presentation_7 q c tools
TRANSCRIPT
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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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PROBLEM SOLVING METHODLOGY - 7 Q.C. TOOLS
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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PROBLEM SOLVING METHODLOGY - 7 Q.C. TOOLS
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
StepstoBuildaParetoChart
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PARETO DIAGRAM
Drawthecumulativepercentagelineshowingcategoriescontribution
Optional
Drawverticallineontherightsideofthechart Plotcumulativevaluesfromlefttoright
Interpretresults
Tallestbarrepresentsbiggestcontributor Performanalysisofcategorythathasthemost
impact
StepstoBuildaParetoChart
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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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CAUSE EFFECT DIAGRAM
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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CAUSE EFFECT DIAGRAM
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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CAUSE EFFECT DIAGRAM
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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CAUSE EFFECT DIAGRAM
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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CAUSE EFFECT DIAGRAM
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?
Questions to Ask When Performing RCA
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CAUSE EFFECT DIAGRAM
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?
Questions to Ask When Performing RCA
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CAUSE EFFECT DIAGRAM
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)?
Questions to Ask When Performing RCA
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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CAUSE EFFECT DIAGRAM
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?
Questions to Ask When Performing RCA
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CAUSE EFFECT DIAGRAM
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?
Questions to Ask When Performing RCA
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CAUSE EFFECT DIAGRAM
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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CAUSE EFFECT DIAGRAM
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.
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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