Post on 08-Apr-2018
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StatisticalProcessControl: Isthecollectionofproblemsolvingtoolsusefulin
achievingprocessstabilityandimprovingprocess
capabilitythroughreductionofvariability
Process monitoring and control
X1
Input raw
materials,
components, and
X2 Xp
Measurement
Evaluation
Monitoring and
control
Product Output
Controllable Inputs
Use of design of experiments to
ascertain the assignable causes
Process
Z2Zp
y = Quality
Characteristic
s - ss s
Z1
Uncontrollable inputs
Output
ProcessKnowledge
Stagesofprocessknowledge Blissfulignorance
Awareness ofignorance(Art)
Measure
Controlthemean
Processcapability
Processcharacterization(knowhow)
Knowwhy(processoptimizationpossible,formulaeforprocess)
Completeknowledge
BiscuitbakeryexampleRogerBohn
Variationandprocessknowledge
8stagesofprocessknowledge bakery
Stage of K Name Comment Typical form knowledge
1. Completeignorance
Nowhere
2. Awareness Pure art Tacit
3. Measure Pre-technolo ical
Written
4 .Control of mean Sc methodfeasible
Written and in hardware
5.Process capabi li ty Local recipe H/W & operat ing manual
6. Processcharacterization
Trade-offs Empirical equation
7. Know why Science Scientific formulae,
algorithm8. Complete K Nirvana
StatisticalProcessControl TheControlProcess
Definevariable Measure
Comparetoastandard Evaluate Takecorrectiveaction
Standard
Process
Input Output
Sensor / measure
Comparator
Feedback
StatisticalProcessControl
VariationsandControl
Randomvariation:Naturalvariationsintheoutputofprocess,createdbycountlessminor
factors
ss gna evar at on: var at onw osesourcecanbeidentified
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StatisticalProcessControlSteps
Produce Good
Provide Service
No
Take Sample
Start
Can weassign
causes?
Stop Process
Yes
Inspect Sample
Find Out WhyCreate
Control Chart
SamplingDistribution
Sampling
distribution
Process
Mean
A number of
small samples.
As sample size
gets
large
eno u h
sampling distribution
becomes almost normal
regardless of
population distribution
of individual samples.
Central Limit TheoremTheoreticalBasisofControlCharts
X
XCLT: The distribution of sample means is normal in shape with means and
Standard Deviation .
If (1) the distribution of population is normal or
( 2) sample size is large enough (n>30)
Xx =nXx =
NormalDistribution
3 2 +2 +3
= Standard deviation(68.26%)
Mean3 2 +2 +3
95.44%
99.74%a b
Relationshipbetweentheprocessandthecontrol
chartStepstoFollowWhenUsingControl
Charts1. Collect 20 to 25 samples ofn=4 orn=5 from a stable
process and compute the mean.
2. Compute the overall means, set approximate controllimits,and calculate the preliminary upper and lower controllimits.If the process is not currently stable, use the desired
mean instead of the overall mean to calculate limits..
3. Graph the sample means and ranges on their respectivecontrol charts and determine whether they fall outside theacceptable limits. Take care of Type 1 & 2 errors.
4. Investigate points or patterns that indicate the process isout of control. Assign causes for the variations
5. Collect additional samples and revalidate the control limits
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ControlCharts
Continuous
Numerical Data
Categorical or Discrete
Numerical Data
ControlChartTypes
R
Chart
VariablesCharts
AttributesCharts
X
Chart
P
ChartC
Chart
X Chart
Typeofvariablescontrolchart
Intervalorratioscalednumericaldata
Showssamplemeansovertime
Monitorsprocessaverage
Example:Weighsamplesofsurf&computemeansofsamples;Plot
ControlChartsfor andR
ControlLimitsforthe chart
x
x
xxRAxUCL 32 +=+=
A2 isfoundinTableforvariousvaluesofn.
xxRAxLCL
xneen er
32 ==
=
ControlChartVisualoperatorcontrol
UCL
Mean
Out ofcontrol
Abnormal variationdue to assignable sources
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
LCL
Sample number
Normal variationdue to chance
Abnormal variationdue to assignable sources
FactorsforComputingControlChartLimitsTableA (or D)
Sample
Size, n
Mean
Factor, A2
Upper
Range, D4
Lower
Range, D3
2 1.880 3.268 0
3 1.023 2.574 0
4 0.729 2.282 05 0.577 2.115 0
6 0.483 2.004 0
7 0.419 1.924 0.076
8 0.373 1.864 0.136
9 0.337 1.816 0.184
10 0.308 1.777 0.223
12 0.266 1.716 0.2840.184
ProcessStandarddeviationfromRange(normaldistribution)
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R Chart
Typeofvariablescontrolchart
Intervalorratioscalednumericaldata Showssamplerangesovertime
erence e weensma es arges va ues ninspectionsample
Monitorsvariabilityinprocess
Example:Weighsamplesofsurf&computerangesofsamples;Plot
ControlChartsfor andR
EstimatingtheProcessStandardDeviation
Theprocessstandarddeviationcanbeestimatedusingafunctionofthesampleaveragerange.
x
Thisisanunbiasedestimatorof2
d
R=
R Chart ControlLimits(tableusedaspopulations.d.notknown)
From Table S6.1
RDLCL
RDUCL
3R
4R
=
=
Range for Sample i
# Samplesn
R
Ri
n
1i=
=
ControlChartfor
(Samplesof9Boxesfilledfor400gmeach)
Variation due to
natural causes
410=UCL
405=Mean
Variation due to
assignable causes
400=LCL
Variation due to
assignable causes
Out of control
1 2 3 4 5 6 7 8 9 10 11 12
Sample Number
Say a sample of 5 packets is taken with weights 401, 403, 405, 407, 409.
Then Mean of sample = 405 AND RANGE = 409 -401=8x
ControlChartVisualoperatorcontrol
UCL
Mean
Out ofcontrol
Abnormal variationdue to assignable sources
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
LCL
Sample number
Normal variationdue to chance
Abnormal variationdue to assignable sources
Surf fillingprocess
Hr 1Hr 8 Hr 7 Hr 6 Hr 5 Hr 4 Hr 3 Hr 2
Fill Hopper
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ObservationsfromSampleDistribution
UCL
Sample number
LCL
1 2 3 4
(process mean is
shifting upward)
SamplingDistribution
MeanandRangeCharts
UCL
LCL
R-chart
x-Chart Detects shift
Does notdetect shift
UCL
LCL
MeanandRangeCharts
(process variability is increasing)Sampling
Distribution
LCL
LC
L
R-chart Reveals increase
x-Chart
UCL
Does not
reveal increase
ProcessControl:ThreeTypesofProcessOutputs
Frequency
Lower control limit Upper control limit
(a) In statistical control andcapable of producing withincontrol limits. Aprocess withonly natural causes ofvariation and capable ofproducing within the specifiedcontrol limits.
Size
(Weight, length, speed, etc. )
(b)In statistical control, but notcapable of producing within control
limits. Aprocess in control (onlynatural causes of variation are present)
but not capable of producing within thespecified control limits; and
(c)Out of control. Aprocess out ofcontrol having assignable causes of
variation.
PatternstoLookforinControlCharts
EngineeringDrawings ShowDimensions,Tolerances,etc.
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ControlChartsfor andR
ControlLimits,SpecificationLimits
Controllimits arefunctionsofthenaturalvariabilit of the rocess usuall set at 3si ma
x
fromthemean)
Specificationlimits aredeterminedbydevelopers/designers.
ControlChartsfor andR
ControlLimitsandSpecificationLimits
Thereisnomathematicalrelationship betweencontrol limits and s ecification limits.
x
Donotplotspecificationlimitsonthecharts
Causesconfusionbetweencontrolandcapability
Ifindividualobservationsareplotted,thenspecificationlimitsmaybeplottedonthechart.
Unacceptable, process needsadjustment back to centre of range.
MaxNominalLimit
Limit
MaxNominalLimit
LimitMax
Acceptable, even if things changeslightly.
MaxNominal
Nominal
Time distributions in the proposal writing process
Unacceptable, needs to reduce thevariability.
Unacceptable, needs to re centre theprocess and reduce variability
MaxNominalLimit
Acceptable now, but the slightestchange will make it unacceptable.
Should reduce the variability
ProcessCapability
LowerSpecification
Upper
Specification
Process variability matches
specificationsLower
SpecificationUpperSpecification
Process variability well within
specificationsLowerSpecification
UpperSpecification
Process variability exceedsspecifications
Factorsinfluencingprocesscapability
1. Condition of machine/ equipment.
2. Type of operation and operational conditions.
3. Raw materials.
. .
5. Measurement method / instruments.
6. Inspectors skill.
ProcessCapabilityRatio
Process capability ratio, Cp =specification width
process width
Cp>1 implies a process has the potential of having more than 99.73% of
outcomes within specifications
Upper specification lower specification
6pCp =
where normal distribution is assumed (number of samples is large):
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ProcessCapabilityCpk
3
LimitionSpecificatLowerx
or,3
xLimitionSpecificatUpperofminimum
=
p
p
pkC
populationprocesstheofdeviationstandard
meanprocessxwhere
=
=
pAssumes that the process is:
under control normally distributed
MeaningsofCpk Measures
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
WHAT IS SIX SIGMA ?
QUALITY BENCHMARK - PRODUCT, PROCESS, SERVICES
DEFECT REDUCTION TECHNIQUE
CORPORATE PHI LOSOPHY
A FEW SIX SIGMA RESULTS
MOTOROLA ( 1987-1994)
REDUCED IN P ROCESS DEFECT LEVELS 200 TIMES
REDUCED MFG. COSTS B Y $ 1.4 BILLION
INCREASED SHARE VALUE 4 TIMES
- CUMULATIVE SAVINGS $ 14 BILLION (UPTO 1997)
GENERAL ELECTRIC
1997 : $ 300 MILLION PROFIT
1998 : $ 600 MILLION PROFIT
OPERATING PROFITS INCREASED TO 16.7% IN 1998
ThreeEmphasisAreasforSixSigma
Focused on product design excellence, design for manufacturability,Customer satisfaction and cost reduction within all components ofthe development and new product introduction process.
Focused on operational excellence, Customer satisfaction and cost
reduction within all components of the operation. Areas of focusinclude Sales, HR, Finance, Materials, etc.
Focused on product production excellence, variation and defectreduction, lean production techniques, Customer satisfaction andcost reduction within all components of the production and deliveryprocess.
Six Sigma touches on allaspects of the BusinessEnterprise
BasicTerminologies
CTQ
Metric
Defect
/
Defective DPU
Opportunity&DPMO
COPQ
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The key measurable characteristics of a product orprocess whose performance standards or specification
limits must be met in order to satisfy the customer.
They align improvement or design efforts withcustomer re uirements.
CTQ - Critical to Quality
Customer level CTQProduct / Process level
CTQ
Order Delivery on time OM process cycle time
Smooth gear shifting Shifter fork movement,
cone clutch
CTQs
Customer Generated
Process Generated
Business Generated
Six Sigma speaks only in terms of MetricsSo measure everything that results in customer satisfaction
Examples of Metric
Process Metric Business results metric
%QC & Rework time -------- Manpower cost
No of defects (DPMO) -------- Rework/Warranty cost
Material residing time -------- Inventory carrying cost
Cost per KM Travel -------- ROI
Hit ratio -------- Order booking value
Process metricTo define the result / output of processes, certain process metrics have to be defined - thestandards which help track and monitor the processes.
Process metric control
Process output is dependent on inputs(X) we provide to theprocess ,that is Y= f (X)
To control Y we must control X i
Measurement
Evaluation
Monitoring andControllable Inputs
Process
1
Z2Zp
y = Quality
Characteristic
Input raw
materials,
components, and
sub-assemblies
Z1
2control
Product Output
Uncontrollable inputs
DefiningProcesses&CTQS
Identify customer driven Critical-to-quality (CTQ)characteristics
Identify Key processes that cause defects in a CTQCharacteristics
For each product or process CTQ-Measure, Analyze, improve &CONTROL
Processidentificationmatrix:linkingprocessandCTQ
Customer driven CTQ Improved CSI Score
Vehicle servicing
Sub CTQ 1Waiting time
for registration
Sub CTQ 2Waiting during
service
Sub CTQ 3Satisfaction
At time ofdelivery
Process1
Process2
Process3
ServiceLevelCTQ
Registration of service request
Servicing process
After service follow up
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BasicTerminologies
CTQ
Metric Defect/Defective
DPU
Opportunity&DPMO
COPQ
Unit
Unit is the basis of measurement of a metric.
Length : Metric
Meter : Unit.
Defect
Duster length = 10.1cm
Defect vs Defective
Defect is within a unit
Defective is for a unit.
Defect Per Unit (DPU)
Shoe No. No. of defects
1 2
2 1
3 3
4 0
Total = 4 Total = 6
DPU = Total no. of defects / Total no. of units
= 6 / 4 = 1.5 defects per unit
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Opportunities:Any measurable event that provides a chance of not meetingspecification limits of a CTQ
DPMO : Defect per million
opportunities
= No. of defects x 106
No. of units x No. of opp.
THE COST OF POOR QUALITY
Sigmalevel
DPMO COPQ
2 308,537 (non-competitive) not applicable
3 66,807 25-40 % of sales
4 6,210 (industry avg.) 15-25% of sales
5 233 5-15% of sales
6 3.4 (world class) < 1% of sales
Each sigma shift provides a 10 % net income improvementSource : Mikel J. Harry & Richard Schroeder in Six Sigma
SixSigmaasaPhilosophy
Internal &
ExternalFailureCosts
Prevention &Appraisal
Costs
Old Belief4C
osts Old Belief
High Quality = High Cost
is a measure of how muchvariation exists in a process
Internal &
ExternalFailure Costs
Prevention &
AppraisalCosts
New BeliefCosts
4
5
6
Quality
Quality
New Belief
High Quality = Low Cost
LSL USL
6 Sigma curve
3 Sigma curve
3 Sigma Vs 6 Sigma
2 3 4 5 6 7 8 9 1210 16151413111
In a 3 sigma process the values are widely spread along the center line,
showing the higher variation of the process. Whereas in a 6 Sigma
process, the values are closer to the center line showing
less variation in the process.
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Off-Target Too Much Variation
TheObjectiveOfSixSigmaTheObjectiveOfSixSigma
UT UTLT LT
Defects
CenterProcess
ReduceSpread
CenteredOn-Target
Reduce Variation & Center Process :Customers feel the variation more than the mean
UTLT
UT : Upper Tolerance
LT : Lower Tolerance
Amountofprocessshiftallowed
LSL USL
SD = 1
1.5 SD 1.5 SD
2 3 4 5 6 7 8 9 1210 16151413111
Breakthrough Strategy: DMAICBreakthrough Strategy: DMAIC
DEFINE D
MEASURE M
ANALYSE A
IMPROVE I
CONTROL C
Process metric control
Process output is dependent on inputs(X) we provide to theprocess ,that is Y= f (X)
To control Y we must control X i
Measurement
Evaluation
Monitoring andControllable Inputs
Process
1
Z2Zp
y = Quality
Characteristic
Input raw
materials,
components, and
sub-assemblies
Z1
2control
Product Output
Uncontrollable inputs
1 2 3
Input1
input2
Input1
input2
Input1
input2
Process Mapping
CTQ1
CTQ2
1
2
Step1:Process mapping
a) Form team using subject matter
experts and process owners
b) Define the current process steps
and input (xs)
c) Identify which process steps
affecteach CT
Use baking example for process map and C& E Matrix and FMEA
Imp.
Rating3 5
CTQ1 CTQ
2
score
Input13 4 29
input23 5 34
(Cause & Effect)
d) Identify the characteristic of
each process input
Step2: C&E Matrix
(Cause & Effect Matrix)
a) List the controllable and
critical inputs vertically in
the C&E matrix.
b ) L is t t he CTQS
horizontally
c) Use the same team to co-
relate and weigh the impact
of each input to each CTQ
Process
Step/Input
Potential Failure
Mode
Potential Failure
Effects
S
E
V
Potential Causes
O
C
C
Current Controls
D
E
T
R
P
N
What is the
rocessste /
In what ways does
the Ke In ut o
What is the impact
ontheKe Out ut sthe
otheWhat causes the Key
In ut to owron ? ause
cu
r?What are the existing
controls and rocedures you
Failure Mode Effect Analysis (FMEA)
Input under
investigation?
Step/Input
wrong?
Variables (Customer
Requirements) or
internal
requirements?How
Severei
effectt
How
oftendoesc
orFM
oc
(inspection and test) that
prevent eith the cause or
the Failure Mode? Should
include an SOP number.How
wellcan
Step3:FMEA
a) List the key inputs which
Rank high in the C&E
matrix in the input column
of FMEA,
b) Work through FMEA with team
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Imp.Rating 3 5
CTQ1 CTQ
2
score
Process
Step/Input
Potential Failure
Mode
Potential Failure
Effects
SE
V
Potential CausesOC
C
CurrentControlsDE
T
RP
N
What is the
process step/
Inwhat ways does
theKey Input go
What is theimpact
onthe Key Output isthe
totheWhat causes theKey
Input togo wrong? ause
ccur?What arethe existing
controls and procedures nyou
FMEA
1 2 3
Input1
input2
Input1
input2
Input1
input2
Process Mapping
C&E Matrix(Cause & Effect)
CTQ1
CTQ2
1
2
3
Input13 4 29
input23 5 34
Step1:Process mapping
a) Form team using subject matter
experts and process owners
b) Define the current process steps
and input (xs)
c) Identify which process steps
affect each CTQ
d) Identify the characteristic of
each process input
Step2: C&E Matrix
(Cause & Effect Matrix)
a) List the controllable and
critical inputs vertically in
the C&E matrix.
b ) L is t th e CTQS
horizontally
c) Use the same team to co-
relate and weigh the impact
of each input to each CTQ
Step3:FMEA
a) List the key inputs which
Rank high in the C&E
matrix in the input coulumn
of FMEA,
b) Work through FMEA with team
Input under
investigation?
Step/Input
wrong? Var iabl es (Customer
Requirements) or
internal
requirements?How
Severe
effectt
How
oftendoesc
orFM
o(inspectionandtest) that
prevent eitht hecause or
theFailure Mode? Should
include anSOPnumber.How
wellca
The Funneling Effect
30+ Inputs
8 -10
10 - 15
All Xs
1st Hit List
Screened List
MEASURE
ANALYZE
Process Maps
FMEAs
C&E Matrix
Critical Input Variables
4 - 8
3 - 6
Found Critical Xs
Controlling Critical Xs
IMPROVE
CONTROL
Multi-Vari Studies
Design of Experiments(DOE)
Control Plans
SIX SIGMA METHODOLOGIES : DMAIC
The 5 - step methodology
Guideposts Define Measures Analyze Improve Control
What are thecustomers needs
& key processes ?
What is thefrequency of
f
When andwhere do
defects occur ?
How can wefix the
How can weensureprocessremains fixed
DIR
ECTION
?
TRANS
PORT
TOOLS
Surveyinterviewsinquiries
processmap
Measurementsigma scorecost of poor
quality
Statisticalanalysispareto
FMEA
DOE SOP riskanalysis actionplanning
Error proofingprocessmonitoring
Process Improvement Tools
Measurement
Project Charter
Process Mapping
Cause & Effect diagram
Descriptive statistics
Gage R & R
Process Capability
Analysis
Pareto Charts
Histogram
ScatterDiagram
Run Chart
FMEA
t-test
Test for equalvariances
ANOVA
Chi-square
2-proportions
Regression
Improvement
Historical DOE
Full factorial DOE
Fractional Factorial DOE
Residual Analysis
Solution design matrix
Pilot
Control
Mistake proofing
X-bar & R chart
I & MR chart
p - Chart
c-chart
SIX SIGMA METHODOLOGIES : DMAIC
The 5 - step methodology
Guideposts Define Measures Analyze Improve Control
Initiate, scope, and
plan the project
Under-standing
customer
needs andi
Developdesign
concepts
and highi
Developdetailed
design and
control / test
Test designand
implement full
- scale
DIRECTI
O
Nspec y s eve des gn p an processes
TRANSPORT
TOOLS
MGP
Project management
Customers research
QFD
Benchmarking
FMEA / error proofing
Process simulation
Design scorecards