© 2002 systex services capability and improvement - from cpk to six sigma
TRANSCRIPT
© 2002 Systex Services
Capability and Improvement
- from Cpk to Six Sigma
© 2002 Systex Services
Capability & ImprovementM
anuf
actu
ring
Pro
cess
es
Statistical Process Control
Par
ts
ContinuousImprovement ProcessesP
eopl
e
Six Sigma
Bus
ines
s P
roce
sses
• Vital for credibility and results
© 2002 Systex Services
Statistical Process Control
- theory and practice
© 2002 Systex Services
Use of Statistical Process Control• Attributes and variables
13.456
AttributeOK or Not OK
VariableMeasurable
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SPC Application
• Initially applied to mechanical components– in mass production – as a control mechanism
• Subsequently applied to any measurable
© 2002 Systex Services
Principles of SPC for Variable Data
• Rules apply when distribution is normalKgs Qty25.0 025.1 1 125.2 1 125.3 1 1 225.4 1 1 225.5 1 1 1 1 425.6 1 1 1 1 1 525.7 1 1 1 1 1 1 625.8 1 1 1 1 1 1 1 1 825.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1326.0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1726.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1326.2 1 1 1 1 1 1 1 1 826.3 1 1 1 1 1 1 626.4 1 1 1 1 1 526.5 1 1 1 1 426.6 1 1 226.7 1 1 226.8 1 126.9 027.0 0
Total 100
Plot
Dimension: 26 Kgs ± 0.5
Bell Curve
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Principles of SPC for Variable Data• Rules do not apply when distribution is abnormal
Skewed Multiple
TruncatedRandom Selection
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Principles of SPC for Variable Data• Normal distribution has consistent variation• Variation unit is ‘Standard Deviation’ -
(Sigma)
• Standard deviation is calculated using:
= (fx2/n) - x2 (Root Mean Square method)
© 2002 Systex Services
Principles of SPC for Variable Data• Standard deviation : = (fx2/n) - x2 (Root Mean Square method)
Weight FrequencyTotal
WeightSquared
WeightSum of
squaresX f fX X2 fX2
25.1 1 25.1 630.01 630.025.2 1 25.2 635.04 635.025.3 2 50.6 640.09 1280.225.4 2 50.8 645.16 1290.325.5 4 102.0 650.25 2601.025.6 5 128.0 655.36 3276.825.7 6 154.2 660.49 3962.925.8 8 206.4 665.64 5325.125.9 13 336.7 670.81 8720.526.0 17 442.0 676.00 11492.026.1 13 339.3 681.21 8855.726.2 8 209.6 686.44 5491.526.3 6 157.8 691.69 4150.126.4 5 132.0 696.96 3484.826.5 4 106.0 702.25 2809.026.6 2 53.2 707.56 1415.126.7 2 53.4 712.89 1425.826.8 1 26.8 718.24 718.2
Totals 100 2599.1 67564.3
X = fX/n = (fX2/n) - X2]= 2599.1/100 = (/100) - (25.991)2]= 25.991 = - 675.532]
= = 0.111 Kgs
Forg
et it
!
- use
MS
Exce
l fun
ctio
ns
- STD
EV, S
TDEV
P
- or s
peci
alis
t sof
twar
e
© 2002 Systex Services
Principles of SPC for Variable Data• Standard Deviation enables calculation of
probability of defects1 1 1 1 1 1
68.26%
95.44%99.73%
Defects with spec. limits at:1 sigma = 31.74% = 317,400 dpm2 sigma = 4.56% = 45,560 dpm3 sigma = 0.27% = 2,700 dpm
© 2002 Systex Services
Principles of SPC for Variable Data• Normal distribution relative to limits
– forecasts scrap– defines process capability– enables process control
‘Normal’ distribution
Upper control limitLower control limit
Lower spec. limit Upper spec. limit
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Capability Studies• Process capability is relative to:
– defined limits– location of process mean– spread of process
LSL USLNOM
Broad spreadGood placement
Moderate spreadModerate placement
Narrow spreadPoor placement
© 2002 Systex Services
Capability Studies• Purpose of capability studies
– to define process capability– to help identify limiting causes– to demonstrate capability to customers– to improve process capability
• reduce defects, waste, cost, customer returns
• undertake higher spec. work
– to employ statistical process controls
© 2002 Systex Services
Capability Studies
Cp
– spec. range 6– no account of placement
Cpk – lower value of
– (USL - X) / 3or (X - LSL) / 3
• Two basic measures of capability
2.402.430
2.385
LSLUSL
X
3 3
2.475
2.50
Cp = (USL-LSL)/6 x 1.111
Cpk = (X-LSL)/3 x 0.667
© 2002 Systex Services
Capability Studies• What is a good Cpk ratio?
• Minimum normally 1.33 Cpk
– based on 4 sigma spread
– extra sigma compensates for
• larger spread over time & larger population
• particularly mean shift
– equivalent to 63 DPM on centred process
• Many companies now looking for 2.0 Cpk
– consistent with 6 sigma concept
– equivalent to 0 DPM
• based on centred process
• allowing up to 2 sigma shift
© 2002 Systex Services
Capability Studies• Capability studies also indicate:
– trends
– cycles
– other influences
Trend - Weight
21.5
22.0
22.5
23.0
23.5
24.0
24.5
25.0
25.5
26.0
26.5
1 3 5 7 9 11 13
15
17
19
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25
27
29
31
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35
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47
49
Gra
ms
Upper Spec. Limit
Lower Spec. Limit
45
50
55
60
65
08:0
008
:30
09:0
009
:30
10:0
010
:30
11:0
011
:30
12:0
0
Av. Viscosity
89.590.0
90.591.0
91.5
Mo
n
We
d
Fri
Tu
e
Th
u
Mo
n
We
d
Fri
Tu
e
Th
u
Mo
n
We
d
Fri
© 2002 Systex Services
X-Bar & Range Charts• X-bar charts plot sample mean values
X-bar
23.80
23.90
24.00
24.10
24.20
24.30
24.40
24.50
24.60
24.70
Process Mean 24.24 24.24 24.24 24.24 24.24 24.24 24.24 24.24 24.24
Subgroup Mean 24.36 24.04 24.50 24.04 24.50 24.00 24.28 24.10 24.50
UCL (Mean+A2*Av.R) 24.56 24.56 24.56 24.56 24.56 24.56 24.56 24.56 24.56
LCL (Mean-A2*Av.R) 23.92 23.92 23.92 23.92 23.92 23.92 23.92 23.92 23.92
1 2 3 4 5 6 7 8 9
UCL
LCL
© 2002 Systex Services
X-Bar & Range Charts• Range charts plot sample range values
Range Chart
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Gra
ms
Range 0.70 0.30 0.80 0.40 0.70 0.20 0.70 0.20 0.70 0.90
UCL (D4*Av.R) 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18
1 2 3 4 5 6 7 8 9 10
UCL
© 2002 Systex Services
Capability Reports
Capability study
results required by many
major customers
STUDY: RESULTS:
Customer: Excellence plc Mean: 24.24 U-Ppk: 1.92 USL: 26.00 + 3 Sigma: 25.16Part Number: 344 834 890 Std Dev: 0.31 L-Ppk: 2.45 LSL: 22.00 - 3 Sigma: 23.33Type: PreliminaryDimension: 24.00Cavity Number: 1Conducted by: John AshcroftDate: 36678
DATA:24.0 24.0 24.2 24.0 24.224.1 24.6 24.1 24.1 24.424.4 24.5 24.8 24.1 24.824.6 24.8 24.7 24.7 24.924.7 24.6 24.7 24.5 24.224.2 24.1 23.9 24.2 23.824.0 23.8 24.0 24.0 24.024.0 23.9 24.0 24.0 23.923.9 24.2 24.1 24.2 24.224.1 24.2 24.0 24.1 24.7
COMMENTS:
Trend Chart Here
Histogram Here
Histogram
0
2
4
6
8
10
12
21
.8
22
.1
22
.4
22
.7
23
.0
23
.3
23
.6
23
.9
24
.2
24
.5
24
.8
25
.1
25
.4
25
.7
26
.0
26
.3
26
.6
Trend
23
24
24
25
25
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
© 2002 Systex Services
Six Sigma
- achieving quantum leaps in competitiveness
© 2002 Systex Services
Six Sigma Application
• Applies Statistical Process Control to ALL business process - not just manufacturing
• Combined with classical Continuous Improvement Techniques
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Six Sigma Objective
Service output
Critical customerrequiremente.g. 3 day delivery
Defects:> 3 days
Reducedvariation
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Six Sigma Example
0
2
4
6
8
10
12
34.1
0
34.2
0
34.3
0
34.4
0
34.5
0
34.6
0
34.7
0
34.8
0
34.9
0
35.0
0
35.1
0
35.2
0
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0
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0
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0
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35.7
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35.9
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36.7
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36.8
0
36.9
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37.6
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37.7
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37.8
0
CCR 36.0
Mean 35.25 36.75
6
3
13
50
DP
M -
sta
ble
pro
cess
22
75
0 D
PM
- 1
Sig
ma
me
an
sh
ift 1 Sigma = 0.25
© 2002 Systex Services
6 Sigma & Quality Loss FunctionNormal DistributionQuality Loss Function
Taguchi: Quality Loss Function = k(x - T)2
Where: k = constant for scrap valuex = value of quality characteristicT = target
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What is Six Sigma?
Suppliers Inputs ProcessesProcessoutputs
Critical customerrequirements
Markets
Defects
Variations in process output cause defects
Root cause analysis of defects leads to permanent defect reduction
Six Sigma Business Improvement...
… a data driven approach to root cause analysis
© 2002 Systex Services
Six Sigma Success FactorsCommitted Leadership
Integration with toplevel strategy
Business process framework
Customer & marketintelligence network
Projects produce realsavings or revenue
Full time six sigmateam leaders
Incentives for all
© 2002 Systex Services
6 Sigma & Business StrategyL
ead
e rs h
i p P
r oc e
s s Business Strategy Development
Core businessProcess
Key PerformanceMeasures
Process OutputMeasures
Critical CustomerRequirements
Marketplace
ProcessSigma
© 2002 Systex Services
6 Sigma Process
MEASUREMENT:- selection
- measurability- acceptability
ANALYSIS:- process capability- experimentation
- root cause
IMPROVEMENT:- actions
- process trials- proving
CONTROL:- selection
- maintenance- reaction
Project by project
© 2002 Systex Services
Implementing 6 SigmaOrganisational
Assessment
• Appoint core team • Process mapping• Current measures• Process owners• Customer knowledge• Customer surveys• Current capabilities• Competitive data• Accountabilities
Over 4 weeks
Exec. Planning Workshop
• Vision/ goals/ 6 sigma• Basis for improvement• Tools & methods• 5 year plan:
• net earnings• growth• improvements
• Opportunities• Select pilot units• Communication plan• Leadership criteria• Resource planning• Commitment
2 days
Pilot BusinessUnit Workshops
• Strategy outline• 6 sigma methods• Integration process• Status assessment• Identify projects• Benefit targets• Force field analysis• Select leaders• Training schedules• Project milestone • Set regular reviews
2 days
6 Sigma LeaderTraining
• High profile launch• Interactive training• Project definition• Mapping• Measurement• Analysis• Analytical tools• Design of experiment• Process sigma• Apply• Facilitate teams• Measurable benefits
4 - 15 weeks
Typical time scales
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6 Sigma Roll Out
OrganisationalAssessment
ExecutiveWorkshop
Pilot UnitWorkshop
Team LeaderTraining
Unit ReviewExecutiveReview
Projects
Projects
Team LeaderTrainingUnit Workshops
© 2002 Systex Services
6 Sigma Black Belt TrainingWEEK 16 sigma & planning overviewProcess mappingQuality function deploymentFailure mode effects analysisOrganizational effectivenessBasic statisticsProcess capabilityMeasurements systems analysis
WEEK 3Design of experiments
- factorial- fractional factorials- balanced block design- evolutionary operation EVOP- response surface designs
ANOVA (Analysis of Variance)Regression (multiple)Facilitation tools
WEEK 2Review of key week 1 topicsStatistical thinkingHypothesis testingCorrelationPassive multi-vari analysis ®ression (simple)Team assessment
WEEK 4Control plansStatistical process control(advanced)Mistake proofingTeam developmentWrap-up of tools
Gre
en B
elt
Bla
ck B
elt
© 2002 Systex Services
6 Sigma Comments
• Large cost reductions: – AlliedSignal $800M (95/7)– GE $600M (3Q97 gain)
• Performance bonus link
• Capability quantified
• Investors & stakeholders understand financial gain
• Customer needs measured
• Year one payback - ROI potential 20% + thereafter
• Large initial investment off putting
• Poor follow through
• Short term thinking
• Changed priorities
• New leadership
• ‘Tried that’ (no longer use it!)
• Fear of statistics
Benefits Risks