National Excellence ProgramElaborating and operating an inland student and researcher personal support system convergence program

Reg.No.: TÁMOP 4.2.4. A/2-11-1-2012-0001

Project period: 2013/09/01-2014/08/31

Name and address of Contractor:University of PannoniaEgyetem utca 10, Veszprém H-8200

Total funding granted by the European Union and the Hungarian Government: 4 200 000 .- HUF.

Design and selection of multidimensional risk-based control charts

Zsolt Tibor KosztyanCsaba Hegedus

Attila Katona

WCIT 2013Brussels, Belgium

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Statistical process control

Values can be:

Sample means (x-bar)

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Statistical process control

Values can be:

Sample means (x-bar)

Moving Avrg of the sample means (MA)

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Statistical process control

Values can be:

Sample means (x-bar)

Moving Avrg of the sample means (MA)

Exponent. Weighted Moving Avg (EWMA)

Etc.

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Constraints and shortcomings of control charts

Control charts work only on probability

base

Not every process is normal

Normality of the values is assumed

Consequences/costs are not taken into

account

Measurements givethe input of the

charts

Measurements havesome uncertainty

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

28,5

29

29,5

30

30,5

31

31,5

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Dia

met

er(m

m)

Sample

X-Bar chart (diameter)

Átlag

UCL

LCL

9898,5

9999,5100

100,5101

101,5

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Axi

slen

gth

(mm

)

Sample

X-Bar chart (axis-length)

UCL

LCL

Multivariate Case

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

0

2

4

6

8

10

12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

T2 é

rték

ek

Sample

Reliability-based T2 chart

T2

UCL

Multivariate Case

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Data sampling

Data sampling:• Distribution type• Mean• Variance• Measurement uncertainty• Specification Limits

1. step 2. step 3. step 4. step

The rewiev of the method

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Data sampling

Design of the controlchart

0

2

4

6

8

10

12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

T2va

lues

Sample

The designed T2 chart

T2

UCL

1. step 2. step 3. step 4. step

The rewiev of the method

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Data sampling Design of the controlchart

Margin-valuecalculation

Conformable NonNon-conformable

Non

-con

form

able

Con

form

able

Conformable ConformableNon-conformable Non-conformable

Conformable

Conformable

Non-conformable

Non-conformable

Decision

Rea

l

1. step 2. step 3. step 4. step

The rewiev of the method

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Data sampling Design of the controlchart

Margin-valuecalculation

Conformable NonNon-conformable

Non

-con

form

able

Con

form

able

Conformable ConformableNon-conformable Non-conformable

Conformable

Conformable

Non-conformable

Non-conformable

1011=r1011-c1011

1111=r1111-c1111 1110=r1110-c1110

1010=r1010-c1010

0001=r0001-c0001

0101=r0101-c0101 0100=r0100-c0100

0000=r0000-c0000p0011=r0011-c0011

0111=r0111-c0111 0110=r0110-c0110

0010=r0010-c0010

1001=r1001-c1001

1101=r1101-c1101 1100=r1100-c1100

1000=r1000-c1000

Decision

Rea

l

1. step 2. step 3. step 4. step

=Margin-valuer=Income

c=Cost

The rewiev of the method

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Data sampling Design of the controlchart

Margin-valuecalculation

Modification of thecontrol limit

0

2

4

6

8

10

12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

T2va

lues

sample

The designed T2 chart

T2

T2(withuncertainty)UCL

1. step 2. step 3. step 4. step

The rewiev of the method

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Data sampling Design of the controlchart

Margin-valuecalculation

Modification of thecontrol limit

0

2

4

6

8

10

12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

T2va

lues

sample

The designed T2 chart

T2

T2(withuncertainty)UCL

New controllimit

1. step 2. step 3. step 4. step

The rewiev of the method

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Industrial Example

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

0

2

4

6

8

10

121 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

T2 va

lues

Sample number

T2

T2(withuncertainty)

UCL

T2

Reliability-based T2 chart

The new control limit

Industrial Example

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

0

2

4

6

8

10

121 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

T2 va

lues

Sample number

T2

T2(withuncertainty)

UCL

T2

Reliability-based T2 chartk

The new control limit

Industrial Example

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

0

2

4

6

8

10

121 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

T2 va

lues

Sample number

T2

T2(withuncertainty)

UCL

RBT2

Risk-based T2 chart

RBT2=Risk-Based T2 The new control limit

Industrial Example

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Aspect T2 RBT 2(Risk-Based T2)

k 0 0,24UCL 9,19 8,95

Total margin value (€) 2.092.000 2.115.000

Margin increment (%) - 1,099

2.092.000 € 2.115.000 €

Results

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Aspect T2 RBT 2(Risk-Based T2)

k 0 0,24UCL 9,19 8,95

Total margin value (€) 2.092.000 2.115.000

Margin increment (%) - 1,099

2,022,032,042,052,062,072,082,092,1

2,112,12

-0,4 -0,2 0 0,2 0,4 0,6 0,8 1

Tota

l mar

gin

valu

e(€)

k parameter

Az The total margin-value related to the kparameter

k: coverage factor

Total marginincreased by

1.1 %

k=0,24

Results

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

1

1,2

1,4

1,6

1,8

2

2,2

2,4

2,6

2,8

3

10 20 30 40 50 60 70 80 90 100 110 120 130

Normal distribution (µ=0, =0,01) Beta distribution (a=0.003, b=5)Weibull distribution (0,003, b=2) Lognormal distribution (µ=0, =0,01)Uniform distribution (a=-0,01, b=-0,02)

The total marginal value- increment related to the costof type II error in case of different distributions

Results

Cost of Type II error (€)

Tota

l Mar

gin

valu

ein

crem

ent(

%)

National Excellence Program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Summary

The reliability centered approach of the control charts does not give the best solutionThe reliability centered approach of the control charts does not give the best solution

The risk of the decision and measurement uncertainty can be taken into account to improve the resultsThe risk of the decision and measurement uncertainty can be taken into account to improve the results

Risk-based approach can be used at multivariate casesRisk-based approach can be used at multivariate cases

The optimal modification of control limits are determined through simulations The optimal modification of control limits are determined through simulations

A new family of control charts can be definedA new family of control charts can be defined

National Excellence Program – Elaborating and operating an inland student and researcher personal support system

convergence program

TÁMOP 4.2.4. A/2-11-1-2012-0001

Thank youfor your

attention!