six sigma green belt part 5 - institute of industrial and ... · pdf filesix sigma green belt...

5-1

Six Sigma Green Belt

Part 5

Process Capability

© 2011 IIE and Aft Systems, Inc.

© 2011 IIE and Aft Systems, Inc. 5-2

Process Capability

• Is the measured, inherent reproducibility of the product turned out by the process. It can be quantified from data which, in turn, are the result of measurements of work performed by the process. It defines limits we would normally expect virtually all individuals to fall within.

• By definition a process is “capable” when it is operating at the three sigma level.


Process Capability

• Is the range over which the natural variation of a process occurs as determined by the system of common causes.

• It is the ability of the combination of people, machines, methods, materials, and measurements to produce a product or service that will consistently meet design specifications.


Measuring Process Capability

• Process capability is measured by the proportion of output that can be produced within design specifications-It is a long term prediction.

• It is a measure of the uniformity of the process.

It can be measured only if all special causes have been eliminated and the process is in a

state of statistical control.


Components of Process Capability

• Design specifications

• Centering of natural variation

• Range or spread of variation


Capability Measures

• Short term measures show the capability at a specific instance in time, e.g., 5 out of 90 samples did not meet customer requirements

• Long term measures show the expected capability of the process based on statistical projections using inherent process variability


Establishing Process Capability

• Histogram

• Control Chart

These must be performed prior to calculating any process capability measures


Statistics

Green Belts are expected to be able to calculate the following:

• Percent or proportion Non-Conforming

• Cp Index

• Cpk Index


Percent Non-Conforming

• Reflects the proportion of the population that we normally expect not to meet the process specifications.

• Corresponds to the

‘tail’ areas on the

normal curve sketch

AcceptableLSLLSL

USL


Calculating

Use z transform. Values in Normal Curve Table

22 d

MR

d

R'

x-Lspec

x-Uspec

or

z

z

l

u

Process must be centered somewhere between the customer requirements.

mean thecalled also is x


Z Value Tail Z Value Tail Z Value Tail Z Value Tail

Prop. Prop. Prop. Prop.

0.01 0.4960 0.31 0.3783 0.61 0.2709 0.91 0.1814

0.02 0.4920 0.32 0.3745 0.62 0.2676 0.92 0.1788

0.03 0.4880 0.33 0.3707 0.63 0.2643 0.93 0.1762

0.04 0.4840 0.34 0.3669 0.64 0.2611 0.94 0.1736

0.05 0.4801 0.35 0.3632 0.65 0.2578 0.95 0.1711

0.06 0.4761 0.36 0.3594 0.66 0.2546 0.96 0.1685

0.07 0.4721 0.37 0.3557 0.67 0.2514 0.97 0.1660

0.08 0.4681 0.38 0.3520 0.68 0.2483 0.98 0.1635

0.09 0.4641 0.39 0.3483 0.69 0.2451 0.99 0.1611

0.10 0.4602 0.40 0.3446 0.70 0.2420 1.00 0.1587

0.11 0.4562 0.41 0.3409 0.71 0.2389 1.01 0.1562

0.12 0.4522 0.42 0.3372 0.72 0.2358 1.02 0.1539

0.13 0.4483 0.43 0.3336 0.73 0.2327 1.03 0.1515

0.14 0.4443 0.44 0.3300 0.74 0.2296 1.04 0.1492

0.15 0.4404 0.45 0.3264 0.75 0.2266 1.05 0.1469

0.16 0.4364 0.46 0.3228 0.76 0.2236 1.06 0.1446

0.17 0.4325 0.47 0.3192 0.77 0.2206 1.07 0.1423

0.18 0.4286 0.48 0.3156 0.78 0.2177 1.08 0.1401

0.19 0.4247 0.49 0.3121 0.79 0.2148 1.09 0.1379

0.20 0.4207 0.50 0.3085 0.80 0.2119 1.10 0.1357

0.21 0.4168 0.51 0.3050 0.81 0.2090 1.11 0.1335

0.22 0.4129 0.52 0.3015 0.82 0.2061 1.12 0.1314

0.23 0.4090 0.53 0.2981 0.83 0.2033 1.13 0.1292

0.24 0.4052 0.54 0.2946 0.84 0.2005 1.14 0.1271

0.25 0.4013 0.55 0.2912 0.85 0.1977 1.15 0.1251

0.26 0.3974 0.56 0.2877 0.86 0.1949 1.16 0.1230

0.27 0.3936 0.57 0.2843 0.87 0.1922 1.17 0.1210

0.28 0.3897 0.58 0.2810 0.88 0.1894 1.18 0.1190

0.29 0.3859 0.59 0.2776 0.89 0.1867 1.19 0.1170

0.30 0.3821 0.60 0.2743 0.90 0.1841 1.20 0.1151


Z Value Tail Z Value Tail Z Value Tail Z Value Tail

Prop. Prop. Prop. Prop.

1.21 0.1131 1.51 0.0655 1.81 0.0351 2.11 0.0174

1.22 0.1112 1.52 0.0643 1.82 0.0344 2.12 0.0170

1.23 0.1093 1.53 0.0630 1.83 0.0336 2.13 0.0166

1.24 0.1075 1.54 0.0618 1.84 0.0329 2.14 0.0162

1.25 0.1056 1.55 0.0606 1.85 0.0322 2.15 0.0158

1.26 0.1038 1.56 0.0594 1.86 0.0314 2.16 0.0154

1.27 0.1020 1.57 0.0582 1.87 0.0307 2.17 0.0150

1.28 0.1003 1.58 0.0571 1.88 0.0301 2.18 0.0146

1.29 0.0985 1.59 0.0559 1.89 0.0294 2.19 0.0143

1.30 0.0968 1.60 0.0548 1.90 0.0287 2.20 0.0139

1.31 0.0951 1.61 0.0537 1.91 0.0281 2.21 0.0136

1.32 0.0934 1.62 0.0526 1.92 0.0274 2.22 0.0132

1.33 0.0918 1.63 0.0516 1.93 0.0268 2.23 0.0129

1.34 0.0901 1.64 0.0505 1.94 0.0262 2.24 0.0125

1.35 0.0885 1.65 0.0495 1.95 0.0256 2.25 0.0122

1.36 0.0869 1.66 0.0485 1.96 0.0250 2.26 0.0119

1.37 0.0853 1.67 0.0475 1.97 0.0244 2.27 0.0116

1.38 0.0838 1.68 0.0465 1.98 0.0239 2.28 0.0113

1.39 0.0823 1.69 0.0455 1.99 0.0233 2.29 0.0110

1.40 0.0808 1.70 0.0446 2.00 0.0228 2.30 0.0107

1.41 0.0793 1.71 0.0436 2.01 0.0222 2.31 0.0104

1.42 0.0778 1.72 0.0427 2.02 0.0217 2.32 0.0102

1.43 0.0764 1.73 0.0418 2.03 0.0212 2.33 0.0099

1.44 0.0749 1.74 0.0409 2.04 0.0207 2.34 0.0096

1.45 0.0735 1.75 0.0401 2.05 0.0202 2.35 0.0094

1.46 0.0721 1.76 0.0392 2.06 0.0197 2.36 0.0091

1.47 0.0708 1.77 0.0384 2.07 0.0192 2.37 0.0089

1.48 0.0694 1.78 0.0375 2.08 0.0188 2.38 0.0087

1.49 0.0681 1.79 0.0367 2.09 0.0183 2.39 0.0084

1.50 0.0668 1.80 0.0359 2.10 0.0179 2.40 0.0082


Z Value Tail Z Value Tail Z Value Tail

Prop. Prop. Prop.

2.41 0.0080 2.71 0.0034 3.10 0.00096760

2.42 0.0078 2.72 0.0033 3.20 0.00068714

2.43 0.0075 2.73 0.0032 3.30 0.00048342

2.44 0.0073 2.74 0.0031 3.40 0.00033693

2.45 0.0071 2.75 0.0030 3.50 0.00023263

2.46 0.0069 2.76 0.0029 3.60 0.00015911

2.47 0.0068 2.77 0.0028 3.70 0.00010780

2.48 0.0066 2.78 0.0027 3.80 0.00007235

2.49 0.0064 2.79 0.0026 3.90 0.00004810

2.50 0.0062 2.80 0.0026 4.00 0.00003167

2.51 0.0060 2.81 0.0025 4.10 0.00002066

2.52 0.0059 2.82 0.0024 4.20 0.00001335

2.53 0.0057 2.83 0.0023 4.30 0.00000854

2.54 0.0055 2.84 0.0023 4.40 0.00000541

2.55 0.0054 2.85 0.0022 4.50 0.00000340

2.56 0.0052 2.86 0.0021 4.60 0.00000211

2.57 0.0051 2.87 0.0021 4.70 0.00000130

2.58 0.0049 2.88 0.0020 4.80 0.00000079

2.59 0.0048 2.89 0.0019 4.90 0.00000048

2.60 0.0047 2.90 0.0019 5.00 0.00000029

2.61 0.0045 2.91 0.0018 5.10 0.00000017

2.62 0.0044 2.92 0.0018 5.20 0.00000010

2.63 0.0043 2.93 0.0017 5.30 0.00000006

2.64 0.0041 2.94 0.0016 5.40 0.00000003

2.65 0.0040 2.95 0.0016 5.50 0.00000002

2.66 0.0039 2.96 0.0015 6.00 0.000000001

2.67 0.0038 2.97 0.0015 6.50 0.00000000

2.68 0.0037 2.98 0.0014 7.00 0.00000000

2.69 0.0036 2.99 0.0014 7.50 0.00000000

2.70 0.0035 3.00 0.0013 8.00 0.00000000


Example

A process has a mean of 600 and a standard deviation of 6. Spec limits are 585 and 615.

1. What is the percent non-conforming? (The total proportion in both tails.)

2. What is the DPMO?

3. What is the sigma level? (The sigma level is the smaller of the two z values.)

LSLLSL

USLUnacceptable

Unacceptable


Example

A process has a mean of 100 and a standard deviation of 4. Spec limits are 95 and 106.

1. What is the percent non-conforming?

2. What is the sigma level?

3. What is the DPM?

LSLLSL

USLUnacceptable

Unacceptable


ExampleContinued

In the preceding example if each incorrect transaction costs $4 and annual volume is 400,000, what is the cost of the incorrect transactions?


ExampleContinued

If in the preceding example the standard deviation were reduced to 2 via a DMAIIC Green Belt project. If this were done at a cost of $100,000 would it be worth it? (One year payback.)


ExampleContinued

What would it take (or be worth) to now reduce the standard deviation to 1?


More Practice

• A process has a mean of 200 and and a standard deviation of 2.

• Upper specification limit is 212.

• Lower specification limit is 188.

• Determine

– Proportion non conforming

– DPMO

– Sigma Level

Motorola Shift


Another Problem

What is the capability of the process, in terms of proportion defective or sigma level or dpmo, we collected data on earlier in the course?

(page 4-12)


Capability Indices

Show the relationship between the process capability and the process specifications

Cp measures potential capability assuming that the process average is equal to the midpoint of the specification limits and the process is operating in statistical control. Cpk reflects the current process mean’s proximity to either specification limit. (When the process is centered Cp = Cpk.)

Although the indices are calculated differently, the interpretation is the same


Cp or Cpk Less than 1.0

Cp or Cpk

Value

Sigma

Level

0.33

0.67

1

2


Cp or Cpk Equal to 1.0

Cp or Cpk

Value

Sigma

Level

0.33

0.67

1.00

1

2

3-4.5

-4.3 -4

-3.8

-3.5

-3.3

-3.1

-2.8

-2.6

-2.3

-2.1

-1.9

-1.6

-1.4

-1.1

-0.9

-0.7

-0.4

-0.2

0.0

7

0.3

1

0.5

5

0.7

9

1.0

3

1.2

7

1.5

1

1.7

5

1.9

9

2.2

3

2.4

7

2.7

1

2.9

5

3.1

9

3.4

3

3.6

7

3.9

1

4.1

5

4.3

9


Cp or Cpk Greater than 1.0

Cp or Cpk

Value

Sigma

Level

0.33

0.67

1.00

1.33

1.67

2.00

2.33

2.67

3.00

1

2

3

4

5

6

7

8

9

No Motorola Shift

-4.5

-4.3 -4

-3.8

-3.5

-3.3

-3.1

-2.8

-2.6

-2.3

-2.1

-1.9

-1.6

-1.4

-1.1

-0.9

-0.7

-0.4

-0.2

0.0

7

0.3

1

0.5

5

0.7

9

1.0

3

1.2

7

1.5

1

1.7

5

1.9

9

2.2

3

2.4

7

2.7

1

2.9

5

3.1

9

3.4

3

3.6

7

3.9

1

4.1

5

4.3

9


Calculating Cp

Cp = (Uspec – Lspec)/6

Process must be centered at the midpoint of the

specification limits.


Cpk Calculation

Smaller of the following:

Cpku = (Uspec – Mean) / 3

Cpkl = (Mean – Lspec) / 3

Cpk also is equal to the sigma level divided by 3

Note:Can also use these for one sided requirements


Capability

What is the capability index for the process we analyzed earlier? (page 4-12)

Interpretation


Capability Measure

Not Capable Capable

More than

Capable

Proportion Non

ConformingMore than

.0027 0.0027Less than

.0027

DPMOMore than

2700 2700Less than

2700

Sigma LevelLess than

3.0 3.0More

than 3.0

CpkLess than

1.0 1More

than 1.0


Another Cost Study

• A process has customer requirements of 50 and 75. It is in control with an adjustable mean and a known standard deviation (based on the Shewhart approximation) of 8.

• Accounting tells us that a “defect” on the low side will cost of $10 and on the high side $5. (Scrap vs. rework.)

• Engineering has not been able to figure out a way to reduce variation.

• What is the optimum location for the process centering in order to minimize cost?


Homework ExerciseU-Bolts

• On the following page is data on U-bolts for the dimension shown at the right.

• Determine the capability of the process regarding the indicated dimension. (Specs are 10.70 + .15)


Sample Observations Average Range

1 10.65 10.70 10.65 10.80 10.55 10.670 0.25

2 10.75 10.85 10.75 10.70 10.65 10.740 0.20

3 10.75 10.80 10.80 10.70 10.75 10.760 0.10

4 10.60 10.70 10.65 10.65 10.90 10.700 0.30

5 10.70 10.75 10.70 10.65 10.65 10.690 0.10

6 10.60 10.75 10.75 10.75 10.70 10.710 0.15

7 10.75 10.80 10.65 10.75 10.45 10.680 0.35

8 10.65 10.80 10.50 10.70 10.80 10.690 0.30

9 10.60 10.70 10.70 10.65 10.60 10.650 0.10

10 10.80 10.75 10.60 10.75 10.65 10.710 0.20

11 10.85 10.70 10.65 10.70 10.65 10.710 0.20

12 10.70 10.75 10.75 10.70 10.65 10.710 0.10

13 10.65 10.70 10.75 10.65 10.50 10.650 0.25

14 10.70 10.80 10.90 10.80 10.70 10.780 0.20

15 10.65 10.80 10.65 10.60 10.65 10.670 0.20

16 10.75 10.70 10.65 10.75 10.65 10.700 0.10

17 10.90 10.70 10.80 10.70 10.75 10.770 0.20

18 10.75 10.65 10.70 10.65 10.55 10.660 0.20

19 10.75 10.60 10.75 10.60 10.90 10.720 0.30

20 10.65 10.55 10.70 10.70 10.65 10.650 0.15

21 10.60 10.65 10.65 10.70 10.65 10.650 0.10

22 10.50 10.60 10.70 10.65 10.75 10.640 0.25

23 10.80 10.70 10.65 10.50 10.65 10.660 0.30

24 10.65 10.65 10.90 10.80 10.65 10.730 0.25

104


Statistics

Mean 10.6958

Average Range .2021

Shewhart Standard Deviation .0869

Calculated Standard Deviation

.0871


28

27

26

25

24

23

22

21

20

19

18

17

16

Frequency 15

14

13

12

11

10

9

8

7

6

5

4

3

2

1


Sample ID

Averages

Ranges


Histogram

0

5

10

15

20

25

30

35

40

10.45

to <=

10.495

10.495

to <=

10.54

10.54

to <=

10.585

10.585

to <=

10.63

10.63

to <=

10.675

10.675

to <=

10.72

10.72

to <=

10.765

10.765

to <=

10.81

10.81

to <=

10.855

10.855

to <=

10.9

Class

# O

bs

erv

ati

on

s


Xbar Chart

UCL=10.81244

LCL=10.57923

CEN=10.69583

10.45

10.5

10.55

10.6

10.65

10.7

10.75

10.8

10.85

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

R Chart

UCL=0.4272

LCL=0.0

CEN=0.20208

0

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24


Process CapabilityCpk Analysis

10

.30

10

.33

10

.35

10

.38

10

.40

10

.43

10

.45

10

.48

10

.50

10

.53

10

.55

10

.58

10

.60

10

.63

10

.65

10

.68

10

.70

10

.73

10

.75

10

.78

10

.80

10

.83

10

.85

10

.88

10

.90

10

.93

10

.95

10

.97

11

.00

11

.02

11

.05

11

.07

Mean = 10.696

StdDev = 0.0869

USL = 10.85

LSL = 10.55

Sigma Level = 1.6801

Cpk = .5600

DPM = 84,654

six sigma green belt part 5 - institute of industrial and ... · pdf filesix sigma green belt...

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