six sigma project - brakes india - wall thickness variation
TRANSCRIPT
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6s Project
DefineMeasure & Analyze
ControlImprove
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Project Number SEL/QA/2006-001Plant SHOWA ENGG.LTD
Name of the Black Belt Mr.S.DORAISWAMY
Team Members Mr.C.SUKUMAR
Mr.D.PONNUVEL
Mr.V.VADIVELU
Mr.A.NANDHAKUMAR
Date of Start 03.07.2006
Six Sigma Project
6
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Caliper Housing
ApprovedComponent
RejectedComponent
Mounting hole less wall thickness
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Define Phase
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Phase 1- Problem Definition
Number of lines/presses/machines used for processing One Machine
Objective of the Project To Reduce this defect to Zero
Annual Savings in Rs. Lakhs if the defect is made zero and horizontally
deployed to other part numbers Rs.1,21,584
Response Variable / Attribute
Specification (if the response is variable)
PCD Dimension : 159.0 0.075 ,Wall thickness: 4.8 mm to 5.8 mm Is R&R study required
Yes / No
If R&R study is required, % R&R to tolerance 10%
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Phase 1- Problem Definition
Problem Statement Pin hole less wall thickness (Up to 4.2 mm as against 4.8mm to 5.8mm)
Part number selected for study 29320155/56
Other similar part numbers having the problem
Nil Process stages where the Problem is detected
Opn No : 30
Pin hole drilling.
Current average rejection for last 6 months
27 Nos/month 0.11% Maximum and Minimum rejection in last 6 months
Maximum rejection in a month - 34 Nos -June06
Minimum rejection in a month - 23 Nos - Mar06
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Phase 1- Problem Definition
Process Mapping
Input MaterialCasting
Opn. 10 - Disc MillingM/C : SPM Milling
Opn. 30 - Pin HoleDrilling
M/C : Systec
Opn. 40 - Feed & BleedM/C : Stama
Opn. 20 - Lug MillingM/C : Cincinnati
Milling
Opn. 60 - Rough BoreM/C : Column Drill
Opn. 50 - Banjo MillingM/C : Cincinnati Milling
Opn. 70 - Finish BoreM/C :1SC & LMW
Rejection occurring
stage
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Phase 1- Problem Definition
Phase
Month Month Month
W1 W2 W3 W4 W1 W2 W3 W4 W1 W2 W3 W4
Define
Measure &Analyze
Improve
Control
Project Planning
PhasesPlannedStart date
PlannedCompletiondate
Actual startdate
Actualcompletion date
Status
Define 03.07.2006 08.07.2006 03.07.2006 07.07.2006 Completed
Measure & Analyze 10.07.2006 05.08.2006 15.07.2006 08.08.2006 Completed
Improve 07.08.2006 26.08.2006 10.08.2006 05.09.2006 Completed
Control 28.08.2006 09.09.2006 08.09.2006 06.10.2006 Completed
Planned Completed
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`Photograph of defect part
CastingPin hole drilling
(Problem operation) Finished component
Min 4.8mm
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Process flow
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Sq.
no Process step
Incoming source of
variation Symbol Desired outcomes Type Process characteristics
10 DISC MILLING 1.HARDNESS 1.DISC MILLING RADIUS BP 1.SPEED
LOADING 2.CASTING DIMENSION 2.RADIUS DEPTH BP 2.FEED
( TOOLING LOCATION W.R.TO 3.CENTER SHIFT OF RADIUS BP 3.COOLANT FLOW
CENTER OF CASTING ) 4.CLAMPING PRESSURE
5.TABLE MOVEMENT
6.LOCATING PIN IN FIXTURE
7.BUTTING THE CASTING BY
OPERATOR
8.SETTING DIMENSION FOR RADIUS
MILLING,RADIUS DEPTH AND
CENTER SHIFT OF RADIUS
20 LUG MILLING CENTER SHIFT OF RADIUS 1.FLANGE THICK NESS BP 1.SPEED
LOADING 2.DIMN. 11.5 MIN. FROM HOLE CENTER BP 2.FEED
3.DIMN 24.20 / 23.80 MM FROM "V" FACE BP 3.SPINDLE AXIAL AND RADIAL
PLAY
30 PIN HOLE 1.CASTING DIMENSION 1.PIN HOLE DIAMETER BP 1.SPEED
DRILLING ( SYMMETRICITY,CAVITY TO 2.PIN HOLE POSITION BP 2.FEED
LOADING CAVITY,CENTER SHIFT OF 3.WALL THICKNESS BP 3.COMPONENT BUTTING LOCATION
RADIUS ) 4.CLAMPING PRESSURE
2.RADIUD DEPTH
3.CENTER SHIFT OF RADIUS
Process flow diagram
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Process
FMEA
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Process FMEAPROCESS
STEPFAILURE MODE POTENTIAL CAUSES OCC
CURRENT PROCESS
CONTROL (TYPE - B)
CURRENT PROCESS
CONTROL (TYPE - C)
CURRENT PROCESS
CONTROL (TYPE - A)DET RPN
DISC MILLING 1.DISC MILLING 1.HARDNESS 1 NIL RECEIVING INSPECTION NIL
RADIUS AS PER SHOWA SINGLE
OVERSIZE SAMPLING PLAN
UNDERSIZE ( ACCEPTANCE LEVEL 0 )
RESP : INSPECTOR
2.RADIUS DEPTH
OVERSIZE 2.CASTING DIMENSION NIL RECEIVING INSPECTION NIL
UNDERSIZE ( TOOLING LOCATION W.R AS PER SHOWA SINGLE
TO CENTER OF CASTING ) SAMPLING PLAN
3.CENTER SHIFT ( ACCEPTANCE LEVEL 0 )
OF RADIUS RESP : INSPECTOR
OVERSIZE
UNDERSIZE 3.BUTTING THE CASTING NIL POKA - YOKE ONCE IN 2 HRS BY QA 6 6
BY OPERATOR PROVIDED PRE-DESPATCH
INSPECTION
AS PER SHOWA SINGLE
SAMPLING PLAN
( ACCEPTANCE LEVEL 0 )
RESP : INSPECTOR
4.TABLE MOVEMENT NIL IT IS IN PM CHECK NIL
LIST
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PROCESS
STEPFAILURE MODE POTENTIAL CAUSES OCC
CURRENT PROCESS
CONTROL (TYPE - B)
CURRENT PROCESS
CONTROL (TYPE - C)
CURRENT PROCESS
CONTROL (TYPE - A)DET RPN
LUG FLANGE 1.CENTER SHIFT OF RADIU 1 PROCESS CONTROL NIL ONCE IN 2 HRS BY QA 6 6
MILLING THICKNESS CHART PRE-DESPATCH
VARIATION CHECK 1 NO/HOUR INSPECTION
RESP: OPERATOR AS PER SHOWA SINGLE
SAMPLING PLAN
( ACCEPTANCE LEVEL 0 )
INSPECTOR
2.SPINDLE AXIAL AND NIL ADDEED IN THE
RADIAL PLAY PM CHECK LIST
Process FMEA
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Process FMEAPROCESS
STEPFAILURE MODE POTENTIAL CAUSES OCC
CURRENT PROCESS
CONTROL (TYPE - B)
CURRENT PROCESS
CONTROL (TYPE - C)
CURRENT PROCESS
CONTROL (TYPE - A)DET RPN
PIN HOLE WALL 1.CASTING DIMENSION 4 NIL RECEIVING INSPECTION NIL 6
DRILLING THICKNESS ( SYMMETRICITY,
UNDERSIZE CAVITY TO CAVITY &
BOSS DIAMETER )
2.RADIUS DEPTH PROCESS CONTROL NIL 100% IN FINAL AREA 5 20
CHART USING GAUGE
CHECK 1 NO/HOUR ONCE IN 2 HRS BY QA
RESP : INSPECTOR PRE-DESPATCH
INSPECTION
3.CENTER SHIFT OF PROCESS CONTROL NIL AS PER SHOW A SINGLE
RADIUS CHART SAMPLING PLAN
CHECK 1 NO/HOUR ( ACCEPTANCE LEVEL 0 )
RESP : INSPECTOR RESP : INSPECTOR
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Calibration
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Variation due toInstrument
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Data Collection
1. Instrument Selected : Vernier Caliper
2. Instrument Number : SM 0200
3. Least Count : 0.01 mm
4. No. of Samples : 5 Nos
5. No. of Appraiser : 3
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Bias Estimation
Following are the readings obtained during calibration of Vernier Caliper
Master Value = 20 mmError = 0.00001 mm
S.No Reading
1 20.01
2 20.00
3 20.00
4 20.01
5 20.02
Average = 20.008
Error = Actual Value Master Value
Error = 20.008 20.000
Error = 0.008
Master Error = 0.01 microns = 0.00001 mm
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Bias Estimation
Standard Deviation( s)= 0.008
Standard Deviation of Averages( s (X bar) )= s/ Sqrt n
= 0.008 / Sqrt 5
=0.008 / 2.236
= 0.0036
t value for 5 data =2.7764
Random Uncertainty = t * (s(X bar))
=2.7764 * 0.0036
=0.009995
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Bias EstimationSystem Uncertainty
Total Uncertainty= Sqrt( (RU)2 + (SU)2 )
= Sqrt( (0.009995)2 + (0.00001)2 )
= 0.0099
Calculating Upper and Lower Boundary
UL= Error + TU
UL= 0.008 + 0.0099
UL= 0.0179
LL= Error - TU
LL = 0.008 - 0.0099
LL= - 0.0019
0 lies between the 2 limits. Hence the Error is 0.
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Conclusion for Uncertainty
Calculate TU/Tolerance %= 0.0099 / 1 * 100
= 0.99 %
0.99 % is < 25%
So the Uncertainty is Acceptable
Bias is 0
Uncertainty percentage is < 25%
Hence this Instrument can be used for ourproject.
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Linearity EstimationMethod-2 :Graphical Method
Following is the data collected after calibration
Master value 20 60 90 120 140
Error 0.00001 0.00000 0.00001 0.00004 0.00003
1 20.01 60.02 89.99 120.02 140.00
2 20.00 59.99 90.01 120.00 140.00
3 20.00 60.02 90.02 120.01 139.98
4 20.01 60.01 90.01 120.00 139.99
5 20.02 60.02 90.00 120.00 139.99
Average 20.008 60.012 90.006 120.006 139.992
Error 0.008 0.012 0.006 0.006 - 0.008
Master Slip Gauge InstrumentVernier Caliper
All dimensions in mm
G hi l M h d
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- 0.015
- 0.010
- 0.005
0.015
0.010
0.005
0.000
20 12010040 8060 140 160
Error
Master Value
Graphical Method
0 lies between the highest and lowest point. So it is Linear
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Gauge R&RStudy
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Appraiser Trial Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
S.DoraisamyT1 12.99 13.08 12.96 12.99 12.98
T2 13.07 13.06 12.96 12.96 12.99
S.GaneshKumar
T1 12.98 12.94 12.92 12.94 12.94
T2 12.90 13.03 12.96 12.99 12.92
V.VadiveluT1 12.97 13.00 12.96 12.99 12.97
T2 12.99 13.02 13.02 12.98 12.99
S.Doraisamy 0.08 0.02 0.00 0.03 0.01
S.Ganesh Kumar 0.08 0.09 0.04 0.05 0.02
V.Vadivelu 0.02 0.02 0.06 0.01 0.02
0.55
15=R
R= 0.037
Maximum Range = 0.09
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To check the Consistency of the range
UCL = D4*R
UCL = 3.267*0.037UCL = 0.121
LCL = 0
With in person Variation = 0.09
UCL is > With in person Variation
So It is Consistent
E i i R bili ( V i i i h i )
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Estimating Standard Deviation
=R
d2s
=0.037
2.48s
s= 0.015
Estimating Variation
5.15s= 5.15*0.015
= 0.077
Estimating Repeatability ( Variation with in person )
m = 5
g = 1
d2= 2.48
At 99% Confidence level
Actual EstimationWith in person 0.09 0.077
Person to Person Variation + With in person variation
Person to Person Variation only
Total R&R
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Mean
S.Doraisamy 13.030 13.070 12.960 12.975 12.985 13.004
S.Ganesh Kumar 12.940 12.985 12.940 12.965 12.930 12.952
V.Vadivelu 12.980 13.010 12.990 12.985 12.980 12.989
Estimating Person to Person and With in person Variation
Range = 0.052
Finding out the Range
R= 0.052
Estimating Standard deviation
=0.052
2.48s
s= 0.021
m = 5
g = 1
d2= 2.48
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Estimate Variation
5.15s= 5.15*0.021
= 0.108
Actual Estimation
With in person 0.090 0.077
Person to Person Variation + With in person variation 0.052 0.108
Person to Person Variation only
Total R&R
At 99% Confidence level
To find Reproducibility (Person to Person Variation) we have toremove Variation with in person from this
E ti ti R d ibilit
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Person to Person Variation
Actual Estimation
With in person 0.090 0.077
Person to Person Variation + With in person variation 0.052 0.108
Person to Person Variation only 0.044 0.105
Total R&R
= Sqrt((AV)2 ((EV)2/(n*r)))
= Sqrt((0.052)2 ((0.090)2/(2*5)))
= 0.044
Estimating Person to Person Variation
= Sqrt((AV)2 ((EV)2/(n*r)))= Sqrt((0.108)2 ((0.077)2/(2*5)))
= 0.105
Estimating Reproducibility
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Actual R&R
Actual Estimation
With in person 0.090 0.077
Person to Person Variation + With in person variation 0.052 0.108
Person to Person Variation only 0.044 0.105
Total R&R 0.100 0.130
= Sqrt((Repeatability)2 + (Reproducibility)2)
= Sqrt((0.090)2 + (0.044)2)
= 0.100
Estimating R&R
= 0.130
= Sqrt((Repeatability)2 + (Reproducibility)2)
= Sqrt((0.077)2 + (0.105)2)
At 99% Confidence level
l l l
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Calculating R&R / Tolerance%
Calculated R&R/Tolerance * 100 = 0.130 / 1*100
= 13 %
Takingsfrom my project
s = 0.082
5.15s= 5.15*0.082
= 0.4223
R&R/Part to Part Variation = 0.130 / 0.4223
= 30.8 %
Calculating R&R / Part to Part Variation%
Since R&R/Part to Part Variation is > 30%. We cannot use thisInstrument for Data Collection in our Project.
We allowed a deviation to our self to use this for data collection
since the deviation is too small.
Ph 1 P bl D fi iti
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Pareto (Based on last 6 months data)
21% of the Total rejection is due to pin hole less wallthickness.
Qty produced - 140782 nos.Total scrap Qty - 787 nos.Scrap Percentage - 0.55 %Pin hole out of pos. scrap 163nos.Pin hole less wall thickness % - 0.11 %
Phase 1- Problem Definition
HOUSING PARETO CHART FOR
THE MONTH OF JAN'06 TO JUNE'06 ( SIX MONTHS)
36 33 29 28
6777
414247 45 44 40 37
58
163
21%
31%
40%47%
53%59%
65% 70%
75% 80%
85% 90%
94% 98% 100%
0
20
40
60
80
100
120
140
160
180
PIN
HOLE
LESS
WALL
THICKNESS
PIN
HOLE
CHAMFE
RD
IAO
/S
BORE
DIA
O/S
FEED
PORTSPOTFA
CE
DAMAGE
FEED
PORTS
.FACE
CHAT.MARK
BLEED
PORTSEATING
DAMAGE
FEED
PORTSHIFT
BLEED
PORTOUTOFPOSITION
LUG
MILLING
STEP
SEALGROOVE
DIA
O/S
FEED
PORTCORE
DIA
O/S
BORE
STEP
M10
THREAD
DAMAGE
BORE
DAMAGE
M10
THREAD
WASH
OUT
DEFECTS
REJECTQTY
0%
20%
40%
60%
80%
100%
120%
CUMULATIVEPERCENTAGE
As per Pareto Pin Hole Less Wall thickness is thehighest rejection. Hence this defect was taken for the
project.
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COPQ (Cost of Poor Quality) Calculation
Phase 1- Problem Definition
Number of pieces rejected last month(for the part number identified for study)
34 ( June06)
Number of pieces scrapped last month 34
Number of pieces reworked last month _
Scrap cost/piece 298
Rework cost/piece _Total scrap cost (Rs. Lakhs) for lastmonth
Rs 10,132
Total rework cost(Rs. Lakhs) for lastmonth
_
Total Rejection cost (Rs. Lakhs) for lastmonth Rs 10,132
Extrapolated Total rejection cost (Rs.Lakhs) for one year
Rs : 1,21,584
Horizontal Deployment N.A
h bl f
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Listing Down Suspected Sources of Variations
Man Input Material
MachineProcess (Pin hole drilling)
Pin hole less wall
thickness
Radial play in Milling &
Systec machines
Cavity to cavity variation
Dia. of the bosses
Symmetricity of the bosses
Radius depth in SPM
Milling
Center Shift of RadiusLoading variation in
pin hole operation
Phase 1- Problem Definition
Clamping variation in Pin hoe operation
Listing Down all SSVs
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Listing Down all SSV s
1.Incoming Material 1.Cavity to Cavity Variation
2.Boss diameter
3.Symmetricity of Boss
4.Radius depth in SPM Milling
5.Center shift of radius
7.Clamping in Pin hole operation
SSVs
6.Loading Variation in pin hole operation
3.Process
4.Machine 8.Spindle Runout in Milling and Systec Machine
2.Operator
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The following SSVs are Constant and Hence are not considered forfurther study for the Y at this Stage
1.Loading - Mistake Proof Arrangement
(Both in previous operation & in problem generated operation)
2.Clamping - Constant
3.Spindle Runout in Systec machine - Constant
Ph 1 P bl D fi iti
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Phase 1- Problem Definition
1. Input MaterialCasting Related
1.Cavity to Cavity Variation
2.Boss diameter
3.Symmetricity of Boss
Previous (Earlier) operation Related
1.Radius Milling depth
2.Center shift of radius
2. SSVs are Nilin the Process (Drilling Operation) at which Y is created
Suspected Sources of Variation (SSVs) for the Problem statement
1st level SSVs
ALL THE ABOVE SSVs ARE VARIABLES
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Phase 1- Problem Definition
SSVsCurrent
Specification
Input Material
Boss diameter 20.0 + 0.60
Cavity number 7,8,9 & 10
Symmetricity 26.50 + 0.60
Previous Operation
related
Radius depth 133.70 + 0.30
Center shift of radius 48.50 / 47.50
Response (Hole ) Y = Wall thickness 4.80 mm to 5.80 mm
P bl St t t
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Problem Statement
Cavity Number
4.8 mm to 5.8 mm.
(Wall thickness)
20+0.6 (Boss dia)
Boss - A Boss - B
47.5 / 48.5
133.7 +0.3
B with respect to A
Y = Wall thickness
X = Symmetricity,Boss diameter,Cavity to Cavity Variation,Radius depth and centershift of radius
Si Si T l d
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Six Sigma Tools used
Phase Tools
Define 1. Process Mapping
2. Process FMEA3. Pareto
4. Calibration
5. Gauge R&R Studies
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Measure andAnalyze Phase
Machines
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Machines
SPM Milling Systec
Root Cause = X Response = Y
Suspected Source Machine Generating Machine
DOE Tool Selection
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DOE Tool Selection
The identified SSVs are Measurable on both Good and Badcomponents and are Input related.
Hence DOE Tool PAIRED COMPARISONwas selected.
Y= f(x)
Y = Response
= Wall Thickness
X = SSVs
Input Material Parameters
1.Cavity to Cavity
2.Boss
3.Symmetricity of Boss
4.Radius Depth
5.Center Shift in Radius
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Measurement
Data Collection
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Data Collection
8 Good parts (Best of Best) and 8 Bad parts (Worst of Worst)
based on Wall thickness (Response) were selected for study.
WOW parts were collected from already rejected lot as thecurrent rejection rate for this defect is 0.11% and need to
wait 8 to 9 thousand numbers (Which is 10 daysproduction) to get 8 Bad components. BOB parts werecollected from a shifts production Quantity.
The parts were marked as B1,B2,B3,B4,B5,B6B7 & B8
W1,W2,W3,W4,W5,W6,W7& W8
Data Collection
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S.No
Input Material SSVs (Casting Related)Earlier Process Related
(Machining Related)Specification
Response CavityNo
Boss
Dia - A200.6mm
Boss
Dia - B200.6 mm
Symmetricity Radius Depth133.70.3mm Center shift ofRadius Response
B1 GOOD 7 21.12 21.38 0.70 133.67 47.82 5.57
B2 GOOD 8 21.00 20.88 0.55 133.75 48.32 5.58
B3 GOOD 9 20.98 21.17 0.60 133.62 48.10 6.00
B4 GOOD 9 20.80 20.80 0.80 133.80 48.00 5.57B5 GOOD 10 21.90 21.00 0.60 133.72 47.80 5.90
B6 GOOD 10 20.97 20.90 0.50 133.55 48.20 5.80
B7 GOOD 8 21.80 21.00 0.80 133.66 48.37 5.70
B8 GOOD 9 20.80 20.80 0.50 133.70 48.20 6.00
W1 BAD 7 21.37 22.00 1.50 133.90 47.88 4.78
W2 BAD 7 21.37 21.33 1.35 134.13 47.70 4.70W3 BAD 7 20.84 20.90 0.78 133.70 48.17 4.70
W4 BAD 7 21.30 21.33 1.10 134.21 47.95 4.75
W5 BAD 8 20.85 20.80 0.70 134.15 47.45 4.79
W6 BAD 10 20.80 20.80 1.12 134.02 47.80 4.78
W7 BAD 7 20.80 21.00 0.80 133.95 47.50 4.57
W8 BAD 7 20.88 21.40 0.70 134.07 47.75 4.76
Data Collection
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Analysis
Analysis Step1
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S.No Response Cavity no
1 GOOD 7
2 GOOD 8
3 GOOD 9
4 GOOD 9
5 GOOD 10
6 GOOD 10
7 GOOD 8
8 GOOD 9
1 BAD 7
2 BAD 7
3 BAD 7
4 BAD 7
5 BAD 8
6 BAD 10
7 BAD 7
8 BAD 7
S.No Response Boss A Boss B
1 GOOD 20.88 20.80
2 GOOD 20.80 20.80
3 GOOD 20.80 20.88
4 GOOD 20.90 20.90
5 GOOD 20.97 21.00
6 GOOD 20.98 21.10
7 GOOD 21.10 21.178 GOOD 21.12 21.38
1 BAD 20.80 20.80
2 BAD 20.80 20..90
3 BAD 20.84 21..90
4 BAD 20.85 21.00
5 BAD 20.88 21.33
6 BAD 21.30 21.33
7 BAD 21.37 21.40
8 BAD 21.37 22.40
Analysis Step1To find out the root causes among the chosen SSVs
Parameter - 1 Parameter - 2
All Cavity numbers are both in goodand bad components. Hence Cavity
Variation is not the cause forVariation in Y
In both Boss s both Max. and Min. sizes are
in Bad Components. Hence these dias are
not the reason for Variation in Y
Analysis Step1
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S.No Response Symmetricity
1 GOOD 0.50
2 GOOD 0.50
3 GOOD 0.55
4 GOOD 0.60
5 GOOD 0.60
6 GOOD 0.70
7 GOOD 0.80
8 GOOD 0.80
1 BAD 0.70
2 BAD 0.70
3 BAD 0.78
4 BAD 0.80
5 BAD 1.10
6 BAD 1.127 BAD 1.35
8 BAD 1.50
S.No ResponseRadiusDepth
1 GOOD 133.55
2 GOOD 133.623 GOOD 133.66
4 GOOD 133.67
5 GOOD 133.70
6 GOOD 133.72
7 GOOD 133.75
8 GOOD 133.80
1 BAD 133.70
2 BAD 133.90
3 BAD 133.95
4 BAD 134.02
5 BAD 134.07
6 BAD 134.13
7 BAD 134.15
8 BAD 134.21
S.No Response CenterShift
1 GOOD 47.80
2 GOOD 47.823 GOOD 48.00
4 GOOD 48.10
5 GOOD 48.20
6 GOOD 48.20
7 GOOD 48.32
8 GOOD 48.37
1 BAD 47.45
2 BAD 47.50
3 BAD 47.70
4 BAD 47.75
5 BAD 47.80
6 BAD 47.88
7 BAD 48.17
8 BAD 47.95
y pParameter - 4Parameter - 3 Parameter - 5
SymmetricityMin & Max do notbelong to the same category. NorMin or Max are in both thecategories. Hence this is one of
the causes.
Radius DepthMin & Max do notbelong to the same category. NorMin or Max are in both thecategories. Hence this is one of
the causes.
Center ShiftMin & Max are not inthe same category. Nor Min orMax are in both the categories.Hence this is one of the cause.
1STlevel funneling
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1.Cavity to
Cavity2.Boss diameter3.Symmetricity4.Radius Depth5.Center Shift
CONCLUSION:
From the above, Cavity to Cavity andBoss Parameter are not the causes for the
response.That leaves with Symmetricity,Radius
Depth and Centre shift of Radius are potentialcauses for the rejection.
g
2ndlevel SSVs
1.Symmetricity2.Radius Depth
3.Center Shift
SSVs remains after 1stlevel funneling
1stlevel funneling ToolDOE-Paired Comparison
1.Symmetricity2.Radius Depth3.Center Shift
Proceeding further to find whether they are the root causes
Analysis Step2
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Arranging values in Ascending order
Sl. No Response
1 G
2 G
3 G
4 G
5 G6 G Top Line
7 B
8 B
9 B
10 B
11 G
12 G Bottom Line
13 B
14 B
15 B
16 B
Symmetricity
0.50
0.50
0.55
0.60
0.600.70
0.70
0.70
0.78
0.80
0.80
1.50
0.80
1.10
1.12
1.35
SSV1 : Symmetricity
Analysis Step2
Top count =51/2
Bottom Count = 4Total Count =91/2
Total Count is > 6.Hence this SSV is oneof the root causes for the response at 95%
confidence level
Analysis Step2
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SSV2 : Radius DepthAnalysis Step2
Top count =41/2
Bottom Count = 7Total Count =111/2
Total Count is > 6.Hence this SSV is oneof the root causes for the response at 95%
Confidence level
Sl. No Response
1 G
2 G
3 G
4 G
5 G Top Line
6 B7 G
8 G
9 G Bottom Line
10 B
11 B12 B
13 B
14 B
15 B
16 B
134.15
134.21
133.95134.02
134.07
134.13
133.72
133.75
133.80
133.90
133.66
133.67
133.70
133.70
Radius depth
133.55
133.62
Analysis Step2
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SSV3 : Center shift of radius
y p
Top count = 5
Bottom Count = 4Total Count = 9
Sl. No Response
1 B2 B
3 B
4 B
5 B Top Line
6 G7 G
8 B
9 G
10 B
11 G12 B Bottom Line
13 G
14 G
15 G
16 G
48.20
48.32
48.37
47.90
48.0048.10
48.17
47.8047.80
47.82
47.88
47.45
47.50
47.70
47.75
Radius centre
47.45
Total Count is > 6.Hence this SSV is oneof the root causes for the response at 95%
Confidence level
Conclusion
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Conclusion
SSV1=Symmetricity
SSV2 =Radius Depth
SSV3= Center shift of Radius
Are the root causes for the Wall thickness Variation (Response Y)
Fixing Specification
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Fixing Specification
Since all the three parameter have count more than 6,New specifications arearrived at
New specifications are based on the sizes from good components.
Parameter Total Count New Specification
Symmetricity 91/2 < 0.60
Radius Depth 111/2 133.55 / 133.67
Center Shift of Radius 9 48.17 / 48.37
Proceeding Further
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Proceeding Further
Can we control the new specification to with in the limits arrived at?
Radius depth and Radius shift are set dimension in the Machine. Hence can becontrolled.
Symmetricity is created at Foundry and they have agreed study to restrictSymmetricity in 0.60 Max.
A l i
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Analysis
Checking the Contribution of Each Root Causefor the Response
Since there are 3 Parameters which affect theResponse, I have selected DOE tool
FullFactorial
for checking the contribution.
Stage 0: Factorial Analysis
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Stage 0:
Identification of (+) Setting and (-) Setting
ParameterIdentified As
Actual ParameterUnit of
Measurement
(+)
Setting
(-)Setting
A Symmetricity In mm < 0.60 > 1.00
B Radius Depth In mm 133.50 134.05
C Center Shift In mm 48.30 47.60
These are the parameters identified as root causes. (+) Settings are those which
produced Good components and (-) Settings are those which produced Bad
components.
Factorial Analysis
Stage 1: Making of Factorial Table
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Stage 1: Making of Factorial Table
A B C
Response A*B B*C A*C A*B*C
Symmetricity Radius Depth
Center Shift
of Radius
- - - + + + -
+ - - - + - +
- + - - - + +
+ + - + - - -
- - + + - - +
+ - + - - + -
- + + - + - -
+ + + + + + +
We have 3 Parameters
Hence No. of Rows = 2n = 2x2x2 = 8No. of Columns = n-1 = 8-1 = 7
Stage 1: Data Collection
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g
+ -
Symmetricity < 0.60 > 1.00
Radius Shift 133.50 134.05
Center Shift 48.30 47.60
Second RunSpecification for Factorial Analysis
Good Response Bad Response
G1 5.88 B1 4.24
G2 5.35 B2 4.46
G3 5.48 B3 5.20
G4 5.58 B4 4.38
G5 5.48 B5 4.78
G6 5.63 B6 4.56
Mean 5.56 Mean 4.60
Range 0.53 Range 0.96
First Run
Good Response Bad Response
G1 5.24 B1 4.82
G2 5.17 B2 4.72
G3 5.18 B3 4.63
G4 5.48 B4 4.79
G5 5.38 B5 4.93
G6 5.50 B6 4.63
Mean 5.33 Mean 4.75
Range 0.33 Range 0.30
Third Run
Good Response Bad Response
G1 5.54 B1 4.84
G2 5.43 B2 4.84
G3 5.32 B3 4.61
G4 5.32 B4 4.75
G5 5.28 B5 4.37
G6 5.28 B6 4.40
Mean 5.36 Mean 4.64
Range 0.26 Range 0.47
+ - - - + - + + -- - -
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S.No Response
1 4.92
2 4.89
3 5.26
4 4.75
5 5.11
6 4.71
Mean 4.94
Range 0.55
+ - +
S.No Response
1 5.17
2 5.50
3 5.11
4 5.30
5 5.27
6 5.45
Mean 5.30
Range 0.39
S.No Response
1 4.79
2 4.94
3 4.76
4 4.78
5 5.06
6 4.68
Mean 4.84
Range 0.38
S.No Response
1 4.70
2 4.71
3 4.70
4 4.69
5 4.14
6 4.71
Mean 4.61
Range 0.57
- + +
S.No Response
1 4.97
2 5.23
3 4.99
4 5.00
5 5.04
6 4.99
Mean 5.03
Range 0.26
- - +
S.No Response
1 5.21
2 5.38
3 5.50
4 5.17
5 5.28
6 5.24
Mean 5.30
Range 0.33
+ + +
S.No Response
1 5.88
2 5.35
3 5.48
4 5.58
5 5.48
6 5.63
Mean 5.56
Range 0.53
S.No Response
1 4.24
2 4.46
3 5.20
4 4.38
5 4.78
6 4.56
Mean 4.60
Range 0.96
Factorial Analysis
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y
A B C Response
Average wall
thickness
Symmetricity Radius Depth Center Shift of Radius
- - - 4.60
+ - - 4.94
- + - 4.84
+ + - 4.61
- - + 5.30
+ - + 5.30
- + + 5.03
+ + + 5.56
To Check Contribution of each Parameter
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o C ec Co t but o o eac a a ete
Response from Collected Data
A B CResponse AxB BxC AxC AxBxC
SymmetricityRadiusDepth
Center Shiftof Radius
- - - 4.60 + + + -
+ - - 4.94 - + - +
- + - 4.84 - - + +
+ + - 4.61 + - - -
- - + 5.30 + - - +
+ - + 5.30 - - + -
- + + 5.03 - + - -
+ + + 5.56 + + + +
+
0.64
-
0.10
+
2.20
-
0.04
+
0.08
+
0.420
+
1.10
+
0.16
-
0.025
+
0.55
-
0.01
+
0.02
+
0.105
+
0.275
Contributionof parameters
Total
Conclusion
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Conclusion
Parameter ContributionWhen the Parameter is moved from- to+,Response Increases or Decreases
A 0.160 Increases
B 0.025 Decreases
C 0.550 Increases
Based on the Factorial Analysis done for the data the Conclusions are given inthe table below
Using Minitab
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Using Minitab
Using Minitab
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g
Using Minitab
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Using Minitab
Six Sigma Tools used
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g
Phase Tools
Measure and
Analyze
1.Paired Comparison
2.Full Factorial
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Improvement
Phase
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Validating the
Root Causes
Selection of DOE Tool
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Since Good and Bad parts Can be created alternately,We selected B Vs C Toolto Validate the root cause(s)
Deciding B and C Condition for the Project
The Tool used for finding out the root cause is Paired Comparison.
Hence the B condition are those corresponding to Good category and
The C condition are those corresponding to Bad condition.
Symmentricity Radius Depth Centre shift of Radius
B Condition < 0.60 133.55 / 133.67 48.17 / 48.37
C Condition > 1.00 133.90 / 134.10 47.50 / 47.70
Symmetricity Radius Depth Center shift of RadiusDeciding Sample Size
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S. No Symmetricity Response
1 0.50 G
2 0.50 G
3 0.55 G
4 0.60 G
5 0.60 G
6 0.70 G
7 0.70 B
8 0.70 B
9 0.78 B
10 0.80 B
11 0.80 G
12 0.80 G
13 1.10 B
14 1.12 B
15 1.35 B
16 1.50 B
S. No Radius Depth Response
1 133.55 G
2 133.62 G
3 133.66 G
4 133.67 G
5 133.70 G
6 133.70 B
7 133.72 G
8 133.75 G
9 133.80 G
10 133.90 B
11 133.95 B
12 134.02 B
13 134.07 B
14 134.13 B
15 134.15 B
16 134.21 B
S. No Center Shift Response
1 47.45 B
2 47.45 B
3 47.50 B
4 47.70 B
5 47.75 B
6 47.80 G
7 47.80 G
8 47.82 B
9 47.88 G
10 47.90 B
11 48.00 G
12 48.10 B
13 48.17 G
14 48.20 G
15 48.32 G
16 48.37 G
Top count=51/2
Bottom count=4
Total count=91/2
Top count=41/2
Bottom count=7
Total count=111/2
Top count=5
Bottom count=4
Total count=9
Top
line
Bottom
line
Top
line
Bottom
line
Top
line
Bottom
line
Symmetricity Radius Depth Ce te s t o ad us
# Since Total Count is less than 16,We need to Machine 6B & 6C
Data Collection
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Deciding Sample Size
Assumption: There could be some overlap in the responses between
B & C condition as while establishing the rootcauses the Total counts were less then 12 for all the 3SSVs. Hence 6B & 6C were selected
Deciding whether 6B & 6C are to be in Nos. or in BatchesSince the response (Wall thickness) is Variable 6B & 6C will be in Nos.
Deciding what big Y will be Monitored
The big Y is Wall thickness (Response) and is Variable.This will be Monitored in Actual Values
Deciding Data collection Methodology
Decided to machine 6B and 6C by creating B and C condition alternatively
Specifications for Current & Better
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Specifications for Current & Bettercondition
CharacteristicBetter condition(New specification)
Current condition
Symmentricity < 0.60 > 1.00
Radius Depth 133.55/ 133.67 133.90 / 134.10
Centre shift of Radius 48.17 / 48.37 47.50 / 47.70
Data Collection
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Example NoResponse Y by
B ConditionResponse Y by
C Condition
1 5.88 4.242 5.35 4.46
3 5.48 5.20
4 5.58 4.38
5 5.48 4.78
6 5.63 4.56
Note :
1. During drilling operation the B Condition & C Condition were alternated for each piece
2. Since there is no overlap, the root causes are correct
Y = 4.80mm to 5.80mm
Analysis for 6B and 6C
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S.No Condition Response Y
1 C 4.24
2 C 4.38
3 C 4.46
4 C 4.56
5 C 4.78
6 C 5.20
7 B 5.35
8 B 5.48
9 B 5.48
10 B 5.58
11 B 5.63
12 B 5.88
Finding Whether the cause is correct (Another Way)
Top Count =6
Bottom Count =6Total Count =12
Since Total Count is >6,the root causes are correct.
if i h f
Analysis
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Quantifying the amount of Improvement
The Average of B = Xb = 5.57 mm
The Average of C = Xc = 4.60 mm
The Difference between Xb & Xc = Xb-Xc = 0.97 mm
Sigma value of B Values = Sigma B = 0.1813
K Value at 95% CL for 6,6 = 2.96
K * Sigma = 2.96 * 0.1813 = 0.537
( Xb Xc ) >= K * Sigma
0.97 > 0.537
Since Xb Xc is greater K * Sigma.
Improvement has taken place at the assumed C.L of 95%
The Amount of Improvement = Xb - Xc
= 0.97 mm
Of th 3 t
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Of the 3 root causes
Symmetricity is Foundry related dimension
Radius Depth and Center shift of radius are machining relateddimension. They are set and locked.
During the middle of the Project stage we discussed with Foundry for
maintaining to new specification of Symmetricity to 0.60 max. They said they
need a tolerance of 1.2 mm max. for their process and they will keep trying tobring it to 0.60 max.
Hence we proceeded with the project with Symmetricity up to 1.20 mm.
6 Nos were produced with Symmetricity 1.00 to 1.20 mm and the other two
dimensions to New specification.The response is as follows.
BOB and WOW Parts specification
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BOB and WOW Parts specification
Characteristic Better condition Current condition
Symmentricity A < 0.60 1.00 to 1.20
Radius Depth B 133.55 133.55
Centre shift of Radius - C 48.30 48.30
Data Collection
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Example NoResponse Y by
B ConditionResponse Y by C Condition with B
Condition data except Symmetricity
1 5.88 4.97
2 5.35 5.23
3 5.48 4.99
4 5.58 5.00
5 5.48 5.04
6 5.63 4.99
Note :
1. Since there is no overlap, the root causes are correct
Y = 4.80mm to 5.80mm
Quantifying the amount of Improvement
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The Average of B = Xb = 5.57 mm
The Average of C = Xc = 5.04 mm
The Difference between Xb & Xc = Xb-Xc = 0.53 mm
Sigma value of B Values = Sigma B = 0.1813
K Value at 95% CL for 6,6 = 2.96
K * Sigma = 2.96 * 0.1813 = 0.54
( Xb Xc ) >= K * Sigma
0.53 < 0.54
Since Xb Xc is Less than K * Sigma.
Improvement has not taken place at the assumed C.L of 95%
Quantifying the amount of Improvement
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The Average of B = Xb = 5.57 mm
The Average of C = Xc = 5.04 mm
The Difference between Xb & Xc = Xb-Xc = 0.53 mm
Sigma value of B Values = Sigma B = 0.1813
K Value at 90% CL for 6,6 = 2.61
K * Sigma = 2.61 * 0.1813 = 0.473
( Xb Xc ) >= K * Sigma
0.53 > 0.473
Since Xb Xc is More than K * Sigma.
Improvement has taken place at the assumed C.L of 90%
The Amount of Improvement = Xb - Xc
= 0.53 mm
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Animation
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Six Sigma Tools used
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Phase Tools
Improve 1. B Vs C
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Control Phase
We have Introduced the following Controls forth SSV
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the SSVs
SSV 1 Symmetricity : Foundry has agreed to study the process and reduce
the variation in Symmetricity to < 0.60. Till then they
will supply castings up to 1.20mm Symmetricity.
However,to ensure the coming castings whether they
are received with in 1.20mm Symmetricity thefollowing check has been introduced.
For every batch 30nos are taken at random and
Symmetricity is measured and the lot is accepted if
6s level is < = 75% of Tolerance.
Symmetricity Variationi i I i i l
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S.NoSymmetricity
in mm
1 0.25
2 0.30
3 0.20
4 0.25
5 0.10
6 0.05
7 0.15
8 0.20
9 0.20
10 0.24
11 0.25
12 0.25
13 0.05
14 0.45
15 0.20
S.NoSymmetricity
in mm
16 0.10
17 0.30
18 0.15
19 0.18
20 0.43
21 0.45
22 0.40
23 0.4524 0.40
25 0.10
26 0.20
27 0.50
28 0.52
29 0.3030 0.10
s = 0.1364
6s= 0.8181
6slevel is lesser than 75% of the Tolerance
Therefore the lot is Accepted
Incoming materialchecked on: 27.09.06
Casting Tolerance = 1.20 mm
Symmetricity VariationS i i I i t i l
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S.NoSymmetricity
in mm
1 0.70
2 0.95
3 0.45
4 0.80
5 0.30
6 0.60
7 1.42
8 0.40
9 0.15
10 0.83
11 0.65
12 0.60
13 0.65
14 0.40
15 0.25
S.NoSymmetricity
in mm
16 0.07
17 0.08
18 0.25
19 0.70
20 0.80
21 0.91
22 0.76
23 0.5324 0.57
25 0.53
26 0.95
27 0.05
28 0.37
29 0.0730 0.80
s = 0.3221
6s= 1.9327
6s
level is greater than 75% of the Tolerance
Therefore the lot is Rejected
Incoming materialchecked on :29.09.06
Casting Tolerance = 1.20 mm
SSV 2 & 3 Radius Depth and Center Shift of Radius :
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These are Setting dimensions in Milling Machine.Hence every
time when setting takes place or tool is changed, the setting will
be controlled based on response . The parameters are locked in
the system and operator cannot change. This can vary only due to
Wear in the Machine parts and Fixture parts. Periodical
Inspection and change of Wear parts have been introduced.
Further a Checking gauge which can give measured value for
SSVs has been provided to check the parameter at periodical
intervals.Currently the parameters are checked once in a day and
whenever fresh setting is done and cutter changed.
Radius checking Gauge with Master
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Gauge No :S GV 7018
This Gauge is added in theControl plan no 29320155/6
Page no: 3 of 52
Q Parts in the Fixture
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Check List for Q parts in fixtures
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Cell Name :Housing
Machine :SPM
Operation :Milling
S.No Part Name CharacteristicsSpecification
In mm
ActualDimensions
Frequencyin Months
ResultsActionTaken
Q1 R.H Side Sliding block
Working
Condition ofretainer spring
Spring load
1kg on44/46mmlength
1kg on
44mmlength
3 OK ---
Q2 L.H Side butting pin 1 Height 26.50 0.01 26.505 3 OK ---
Q3 L.H Side butting pin 1 Height 25.50 0.01 25.504 3 OK ---
Q4 Bottom butting pin 1 Height 17.00 0.01 17.005 3 OK ---
Q5 Bottom butting pin 2 Height 23.96 0.01 23.962 3 OK ---
Q6 Bottom butting pin 3 Height 23.96 0.01 23.959 3 OK ---
Q7 Bottom butting pin 3 Height 10.50 0.01 10.505 3 OK ---
Checked on: 17.08.06
Check List for Q parts in Machine
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S.No Part NameSpecification
In mm
ActualDimensions
Frequencyin Months
ResultsActionTaken
1 Bearing Worn-out --- 12 OK ---
2 Spindle axial play 0.020.03 mm 0.022 mm 12 OK ---
3 Spindle Radial play 0.020.03 mm 0.027mm 12 OK ---
4X Axis
Repeatability0 - 0.02 mm 0.017 mm 12 OK ---
5 Z AxisRepeatability
0 - 0.02 mm 0.010 mm 12 OK ---
Cell Name :Housing
Machine :SPM
Operation :Milling
Checked on: 04.06.06
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Variation Analysis for Root
Cause and Response
Step 1: Identifying Parameters
R di D h d C Shif f R di h
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Radius Depth and Center Shift of Radius are the two root cause
parameters identified for Variation Analysis as they are
1. Measurable and Variable
2. These root causes are generated from the milling process andnot functional parameters.
3. These are generated from discrete production process and not
from a batch process.4. Can be measured with Non-destructive method.
5. We can detect the parameter immediately if something goeswrong immediately after generation.
6. Apart from the root causes,Variation Analysis for Response (Y)I.e., Wall thickness was also decided to be done to find outwhether the estimated Variation is < = 50% i.e.,6s level
Step 2: Identifying Product / Process StreamIn this case only one Stream is there.
Step 3: Deciding Sample Size
Th f ll i d id d d f ll d
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The following were decided and followed
1. Sample size - 3 Nos
2. Time block chosen - 25
3. Period of Coverage - 4 Hrs
4. Planned events between the Time blocks were captured.
5. Randomized Time intervals were followed.
6. Time blocks were closer because Cycle time is < 3 mins
(Actual is 56 Secs)
Step 4: Collection of Data
Instrument and Dial Gauge with Accuracy which is less than 10%of Tolerance is used.
Step 5: Multi Vari Analysis
Not done as products are not produced from different Streams
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Variation Analysis for
Root Causes (X)
Variation Analysis for Root Cause (X)
P t D t il
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Part Details
CharacteristicRadiusDepth
Part Number 29320155/6 Gauge Number S GV 7018
Unit ofMeasurement
MM PartDescription
HousingMachining
GaugeDescription
RadiusGauge
Target Value Date 08.02.06Gauge Least
Count0.01 mm
Tolerance 0.20 mm
Gauge R&RValue 7.98USL 133.600
Study Dates& Shift
06.07.06
1stShift
LSL 133.400Any other
details----
Data Grouping and Sample details
Number of Groups (Number of Time blocksx number of Streams)
26
Number of Samples in each group (It ispreferable to collect 5 samples continuously
from the process so that the inherentvariations are captured)
3
Study taken to check the variation in the Process at randomized time blocks in SPMMilling for Radius Depth and Center Shift
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S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
1 0.00 4 -0.01 7 0.00 10 -0.01 13 -0.02 16 -0.01 19 0.01 22 -0.03
2 -0.01 5 0.03 8 0.01 11 0.01 14 0.01 17 -0.03 20 0.00 23 0.00
3 0.00 6 -0.01 9 0.01 12 -0.01 15 -0.01 18 0.00 21 0.01 24 -0.02
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
25 -0.02 28 -0.02 31 0.00 34 0.03 37 -0.03 40 -0.03 43 -0.01 46 -0.04
26 -0.02 29 0.00 32 0.00 35 -0.04 38 0.00 41 0.00 44 -0.03 47 -0.05
27 0.02 30 0.00 33 0.02 36 0.02 39 -0.01 42 -0.01 45 -0.02 48 -0.02
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
49 0.00 52 -0.01 55 -0.01 58 -0.08 61 -0.03 64 -0.04 67 0 70 -0.04
50 0.01 53 0.00 56 0.00 59 -0.03 62 -0.03 65 -0.07 68 -0.04 71 -0.0651 -0.01 54 -0.02 57 -0.06 60 -0.03 63 -0.03 66 -0.04 69 -0.03 72 -0.04
S.No Response S.No Response
73 -0.01 76 0.00
74 0.00 77 -0.02
75 0.00 78 -0.02
T17 T18 T19 T20 T21 T22
T6 T7 T8
T25 T26
T16T11 T12
T23 T24
T13 T14 T15
Actual time=1:44 Actual time=2:00 Actual time=2:10
T1 T2 T3 T4
T9 T10
Actual time=1:30 Actual time=1:35
Actual time=2:45 Actual time=3:05 Actual time=4:02 Actual time=4:11
Actual time=6:17
Actual time=2:20 Actual time=2:28 Actual time=2:36
Actual time=4:25 Actual time=4:38 Actual time=4:50
T5
Actual time=6:24 Actual time=6:30
Actual time=4:55
Actual time=5:13 Actual time=5:20 Actual time=5:28 Actual time=5:48 Actual time=5:54 Actual time=6:00 Actual time=6:07
Time between Time blocks in Minutes
1) 5
2) 9
3) 16
4) 10
5) 10
6) 8
7) 8
8) 9
9) 20
10) 57
11) 9
12) 14
13) 13
14) 12
15) 5
16) 19
17) 7
18) 22
19) 6
20) 6
21) 10
22) 3
23) 10
24) 7
25) 6
Study taken to check the variation in the Process at randomized time blocks in SPMMilling for Radius Depth and Center Shift
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# Part to Part Variation = Max. Value of R = 0.07 mm
# Time to Time Variation = Max. Value of Ave.Min. Value of Ave. = 0.057 mm
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
1 0.00 4 -0.01 7 0.00 10 -0.01 13 -0.02 16 -0.01 19 0.01 22 -0.03
2 -0.01 5 0.03 8 0.01 11 0.01 14 0.01 17 -0.03 20 0.00 23 0.00
3 0.00 6 -0.01 9 0.01 12 -0.01 15 -0.01 18 0.00 21 0.01 24 -0.02
Ave -0.003 Ave 0.003 Ave 0.007 Ave -0.003 Ave -0.007 Ave -0.013 Ave 0.007 Ave -0.017
R 0.01 R 0.04 R 0.01 R 0.02 R 0.03 R 0.03 R 0.01 R 0.03
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
25 -0.02 28 -0.02 31 0.00 34 0.03 37 -0.03 40 -0.03 43 -0.01 46 -0.04
26 -0.02 29 0.00 32 0.00 35 -0.04 38 0.00 41 0.00 44 -0.03 47 -0.05
27 0.02 30 0.00 33 0.02 36 0.02 39 -0.01 42 -0.01 45 -0.02 48 -0.02
Ave -0.007 Ave -0.007 Ave 0.007 Ave 0.003 Ave -0.013 Ave -0.013 Ave -0.020 Ave -0.037
R 0.04 R 0.02 R 0.02 R 0.07 R 0.03 R 0.03 R 0.02 R 0.03
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
49 0.00 52 -0.01 55 -0.01 58 -0.08 61 -0.03 64 -0.04 67 0.00 70 -0.04
50 0.01 53 0.00 56 0.00 59 -0.03 62 -0.03 65 -0.07 68 -0.04 71 -0.06
51 -0.01 54 -0.02 57 -0.06 60 -0.03 63 -0.03 66 -0.04 69 -0.03 72 -0.04
Ave 0.000 Ave -0.010 Ave -0.023 Ave -0.047 Ave -0.030 Ave -0.050 Ave -0.023 Ave -0.047
R 0.02 R 0.02 R 0.06 R 0.05 R 0.00 R 0.03 R 0.04 R 0.02
S.NoResponse S.No Response
73 -0.01 76 0.00
74 0.00 77 -0.02
75 0.00 78 -0.02
Ave -0.003 Ave -0.013
R 0.01 R 0.02
T25 T26
T21 T22 T23 T24T17 T18 T19 T20
T13 T14 T15 T16T9 T10 T11 T12
T1 T2 T3 T4 T5 T6 T7 T8
The tolerance is 0.20 mm. Variation 0.07 mm is with in 75% of the Tolerance
Calculating Upper Control Limit
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R (Average of all Ranges) = 0.027 mm
(Rounded off to one decimal more than the data)
UCL = D4 x R
= 2.575 x 0.027 (D4 Value taken from table for 3 Sample Size)
= 0.0695 mm
Rounding off to the same decimal of data = 0.07 mm
Step 7: Checking the Consistency of Part to Part Variation
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20100
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
Sample Number
SampleRa
nge
R Chart for Response
R=0.02731
UCL=0.07030
LCL=0
Checking the Consistency of Part to PartVariation
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Variation
1. All points lie with in the Limits
2. The Stratification level is > 3
3. There are no 7 points continuously increasing
4. There are no 7 points continuously decreasing
5. There are no 7 points in any of the 2 zones
ThereforePart to Part Variation is Consistent
Consistency of Part to Part Variation
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Checking the Consistency of Part to Part Variation (Step 7)
Average range (R-Bar) (Round off to onedecimal more than the data)
0.027Samples D3 D4
2 0 3.267
Upper control limit (UCL) = D4*R-Bar
(Round off to the same decimals as data)0.07
3 0 2.575
4 0 2.282
5 0 2.115
Lower control limit (LCL) = D3*R-Bar 0 6 0 2.004
Is the Part to Part Variation Consistent YES / NO
If the Part to Part variation is consistent, STOP, do not proceed further. Plan forDOE
Is the range chart plotted YES / NO
Are the stratification level more than 3 YES / NO
If the stratification level
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s
= Estimated Part to Part Variation
s= R/d2 (d2is a Constant and depends on Sample size.d2 for 3samples is 1.693)
= 0.027 / 1.693
= 0.0159 (To be rounded off to one decimal more than the data)
= 0.016
6s 0.096
Estimated Part to Part Variation Confidential level = 99.73%
Step 10 : Normality Check
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0.00-0.05-0.10
20
10
0
Response
Frequenc
y
Step 11 : Estimating Rejection Percentage
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Average 0.027 Z (usl) 4.563
s
0.016 Z (lsl) 7.938
6s 0.096Estimated Rejection
above USL0
USL 0.100Estimated Rejectionabove LSL
0
LSL -0.100 Cpk (usl) 1.521
Cpk (lsl) 2.646
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Variation Analysis forResponse to arrive at Control
method for Y
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Variation Analysis for
Response (Y)
Variation Analysis for Response (Y)Part Details
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Part Details
CharacteristicWall
thicknessPart Number 29320155/6 Gauge Number SM 200
Unit ofMeasurement
MM PartDescription
HousingMachining
GaugeDescription
VernierCaliper
Target Value Date 07.07.06Gauge Least
Count0.01 mm
Tolerance 1.00 mm
Gauge R&RValue 13%USL 5.80 mm
Study Dates& Shift
07.07.06
1stShift
LSL 4.80 mmAny other
details----
Data Grouping and Sample details
Number of Groups (Number of Time blocksx number of Streams)
26
Number of Samples in each group (It ispreferable to collect 5 samples continuously
from the process so that the inherentvariations are captured)
3
Study taken on Response at randomized time blocksActual time=3:26 Actual time=3:38 Actual time=3:48Actual time=3:05 Actual time=3:17 Actual time=4:04 Actual time=4:11 Actual time=4:21
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S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
1 5.10 4 5.03 7 5.14 10 5.24 13 5.21 16 5.14 19 5.11 22 5.14
2 5.10 5 5.24 8 5.22 11 5.31 14 5.19 17 5.14 20 5.19 23 5.17
3 5.16 6 5.15 9 5.22 12 5.24 15 5.18 18 5.19 21 5.20 24 5.16
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
25 5.30 28 5.25 31 5.06 34 5.10 37 5.23 40 5.14 43 5.18 46 5.28
26 5.23 29 5.13 32 5.21 35 5.23 38 5.14 41 5.19 44 5.12 47 5.40
27 5.02 30 5.05 33 5.18 36 5.14 39 5.08 42 5.10 45 5.28 48 5.06
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
49 5.21 52 5.17 55 5.03 58 4.97 61 5.03 64 5.08 67 5.24 70 5.04
50 4.92 53 5.15 56 5.00 59 5.03 62 5.10 65 5.17 68 5.11 71 5.09
51 5.18 54 4.93 57 5.09 60 5.09 63 5.35 66 5.10 69 5.21 72 5.02
S.No Response S.No Response
73 5.07 76 5.10
74 5.04 77 5.11
75 5.08 78 5.01
T17 T18 T19 T20 T21 T22
T6 T7 T8
T25 T26
T16T11 T12
T23 T24
T13 T14 T15
T1 T2 T3 T4
T9 T10
Actual time=4:28 Actual time=4:35 Actual time=4:45 Actual time=4:51
Actual time=6:56
Actual time=5:00 Actual time=5:08 Actual time=5:20
T5
Actual time=7:02 Actual time=7:12
Actual time=5:33
Actual time=5:43 Actual time=5:56 Actual time=6:10 Actual time=6:20 Actual time=6:31 Actual time=6:38 Actual time=6:48
Time between Time blocks in Minutes
1) 12
2) 9
3) 12
4) 10
5) 16
6) 7
7) 10
8) 5
9) 9
10) 10
11) 6
12) 9
13) 8
14) 12
15) 13
16) 10
17) 13
18) 14
19) 10
20) 11
21) 7
22) 10
23) 8
24) 6
25) 10
Total = 247 mins = 4Hrs 7Mins
5.5
Randomised time block
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4.8
5.3
5.2
5.1
5.0
4.9
5.5
5.4
706560555045403530252015105 75 8580 1009590
T1 T5T4T3T2 T9T8T7T6
Re
sponse"Y"
Time interval in mins
Just before
event
Just after
event
Event
Time
T1 T2 T3 T4 T5 T6 T7 T8
Step 6: Checking whether the Part to Part is highest
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S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
1 5.10 4 5.03 7 5.14 10 5.24 13 5.21 16 5.14 19 5.11 22 5.14
2 5.10 5 5.24 8 5.22 11 5.31 14 5.19 17 5.14 20 5.19 23 5.17
3 5.16 6 5.15 9 5.22 12 5.24 15 5.18 18 5.19 21 5.20 24 5.16
Ave 5.12 Ave 5.14 Ave 5.19 Ave 5.26 Ave 5.19 Ave 5.16 Ave 5.17 Ave 5.16
R 0.06 R 0.21 R 0.08 R 0.07 R 0.03 R 0.05 R 0.09 R 0.03
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
25 5.30 28 5.25 31 5.06 34 5.10 37 5.23 40 5.14 43 5.18 46 5.28
26 5.23 29 5.13 32 5.21 35 5.23 38 5.14 41 5.19 44 5.12 47 5.40
27 5.02 30 5.05 33 5.18 36 5.14 39 5.08 42 5.10 45 5.28 48 5.06
Ave 5.18 Ave 5.14 Ave 5.15 Ave 5.16 Ave 5.15 Ave 5.14 Ave 5.19 Ave 5.25
R 0.28 R 0.20 R 0.15 R 0.13 R 0.15 R 0.09 R 0.16 R 0.34
S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response S.No Response
49 5.21 52 5.17 55 5.03 58 4.97 61 5.03 64 5.08 67 5.24 70 5.04
50 4.92 53 5.15 56 5.00 59 5.03 62 5.10 65 5.17 68 5.11 71 5.09
51 5.18 54 4.93 57 5.09 60 5.09 63 5.35 66 5.10 69 5.21 72 5.02
Ave 5.10 Ave 5.08 Ave 5.04 Ave 5.03 Ave 5.16 Ave 5.12 Ave 5.19 Ave 5.05
R 0.29 R 0.24 R 0.09 R 0.12 R 0.32 R 0.09 R 0.13 R 0.07
S.No Response S.No Response
73 5.07 76 5.1
74 5.04 77 5.11
75 5.08 78 5.01
Ave 5.06 Ave 5.07
R 0.04 R 0.10
T9 T10 T11 T12 T13 T14 T15 T16
T23 T24T17 T18 T19 T20
T25 T26
T21 T22
# Part to Part Variation = Max. Value of R = 0.34
# Time to Time Variation = Max. Value of Ave.Min. Value of Ave. = 0.23
Part to Part variation is highestand hence we proceeded further
Calculating Upper Control Limit
R (A f ll R ) = 0 139
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R (Average of all Ranges) = 0.139 mm
(Rounded off to one decimal more than the data)
UCL = D4 x R
= 2.575 x 0.139 (D4 Value taken from table for 3 Sample Size)
= 0.3579
Rounding off to the same decimal of data = 0.36 mm
Step 7: Checking the Consistency of Part to PartVariation
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0 10 20
0.0
0.1
0.2
0.3
0.4
Sample Number
SampleRang
e
R Chart for response
R=0.1388
UCL=0.3574
LCL=0
Checking the Consistency of Part to Part Variation
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1. All points lie with in the Limits
2. The Stratification level is > 3
3. There are no 7 points continuously increasing
4. There are no 7 points continuously decreasing
5. There are no 7 points in any of the 2 zones
Therefore Part to Part Variation is Consistent
Consistency of Part to Part Variation
Checking the Consistency of Part to Part Variation (Step 7)
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Checking the Consistency of Part to Part Variation (Step 7)
Average range (R-Bar) (Round off to onedecimal more than the data)
0.139Samples D3 D4
2 0 3.267
Upper control limit (UCL) = D4*R-Bar
(Round off to the same decimals as data)0.36
3 0 2.575
4 0 2.282
5 0 2.115
Lower control limit (LCL) = D3*R-Bar 0 6 0 2.004
Is the Part to Part Variation Consistent YES / NO
If the Part to Part variation is consistent, STOP, do not proceed further. Plan forDOE
Is the range chart plotted YES / NO
Are the stratification level more than 3 YES / NO
If the stratification level
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s
= Estimated Part to Part Variation
s= R/d2 (d2is a Constant and depends on Sample size.d2 for 3samples is 1.693)
= 0.139 / 1.693
= 0.0821 (To be rounded off to one decimal more than the data)
= 0.082
6s= 0.492
Estimated Part to Part Variation Confidential level = 99.73%
Step 10 : Normality Check
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4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40
0
5
10
15
response
Frequenc
y
Step 11 : Estimating Rejection Percentage
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Average 5.141 Z (usl) 8.037
s
0.082 Z (lsl) 4.159
6s 0.492Estimated Rejection
above USL
0
USL 5.800Estimated Rejectionabove LSL
0
LSL 4.800 Cpk (usl) 2.679
Cpk (lsl) 1.390
Step 12 : Decision on the type of Monitoring
6 Analysis
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6s
Analysis
In our case Tolerance = 1.00 mm
6s= 0.492
6s
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Pre control limit for On job
Hour Wall thickness (Response)1stJob 2ndJob
1 5.33 5.11
2 5.41 5.61
3 5.28 5.39
4 5.14 5.26
5 5.09 5.06
6 5.45 5.51
7 5.12 5.25
8 5.47 5.21
Step 14 : On line Monitoring
Pre control limit for On job
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j
USL
UCL
LCL
LSL
Time interval
WallThickness(Response)inmm
5.80
5.30
5.55
5.05
4.80
5.000
4.85
4.95
4.90
5.65
5.70
5.60
5.50
5.45
5.405.35
5.25
5.20
5.15
5.10
5.75
1 2
43
5 6
7
8
Controls
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1. Drawing updated for new specification
2. Control plan updated
3. FMEA updated
4. The new parameters have been programmed and
locked in the system
5. A Setting Gauge has been introduced in milling
operation to check the new parameter settings at
periodical intervals.This has been incorporated in
Control plan and FMEA
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Control plan
Reaction Plan
Product Process
Product/Process
Specification
Tolerance
Evaluation/
Measurement
Technique
Sample Control
method Resp. Recording (Y/N)
CharacteristicsSpecial
Character
istic class
Methods
Control Plan
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Size Frequency
DISC 1.RADIUS DEPTH 133.7 0.30 MM CMM 1 PER DAY INSPECTIO INSPECTO YES HOLD,REINSPECT
MILLING
2.CENTER SHI FT OF 47.50 / 48.50 MM CMM 1 PER AY INSPECTIO INSPECTO YES HOLD,REINSPECT
RADIUS
3.CASTING LEVER DIAL 100% - INSPECTION QA NO SEGREGATE AND
DIMENSION AND FIXTURE KEEP
( TOOLING
LOCATION W.R.TO
CENTER OF
CASTING )
4.HARDNESS 165 - 250 BHN HARDNESS AS PER - INSPECTION QA NO SEGREGATE AND
MEASURING SHOWA KEEP
INSTRUMENT SINGLE
SAMPLING
PLAN
4.BUTTING OF VISUAL 100% - INSPECTION OPERATOR NO SEGREGATE AND
COMPONENT KEEP
5.CLAMPING PRESSURE ONCE PER DAY CHECKING OPERATOR YES INFORM
PRESSURE GAUGE MAINTENANCE
Tolerance Technique
Reaction Plan
CharacteristicsSpecial
Character
Methods
Product/Process Evaluation/
Control Plan
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Size Frequency
LUG 1.FLANGE 13.15 / 12.85 MM VERNIER 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
MILLING THICKNESS 11 GG 5092
2.POSITION FROM 11.5 MM VERNIER 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
HOLE CENTER
3.LUG FACE TO 24.20 / 23.80 MM HEIGHT GAUGE 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
"V" FACE S GD 7091 KEEP
4.CENTER SHIFT OF 47.50 / 48.50 MM S GV 7018 GAUG 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
RADIUS
Reaction Plan
Product Process Resp. Recording (Y/N)
Character
istic class
Product/Process
Specification
Tolerance
Evaluation/
Measurement
Technique
Sample Control
method
MethodsCharacteristicsSpecial
Control Plan
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Size Frequency
WALL 4.80 / 5.80 MM VERNIER 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
THICKN ESS
1.RADIUS DEPTH CMM 1 PER DA INSPECTIO OPERATOR YES HOLD,REINSPECT
2.CENTER SHIFT OF CMM 1 PER DAY INSPECTIO OPERATOR YES HOLD,REINSPECT
RADIUS
3.CASTING LEVER DIAL 100% - INSPECTION QA NO SEGREGATE AND
DIMENSION AND FIXTURE KEEP
( SYMMENTRICITY )
5.CLAMPING PRESSURE ONCE PER DAY CHECKING OPERATOR YES INFORM
PRESSURE GAUGE MAINTENANCE
Control
methodResp. Recording (Y/N)
Reaction PlanSample
Product/Process
Specification
Tolerance
Evaluation/
Measurement
Technique
Special
Character
istic classProcessProduct
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Control plan &
Process FMEAafter 6 Sigma
Process FMEA after 6 Sigma
PROCESS
STEPFAILURE MODE POTENTIAL CAUSES OCC
CURRENT PROCESS
CONTROL (TYPE - B)
CURRENT PROCESS
CONTROL (TYPE - C)
CURRENT PROCESS
CONTROL (TYPE - A)DET RPN
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STEP CONTROL (TYPE - B) CONTROL (TYPE - C) CONTROL (TYPE - A)
DISC MILLING 1.DISC MILLING 1.HARDNESS 1 NIL RECEIVING INSPECTION NIL
RADIUS AS PER SHOWA SINGLE
OVERSIZE SAMPLING PLAN
UNDERSIZE ( ACCEPTANCE LEVEL 0 )
RESP : INSPECTOR
2.RADIUS DEPTH
OVERSIZE 2.CASTING DIMENSION NIL RECEIVING INSPECTION NIL
UNDERSIZE ( TOOLING LOCATION W.R AS PER SHOWA SINGLE
TO CENTER OF CASTING ) SAMPLING PLAN
3.CENTER SHIFT ( ACCEPTANCE LEVEL 0 )
OF RADIUS RESP : INSPECTOR
OVERSIZE
UNDERSIZE 3.BUTTING THE CASTING NIL POKA - YOKE ONCE IN 2 HRS BY QA 6 6
BY OPERATOR PROVIDED PRE-DESPATCH
INSPECTION
AS PER SHOWA SINGLE
SAMPLING PLAN
( ACCEPTANCE LEVEL 0 )
RESP : INSPECTOR
4.TABLE MOVEMENT NIL IT IS IN PM CHECK NIL
LIST
PROCESSFAILURE MODE POTENTIAL CAUSES OCC
CURRENT PROCESS CURRENT PROCESS CURRENT PROCESSDET RPN
Process FMEA after 6 Sigma
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STEPFAILURE MODE POTENTIAL CAUSES OCC
CONTROL (TYPE - B) CONTROL (TYPE - C) CONTROL (TYPE - A)DET RPN
LUG FLANGE 1.CENTER SHIFT OF RADIU 1 PROCESS CONTROL NIL ONCE IN 2 HRS BY QA 6 6
MILLING THICKNESS CHART PRE-DESPATCH
VARIATION CHECK 1 NO/HOUR INSPECTION
RESP: OPERATOR AS PER SHOWA SINGLE
SAMPLING PLAN
( ACCEPTANCE LEVEL 0 )
INSPECTOR
2.SPINDLE AXIAL AND NIL ADDEED IN THE
RADIAL PLAY PM CHECK LIST
Process FMEA after 6 SigmaPROCESS
STEPFAILURE MODE POTENTIAL CAUSES OCC
CURRENT PROCESS
CONTROL (TYPE - B)
CURRENT PROCESS
CONTROL (TYPE - C)
CURRENT PROCESS
CONTROL (TYPE - A)DET RPN
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PIN HOLE WALL 1.CASTING DIMENSION 1 NIL RECEIVING INSPECTION NIL 6
DRILLING THICKNESS ( SYMMETRICITY, AS P ER SHOW A SINGLE
UNDERSIZE CAVITY TO CAVITY & SAMPLING PLAN
BOSS DIAMETER ) ( ACCEPTANCE LEVEL 0 )
RESP : INSPECTOR
2.RADIUS DEPTH PROCESS CONTROL NIL ONCE IN 2 HRS BY QA 5 5
CHART PRE-DESPATCH
CHECK 1 NO/HOUR INSPECTION
RESP : INSPECTOR AS PER SHOWA SINGLE
SAMPLING PLAN
3.CENTER SHIFT OF PROCESS CONTROL NIL ( ACCEPTANCE LEVEL 0 )
RADIUS CHART RESP : INSPECTOR
CHECK 1 NO/HOUR
RESP : INSPECTOR
Size Frequency
Special
Character
istic class
Methods
Reaction Plan
Product Process
Product/Process
Specification
Tolerance
Evaluation/
Measurement
Technique
Sample Control
method Resp. Recording (Y/N)
Characteristics
Control Plan after
6 Sigma
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Size Frequency
DISC 1.RADIUS DEPTH 133.55 / 133.67 MM S GV 7018 GAU 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
MILLING (PROCESS)
2.CENTER SHIFT OF 48.17 / 48.37 MM S GV 7018 GAU 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
RADIUS (PROCESS)
3.CASTING LEVER DIAL 100% - INSPECTION QA NO SEGREGATE AND
DIMENSION AND FIXTURE KEEP
( TOOLING
LOCATION W.R.TO
CENTER OF
CASTING )
4.HARDNESS 165 - 250 BHN HARDNESS AS PER - INSPECTION QA NO SEGREGATE AND
MEASURING SHOWA KEEP
INSTRUMENT SINGLE
SAMPLING
PLAN
Sample ControlReaction Plan
CharacteristicsSpecial
Character
Methods
Product/Process Evaluation/
Control Plan after 6 Sigma
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Size Frequency
LUG 1.FLANGE 13.15 / 12.85 MM VERNIER 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
MILLING THICKNESS 11 GG 5092
2.POSITION FROM 11.5 MM VERNIER 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
HOLE CENTER
3.LUG FACE TO 24.20 / 23.80 MM HEIGHT GAUGE 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
"V" FACE S GD 7091 KEEP
4.CENTER SHIFT OF 48.17 / 48.37 MM S GV 7018 GAUG 1 PER HOUR INSPECTIO OPERATOR YES HOLD,REINSPECT
RADIUS (PROCESS)
Sample Control
methodProduct Process Resp. Recording (Y/N)istic class Specification
Tolerance
Measurement
Technique
Control Plan after 6 Sigma
MethodsCharacteristics
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Size Frequenc
WALL 4.80 / 5.80 MM VERNIER 1 PER HOUR INSPECTIO OPERATOR YES
THICKNESS S GG 7167
1.RADIUS DEPTH S GV 7018 GAUGE 1 PER HOUR INSPECTIO OPERATOR YES
2.CENTER SHIFT OF S GV 7018 GAUGE 1 PER HOUR INSPECTIO OPERATOR YES
RADIUS
3.CASTING LEVER DIAL AS PER - INSPECTION QA NO
DIMENSION AND FIXTURE SAMPLING
( SYMMENTRICITY )
Recording (Y/N)
MethodsCharacteristics
Product/Process
Specification
Tolerance
Evaluation/
Measurement
Technique
Special
Character
istic classProcessProductSample Control
methodResp.
HOLD,REINSPECT
HOLD,REINSPECT
HOLD,REINSPECT
SEGREGATE AND
KEEP
Reaction Plan
Six Sigma Tools used
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Phase Tools
Control 1. Variation Analysis
2. Pre-Control chart3. Control plan
BenefitsRejection reduced to Zero
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Rejection due to M/H Less Wall thickness
000000
67
5
001
2
3
4
56
7
8
Week36
Week37
Week38
Week39
Week40
Week41
Week42
Week43
Week44
Week45
QtyinNos
Improvement
through 6s
Qty Produced from week 39 week 45
= 39785 Nos
Estimated Cost Saving by Rejection reduction is Rs. 1,21,589 / Annum
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