the six sigma black belt primer - quality council of · pdf filethe six sigma black belt...

© QUALITY COUNCIL OF INDIANACSSBB 2014

INTRO-1 (1)

THESIX SIGMA

BLACK BELTPRIMER

© by Quality Council of Indiana - All rights reserved

Fourth Edition - September, 2014

Quality Council of Indiana602 West Paris AvenueWest Terre Haute, IN 47885TEL: 800-660-4215FAX: [email protected]://www.qualitycouncil.com

000


INTRO-7 (2)

CSSBB Primer Contents

I. CERTIFICATION OVERVIEW . . . . . . . . . . . . . . . . . I-1CSSBB EXAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-3CSSBB BODY OF KNOWLEDGE . . . . . . . . . . . . . . I-6

II. ENTERPRISE-WIDE DEPLOYMENT . . . . . . . . . . . II-1ORGANIZATION-WIDE CONSIDERATIONS . . . . . II-2

SIX SIGMA/LEAN FUNDAMENTALS . . . . . . . . . II-2IMPROVEMENT METHODOLOGIES . . . . . . . . II-34SYSTEMS AND PROCESSES . . . . . . . . . . . . . . II-42STRATEGIC PLANNING . . . . . . . . . . . . . . . . . . II-47

LEADERSHIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-57ROLES AND RESPONSIBILITIES . . . . . . . . . . II-57ORGANIZATIONAL ROADBLOCKS . . . . . . . . . II-63

III. PROCESS MANAGEMENT . . . . . . . . . . . . . . . . . III-1OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-2STAKEHOLDER IMPACT . . . . . . . . . . . . . . . . . . . III-8CRITICAL REQUIREMENTS . . . . . . . . . . . . . . . . III-11BENCHMARKING . . . . . . . . . . . . . . . . . . . . . . . . III-11BUSINESS MEASURES . . . . . . . . . . . . . . . . . . . III-15

PERFORMANCE MEASURES . . . . . . . . . . . . III-15FINANCIAL MEASURES . . . . . . . . . . . . . . . . . III-20


III. PROCESS MANAGEMENT II.C.1 BUSINESS MEASURES/PERFORMANCE MEASURES

III-16 (138)

Business Level Metrics

Business level metrics are typically financial (external)and operational (internal) summaries for shareholdersand management.

Business (executive) level metrics comprise summariesof detailed operations and financial results reportedmonthly, quarterly, or annually.


III. PROCESS MANAGEMENT II.C.1 BUSINESS MEASURES/PERFORMANCE MEASURES

III-16 (139)

Operations Level Metrics

Six sigma provides new metrics for managing complexoperations. Business effectiveness measures track howwell products are meeting customer needs (externalfocus). Breyfogle indicates that they should have alonger-term perspective and reflect the total variationthat the customer sees.

Operational efficiency measures relate to the cost andtime required to produce the products. They providekey linkages between detailed process measures andsummary business results, and help identify importantrelationships and root causes.


V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION

V-7 (320)

External Customer Segmentation (Cont’d)

The consumer customer market differs from thebusiness market as follows:

C The consumer market has a large number ofcustomers

C The majority of consumer purchases are small inactual dollar amounts

C The transaction is usually a simple purchase

C Most consumers are not very knowledgeable aboutthe product

C The supplier does not share proprietary informationwith the consumer



V-7 (321)

External Customer Segmentation (Cont’d)

In contrast, the business customer acts in the followingmanner:

C There are a very small number of businesscustomers

C The amount purchased per transaction is quite large

C The purchase is handled through specializedpersonnel

C The customer may know more about therequirements than the producer

C The supplier may allow the customer access to allsorts of information

It is also important to look at the market for the next twoto five years and estimate how it will change and grow.



V-8 (322)

Customer Service

The customer driven company is beginning to emerge inAmerica. The public demands and expects betterquality products and service. One sample programfollows:

C Listen to the customer and determine needsC Define a service strategyC Set standards of performanceC Select and train the right employeesC Recognize and reward accomplishment

There is the need to listen to the customer, provide avision, provide training, improve the process, find ordevelop response metrics, and measure the results. About 70% of customers who leave a company do sobecause of service quality.



V-8 (323)

Customer Retention

Most organizations spend the bulk of their resources onattaining new customers and smaller amounts onretaining customers. High customer satisfactionnumbers do not necessarily mean the company hasgood customer retention and good customer loyalty. Ithas been found that current customers are worth asmuch as five times more than new customers. The costof retaining a current customer is only one-fourth thecost of acquiring a new customer.

Another study showed that companies will boost profitsby about 100% by just retaining 5% more of theircustomers.



V-9 (324)

Customer Retention (Continued)

Furlong lists some techniques for getting to knowcustomers better:

C Don’t use your own instincts as dataC See the world from the customer’s sideC People high in the organization are out of touchC Get customers to talkC 90% of unhappy customers won’t complainC Do research to retain customersC Determine how satisfied customers areC Conduct research on customer expectationsC Develop a customer profileC Share the results of customer research studiesC Don’t go overboard on the details and measurementC Coordinate and use research effortsC Understand that sometimes research does not help



V-9 (325)

Customer Loyalty

The value of a loyal customer is not measured on thebasis of one gigantic purchase, but rather on his/herlifetime worth. Loyal customers account for a highproportion of sales and profit growth. Customerretention generates repeat sales, and it is cheaper toretain customers. Customer loyalty is something thatmust be demonstrated through an act of execution,trust, or delightful service. Customers become partners.


VI. MEASURE - DATA V.A.2 PROCESS CHARACTERISTICS/ANALYSIS TOOLS

VI-33 (473)

1. PLAN

2. DO3. CHECK

4. ACT

The PDCA Cycle

Precise, butBiased

Unbiased, butnot Precise

Unbiased and Precise

Bias and Precision Distinction

Circle Diagrams (Continued)


VI. MEASURE - DATA V.A.2 PROCESS CHARACTERISTICS/ANALYSIS TOOLS

VI-34 (474)

Circle Diagrams

On occasion, a circle diagram can help conceptualizethe relationship between work elements in order tooptimize work activities. Shown below is a hypotheticalanalysis of the work load for a shipping employee usinga Venn (or circle) diagram.

0.04

0.06PullingStock0.25

Packing0.30

ShippingDataEntry0.20

MakingCDs0.10


VII. MEASURE - STATISTICS V.E.2 PROBABILITY/OTHER DISTRIBUTIONS

VII-43 (623)

nm nm m N - n = = 1 -

N N N N - 1

5 15n5 5r20

10

C C n!P r = note that C =

C r! n - r !

5! 15!15! 10!10!5!10! 5!10!

P r = = = 0.0163 = 1.63%20! 5!10! 20!

10!10!

Hypergeometric Distribution (Continued)

From a group of 20 products, 10 are selected at randomfor testing. What is the probability that the 10 selectedcontain the 5 best units?

N = 20, n = 10, d = 5, (N-d) = 15 and r = 5

The mean and the variance of the hypergeometricdistribution are:



VII-44 (624)

Modeling a rate with no upper bound for the number of successes?

Poisson

Fixed number of trials?

Probability of successthe same on all trials

and number of successes = 1?

Start

Probability of success same on all trials?

Binomial

Geometric

Hypergeometric

NegativeBinomial

Yes

No Yes

Yes

Yes

No

No

No

Choosing A Discrete Distribution



VII-45 (625)

Bivariate Normal Distribution

The joint distribution of two variables is called abivariate distribution. Bivariate distributions may bediscrete or continuous.

The graphical representation of a bivariate distributionis a three dimensional plot, with the x and y-axisrepresenting the independent variables and the z-axisrepresenting the frequency for discrete data or theprobability for continuous data.

A special case of the bivariate distribution is thebivariate normal distribution shown below:


VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES

VII-54 (637)

Identifying Characteristics

The identification of characteristics to be measured in aprocess capability study should meet the followingrequirements:

C The characteristic should be indicative of a keyfactor in the quality of the product or process

C It should be possible to adjust the value of thecharacteristic

C The operating conditions that affect the measuredcharacteristic should be defined and controlled

Selecting one, or possibly two, key dimensions providesa manageable method of evaluating the processcapability. The characteristic selected may also bedetermined by the history of the part and the parameterthat has been the most difficult to control.

Customer purchase order requirements or industrystandards may also determine the characteristics thatare required to be measured.



VII-55 (638)

R2

R d

Identifying Specifications/Tolerances

The process specifications or tolerances are determinedeither by customer requirements, industry standards, orthe organization’s engineering department.

Developing Sampling Plans

The appropriate sampling plan for conducting processcapability studies depends upon the purpose andwhether there are customer or standards requirementsfor the study.

If the process is currently running and is in control,control chart data may be used to calculate the processcapability indices. If the process fits a normaldistribution and is in statistical control, then thestandard deviation can be estimated from:

For new processes a pilot run may be used to estimatethe process capability. A design of experiments can beused to determine the optimum values of the processvariables which yield the lowest process variation.



VII-56 (639)

Verifying Stability and Normality

If only common causes of variation are present in aprocess, then the output of the process forms adistribution that is stable over time and is predictable. If special causes of variation are present, the processoutput is not stable over time.

The Figure below depicts an unstable process with bothprocess average and variation out-of-control. Theprocess may also be unstable if either the processaverage or variation is out-of-control.



VII-57 (640)

Verifying Stability and Normality (Cont’d)

The validity of the normality assumption may be testedusing the chi square hypothesis test. To perform thistest, the data is partitioned into data ranges. Thenumber of data points in each range is then comparedwith the number predicted from a normal distribution.

Continuous data may be tested using a variety ofgoodness-of-fit tests.



VII-58 (641)

68.27%

95.45%

99.73%:-3F :-2F :-1F : :+1F :+2F :+3F

The Normal Distribution

When all special causes of variation are eliminated,many variable data processes, when sampled andplotted, produce a bell-shaped distribution. If the baseof the histogram is divided into six (6) equal lengths(three on each side of the average), the amount of datain each interval exhibits the following percentages:



VII-58 (642)

LOWER UPPER

X - LSL USL - XZ Z

S S

X - Z =

The Z Value

The area outside of specification for a normal curve canbe determined by a Z value.

The Z transformation formula is:

This transformation will convert the original values tothe number of standard deviations away from the mean. The result allows one to use a single standard normaltable to describe areas under the curve (probability ofoccurrence).



VII-59 (643)

0 1.0

0 1.0

Z Value (Continued)

There are several ways to display the normal(standardized) distribution:

1. As a number under the curve, up to the Z value.

P(Z = - to 1) = 0.8413

2. As a number beyond the Z value.

P(Z =1 to + ) = 0.1587



VII-59 (644)

Z Value (Continued)

3. As a number under the curve, and at a distance fromthe mean.

P(Z = 0 to 1) = 0.3413

The standard normal table in this Primer uses thesecond method of calculating the probability ofoccurrence.



VII-60 (645)

X- μZ =

σ100 - 150 50

Z = = - = -2.520 20

Z Value Example

Tenth grade students weights follow a normaldistribution with a mean μ = 150 lb and a standarddeviation of 20 lb. What is the probability of a studentweighing less than 100 lb?

μ = 150

x = 100

σ = 20

Since the normal table has values about the mean, a Zvalue of - 2.5 can be treated as 2.5.

P(Z = - to -2.5) = 0.0062. That is, 0.62% of the studentswill weigh less than 100 lb.


VII. MEASURE - STATISTICS V.F.1 PROCESS CAPABILITY / CAPABILITY INDICES

VII-62 (646)

Capability Index Failure Rates

There is a direct link between the calculated Cp (and Pp

values) with the standard normal (Z value) table. A Cp of1.0 is the loss suffered at a Z value of 3.0 (doubled, sincethe table is one sided). Refer to the Table below.

CpZ

valueppm

0.33 1.00 317,311

0.67 2.00 45,500

1.00 3.00 2,700

1.10 3.30 967

1.20 3.60 318

1.30 3.90 96

1.33 4.00 63

1.40 4.20 27

1.50 4.50 6.8

1.60 4.80 1.6

1.67 5.00 0.57

1.80 5.40 0.067

2.00 6.00 0.002


VII. MEASURE - STATISTICS V.F.1 PROCESS CAPABILITY / CAPABILITY INDICES

VII-62 (647)

Index Failure Rates (Continued)

In the prior Table, ppm equals parts per million ofnonconformance (or failure) when the process:

C Is centered on XC Has a two-tailed specificationC Is normally distributedC Has no significant shifts in average or dispersion

When the Cp, Cpk, Pp, and Ppk values are 1.0 or less, Zvalues and the standard normal table can be used todetermine failure rates. With the drive for increasinglydependable products, there is a need for failure rates inthe Cp range of 1.5 to 2.0.


X. CONTROL VIII.A.4 SPC/CONTROL CHART SELECTION

X-12 (937)

Ave

rag

esR

ang

es

0

1

2

3

4

5

6

7

8

Date Start 1/12/10Time

SampleMeasurement

Total

TimeTimeTimeTimeTime

Average xRange R

1234

5

1/12 1/13

7:05 7:10 7:35 8:10 8:15 9:10 9:12 9:33 11:40 11:43 12:05 13:05 13:55 14:20 14:55 7:00 7:55 9:0013:45 9:12 9:32

12

121315

12

6412.8

15

171617

18

8316.6

13

1814

15

7414.8

14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

101211

1154

10.8

10

13 1515 1515 1622 16

17

16 17 19 16 16 17 19

14

16 1613 16 1515

16 15

12

121115

15

15

1514

14

14.472 66

17

1717

17

17

1414

16161618

18

77 74 85 81 82

1616

16 16

1616

15 15

15 15 15 15 15

151717

1717

17

17

17 17 17

1717

1719 19

151518

1818

18

14

14

1414

13

16

16

13

3 3 35 2 4 1 5 8 3 3 32 2 4 4 4 4 435

79 79 83 8385 80 82 76 85 7413.2 15.4 14.8 16.2 16.4 15.8 15.8 16.6 16.6 16 16.4 15.2 14.8

special

specialspecial

special10.5

11

12

13

14

15

16

17

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Removal TorquesVariable:Product Name: Tablets Process Closure Department

Specification Limits: LSL = 10 LBS USL = 22 LBS Units of Measure: LBSOperator BillChart No. 1

UCL =17.5X

X = 15.4

LCL =13.3X

UCL = 7.6R

LCL = 0R

R = 3.6

run

X̄ - R Control Chart

This start up process smoothed out from data set 10 on. The chart would need new control limits from that point.


X. CONTROL VIII.A.6 SPC/CONTROL CHART ANALYSIS

X-35 (962)

(Rule 2) 4 out of 5points in zone B

(Rule 4) 8 or more consecutivepoints on one side of center line

(Rule 1) A point beyond the control limit

Comment: Some authorities say 7 or more consecutive points for both Rules 4 and 5.

(Rule 6) Stratification15 or more points in zone C

(Rule 7) Mixture orsystematic variation

Zone A

UCL

Zone B

Zone C

Zone C

Zone B

Zone A

UCL

Zone A

UCL

Zone B

Zone C

Zone C

Zone B

Zone A

UCL

Zone A

UCL

Zone B

Zone C

Zone C

Zone B

Zone A

UCL(Rule 3) 2 out of 3 pointsin zone A

(Rule 5) A trend is 6 or more consecutive points increasing or decreasing

Control Chart Interpretation

Five Common Rules

Other Unusual Patterns


XII. APPENDIX

XII-8 (1055)

Table V - t Distribution

tα

d.f. t.100 t.050* t.025** t.010 t.005 d.f.

123456789

1011121314151617181920212223242526272829inf.

3.0781.8861.6381.5331.4761.4401.4151.3971.3831.3721.3631.3561.3501.3451.3411.3371.3331.3301.3281.3251.3231.3211.3191.3181.3161.3151.3141.3131.3111.282

6.3142.9202.3532.1322.0151.9431.8951.8601.8331.8121.7961.7821.7711.7611.7531.7461.7401.7341.7291.7251.7211.7171.7141.7111.7081.7061.7031.7011.6991.645

12.7064.3033.1822.7762.5712.4472.3652.3062.2622.2282.2012.1792.1602.1452.1312.1202.1102.1012.0932.0862.0802.0742.0692.0642.0602.0562.0522.0482.0451.960

31.8216.9654.5413.7473.3653.1432.9982.8962.8212.7642.7182.6812.6502.6242.6022.5832.5672.5522.5392.5282.5182.5082.5002.4922.4852.4792.4732.4672.4622.326

63.6579.9255.8414.6044.0323.7073.4993.3553.2503.1693.1063.0553.0122.9772.9472.9212.8982.8782.8612.8452.8312.8192.8072.7972.7872.7792.7712.7632.7562.576

123456789

1011121314151617181920212223242526272829inf.

* one tail 5% α risk ** two tail 5% α risk


XII. APPENDIX

XII-12 (1059)

x

R

R

X S Charts

CL x A S

UCL B S

LCL B S

3

4

3

x

R

R

X R Charts

CL x A R

UCL D R

LCL D R

2

4

3

Approximate capability

R

d

2

Table IX - Control Chart Factors

CHART FORAVERAGES

CHART FOR STANDARDDEVIATIONS

CHART FOR RANGES

SampleObservations

Control limitFactors

CenterLine

Factors

Control LimitFactors

CenterLine

Factors

Control LimitFactors

n A2 A3 c4 B3 B4 d2 D3 D4

2 1.880 2.659 0.7979 0 3.267 1.128 0 3.267

3 1.023 1.954 0.8862 0 2.568 1.693 0 2.574

4 0.729 1.628 0.9213 0 2.266 2.059 0 2.282

5 0.577 1.427 0.9400 0 2.089 2.326 0 2.114

6 0.483 1.287 0.9515 0.030 1.970 2.534 0 2.004

7 0.419 1.182 0.9594 0.118 1.882 2.704 0.076 1.924

8 0.373 1.099 0.9650 0.185 1.815 2.847 0.136 1.864

9 0.337 1.032 0.9693 0.239 1.761 2.970 0.184 1.816

10 0.308 0.975 0.9727 0.284 1.716 3.078 0.223 1.777

15 0.223 0.789 0.9823 0.428 1.572 3.472 0.347 1.653

20 0.180 0.680 0.9869 0.510 1.490 3.735 0.415 1.585

25 0.153 0.606 0.9896 0.565 1.435 3.931 0.459 1.541

Approximate capability

S

c

4

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