© 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
© QUALITY COUNCIL OF INDIANACSSBB 2014
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
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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.
© QUALITY COUNCIL OF INDIANACSSBB 2014
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.
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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
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V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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.
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V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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.
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V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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.
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V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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
© QUALITY COUNCIL OF INDIANACSSBB 2014
V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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.
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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)
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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
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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:
© QUALITY COUNCIL OF INDIANACSSBB 2014
VII. MEASURE - STATISTICS V.E.2 PROBABILITY/OTHER DISTRIBUTIONS
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
© QUALITY COUNCIL OF INDIANACSSBB 2014
VII. MEASURE - STATISTICS V.E.2 PROBABILITY/OTHER DISTRIBUTIONS
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:
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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.
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VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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.
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VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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.
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VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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.
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VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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:
© QUALITY COUNCIL OF INDIANACSSBB 2014
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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).
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VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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
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VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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.
© QUALITY COUNCIL OF INDIANACSSBB 2014
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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.
© QUALITY COUNCIL OF INDIANACSSBB 2014
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
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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.
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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.
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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
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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
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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