© 2002 systex services capability and improvement - from cpk to six sigma

© 2002 Systex Services

Capability and Improvement

- from Cpk to Six Sigma


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


Statistical Process Control

- theory and practice


Use of Statistical Process Control• Attributes and variables

13.456

AttributeOK or Not OK

VariableMeasurable


SPC Application

• Initially applied to mechanical components– in mass production – as a control mechanism

• Subsequently applied to any measurable


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


Principles of SPC for Variable Data• Rules do not apply when distribution is abnormal

Skewed Multiple

TruncatedRandom Selection


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)


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

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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


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


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


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


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


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


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

21

23

25

27

29

31

33

35

37

39

41

43

45

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


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


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


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


Six Sigma

- achieving quantum leaps in competitiveness


Six Sigma Application

• Applies Statistical Process Control to ALL business process - not just manufacturing

• Combined with classical Continuous Improvement Techniques


Six Sigma Objective

Service output

Critical customerrequiremente.g. 3 day delivery

Defects:> 3 days

Reducedvariation


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

35.3

0

35.4

0

35.5

0

35.6

0

35.7

0

35.8

0

35.9

0

36.0

0

36.1

0

36.2

0

36.3

0

36.4

0

36.5

0

36.6

0

36.7

0

36.8

0

36.9

0

37.0

0

37.1

0

37.2

0

37.3

0

37.4

0

37.5

0

37.6

0

37.7

0

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


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


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


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


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


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


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


6 Sigma Roll Out

OrganisationalAssessment

ExecutiveWorkshop

Pilot UnitWorkshop

Team LeaderTraining

Unit ReviewExecutiveReview

Projects

Projects

Team LeaderTrainingUnit Workshops


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 &regression (simple)Team assessment

WEEK 4Control plansStatistical process control(advanced)Mistake proofingTeam developmentWrap-up of tools

Gre

en B

elt

Bla

ck B

elt


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

© 2002 systex services capability and improvement - from cpk to six sigma

Documents

sigma spreadextra sigma

xlsl3 s

variable datarules

sigma conceptequivalent

dpm2 sigma

dpm3 sigma

capability studieswhat

measurableprinciples