Presentation_7 q c Tools

7/30/2019 Presentation_7 q c Tools

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PROBLEM SOLVING METHODLOGY - 7 Q.C. TOOLS


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WhatDoYouMeanByQuality?

Conformancetospecifications?

FitnessforUse?

CustomerSatisfaction?

Degreetowhichasetofinherentcharacteristicsfulfillsthe

requirement?

(

ISO

9000

)


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QUALITYCONTROLemphasizestestingandblockingthereleaseof

defectiveproducts.

QUALITYASSURANCEisaboutimprovingandstabilizingproductionand

associatedprocessestoavoidoratleastminimizeissuesthatleadtothe

defectsinthefirstplace.

QUALITY CONTROL & QUALITY ASSURANCE


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QUALITY IMPROVEMENT

Inspection with the aim of finding the bad ones and throwing them out is

too late ,ineffective and costly. Quality comes not from inspection but from the improvement of the

processes.

Various Tools and Approaches used for IMPROVEMENT.

TQM Systematic activities with total involvement to achieve the company goal.

TPM Improve Productivity. ( O.E.E.)

TPS / LEAN MANUCTURING Reduce Waste.

ISO / TS 16949 : 2002 Reduction in Variation, Wastages , Defect Prevention.

SIX SIGMA Highly structured bottom line improvement .


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WHAT IS PROBLEM ?

A problem is the gap between the Actual Situation and the Ideal Situation.

Ideal Situation

Actual Situation

Gap


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WHY THE PROBLEM ?

PhilosophyOfSystem Nobodymakesmistakewillingly.

Many problems are due to -

- Nosystemexists.

- Nocommunication.

Systemnotsuitable.

Systemnoteffective.


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WHYDEFECTIVEPARTSGENERATE?

GoodpartsanddefectivepartsareproducedbytheSameprocesses.

WhysomepartsaredefectiveandsomepartsareO.K.?

Defectsareduetothevariations.

Variationinwhat?

Input (IncomingMaterial)

Processes(Man,Machine,Material,Method)

We need to understand Process & Input to understand the causes of variations .


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WHYDOWENEEDTOOLS&METHODS?

Howtoidentifytheinput /processcharacteristicswhichiscreating

variationinoutput?

BYUNDERSTANDINGTHEBEHAVOIROFTHEPROCESS.

Howtounderstandthebehavioroftheprocess?

Databasedapproachismorereliablethanopinion.

But,weshouldknowhowtocollectthedataandanalyzethedata.

OBSEVATION ,DATAOROPINION/EXPERIENCE.


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7 Q.C. TOOLS -

1. Check Sheet

0

20

40

60

80

100

120

Quantity

Defects 104 42 20 14 10 6 4

Dent Scratch Hole Others Crack Stain Gap

2. Stratification

3. Pareto Analysis 4. Cause & Effect Diagram


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7 Q.C. TOOLS -

Variable 1

5. Histogram6 . Scatter Diagram

7 . Control Chart


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CHECK SHEET -

Check sheet is a simple tool for collecting data so that the errors that

probably occurred can be avoided.

Checklist can be used

For the production process distribution - Application

- Tool used to record and compile frequency of observations as they occur

- Used for Pareto charts and histograms

- Design varies depending on information needed


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CHECK SHEET -

Production process distribution check list -


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CHECK SHEET -

Defective Item Check list - Application

- Generally used in final inspection of the process

- Helps to calculate number of defects and defectives .

Sr.No DefectFrequencymarksFrequencyf FrequencyMarks Frequency

1 Scratch ////// 6

2 Dent //////// 8

3 Blowhole ////////// 10

4 undersize ////////////// 14

5 Mark //////////////////////////////////////// 40

6 Crack ////////////////// 18

7 Blackspot //////////// /// 15

8 Bulge //////////////////////// 24

9 Misc /////////////// 15

Total 150


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CHECK SHEET -

Defect location check list

External defects like scratch,dentmark etc are found some time on specific

area of the product . This check sheet helps to identify the location where more

defects are produced and hence it helps to detect the cause of the problem.

It helps to know the distribution of the defect within the component.

Defectlocationmatrix.

Radial1 2 3 4 5 6 7 8

Circular

1

2

34

5

6

7

8


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CHECK SHEET -

Defect cause check list

If we want to stratify based on causes like operator wise , machine wise ,

shift wise along with the types of defects occurred , it is possible apply cause

check sheet .

It helps in analyzing the data cause wise and improves the understanding of

the process.

MACHINE OPERATORMON TUE

IShift IIShift IShift IIShift

1 A

x xx xx xxx

oo o o oo

**** ** ** *

2 B

xx xxx x xx

o oo oo o

** * **** **

x Dent

o Scratch

* BM


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STARTIFICATION -

What is Stratification ?

Stratification means to divide the whole into smaller portionsaccording to certain criteria. In case of quality control, stratification

generally means to divide data into several groups according to

common factors or tendencies (e.g., type of defect and cause of

defect).

Dividing into groups fosters understanding of a situation. This

represents the basic principle of quality control.


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STARTIFICATION -

When is it used and what results will be obtained?

The common and basic principle of quality control is stratification, i.e., to

think a matter out by breaking it into smaller portions. Stratification has a

number of useful purposes. The table below shows only a few examples of

these purposes.

Item Method of Stratification

Elapse of timeHour, a.m., p.m., immediately after start of work,shift, daytime, nighttime, day, week, month

Variations among workersWorker, age, male, female, years of experience,shift, team, newly employed, experienced worker

Variations among workmethods

Processing method, work method, working

conditions (temperature, pressure, and speed),temperature

Variations amongmeasurement/inspectionmethods

Measurement tool, person performingmeasurement, method of measurement, inspector,sampling, place of inspection


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PARETO DIAGRAM

TheVitalFewandTrivialManyRule

Predictable Imbalance

80:20 Rule


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PARETO DIAGRAM

Method of prioritizing problems or causes by frequency of occurrence or cost

Based in the 80-20 rule:

80% of the problem is caused by 20% of the sources

Vital few and trivial many

Depicted by a vertical bar graph arranged from

left to right descending order


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PARETO DIAGRAM

Advantages of a Pareto Chart

Focuseseffortsonproblemswithgreatest potentialforimprovement Distinguishesthecriticalcausesfromthelesssignificantcauses

Helpspreventshiftingtheproblemwherethesolutionremovessomecausesbut

worsensothers

Measuretheimpactofimprovementprojects whencomparingchartsbeforeand

after

Thechartshowstherelativeimportanceofproblemsinasimple,quickly

interpreted,visualformat.

Progressismeasuredinahighlyvisibleformatthatprovidesincentivetopushon

formoreimprovement.


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PARETO DIAGRAM

Identifyproblem

Choosecategoriesthatwillbemonitored

Choosethemostmeaningfulunitofmeasurement

Frequency

Cost

Determinetimeperiod

Longenoughtorepresentsituation

Scheduledtimetocollectdataistypicalofaworkday.

StepstoBuildaParetoChart


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PARETO DIAGRAM

Collectdata

Comparethefrequencyofeachcategory

Drawchart:

Listthecategoriesonthehorizontalline

Descendingorder,fromlefttoright

Frequenciesontheverticalline



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PARETO DIAGRAM

Drawthecumulativepercentagelineshowingcategoriescontribution

Optional

Drawverticallineontherightsideofthechart Plotcumulativevaluesfromlefttoright

Interpretresults

Tallestbarrepresentsbiggestcontributor Performanalysisofcategorythathasthemost

impact



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PARETO DIAGRAM

ExampleofaParetoChart

Benefits: Pareto analysis

helps graphically

display results sothe significant few

problems emerge

from the general

background It tells you what to

work on first

Lo

oseconnectionofnuts&bolts

DamagedGlandPackin

g

AirLeakInSuctionPipe

TriangularFlangeBroken

Shaftinjammedcondition

Im

pellerDamaged

Presenceofair

CoolingFanBroken

MountingNuts&Boltsinloose

condition

DamagedMechanicalS

eal

AirBlockage

TighteningofNuts&Bo

lts

CoolingFanCoverDen

t

CouplingNuts&Boltsloose

PumpBodyBroken

AirremovedfromPump

BearingWornout

FootValveOpencondition

0%

20%

40%

60%

80%

100%

0

2

4

6

8

10

12

14

16

18

20

C

umulative%

Defects

Causes

Vital Few Useful Many Cumulative% Cut Off %


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PARETO DIAGRAMTardiness events by school

0

50

100

150

200

250

B re nt wo od F or es t H i ll s C r aven s ro ft G le nd al e W en de ll S m it h M ap l e S tr ee t R a nd al l

School

#

ofTardy

Events

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1st level Pareto Chart

Tardiness by Grade

0

20

40

60

80

100

5th grade 4th grade 3rd grade 2nd grade 1st grade

Grade

No.ofTardin

ess

Events

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2ndlevel Pareto Chart

Tardiness by Student

0

10

20

30

40

50

60

70

Joe Tim Sofia Ann Maria Laura Jam es Leroy Ken Other

Student

No.ofTardiness

Events

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

3rd level Pareto Chart

If the data from the Pareto chart can

be stratified further, create 2nd or even

3rd level charts.

Analyze these charts to determine if

the Pareto Principle applies.

When youve narrowed down the

problems on the deepest levels

you will start finding root causes.


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CAUSE EFFECT DIAGRAM

THEAnalysisof

CauseAndEffectDiagram

What?

Why?

For

Is

Pictorialrepresentationofallpossiblecausescontributingtoaproblem.


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WHAT IS IT?

The Fishbone Diagram (also known as the Cause & Effect Diagram) is a

technique to graphically identify and organize many possible Causes of aproblem (effect).

WHY IS IT USEFUL?

Fishbone Diagrams help identify the most likely ROOT CAUSES of a problem.

They can also help teach a team to reach a common understanding of theproblem. This tool can help focus problem solving and reduce subjective

decision making.

WHEN IS IT USED?

When the need exists to display and explore many possible causes of a

specific problem or condition. This diagram allows the team to systematically

analyze cause & effect relationships. It can also help with the identification of

ROOT CAUSES.


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HOW IS IT DONE?

Name the effect; determine the specific problem to be analyzed. Draw the diagram

with a process arrow to the effect and draw a box around it.

Decide what the major categories of the causes are (i.e., people, machines,

measurement, materials, methods, environment, policies, etc.).

Label categories important to your situation. Make it work for you.

Brainstorm all possible causes and label each cause under the appropriate

category.

Post the diagram where others can add causes to it (i.e., experts, affected people,

process owners, etc..).

Analyze causes and eliminate trivial and/or frivolous ideas.


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Rank causes and circle the most likely ones for further consideration and study.

Investigate the circled causes. Use other techniques to gather data and prioritize

findings.

GUIDELINES

Try not to go beyond the span of control of the group.

Promote participation by everyone concerned.Keep chart up to date so it can be used throughout the improvement cycle.


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PEOPLE Was the document properly interpreted?

Was the information properly disseminated?

Did the recipient understand the information?

Was the proper training to perform the task administered to the person? Was too much judgment required to perform the task?

Were guidelines for judgment available?

Did the environment influence the actions of the individual?

Are there distractions in the workplace? Is fatigue a mitigating factor?

How much experience does the individual have in performing this task?

Questions to Ask When Performing RCA


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MACHINES Was the correct tool used?

Is the equipment affected by the environment?

Is the equipment being properly maintained (i.e., daily/weekly/monthly

preventative maintenance schedule)

Was the machine properly programmed?

Is the tooling/fixturing adequate for the job?

Does the machine have an adequate guard?

Was the tooling used within its capabilities and limitations?

Are all controls including emergency stop button clearly labeled and/orcolor coded or size differentiated?

Is the machine the right application for the given job?



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MEASUREMENT Does the gage have a valid calibration date?

Was the proper gage used to measure the part, process, chemical,

compound, etc.?

Was a gage capability study ever performed?

Do measurements vary significantly from operator to operator?

Do operators have a tough time using the prescribed gage?

Is the gage fixturing adequate?

Does the gage have proper measurement resolution?

Did the environment influence the measurements taken?



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MATERIAL Is a Material Safety Data Sheet (MSDS) readily available?

Was the material properly tested?

Was the material substituted?

Is the suppliers process defined and controlled?

Were quality requirements adequate for part function?

Was the material contaminated?

Was the material handled properly (stored, dispensed, used & disposed)?


ENVIRONMENT

Is the process affected by temperature changes over the course of a day?

Is the process affected by humidity, vibration, noise, lighting, etc.?

Does the process run in a controlled environment?


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METHODS

Was the canister, barrel, etc. labeled properly?

Were the workers trained properly in the procedure?

Was the testing performed statistically significant?

Have I tested for true root cause data?

How many if necessary and approximately phrases are found in this process? Was this a process generated by an Integrated Product Development (IPD) Team?

Was the IPD Team properly represented?

Did the IPD Team employ Design for Environmental (DFE) principles?

Has a capability study ever been performed for this process? Is the process under Statistical Process Control (SPC)?

Are the work instructions clearly written?

Are mistake-proofing devices/techniques employed?



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METHODS

Are the work instructions complete?

Is the tooling adequately designed and controlled?

Is handling/packaging adequately specified?

Was the process changed?

Was the design changed? Was a process Failure Modes Effects Analysis (FMEA) ever performed?

Was adequate sampling done?

Are features of the process critical to safety clearly spelled out to the Operator?



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Cast Patch

after roughmachining

Man MachineMethod

Material ToolingOther

Excess

grinding

Improper

averaging

Core fall outExcess core paint

Core assembly

shift while transfer

Rough

machining shift

Lock position

incorrect

Transfer fixture

lever position &

setting not OK

Core repairLow mould hardness

Core lock damage

Improper paint viscosity

Uneven clamping

pressure

Lack of skill

Less jolt & squeeze

time

Less scratch hardness

Job not located in dowel

hole

Uneven clampingpressure while

transfer

In consistency in

incoming air pressure

Less machining

stock on tooling

itself

Tooling wear out

Unfilled core

Mould box pin wear

out

Setting fixture

reference wear out

Improper sand properties

like GCS, compactability


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Drill Breakage

ManMachine

Method Material

Wrong drill selection

Wrong drill bushselection

Wrong diameter

Wrong length

Worn out drill

Worn out bush

Drill guide diameterless or more

Keeping high speedand feed

Chuck Clamping

pressure more

Vibration

Intermittent coolantfeeding

Error inProgramme Wrong

programming

Speed variation

Feed variation

Power failure

Spindle bearingfailure

Improper bush seating overthe piston

Collet not working

Burr Entrapment

Improper Coolant flow

Too much drill over hang

Drill vibration

Wrong drill size

Dia more or less

Guide Bush length & dialess or more

Hardness variation inthe piston

More stock on pistonouter diameter

Material of the drill

Bush material

Wrong indexing

Tool life of drill


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HISTOGRAM -

Purpose:Todeterminethespreadorvariationofasetofdatapointsinagraphical

form

Dataobtainedfromsampleservesasabasisforadecisiononthepopulation

We

need

a

method

which

will

enable

ustounderstandthepopulation

inanobjectivemanner

ataglance.

SuchamethodiscalledHistogram


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HISTOGRAM -

Howisitdone?

Collect data, 50-100 data point

Determine the range of the data Calculate the size of the class interval

Divide data points into classes determine

the class boundary

Count # of data points in each class Draw the histogramStable process, exhibiting bell shape


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HISTOGRAM -

Letusmakeahistogramusinganexample.

Example

To investigate distribution of piston bottom O.D.

STEP - 1

Calculate the range = ( Largest observed value Smallest observed value )

R = ( 114.235 114.160 ) = 0.075

SNO. 1 2 3 4 5 6 7 8 9 10

1 114.200 114.195 114.200 114.206 114.205 114.215 114.205 114.210 114.210 114.208

2 114.175 114.202 114.213 114.216 114.198 114.184 114.211 114.212 114.218 114.215

3 114.193 114.194 114.216 114.186 114.190 114.220 114.188 114.195 114.180 114.2004 114.205 114.200 114.201 114.200 114.200 114.205 114.185 114.212 114.196 114.215

5 114.212 114.199 114.204 114.218 114.235 114.212 114.160 114.223 114.202 114.200

XLARGE 114.212 114.202 114.216 114.218 114.235 114.220 114.211 114.223 114.218 114.215

XSMALL 114.175 114.195 114.200 114.186 114.198 114.184 114.160 114.195 114.180 114.20


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HISTOGRAM -

STEP - 2

Determine the class interval :

Class Interval = R / n = 0.075 / 7 = 0.011 ( approx )

Class interval is determined so that range will include the maximum and

minimum values

The no. of class interval can be calculated by formula

The no. of class interval = n ( where n = total no. of observations )= 50 = 7.07 = 7 ( rounding to nearest )

Divide the range by 1,2,5 or 0.1,0.2 ,0.5, or 10,20,50,etc.as the values are

obtained from 5 to 20 class intervals of equal width.

Where there are two possibilities , use narrower interval ( more classes ) for

below 100 readings and for 100 & above readings, use wider intervals

( less classes )


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HISTOGRAM -

STEP - 3

Prepare a frequency table form -

Prepare a frequency table form as shown below containing class, mid point,

Frequency marks & frequency.

Sr.No. Class Midpoint FrequencyMarks(Tally) Frequency


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HISTOGRAM -

STEP - 4

Determine the class boundaries

Boundaries for first class should include the smallest value 114.160

hence it has to be less than 114.160

The lower boundaries of the first class interval can be 114.1595.

Therefore , 114.1595 + class interval

i.e. 114.1595 + 0.011 = 114.1705

Therefore , first class boundary : 114.1595 ~ 114.1705

The second class boundary : 114.1705 ~ 114..1815

Note that this has to contain the largest recorded value . Therefore ,7 th class boundary : 114.225 ~ 114.236.5


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HISTOGRAM -

STEP - 5

CalculatetheMid PointOfTheClass

Using the following equation , calculate the mid point of the class & write this

down on the frequency table

Sum of upper & lower boundaries of each class

Mid Point of each class =2

STEP 6

Prepare the fill up the frequency table with tally marks and count the

frequency.

STEP 7

Draw the bar graph with X axis as mid point of interval and Y axis as

frequency . Draw the smooth curve of Histogram.


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HISTOGRAM -

Sr.No. Class Midpoint FrequencyMarks(Tally) Frequency

1 114.1595 114.1705 114.165 / 1

2 114.1705 114.1815 114.176 // 2

3 114.1815 114.1925 114.187 // 64 114.1925 114.2035 114.298 //////// 19

5 114.2035 114.2145 114.209 ///////////////// 14

6 114.2145 114.2255 114.220 /////////////////// 7

7 114.2255 114.2365 114.231 / 1

TOTAL 50

114.1595

114.1705

114.1705

114.1815

114.1815

114.1925

114.1925

114.2035

114.2035

114.2145

114.2145

114.2255

114.2255

114.2365

Series1 1 2 6 19 14 7 1

0

5

10

15

20

Freq

uency

Diamensions

BottomO.D.


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HISTOGRAM -

Benefits:

Allows you to understand at a glance the variation that exists in aprocess

The shape of the histogram will show process behavior

Often, it will tell you to dig deeper for otherwise unseen causes of

variation. The shape and size of the dispersion will help identify otherwise

hidden sources of variation

Used to determine the capability of a process

Starting point for the improvement process


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HISTOGRAM -

TYPES OF HISTOGRAMS -

The shape that your histogram takes tells a lot about your process. Often, it

ill tell you to dig deeper for otherwise unseen causes of variation.

The symmetrical or bell-shaped type of

histogram:

The mean value is in the middle of the range of

data.

The frequency is high in the middle of therange and falls off fairly evenly to the right and

left.

This shape occurs most often.


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HISTOGRAM -

The comb or multi-modal type of

histogram:

Adjacent classes alternate higher

and lower in frequency.

This usually indicates a data

collection problem. The problemmay lie in how a characteristic was

measured or how values were

rounded.

It could also indicate an error in the

calculation of class boundaries.


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HISTOGRAM -

If the distribution of frequencies is shifted noticeably to either side of thecenter of the range, the distribution is said to be skewed.

When the histogram is positively skewed

The mean value is to the left of the center

of the range, and the frequency decreasesabruptly to the left but gently to the right.

This shape normally occurs when the lower

limit, the one on the Left, is controlled

either by specification or because values

lower than a certain value do not occur for

some other reason.


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HISTOGRAM -

If the classes in the center of the distribution have

more or less the same frequency, the resulting

histogram looks like a plateau.

This shape occurs when there is a mixture of two

distributions with different mean values blended

together.

Look for ways to stratify the data to separate the

two distributions. You can then produce two

separate histograms to more accurately depict

what is going on in the process.


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HISTOGRAM -

TYPESOFHISTOGRAMS

If two distributions with widely differentmeans are combined in one data set, the

plateau splits to become twin peaks.

The two separate distributions becomemuch more evident than with the plateau.

Examining the data to identify the two

different distributions will help you

understand how variation is entering the

process.


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HISTOGRAM -

ISOLATED PEAKS

If there is a small, essentially

disconnected peak along with

a normal, symmetrical peak,this is called an isolated-peak

histogram.

It occurs when there is asmall amount of data from a

different distribution included

in the data set.

This could also represent ashort-term process

abnormality, a measurement

error or a data collection

problem.


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HISTOGRAM -

If specification limits are involved in your process, the histogram is an especially

valuable indicator for corrective action.

The histogram shows that the process is centered between the limits with a

good margin on either side. Maintaining the process is all that is needed.


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HISTOGRAM -

When the process is centered but with no margin, it is a good idea to work at

reducing the variation in the process since even a slight shift in the process

center will produce defective material.


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HISTOGRAM -

A process that would have produced material within specification limits if itwere centered is shifted to the left.

Action must be taken to bring the mean closer to the center of the specification

limits.


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HISTOGRAM -

A histogram that shows a process that has too much variation to meet

specifications no matter how it is centered.

Action must be taken to reduce variation in this process.


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HISTOGRAM -

A process that is both shifted, in this case to the right, and has too much

variation.Action is necessary to both center the process and reduce variation.

Conclusion:

A histogram is a picture of the statistical variation in your process. Not only can

histograms help you know which processes need improvement, they can also help

you track that improvement.


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SCATTER DIAGRAM -

Purpose:

To identify the correlations that might exist between a

quality characteristic and a factor that might be drivingit.

A scatter diagram shows the correlation between twovariables in a process.

These variables could be a Critical To Quality (CTQ)characteristic and a factor affecting it two factorsaffecting a CTQ or two related quality characteristics.

Dots representing data points are scattered on theDiagram.

The extent to which the dots cluster together in a lineacross the diagram shows the strength with which thetwo factors are related.


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SCATTER DIAGRAM -

How is it done?:

Decide which paired factors you want to examine. Both factors must

be measurable on some incremental linear scale.

Collect 30 to 100 paired data points.

Find the highest and lowest value for both variables.

Draw the vertical (y) and horizontal (x) axes of a graph. Plot the data

Title the diagram

The shape that the cluster of dots takes will tell you something about therelationship between the two variables that you tested.


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SCATTER DIAGRAM -

CORRELATIONCOEFFICIENT(r):

Thequantitativemeasureofcorrelationbetweenvariables.

rwillrangefrom 1to +1.

1indicatesverystrong ve correlation.

+1indicatesverystrong+ve correlation. Scoreof 0 indicatesnocorrelation.

S(xy)r=

S(xx)*S(yy) POSITIVE NEGATIVE

STRONG r 0.8 r 0.8

MODERATE 0.5 r0.8

WEAK r0.5


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SCATTER DIAGRAM -

= 0.124 / 2.88 * 0.1254

r = 0.2

S(XX) = Xi ( Xi ) / n= 2312.02 (263.2) / 30 = 2.88

Sr.No X Y X Y XY

1 8.6 0.889 73.96 0.790321 7.6454

2 8.9 0.884 79.21 0.781456 7.8676

3 8.8 0.874 77.44 0.763876 7.6912

4 8.8 0.891 77.44 0.793881 7.8408

5 8.4 0.874 70.56 0.763876 7.3416

6 8.7 0.886 75.69 0.784996 7.7082

7 9.2 0.991 84.64 0.982081 9.1172

8 8.6 0.912 73.96 0.831744 7.8432

9 9.2 0.895 84.64 0.801025 8.234

10 8.7 0.896 75.69 0.802816 7.7952

11 8.4 0.894 70.56 0.799236 7.5096

12 8.2 0.864 67.24 0.746496 7.0848

13 9.2 0.922 84.64 0.850084 8.4824

14 8.7 0.909 75.69 0.826281 7.9083

15 9.4 0.905 88.36 0.819025 8.50716 8.7 0.892 75.69 0.795664 7.7604

17 8.5 0.877 72.25 0.769129 7.4545

18 9.2 0.885 84.64 0.783225 8.142

19 8.5 0.866 72.25 0.749956 7.361

20 8.3 0.896 68.89 0.802816 7.4368

21 8.7 0.896 75.69 0.802816 7.7952

22 9.3 0.928 86.49 0.861184 8.6304

23 8.9 0.886 79.21 0.784996 7.885424 8.9 0.908 79.21 0.824464 8.0812

25 8.3 0.881 68.89 0.776161 7.3123

26 8.7 0.882 75.69 0.777924 7.6734

27 8.9 0.904 79.21 0.817216 8.0456

28 8.7 0.912 75.69 0.831744 7.9344

29 9.1 0.925 82.81 0.855625 8.4175

30 8.7 0.872 75.69 0.760384 7.5864

Total 263.2 26.896 2312.02 24.1305 236.093 Xi Yi Xi Yi XY

S(YY) = Yi ( Yi ) / n= 24.1305 (263.2) / 30 = 0.0173

S(XY) = XiYi ( Xi ) * ( Yi )n

= 236.093 (263.2) * (26.896)30

= 0.1254

S ( x y )r = S (xx)*S(y y)


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SCATTER DIAGRAM -

If the variables are correlated, when

one changes the other probably also

changes.

Dots that look like they are trying to

form a line are strongly correlated.

Sometimes the scatter plot may show

little correlation when all the data are

considered at once.

9 Stratifying the data, that is,

breaking it into two or more

groups based on some

difference such as the

equipment used, the time of day,

some variation in materials or

differences in the people

involved, may show surprising

results


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SCATTER DIAGRAM -

You may occasionally get scatter diagrams that

look boomerang- orbanana-shaped.

9To analyze the strength of the correlation,divide the scatter plot into two sections.

9Treat each half separately in your analysis

Benefits:

Helps identify and test probable causes.

By knowing which elements of your process are

related and how they are related, you will know

what to control or what to vary to affect a qualitycharacteristic.


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CONTROL CHARTS -

Purpose:

The primary purpose of a control chart is to predict expected product outcome.

Benefits:

Predict process out of control and out of specification limits Distinguish

between specific, identifiable causes of variation Can be used for statistical

process control


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CONTROL CHARTS -Every process varies. If you write your name ten times, your signatures will all

be similar, but no two signatures will be exactly alike. There is an inherent

variation, but it varies between predictable limits. If, as you are signing your

name, someone bumps your elbow, you get an unusual variation due to whatis called a "special cause" . If you are cutting diamonds, and someone bumps

your elbow the special cause elbow, can be expensive. For many, many processes, it

is important to notice special causes of variation as soon as they occur.

There's also "common cause" variation. Consider a baseball pitcher. If he has

good control, most of his pitches are going to be where he wants them. There

will be some variation, but not too much. If he is "wild", his pitches aren't

going where he wants them; there's more variation. There may not be any

special causes - no wind, no change in the ball - just more "common cause"variation. The result: more walks are issued, and there are unintended fat

pitches o t o e the plate he e batters can hit them In baseball control ins

out over where batters them. baseball, control wins ballgames. Likewise, in most

processes, reducing common cause variation saves money.

O SO G O OG Q C OO S


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CONTROL CHARTS -

Proposed by W.A. Shewhart in 1924

A control chart consists of a center line, a pair of control limits, one each

allocated above and below the center line, the characteristic values plottedon the chart representing the state of the process

Chance cause variation by chance cause is unavoidable and inevitably

occurs in a process. It is not possible to eliminate chance cause practicallyand economically

Assignable cause -Variation by assignable cause means that there are

meaningful factors to be investigated. It is avoidable and cannot be

overlooked.

PROBLEM SOLVING METHODLOGY 7 Q C TOOLS


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CONTROL CHARTS -

Advantages of Control Charts

Focuses attention on detecting and monitoring process variation

over time

Distinguishes special from common causes

Helps predict performance of a process

Helps improve a process to perform consistently

Provides a common language to discuss process behavior



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CONTROL CHARTS -Types of control charts

X R chart used for controlling and analyzing a process using continuous values

of product quality variable quality characteristics. X bar represent average of sub

group and R range of the subgroup.

X chart when data is obtained after long intervals or subgroup of data is not

effective. R can not be obtained. The moving range R of successive data is used for

calculation of control limits. Pn chart, p chart These charts are used when the quality characteristic is

represented by number of defective units or fraction defective. For a sample of

constant size, pn chart of number of defective units is used, whereas a p chart of the

fraction defect9ive is used for a sample of varying size

C chart, u chart - These are used for controlling and analyzing a process by defects

of a product, such as scratches on plated metal, number of defective soldering inside

or unevenly woven texture of fabrics. A c chart of the number of defects is used for

product of constant size, while a u chart is used for product of varying size



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CONTROL CHARTS -

How to plot a X-R Chart

_

Step 1Collect approx 100 data. Divide them into 20-25 subgroups with 4-5 in each.

Fill a data sheet. When there is no technical reason for sub grouping, divide

the data in order it is obtained.

The size of a group is usually 2 10.

Step 2

Calculate the average value for each subgroup

x1+x2+x3+xi+.. Xn n is size of subgroup

n

Step 3 _ _ _

Calculate x = x1+x2+x3+ .. xk k is number of subgroups

k

=



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CONTROL CHARTS -

Step 6

Calculate the control limits

Step 4

Calculate R = max value in sub group min value in subgroup

Step 5 _Calculate R = R1+R2+R3+ .. Rk

k

Central line CL = x=

Upper control limit UCL = x + A2 R=

_

Lower Control Limit LCL = x - A2 R=

_



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CONTROL CHARTS -

R chart

Central line = CL = R_

Upper control limit UCL = D4 R_

Lower control limit LCL = D3 R

_

List Of Coefficients

Subgroup SizeX Chart R Chart

A2 D3 D4 d2

2 1.88 0 3.267 1.128

3 1.023 0 2.575 1.1693

4 0.729 0 2.282 2.059

5 0.577 0 2.115 2.326



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CONTROL CHARTS -

Step 7

Take a squared paper and mark the left hand vertical axis with the values of x

and R and horizontal axis with subgroup number.

Draw solid line for center line and dotted lines for UCL and LCL

Step 8 __

Plot the points. Mark values of x and R in each subgroup

Step 9

Write the necessary information such as process, product, period, measuring

method , shift, working conditions etc.

__



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CONTROL CHARTS -PART NAME: Piston INSTRUMENT: O.D.Comparator L.COUNT: 0.001 SUPPL

IERxxx

PART NO.: 114.3 SPECIFIC: Dia-114.22/114.19 MACHINE:

SAMPLE SIZE: 50 NOS. OPERATION: Bottom O.DNO.OF

DECIMALS:3

D.C.

NO.QTY. 50

DATA COLLECTION: - ALL DIMENSIONS ARE IN INCHESMM /

SNO. 1 2 3 4 5 6 7 8 9 10

U.T.L. 114.2200

SAMP

LED2 A2 D4

1 114.200 114.220 114.200 114.206 114.205 114.215 114.205 114.210 114.210 114.208 1 1.123 2.560 3.270

2 114.175 114.220 114.213 114.216 114.220 114.184 114.211 114.212 114.218 114.215 2 1.128 1.880 3.270

3 114.193 114.217 114.216 114.207 114.210 114.220 114.213 114.195 114.180 114.200

L.T.L. 114.1900

3 1.693 1.020 2.570

4 114.205 114.218 114.225 114.200 114.200 114.205 114.185 114.212 114.218 114.215 4 2.059 0.730 2.230

5 114.212 114.217 114.204 114.218 114.235 114.212 114.160 114.223 114.216 114.218 5 2.326 0.590 2.110

CALCULATIONS: -

FOR HISTOGRAM

XLARG

E

114.21

2114.22

114.22

5

114.21

8

114.23

5114.22

114.21

3

114.22

3

114.21

8

114.21

8Xmax.=

114.23

50 NO.OF NON

CONFORMING PART

=

8NOS.

XSMALL

114.175

114.217

114.2 114.2 114.2 114.184

114.16 114.195

114.18 114.2 Xmin.= 114.1600

RANG

E0.037 0.003 0.025 0.018 0.035 0.036 0.053 0.028 0.038 0.018 2 =

0.0291

0

NO. OF PARTS

ABOVE U.T.L. =3NOS.

AVG.114.19

7

114.21

84

114.21

16

114.20

94

114.21

4

114.20

72

114.19

48

114.21

04

114.20

84

114.21

128 =

114.20

83

NO. OF PARTS

BELOW L.T.L. =5NOS.



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CONTROL CHARTS -

114.17

114.18

114.19

114.2

114.21

114.22

114.23

1 2 3 4 5 6 7 8 9 10

VALUE

SAMPLE

X - CHART

AVG.

U.C.L.

L.C.L.

X-BAR

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1 2 3 4 5 6 7 8 9 10

VALU

E

SAMPLE

R - CHART

RANGE

U.C.L.

L.C.L.

R-BAR

=

__



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CONTROL CHARTS -

Things to look for:

The point of making control charts is to look at variation, seeking special causesand tracking common causes. Special causes can be spotted using several tests:

1 data point falling outside the control limits

6 or more points in a row steadily increasing or decreasing

8 or more points in a row on one side of the centerline 14 or more points alternating up and down In those charts that pair two charts

together, you will want to look for these anomalies in both charts

The simplest interpretation of the control chart is to use only the first test listed.

The others may indeed be useful (and there are more not listed here), but be

mindful that, as you apply more tests, your chances of making Type I errors, i.e.

getting false positives, go up significantly.



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CONTROL CHARTS -

Basic Control Chartsinterpretation rules:

Specials are any points abovethe UCL or below the LCLA Run violation is seven or

more consecutive pointsabove or below the center

(20-25 plot points)A trend violation is any upwardor downward movementof five or more consecutivepoints or drifts of seven or

more points (10-20 plotpoints)

A 1-in-20 violation is morethan one point in twentyconsecutive points close to

the center line

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