 17/8 185 19 10.27

16. 18/8 203 21 10.34

17. 19/8 186 19 10.22

18. 20/8 125 14 11.20

19. 21/8 135 15 11.11

20. 22/8 185 19 10.27

21. 23/8 210 22 10.48

22. 24/8 167 18 10.78

23. 25/8 168 19 11.31

24. 26/8 123 14 11.38

25. 27/8 145 16 11.03

Total 4236 438

No. DateNo. of

defec-

tives

No.

In-

spected

% of

defec-

tive

1. 185 17 9.19 13.60 0.221 0.067 17.00 3.602. 210 22 10.48 14.49 0.207 0.063 16.60 4.003. 196 16 8.16 14.00 0.214 0.065 16.80 3.804. 214 26 12.15 14.63 0.205 0.062 16.50 4.105. 225 22 9.78 15.00 0.200 0.061 16.40 4.206. 176 18 10.23 13.27 0.226 0.069 17.20 3.407. 182 16 8.79 13.49 0.222 0.067 17.00 3.608. 203 25 12.32 14.25 0.211 0.064 16.70 3.909. 176 18 10.23 13.27 0.226 0.069 17.20 3.4010. 95 10 10.53 9.75 0.308 0.094 19.70 0.9011. 115 13 11.30 10.72 0.280 0.085 18.80 1.8012. 202 19 9.41 14.21 0.211 0.064 16.70 3.9013. 65 6 9.23 8.06 0.372 0.113 21.60 0.0014. 160 14 8.75 12.65 0.237 0.072 17.50 3.1015. 185 19 10.27 13.60 0.221 0.067 17.00 3.6016. 203 21 10.34 14.25 0.211 0.064 16.70 3.9017. 186 19 10.22 13.64 0.220 0.067 17.00 3.6018. 125 14 11.20 11.18 0.268 0.081 18.40 2.2019. 135 15 11.11 11.62 0.258 0.078 18.10 2.5020. 185 19 10.27 13.60 0.221 0.067 17.00 3.6021. 210 22 10.48 14.49 0.207 0.063 16.60 4.0022. 167 18 10.78 12.92 0.232 0.071 17.40 3.2023. 168 19 11.31 12.96 0.231 0.070 17.30 3.3024. 123 14 11.38 11.09 0.271 0.082 18.50 2.1025. 145 16 11.03 12.04 0.249 0.076 17.90 2.70

Tl. 4236 438 438 ÷ 4236 = 0.103

No.

No.inspected

(n)

% of

defective(p%)

No.of

defective (d)

PERCENTAGE DEFECTIVE CHART - P CHART

Place: Arcee Jute Mills Part: Gunny Bags Inspected by: DK Srivastava

20

18

16

14

12

10

8

6

4

2

3/8 4/8 5/8 6/8 7/8 8/8 9/8 10/8 11/8 12/8 13/8 14/8 15/8 16/8 17/8 18/8 19/8 20/8 21/8 22/8 23/8 24/8 25/8 26/8 27/8

Date

P %

P -CHART FO R % DEFECTIVE JUTE BAGSJUTE BAGS



LCL np = np-3 np (1- p )√

UCLnp = np+3 np (1- p )√

NUMBER DEFECTIVE CONTROL CHART - NP CHART

Place: Arcee Jute Mills Part: Gunny Bags

Inspected by: DK Srivastava Sample Size: 50

√ CUCLc = C + 3 √ CLCLc = C - 3

NUMBER DEFECTS CONTROL CHART - C CHART

Org: Balaji Carpet Ltd. Process: Final Inspection

Basis: Visual Inspector: Sanjay

UCLu = U+ 3 U/n

LCLu = U- 3 U/n

√√

NUMBER DEFECTS CONTROL CHART - U-CHART

Org: Balaji Carpet Ltd. Process: Final Inspection

Basis: Visual Inspector: Sanjay

Time Inspc.unit No. of Defects

08.00 1.00 308.30 1.00 409.00 1.00 609.30 1.00 110.30 1.00 410.30 1.00 311.00 1.50 711.30 1.50 412.00 1.50 212.30 1.50 013.00 1.50 513.30 1.50 614.00 1.80 714.30 1.80 415.00 1.80 315.30 1.80 216.00 1.80 316.30 1.80 417.00 1.80 1

Number defective due to

No.

Date

No. ins-

pected

No.of

def.bags

Cal.

cut

Snarl

Gaw

Warp

bkg.

Weft

bkg.

Bias

Stit.

gap

1. 3/8 50 4 1 2 12. 4/8 50 5 1 3 13. 5/8 50 8 1 2 3 24. 6/8 50 6 1 1 1 35. 7/8 50 7 2 2 36. 9/8 50 12 3 1 2 2 1 1 27. 10/8 50 9 2 4 38. 11/8 50 4 1 39. 12/8 50 3 2 110. 13/8 50 2 211. 14/8 50 1 112. 15/8 50 5 1 1 1 213. 16/8 50 10 2 2 3 314. 17/8 50 4 1 2 115. 18/8 50 6 1 2 1 216. 19/8 50 7 1 3 1 217. 20/8 50 4 1 1 218. 21/8 50 9 1 1 719. 22/8 50 8 1 4 320. 23/8 50 6 1 2 1 2

14

12

10

8

6

4

2

UCL np

np

LCL np

3/8 4/8 5/8 6/8 7/8 8/8 9/8 10/8 11/8 12/8 13/8 14/8 15/8 16/8 17/8 18/8 19/8 20/8 21/8 22/8

Dates/Monthnp Control Chart ; n = 50

8

6

4

2

8 9 10 11 12 13 14 15 16 17 18

Time in Hrs.

‘C’ Control Chart

UCL c

c

10

8

6

4

2

UCL u

U

Time in Hrs.

‘U’ Chart

3/8 4/8 5/8 6/8 7/8 8/8 9/8 10/8 11/8 12/8 13/8 14/8 15/8 16/8 17/8 18/8 19/8 20/8 21/8 22/8

n= 1.0 Sq .m.

n= 1.5 Sq .m.n= 1.0 Sq .m.

u

5220

= 2.6

DefectsTime

08.00 408.30 309.00 209.30 010.00 110.30 511.00 611.30 412.00 012.30 3

13.00 113.30 414.00 314.30 215.00 015.30 016.00 316.30 217.00 517.30 4

DefectsTime

5220

= 2.6

DefectsTime

08.00 408.30 309.00 209.30 010.00 110.30 511.00 611.30 412.00 012.30 3

13.00 113.30 414.00 314.30 215.00 015.30 016.00 316.30 217.00 517.30 4

DefectsTime



CentralLine

UppercontrolLimit

LowercontrolLimit

VARIOUS OUT OF CONTROL PROCESS CONDITIONSPOINTS OUTSIDE CONTROL LIMITS

CentralLine

3 Sigma line

3 Sigma line

1.5 Sigma line

WHEN MOST OF THE POINTS ARE WITHIN 1.5 SIGMALINE

CentralLine

UppercontrolLimit

LowercontrolLimit

Seven-point length ofrun is abnormal

10 out of 11 consecutivepoints occuring on one

side is abnormal

WHEN POINTS OCCUR CONTINUOUSLY ON ONE SIDEOR MORE

CentralLine

UppercontrolLimit

LowercontrolLimit

Seven upwards points Drastic downward trend

WHEN POINTS FORM CONTINUOUS UPWARD/DOWNWARDTREND

•

• •

••

•• •

•

••

••

•

•

•• •

•

WHEN 2 OUT OF 3 POINTS OCCUR OUTSIDE 2 SIGMA LINE

WHEN CURVE SHOWS REPEATEDLY UP ANDDOWNWARD TREND

• • •• •

•

•• •

•

•• •

• •

• •

18

RUN

TREND APPROACH TO CONTROL LIMIT

APPROACH TO CENTRAL LINE PERIODICITY

Documents

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