six sigma - prof. sanjit ray
TRANSCRIPT
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
THE MANY FACETS OF SIX SIGMATHE MANY FACETS OF SIX SIGMA
�Metrics
� Benchmark
� Vision
� Philosophy
�Method
� Tool
� Symbol
� Goal
� Value
�Metrics
� Benchmark
� Vision
� Philosophy
�Method
� Tool
� Symbol
� Goal
� Value
S
I
X
S
I
G
M
A
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
WHAT IS THIS SIX SIGMA ?WHAT IS THIS SIX SIGMA ?
• A Philosophy
• A Statistical Measurement
• A Metric
• A Business Strategy
• make fewer mistakes in all that we
do.
• helps gage adequacy of product,
process and services
• A measuring system
• good quality reduces cost
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
SIGMA RATING AND PPM ARE CORRELATEDSIGMA RATING AND PPM ARE CORRELATED
Sigma Rating PPM
2 308,537
3 66,807
4 6,210
5 233
6 3.4
Process Defects per
Capability Million Opportunities
Sigma Rating PPM
2 308,537
3 66,807
4 6,210
5 233
6 3.4
Process Defects per
Capability Million Opportunities
SIGMA RATING A PERFORMANCE MEASURE
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• TO REDUCE VARIATION
• TO REDUCE DEFECTS
• TO IMPROVE YIELD
• TO ENHANCE CUSTOMER SATISFACTION
• TO IMPROVE THE BOTTOMLINE
THE GOALS OF SIX SIGMATHE GOALS OF SIX SIGMA
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
To get results should we focus on Y or X?
• Y
• Dependent variable
• Output of the process
• Effect
• Symptom
• It is monitored
• X1, X2, …….., Xn
• Independent variable
• Input to the process
• Cause
• Problem
• It is controlled
Y = f(X)
THE FOCUS OF SIX SIGMATHE FOCUS OF SIX SIGMA
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
APPROACH TO DEFINEAPPROACH TO DEFINE
Develop Business
Case and
Team Charter
Develop Business
Case and
Team Charter
Map the
current
process
Map the
current
process
Listen to the
Voice of the
Customer
Listen to the
Voice of the
Customer
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
PREVIEW OF DEFINE STEPPREVIEW OF DEFINE STEP
• The subsequent discussions will take you through
– Selecting a project and drafting a charter
– A basic SIPOC analysis
– Gathering/confirming the “Voice of the Customer”
(Effectiveness goals e.g. On time delivery) and/or the
“Voice of the Business” (Efficiency goals e.g. reduction
of inventory).
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
GOALSGOALS– Understand the organizational context for process
improvement projects.
– Understand how to select a DMAI²C project and be able
to apply the criteria to your own project.
– Know the basic elements of the project charter and be able
to develop a charter for your own project.
– Understand the basics of estimating the business impact of
a project and be able to relate them to your own project.
– Be able to identify key players and stakeholders and
incorporate them into the communication plan for your
own project.
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
ORGANIZATIONAL CONTEXT FOR PROJECTSORGANIZATIONAL CONTEXT FOR PROJECTS
Champions/
Sponsors
Black Belt
Green Belt
Team Members
Master
Black BeltCoordinators
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
DMAI²C PROJECT SELECTION CRITERIADMAI²C PROJECT SELECTION CRITERIA
• Projects will likely have greater success if…
– The problem is related to a key business issue.
– The problem is linked to a clearly defined process
(you can identify the starting and ending points).
– You can identify the internal or external
customers who use or receive the output from this
process.
• You know or can find out how the customers
use the output.
• You know or can find out what is important to
the customer about the output.
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
– You can clearly identify what a defect is and count its
occurrence
– You can demonstrate how improvements could
enhance financial performance
– There is appropriate organizational support
• The champion cares about this work and wants to
make it happen
• The champion has the authority to commit time
and resources
• A process owner has been identified
DMAI²C PROJECT SELECTION CRITERIADMAI²C PROJECT SELECTION CRITERIA
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
COMMON PROBLEMS AND COMMON PROBLEMS AND
RECOMMENDATIONSRECOMMENDATIONS
• Many projects encounter one or more of the following problems:
– Not relevant to customers or to business needs
– Project scope too large; won’t have authority to commit time/resources or to make changes in the process; can’t easily identify starting and ending points
– Relevant data hard to collect or too much data
– Can’t define what a defect is
– Process doesn’t cycle often enough
– Problem written as solution
– Recent changes in the process
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
ELEMENTS OF A PROJECT CHARTERELEMENTS OF A PROJECT CHARTER
– Project Description
– Scope
– Goals and Measures (indicators)
– Expected Business Results
– Team Members
– Support Required
– Expected Customer Benefits
– Schedule
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
QUALITY AND PROCESSESQUALITY AND PROCESSES
– Quality is judged by customers based on the output of a process.
– Focusing on the work of the individual worker will not lead to greatly improved quality.
– To improve quality, the process must be improved.
– Simply focusing on or defining a process is NOT improvement—we have to make changes and use data to show the change really is an improvement.
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
WORK AS A PROCESSWORK AS A PROCESS
– Applies to all kinds of work, whether repetitive in
nature or “one-of-a-kind.”
– Having a high-level view of a process helps to:
• define project boundaries (starting and ending points);
• describe where to collect data.
S U P P L I ER S
C U S T O M E R S
OutputsInputs Process
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
SIPOC EXAMPLESIPOC EXAMPLESuppliers Inputs Process Outputs Customers
Copier
Toner
Electricity
OriginalYourself
Power Company
Office Supply
Company
CopiesManufacturer
Making a
photocopy
You
File
Others
Put original
on glass
Put original
on glass Close LidClose Lid Adjust
Settings
Adjust
SettingsPress
START
Press
START
Remove
originals
and copies
Remove
originals
and copies
Process Steps
Paper
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
TRANSLATING VOC/VOB INTO CTQsTRANSLATING VOC/VOB INTO CTQs
• (CTQ = Critical to Quality)
need
VOC/VOB CTQ Tree
I want
CTQ
CTQ
CTQ
CTQ
CTQ
CTQ
CTQ
CTQ
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
EXAMPLE: CTQ TREEEXAMPLE: CTQ TREE
Need Drivers CTQs
General Specific
Hard to measure Easy to measure
Ease of Operation
and Maintenance
Operation
Low qualification of operator
Easy to setup
(training / documentation)
Digital Control
MaintenanceMTBF
Mistake Proofing
Documentation
Minimum special tools /
equipment required
Modification
Skills and Knowledge
Mistake Proofing
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
APPROACH TO MEASUREAPPROACH TO MEASURE
Collect
baseline
data on
defects
and
possible
causes
Develop a
Sampling
Strategy
Validate
your
measurement
system
using
Gage R&R
Analyze
patterns
in data
Determine
process
capability
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• What is Data ?
Data is a numerical expression of an activity.
Conclusions based on facts and data are necessary for
any improvement.
-K. Ishikawa
If you are not able to express a phenomenon in
numbers, you do not know about it adequately.
-Lord Kelvin
DATA GATHERINGDATA GATHERING
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
TYPES OF DATATYPES OF DATA
CONTINUOUS DISCRETE
Measurable
e.g. :Length, Temperature
Subjective Assessment
e.g. :Score in a beauty
contest
Countable
e.g. :Number of defects
Data if properly collected
• Least influenced by individual biases
• Could be subject to critical analysis
• Generally beyond language barriers and therefore universal in
expression.
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
WHICH OF THE BELOW ARE CONTINUOUS WHICH OF THE BELOW ARE CONTINUOUS
AND DISCRETE DATA?AND DISCRETE DATA?• Width of sheet
• No. of liners thinned
• Tubes rejected by Go- Nogo Gauge
• Diameter of Piston
• Height of a Man
• Sheet thickness
• Out of 100 sheets the numbers that meet the thickness
4 ± 0.9
• Time taken to process a purchase order
• No. of bugs in a program
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--MEASURE PHASEMEASURE PHASE
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
WHAT IS THE MEASUREOF CENTRAL TENDENCY OF A SET OF
NUMBERS?
WHAT IS THE MEASUREWHAT IS THE MEASUREOF CENTRAL TENDENCY OF A SET OF OF CENTRAL TENDENCY OF A SET OF
NUMBERS? NUMBERS?
• There are three ways in which Central
Tendency of Numbers can be measured.
• These are the 3 M’s
�MEAN
�MEDIAN
�MODE
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
MEASURES OF DISPERSIONMEASURES OF DISPERSIONMEASURES OF DISPERSION
� The extent of the spread of the values from the
mean value is called Dispersion.
� The measures of Dispersions are– Range (R)– Standard Deviation (s)– Variance (s2)– Co-efficient of Variation (CV)
�Standard deviation is the most commonly used measure of dispersion.
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• No two things in nature are alike.
• This is also true for manufactured products.
• This dissimilarity between two products for the same characteristic is called variation.
• The variation may be or can be made to be so small so as to make the product SEEM similar.
•When we say that 2 things are similar we actually mean that it is not possible to measure the variation present within the accuracy of the existing measuring equipment.
• Variation between 2 products are compared for SIMILAR features or characteristics.
WHAT IS VARIATION ?WHAT IS VARIATION ?
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• Variations among pieces at the same
time
• Variations across time
TYPES OF VARIATIONTYPES OF VARIATION
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
GRAPHICAL DISPLAY OF GRAPHICAL DISPLAY OF VARIABILITIESVARIABILITIES
InherentVariability
Assignable Variability
Assignable Variability
TOTAL
VAR I A B I L I T Y
Assignable Variability
Assignable Variability
Aimed Value
CASE I
CASE II CASE III
(Black noise)
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
GENERIC CAUSES OF VARIATIONGENERIC CAUSES OF VARIATION
Machines
Materials
Methods
Measurements
Mother Nature
People
P
R
O
C
E
S
S
PP
RR
OO
CC
EE
SS
SS
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
THE NORMAL DISTRIBUTIONTHE NORMAL DISTRIBUTION
95.46
68.26
99.73-3 -2 +3-1 +1 +2
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
IMPORTANT SPC RATIOS USEDIMPORTANT SPC RATIOS USED
This compares the requirement of the process output vis-a-vis the
inherent variability of the process. Higher value than 1 implies that the
process has got the capability to give the product within the set limits.
LSL x USL
- 3 + 3
s 6
LSL-USL
s 6
Tolerance
process of variation Normal
sticcharacteri ofrange allowable Maximum Cp
========
====
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
This gives us the positioning of the mean vis-a-vis the USL and the relationship between the two.
This gives us the positioning of the mean vis-a-vis the LSL and the relationship between the two.
Cpk - Process Performance Index. This is important
Cpk = Minimum of (Cpu and Cpl) ; for bilateral tolerances
= Cpu ;for unilateral tolerance on upper side i.e..
= Cpl ;for unilateral tolerance on lower side i.e..
X+Y-O
X+O-Y
s3
X-USL Cpu ====
s3
LSLX Cpl
−−−−====
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• Every possibility of making an error is called an opportunity
• The total opportunities available for an error to take place areNos.Chkd. x Opp
• If there are more than 1 opp. The sigma can be calculated by finding DPMO.
• Knowing DPMO we refer to the Normal Dist. Table to get the Sigma value
• One could inflate the opp. and hence get an enhanced Sigma But the opp.are limited to what exactly is checked for.
E.g. a sheet is checked for thickness, length & width and can berejected for either.Hence the opp. is 3
THE CONCEPT OF OPPORTUNITYTHE CONCEPT OF OPPORTUNITY
DPMO = Defects x 106
Units chkd. x Opp.
DPMO = Defects x 106
Units chkd. x Opp.
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
•Defect : Any non-conformity in a product or service
– e.g. Late delivery or no. of tubes rejected
•Units : The nos. checked or inspected
– 100 deliveries were monitored for being late, no. of units are 100
– 1000 tubes were checked for oversize dia., no. of units are 1000
•Opportunity : Anything that you measure or check for.
– Finished refrigerator is checked for 25 defects at final inspection, the no. of opportunities is 25
A FEW TERMINOLOGIESA FEW TERMINOLOGIES
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• This Z value is known as the SIGMA RATING
• Knowing the sigma rating we can establish the rejections that can be expected from the process
• The average, the standard deviation & the specification limits are required to get the sigma rating
• There are 2 kinds of sigma ratings.The short term Sigma & the long term Sigma (to be seen in detail later)
• One should not confuse between the sigma rating & the standard deviation
THE SIGMA RATINGTHE SIGMA RATING
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO
0.01 931888 0.26 892512 0.51 838913 0.76 770350 1.01 687933 1.26 594835 1.51 496011 1.76 397432
0.02 930563 0.27 890651 0.52 836457 0.77 767305 1.02 684386 1.27 590954 1.52 492022 1.77 393580
0.03 929219 0.28 888767 0.53 833977 0.78 764238 1.03 680822 1.28 587064 1.53 488033 1.78 389739
0.04 927855 0.29 886860 0.54 831472 0.79 761148 1.04 677242 1.29 583166 1.54 484047 1.79 385908
0.05 926471 0.30 884930 0.55 828944 0.80 758036 1.05 673645 1.30 579260 1.55 480061 1.80 382089
0.06 925066 0.31 882977 0.56 826391 0.81 754903 1.06 670031 1.31 575345 1.56 476078 1.81 378281
0.07 923641 0.32 881000 0.57 823814 0.82 751748 1.07 666402 1.32 571424 1.57 472097 1.82 374484
0.08 922196 0.33 878999 0.58 821214 0.83 748571 1.08 662757 1.33 567495 1.58 468119 1.83 370700
0.09 920730 0.34 876976 0.59 818589 0.84 745373 1.09 659097 1.34 563559 1.59 464144 1.84 366928
0.10 919243 0.35 874928 0.60 815940 0.85 742154 1.10 655422 1.35 559618 1.60 460172 1.85 363169
0.11 917736 0.36 872857 0.61 813267 0.86 738914 1.11 651732 1.36 555670 1.61 456205 1.86 359424
0.12 916207 0.37 870762 0.62 810570 0.87 735653 1.12 648027 1.37 551717 1.62 452242 1.87 355691
0.13 914656 0.38 868643 0.63 807850 0.88 732371 1.13 644309 1.38 547758 1.63 448283 1.88 351973
0.14 913085 0.39 866500 0.64 805106 0.89 729069 1.14 640576 1.39 543795 1.64 444330 1.89 348268
0.15 911492 0.40 864334 0.65 802338 0.90 725747 1.15 636831 1.40 539828 1.65 440382 1.90 344578
0.16 909877 0.41 862143 0.66 799546 0.91 722405 1.16 633072 1.41 535856 1.66 436441 1.91 340903
0.17 908241 0.42 859929 0.67 796731 0.92 719043 1.17 629300 1.42 531881 1.67 432505 1.92 337243
0.18 906582 0.43 857690 0.68 793892 0.93 715661 1.18 625516 1.43 527903 1.68 428576 1.93 333598
0.19 904902 0.44 855428 0.69 791030 0.94 712260 1.19 621719 1.44 523922 1.69 424655 1.94 329969
0.20 903199 0.45 853141 0.70 788145 0.95 708840 1.20 617911 1.45 519939 1.70 420740 1.95 326355
0.21 901475 0.46 850830 0.71 785236 0.96 705402 1.21 614092 1.46 515953 1.71 416834 1.96 322758
0.22 899727 0.47 848495 0.72 782305 0.97 701944 1.22 610261 1.47 511967 1.72 412936 1.97 319178
0.23 897958 0.48 846136 0.73 779350 0.98 698468 1.23 606420 1.48 507978 1.73 409046 1.98 315614
0.24 896165 0.49 843752 0.74 776373 0.99 694974 1.24 602568 1.49 503989 1.74 405165 1.99 312067
0.25 894350 0.50 841345 0.75 773373 1.00 691462 1.25 598706 1.50 500000 1.75 401294 2.00 308538
Sigma and DPMO conversion table
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ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
Sigma and DPMO conversion tableSigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO
2.01 305026 2.26 223627 2.51 156248 2.76 103835 3.01 65522 3.26 39204 3.51 22216 3.76 11911
2.02 301532 2.27 220650 2.52 153864 2.77 102042 3.02 64256 3.27 38364 3.52 21692 3.77 11604
2.03 298056 2.28 217695 2.53 151505 2.78 100273 3.03 63008 3.28 37538 3.53 21178 3.78 11304
2.04 294598 2.29 214764 2.54 149170 2.79 98525 3.04 61780 3.29 36727 3.54 20675 3.79 11011
2.05 291160 2.30 211855 2.55 146859 2.80 96801 3.05 60571 3.30 35930 3.55 20182 3.80 10724
2.06 287740 2.31 208970 2.56 144572 2.81 95098 3.06 59380 3.31 35148 3.56 19699 3.81 10444
2.07 284339 2.32 206108 2.57 142310 2.82 93418 3.07 58208 3.32 34379 3.57 19226 3.82 10170
2.08 280957 2.33 203269 2.58 140071 2.83 91759 3.08 57053 3.33 33625 3.58 18763 3.83 9903
2.09 277595 2.34 200454 2.59 137857 2.84 90123 3.09 55917 3.34 32884 3.59 18309 3.84 9642
2.10 274253 2.35 197662 2.60 135666 2.85 88508 3.10 54799 3.35 32157 3.60 17864 3.85 9387
2.11 270931 2.36 194894 2.61 133500 2.86 86915 3.11 53699 3.36 31443 3.61 17429 3.86 9137
2.12 267629 2.37 192150 2.62 131357 2.87 85344 3.12 52616 3.37 30742 3.62 17003 3.87 8894
2.13 264347 2.38 189430 2.63 129238 2.88 83793 3.13 51551 3.38 30054 3.63 16586 3.88 8656
2.14 261086 2.39 186733 2.64 127143 2.89 82264 3.14 50503 3.39 29379 3.64 16177 3.89 8424
2.15 257846 2.40 184060 2.65 125072 2.90 80757 3.15 49471 3.40 28716 3.65 15778 3.90 8198
2.16 254627 2.41 181411 2.66 123024 2.91 79270 3.16 48457 3.41 28067 3.66 15386 3.91 7976
2.17 251429 2.42 178786 2.67 121001 2.92 77804 3.17 47460 3.42 27429 3.67 15003 3.92 7760
2.18 248252 2.43 176186 2.68 119000 2.93 76359 3.18 46479 3.43 26803 3.68 14629 3.93 7549
2.19 245097 2.44 173609 2.69 117023 2.94 74934 3.19 45514 3.44 26190 3.69 14262 3.94 7344
2.20 241964 2.45 171056 2.70 115070 2.95 73529 3.20 44565 3.45 25588 3.70 13903 3.95 7143
2.21 238852 2.46 168528 2.71 113140 2.96 72145 3.21 43633 3.46 24998 3.71 13553 3.96 6947
2.22 235762 2.47 166023 2.72 111233 2.97 70781 3.22 42716 3.47 24419 3.72 13209 3.97 6756
2.23 232695 2.48 163543 2.73 109349 2.98 69437 3.23 41815 3.48 23852 3.73 12874 3.98 6569
2.24 229650 2.49 161087 2.74 107488 2.99 68112 3.24 40929 3.49 23295 3.74 12545 3.99 6387
2.25 226627 2.50 158655 2.75 105650 3.00 66807 3.25 40059 3.50 22750 3.75 12224 4.00 6210
38
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
Sigma and DPMO conversion table
Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO
4.01 6037 4.26 2890 4.51 1306 4.76 557 5.01 224 5.26 85 5.51 30.4 5.76 10.2
4.02 5868 4.27 2803 4.52 1264 4.77 538 5.02 216 5.27 82 5.52 29.1 5.77 9.8
4.03 5703 4.28 2718 4.53 1223 4.78 519 5.03 208 5.28 78 5.53 27.9 5.78 9.4
4.04 5543 4.29 2635 4.54 1183 4.79 501 5.04 200 5.29 75 5.54 26.7 5.79 8.9
4.05 5386 4.30 2555 4.55 1144 4.80 483 5.05 193 5.30 72 5.55 25.6 5.80 8.5
4.06 5234 4.31 2477 4.56 1107 4.81 467 5.06 185 5.31 70 5.56 24.5 5.81 8.2
4.07 5085 4.32 2401 4.57 1070 4.82 450 5.07 179 5.32 67 5.57 23.5 5.82 7.8
4.08 4940 4.33 2327 4.58 1035 4.83 434 5.08 172 5.33 64 5.58 22.5 5.83 7.5
4.09 4799 4.34 2256 4.59 1001 4.84 419 5.09 165 5.34 62 5.59 21.6 5.84 7.1
4.10 4661 4.35 2186 4.60 968 4.85 404 5.10 159 5.35 59 5.60 20.7 5.85 6.8
4.11 4527 4.36 2118 4.61 936 4.86 390 5.11 153 5.36 57 5.61 19.8 5.86 6.5
4.12 4397 4.37 2052 4.62 904 4.87 376 5.12 147 5.37 54 5.62 19.0 5.87 6.2
4.13 4269 4.38 1988 4.63 874 4.88 362 5.13 142 5.38 52 5.63 18.1 5.88 5.9
4.14 4145 4.39 1926 4.64 845 4.89 350 5.14 136 5.39 50 5.64 17.4 5.89 5.7
4.15 4025 4.40 1866 4.65 816 4.90 337 5.15 131 5.40 48 5.65 16.6 5.90 5.4
4.16 3907 4.41 1807 4.66 789 4.91 325 5.16 126 5.41 46 5.66 15.9 5.91 5.2
4.17 3793 4.42 1750 4.67 762 4.92 313 5.17 121 5.42 44 5.67 15.2 5.92 4.9
4.18 3681 4.43 1695 4.68 736 4.93 302 5.18 117 5.43 42 5.68 14.6 5.93 4.7
4.19 3573 4.44 1641 4.69 711 4.94 291 5.19 112 5.44 41 5.69 14.0 5.94 4.5
4.20 3467 4.45 1589 4.70 687 4.95 280 5.20 108 5.45 39 5.70 13.4 5.95 4.3
4.21 3364 4.46 1538 4.71 664 4.96 270 5.21 104 5.46 37 5.71 12.8 5.96 4.1
4.22 3264 4.47 1489 4.72 641 4.97 260 5.22 100 5.47 36 5.72 12.2 5.97 3.9
4.23 3167 4.48 1441 4.73 619 4.98 251 5.23 96 5.48 34 5.73 11.7 5.98 3.7
4.24 3072 4.49 1395 4.74 598 4.99 242 5.24 92 5.49 33 5.74 11.2 5.99 3.6
4.25 2980 4.50 1350 4.75 577 5.00 233 5.25 88 5.50 32 5.75 10.7 6.00 3.4
39
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• Brainstorm on X’s
• Find change of which X’s affect Y and in what
manner
• Ultimately find which X’s are critical to move the
Y in the desired direction
IN THE ANALYSIS PHASE YOU WILL...IN THE ANALYSIS PHASE YOU WILL...
IN MEASURE PHASE, WE DEALT WITH Y’s.
IN ANALYSIS PHASE, WE WILL DISCOVER
& DEAL WITH X’s.
IN MEASURE PHASE, WE DEALT WITH Y’s.
IN ANALYSIS PHASE, WE WILL DISCOVER
& DEAL WITH X’s.
40
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
To get results should we focus on Y or X?
• Y
• Dependent variable
• Output of the process
• Effect
• Symptom
• It is monitored
• X1, X2,…….., Xn
• Independent variable
• Input to the process
• Cause
• Problem
• It is controlled
Y = f(X)
THE FOCUS OF SIX SIGMATHE FOCUS OF SIX SIGMA
41
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
B e com e A w a r e o f th e P r o b lem
S e le c t L ik e ly C a u se s
Id e n t if y P o ten t ia l C a u se s
D e f in e a n d V e r ify R o o t C a u se s
D e s c r ib e th e P r o b lem
Id en t if y A lt e rn a t iv e S o lu t io n s
I s th e P o te n t ia l C a u se a R o o t C a u se ?
C o n g r a tu la t e y o u r T e am
Im p lem en t p e rm a n a n t a c t io n s
V e r i fy C o r r e c t io v e A c t io n s
P r e v e n t R e c u r r e n c e
Y e s
42
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
High Petrol
Consumption
Procedure Driver Vehicle
MaterialsMaintenanceRoad
Restrictions
No turnOne way
Circuitous
Road
Frequent
stops
Crossings
Traffic
Speed Breakers
Steep
Poor
condition
Potholes Irregular
servicing
False
economy
Negligence
Clogged
filters
Low pressureIgnorance
Faulty
pressure
Tyres
Petrol
Oil
Not changed
Low level
Incorrect viscosity
ImpuritiesIncorrect
Octane no.
Additives
SparesSpurious
Inferior
Impatience
Craze
Always
late
Riding on
clutch
Lack of
awareness
Poor
anticipation
Wrong
gears
Poor
skill
Wrong
culture
Bad
attitude
Inexperience
Body
Heavy
Shape
Technical
details
Carburetor
Spark plugs
LifeContacts
Fuel mix
Engine
High H.P
Cylinders
Cause and Effect Diagram for High Petrol ConsumptionCause and Effect Diagram for High Petrol Consumption
43
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
Validation of CausesValidation of Causes
⌦GEMBA (Work Place) Investigation
⌦ List each cause and verify them through workplace
observations.
Causes Specifications/ Desired
states
Observations Remarks
Bunching
of car
Maximum 2 at a
time
6 out of 10
moments
May be a potential
root cause for
Delay in servicing
44
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
CTQ(y)
Type
Cause(x)
Type
Question to
Answer
Type of
Analysis
Single
Continuous
(Noise)
Discrete in
Two categories
(Bearing-1 & 2)
Do bearing have any effect on
Variation in Noise?2 Variance test
(F-test)
Single
Continuous
(Noise)
Discrete in two
categories
(Bearing-1& 2)
Do bearing have any effect on
Noise level?2-sample t-test.
Data Based validation of Causes
Single
Continuous
(Cycle time)
Discrete in more
than two categories
(Machine-1,2& 3)
Do machine have any effect
on Cycle time?
Analysis of Variance/
Analysis of Means
Single
Continuous
(Cycle time)
Discrete in more
than two categories
(Machine-1,2& 3)
Do machine have any effect
on variation in Cycle time?
Bartlett’s test for
equal variances.
Single
Discrete
(defectives)
Discrete in two
categories
(Month -1& 2)
Do time have any effect on
defectives?
2-proportions test
Single
Discrete
(Error/defect)
Discrete in more
than two/more
categories
(Type of jobs)
Do type of jobs have any effect
on error level?χχχχ2 test (Chi- square
test)
45
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
CTQ(y)Type
Cause(x)Type
Question toAnswer
Type of
AnalysisSingle
Continuous
(Cycle time)
Single continuous
(Time taken in
Process step 1)
Do time taken in process step 1
Influence the cycle time?
Simple correlation and
Regression analysis.
Data Based validation of Causes (Contd.)
Single
Discrete
(defectives)
Single
Continuous
(Cycle time)
Multiple continuous
(Time taken in
Process steps 1,2&3)
Multiple
Regression analysis.
Single continuous
(machine speed).
Logistic
Regression
Which process steps
Influence the cycle time
maximum?Does the machine speed
influence defectives?
Single
Discrete
(defectives)
Single continuous
(machine speed).Does the machine speed
influence defectives?
Multiple Logistic
Regression
Single
Continuous
On same
Subject
(Noise level at
Two different
speed)
Discrete in two
categories
(machine speed).
Does the machine speed
influence noise level?Paired t-test
46
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
CTQ(y)Type
Cause(x)Type
Question toAnswer
Type of
AnalysisSingle discrete in
two categories
(Two supplier)
Do the supplier have different
cycle time?
Wilcoxon signed rank
test
Data Based validation of Causes (Contd.)
Single
Continuous
but non normal
(Cycle time)
Single
Continuous
but non normal
(Cycle time)
Single discrete in
More than two
categories
(Supplier 1,2 & 3)
Do the supplier have different
cycle time?Kruskal-wallis test
47
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
� Learn, how to select the solution
� How to pilot the solutions
� How to assess the risks
� How to implement the solutions
IN THE IMPROVE PHASE YOU WILL…IN THE IMPROVE PHASE YOU WILL…
48
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
GENERATING SOLUTION IDEASGENERATING SOLUTION IDEAS– Review what you know about the process and the verified cause.
– Brainstorm solution ideas; use creativity techniques.
– Combine ideas into solutions.
49
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
A PATH TO BETTER SOLUTIONSA PATH TO BETTER SOLUTIONS• In order to get better solutions, we will follow these steps:
– Generate Criteria
– Weight Criteria
– Evaluate Ideas
• The tool we will use for this is the Solution Prioritization Matrix.
Solution
A
B
C
D
0.2 1.25 0.3 1.65 0.6
Easy Quick Tech Hi Impact Customers
SUM
2.6
3.0 2.4
2.7
19.8
8.25
8.4
4.8
10
13.75
43.6
1.2 2.7 19.8 5.47.5 36.6
32.1
4.2 18.15 5.418.75 47.71.2
Criteria and Weights
50
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
WHY PILOT?WHY PILOT?
– Improve the solution
– Understand risks
– Validate expected results
– Smooth implementation
– Facilitate buy-in
– Identify previously unknown performance
problems
51
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
WHEN TO PILOTWHEN TO PILOT
Pilot when:
– You need to confirm the expected results and
practicality of the solution.
– You want to reduce the risk of failure.
– The scope of the change is large, and reversing the
change would be difficult.
– Implementing the change will be costly.
– Changes would have far-reaching, unforeseen
consequences.
52
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
EVALUATE THE PILOTEVALUATE THE PILOT
– Compare results against the original definition of a
defect and against CTQs.
– Recalculate process sigma and process capability.
– Analyze causal relationships and process conditions.
53
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
PLANNING GRIDS DEFINITIONPLANNING GRIDS DEFINITION• A planning grid helps to identify the resources and outcomes for each step in the process.
Due Date
Respon-sibility
DeliverableStepWhom to
Involve
Budget/ Cost
Other Topics
Step Number
1
2
4
3
Develop new wiring
schematic
Wiring PlanCalvin,Max,Sheryl
6/12 N/ADept.staff,Maria
Conduct ChangesMaria 6/12 N/A
Dept.staff
Revalidate SystemMaria 6/16 N/A
Update
documentationCalvin 6/8 N/A
Otherdeptsupv
Machine
Changes
Documentation
Documentation
54
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
PLANNING GRID FEATURESPLANNING GRID FEATURESPerson(s)responsibleidentified
Steps listedsequentially
Outcome of eachstep clearlyidentified
Timing andother factors
tracked
Due Date
Respon-sibility
DeliverableStepWhom to
Involve
Budget/ Cost
Other Topics
Step Number
1
2
4
3
Develop new wiring
schematic
Wiring PlanCalvin,Max,Sheryl
6/12 N/ADept.staff,Maria
Conduct ChangesMaria 6/12 N/A
Dept.staff
Revalidate SystemMaria 6/16 N/A
Update
documentationCalvin 6/8 N/A
Otherdeptsupv
Machine
Changes
Documentation
Documentation
55
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
THE PEOPLE SIDETHE PEOPLE SIDE
– Too often we spend all our time on the “technical” side of a
change—what has to happen by when, etc.
– We ignore the people side of the change—how to help those
who will have to change their ways of doing things in order
to realize the new change.
– There are three elements of the people side:
• Communication: the exchange of information both from you to
others and from others to you.
• Participation: involving people in the planning and execution of a
change so they can develop shared ownership and commitment.
• Education: providing people with what they will need to know
before they successfully implement the desired changes.
56
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
BENEFITS OF PEOPLEBENEFITS OF PEOPLE--SIDE PLANNINGSIDE PLANNING
– Increased understanding ���� decreased confusion
– Increased commitment ���� decreased resistance
– Increased capability ���� decreased fear of failure
57
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
APPROACH TO CONTROLAPPROACH TO CONTROL
Quality Control &
Process Change
Management
Quality Control &
Process Change
Management
Standardize and
Document
Effective
Methods
Standardize and
Document
Effective
Methods
Establish
Ongoing
Project
Monitoring
Establish
Ongoing
Project
Monitoring
Evaluating
Results
Evaluating
Results
Hand Off,
Summarize Key
Learnings and
Draft Future Plans
Hand Off,
Summarize Key
Learnings and
Draft Future Plans
58
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
CONTROL PHASECONTROL PHASE
Till now you may have
• Described your ‘Y’ and got the direction of action.
• Isolated your critical Xs.
• Optimized the process by deciding on the level of these Xs.
IN THE CONTROL PHASE YOU DEAL
WITH HOLDING THE GAINS THROUGH
CONTROL OF Xs.
59
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
SOME WAYS TO MAINTAIN/CONTROL SOME WAYS TO MAINTAIN/CONTROL
YOUR NEW PROCESS CAN BE BYYOUR NEW PROCESS CAN BE BY
�Standardizing : Put it in audit checklist, quality
plan, documented procedure etc.
�Fool-Proofing : To ensure that it can be done in
no other way except how you want it to be done.
�Have Advance Warning Systems : If
something goes wrong, it tells that to you NOW
What you would as such come to know of it over
a period of time.
e.g. : Control Charts
60
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
PROCESSES CAN BE CONTROLLED BY PROCESSES CAN BE CONTROLLED BY
BUT NOT LIMITED TOBUT NOT LIMITED TO
• SPC and Advance Warning Systems
• Inspection & Audits
• 100% checking of output
• Fool-Proofing
• Sampling Plans
• Control / Quality Plans
• Quality Systems
61
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
• Different processes would be sensitive to
different parameterse.g.: Man, Machine
• Hence different processes would require
different controls which in turn would
depend on that specific parameter to which
it is sensitivee.g.: Brazing may be welder dependent. Hence
training would be an important control parameter.
Thus leading to concept of brazer qualification.
62
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
IN A NUT SHELL IN A NUT SHELL Your Process may be:
AFFECTED BY CAN BE MAINTAINED BY
� Initial Setup
� Equipment/
machine settings
� Fixtures
� Tooling
� Man
� Material
� Maintenance
� Environment
� FPI in between the checks
� Parameters feedback system
� First approvals, monitor the assignable causes
� Tool approval, Fool-Proofing of mating parts, FPI,
Audit checks
� Training and Fool-Proofing
� Certification before use
� PM schedules, FPI check after each maintenance
� Control environment and PM of environment
controlling equipment
63
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
CONTROL PLANCONTROL PLAN Page 01 of 02
PROTOTYPE PRE-LAUNCH PRODUCTION
CONTROL PLAN NUMBER : CP-M13-02
KEY CONTACT / PHONE : Head, Quality & C.S. DATE (ORI.) : 08.09.99 DATE (REV.) : 27.06.00
PART NUMBER / LATEST CHANGE LEVEL : ML CORE TEAM : BSK, HA, GVS, KSK CUSTOMER ENGG. APPROVAL / DATE (IF REQD.) : N.A.
PART NAME / DESCRIPTION : Generic SUPPLIER / PLANT APPROVAL / DATE : 01.10.99 CUSTOMER QUALITY APPROVAL / DATE (IF REQD.) : N.A.
SUPPLIER PLANT : Nanjangud SUPPLIER CODE : N.A. OTHER APPROVAL / DATE (IF REQD.) : N.A. OTHER APPROVAL / DATE (IF REQD.) : N.A.
CHARACTERISTICS METHODS
SAMPLE
PART /
PROCESS
NUMBER
PROCESS NAME /
OPERATION
DESCRIPTION
MACHINE,
DEVICE, JIG,
TOOLS FOR
MFG.
NO. PRODUCT PROCESS
SPL.
CHAR.
CLASSPRODUCT /
PROCESS
SPEC. /
TOLERANCE
EVALUATION /
MEASUREMENT
TECHNIQUE SIZE FREQ.
CONTROL
METHOD
REACTION
PLAN
1 Drill hole
position
* + 50 µ - X
+ 50 µ - Y
True measure Every spindle SPC chart Check &
adjust
2 Hole quality * As per SOP Cross Section Once / week
All layer counts
Hole
quality
chart / log
book
Check &
adjust
3 Hole diameter As per traveler Pin gauge Bottom
panel
Every
lot
Visual Check &
adjust
4 Hole count As per
program
Drill check sheet Bottom
panel
Every
stack
Visual Check &
adjust
Machine setup
M13 Drilling Drilling
machines,
Drill bits,
Aluminium
Entry & backup
5 Scope drill target pad
distance
As per traveler Scope drill m/c. All
panels
100% Log book Quarantine
& adjust
previous
process
�
64
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
POKAPOKA--YOKE (JAPANESE TERM)YOKE (JAPANESE TERM)
• Fail Safe
– Methods used to either make the occurrence of a
nonconformity impossible or to ensure that it
does not pass undetected.
• However…
As we get better at fool-proofing,
we get better fools.
65
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
STANDARDIZATIONSTANDARDIZATION
– Making sure that important elements of a process are performed
consistently in the best possible way.
– Changes are made only when data shows that a new alternative
is better.
– Documentation is key
• Making sure documentation is up to date and used encourages ongoing
use of standardized methods.
– Discussion
• What images come to mind when you think of process standardization?
66
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
BENEFITS OF STANDARDIZATIONBENEFITS OF STANDARDIZATION
• Standardization helps us compete more
successfully in the marketplace by providing:
– Increased reliability
– Reduced costs
– Improved employee performance
– Increased safety
– Processes that remain in control
– Continuous improvement
– Flexible practices that allow for quick
response to customer needs
67
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
STANDARDIZATION = “STANDARD STANDARDIZATION = “STANDARD
PRACTICES AND PROCEDURES”PRACTICES AND PROCEDURES”
• A standard practice is…
“A definition of a work method wherein all
variables of the method have been specified
in detail.”
• It is a written agreement between the worker
and the company regarding how the job will
be done.
68
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
WHAT DEFINES A STANDARD PRACTICE?WHAT DEFINES A STANDARD PRACTICE?
•Purpose: To gather technology and process skill in written form and to make it easier for everyone to do their work.
•Contents:
– Written so even workers who are not fully trained can use them easily
– Specific to the job, written at an appropriate level of detail
– Describe how to prevent variation
– Provide clear instructions
– Considered priorities
69
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
TRAININGTRAINING
– When you have completed the documentation, you need to make sure that everyone using a common process is trained in the new methods.
– Even experienced employees need to be trained in the new methods.
70
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
� It is an important tool to give advance warnings
about the drift from the normal behavior.
�To draw control charts, for a process we need to
know the average and standard deviation
obtained from the process.
SHEWHART CONTROL CHARTSSHEWHART CONTROL CHARTS
71
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
DISPLAYING BEFORE & AFTER DATADISPLAYING BEFORE & AFTER DATA
• Add more data to an
existing run chart or
control chart.
• Prepare new Pareto charts
for those you created in
Step 2. Make scale and
dimensions the same so you
can more accurately judge
degree of improvement.
• Draw new frequency plots
on the same scale as the
original plots.
Before After
}Improvement
Target
}Remaining Gap
Good
Step 4 changesimplemented
} Improvement
Before After
A1 A2 A3 A4 A2 A1 A3 A4
Before After
72
ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SSSS--DEFINE PHASEDEFINE PHASE
RECALCULATE PROCESS SIGMARECALCULATE PROCESS SIGMA
Step BEFOREOpportunitiesUnits
1
2
3
4
5
6
7
8
9
10
11
12
40
40
2 x 40 = 80 61
37
113
34
142
38
69
143
37
64
72
35
1 x 40 = 40
3 x 40 = 120
1 x 40 = 40
4 x 40 = 160
1 x 40 = 40
2 x 40 = 80
4 x 40 = 160
1 x 40 = 40
2 x 40 = 80
2 x 40 = 80
1 x 40 = 40
40
40
40
40
40
40
40
40
40
40
960 846
AFTER
17
1
12
0
8
0
3
37
0
5
2
1
86
Yield = 1 –
= 1 – .88
= 12%
Sigma = 0.3
960
846
Yield = 1 –
= 1 – .09
= 91%
Sigma = 2.8
960
86
BEFORE
AFTER