Six Sigma Foundations
Not publishedof exam
Lean Concepts
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DMAIC + Project Tools
Not publishedof exam
Statistics + Measurement
Not publishedof exam
SPC + Capability
Not publishedof exam
Quick Facts
- Exam
- CSSC Green Belt
- Path
- Standard Exam
- Questions
- 100
- Types
- Multiple choice, true/false
- Time
- 2 hours
- Pass
- 280 of 400 points
- Percent
- 70%
- Books
- Open book
- Fee
- $195 USD
- Attempts
- 3 within 1 year
- Prerequisites
- None
- Project
- Not required
- Validity
- No expiration
- Blueprint
- 24 sections, no weights
SIPOC
Suppliers Inputs Process Outputs Customers
Drafted in DefineOne brainstorming sessionScales to any process
Belt Levels + Roles
- Belt order
- White, Yellow, Green, Black, Master
- Green Belt
- Collects data under Black Belt
- Green Belt scope
- Keeps day job; smaller projects
- Black Belt
- Directs Green Belt analysis
- Master Black Belt
- Reviews analysis before presenting
- Sponsor / champion
- Senior leader owning the resultOwns
- Champion duties
- Funds, resources, corporate politics
- Process owner
- Metrics, procedures, control plan
Related Quality Methods
- Six Sigma
- Reduces variation and defects
- Lean
- Removes waste (muda)
- Kaizen
- Change for the better
- TQM
- Early enterprise-wide quality program
- BPR
- Radical technical process redesign
- Rummler-Brache
- Nine Boxes performance model
- Nine Boxes grid
- Performer, process, organization levels
- JumpStart
- Fast fix, no statisticsLow risk only
Problem + Quality Framing
- y = f(x)
- Output caused by inputs
- 5 Whys
- Drill past the symptom
- Problem statement
- Where, when, magnitude, metric
- Statement excludes
- No cause, no solution
- VOC
- Voice of the customer
- CTQ tree
- Need, drivers, measurable requirements
- CoPQ
- Cost of poor quality
- Internal failure
- Caught before delivery
- External failure
- Found by the customer
Project + Team Setup
- Project charter
- Output of Define phase
- Charter contents
- Problem, CTQs, roles, duration
- SIPOC
- Suppliers Inputs Process Outputs Customers
- Is / Is Not matrix
- Fixes scope boundaries early
- Stakeholder analysis
- Power versus interest grid
- Project viability model
- 15 weighted selection criteria
- Critical path method
- Dependencies set the schedule
- Tollgate review
- Sponsor approves phase exit
5S Phases
Sort, Straighten, Shine, Standardize, Sustain
Sort: remove clutterStraighten: a place for eachShine: clean and inspectStandardize: written standardSustain: everyone commits
Type I vs Type II Muda
Type I
- Non-value-added
- Currently essential
- Make it efficient
Type II
- Non-value-added
- Not essential
- Remove immediately
Streamline vs delete
Waste Picker
- Made too early→Overproduction
- Stock stacks before step→Inventory(Bottleneck)
- Fixing defective output→Correction(Rework)
- People walking needlessly→Motion
- Parts moved needlessly→Conveyance
- Idle between steps→Waiting
- Steps customer never values→Over-processing
- Skills going unused→Talent(CSSC addition)
Seven Muda + Extras
- Overproduction
- Too much, too soon
- Correction
- Rework and defect fixing
- Inventory
- Stock piling before a step
- Motion
- Needless movement of people
- Conveyance
- Needless movement of material
- Over-processing
- More work than required
- Waiting
- Idle time between steps
- CSSC additions
- Talent, ideas, capital
- Type I muda
- Non-value-added but currently essential
- Type II muda
- Non-essential; remove immediately
Seven Muda
Overproduce, Correct, Inventory, Motion, Convey, Process, Wait
Plus talentPlus ideasPlus capital
Lean Tools + Process
- 5S
- Sort Straighten Shine Standardize Sustain
- Sustain
- Hardest phase; needs commitment
- Just-in-time
- Produce only what's needed
- Value stream map
- Exposes waste across process
- Bottleneck
- Slowest step caps output
- Smaller batches
- Cut lead time, inventory
- Process components
- Inputs outputs events tasks decisions
- Process definition layers
- Steps, time, dependencies, resources
- Poka yoke
- Mistake-proofs the process
DMAIC Order
Define Measure Analyze Improve Control
Define: charterMeasure: baselineAnalyze: root causeImprove: pilotControl: control plan
DMAIC vs DMADV
DMAIC
- Improves existing process
- Define Measure Analyze
- Improve then Control
DMADV
- Creates new process
- Define Measure Analyze
- Design then Verify
Fix existing vs design new
DMAIC Phase Deliverables
- Define
- Charter, SIPOC, scope
- Measure
- Baseline data, FMEA, metrics
- Analyze
- Root causes, validated statistically
- Improve
- Select, pilot, implement
- Control
- Control plan, SPC, handoff
- Design (DMADV)
- Build the new process
- Verify (DMADV)
- Confirm the design performs
- Phase purpose
- Eat the elephant gradually
FMEA RPN
RPN = Severity x Occurrence x Detection
Score each 1-10Highest RPN firstRescore after the fix
Repeatability vs Reproducibility
Repeatability
- One appraiser
- Same part, same gauge
- Same reading twice
Reproducibility
- Different appraisers
- Same part, same gauge
- Do they agree
One person vs several people
Analyze + Improve Tools
- Fishbone bones
- People Process Materials Procedure
- Optional bones
- Equipment and Environment
- Pareto principle
- 20% causes, 80% effects
- FMEA RPN
- Severity x Occurrence x Detection
- Solutions selection matrix
- Ranks fixes against causes
- Cost benefit analysis
- Weighs gain against spend
- Pilot
- Limited live trial first
- Control plan
- Who monitors what, when
- Visual management
- Status visible at a glance
- Gage R&R
- Tests the measurement system
Type I vs Type II
Type I (alpha)
- Reject a true null
- False alarm
- Set by alpha
Type II (beta)
- Keep a false null
- Missed difference
- Power = 1 - beta
False alarm vs missed signal
Hypothesis Test Picker
- One proportion versus target→1-Proportion test(Discrete data)
- Two proportions compared→2-Proportion test(Discrete data)
- Mean versus target, normal→1-Sample t test(Small sample)
- Same group before, after→Paired t test(Same x factor)
- Means of two populations→2-Sample t test(Different x factors)
- Comparing variance or deviation→Chi-Square test(Also 1-Variance test)
- Median versus target, non-normal→1-Sample Wilcoxon(Fairly symmetrical data)
- Non-normal and badly skewed→1-Sample Sign test(Wilcoxon alternative)
- Two medians, non-normal→Mann-Whitney test(Two x factors)
Defect + Yield Formulas
- DPMO
- (defects / opportunities) x 1,000,000
- DPMO example
- (2 / 900) x 1,000,000 = 2,222
- DPU
- defects / units sampled
- DPU example
- 9 / 50 = 0.18
- Yield
- (opportunities - defects) / opportunities
- FTY
- good units / units entering
- RTY
- (entering - scrap - rework) / entering
- Multi-step yield
- Multiply each step's yield
- Why RTY is lower
- It charges rework as loss
Discrete vs Continuous Data
Discrete
- Nominal, ordinal, binary
- Counted categories
- Needs larger samples
Continuous
- Measured in units
- More precise
- Collect this where possible
Continuous converts down, not up
Distribution Picker
- Pass or fail, fixed trials→Binomial(Discrete)
- Metric reads 'per unit'→Poisson(Discrete counts)
- Trials until first defect→Geometric(Waiting time)
- Time between failures→Exponential(Continuous)
- Skewed durations above zero→Lognormal(Continuous)
- Reliability, shape varies→Weibull(Distribution family)
- Symmetrical continuous data→Normal(Still test normality)
Sigma Conversion Table
- 99.7450% yield
- 2,550 DPMO = 4.3 sigma
- 99.6540% yield
- 3,460 DPMO = 4.2 sigma
- 99.5340% yield
- 4,550 DPMO = 4.1 sigma
- 99.3790% yield
- 6,210 DPMO = 4.0 sigma
- 99.1810% yield
- 8,190 DPMO = 3.9 sigma
- Six sigma
- 3.4 DPMO, 99.99966% yieldGoal
- Worked example
- 99.5% yield = 4.0-4.1 sigma
FTY vs RTY
FTY
- Good units / units in
- Ignores rework
- Looks better
RTY
- Subtracts scrap and rework
- Probability of defect-free unit
- Always lower
Rework hidden vs rework charged
Distribution Basics
- Normal
- Symmetrical continuous bell curve
- Binomial
- Two outcomes, independent trials
- Poisson
- Counts per time or space
- Poisson clue
- The word 'per' in metric
- Geometric
- Trials before first occurrence
- Exponential
- Arrival times, between failures
- Lognormal
- Right-skewed durations above zero
- Weibull
- Family imitating other shapes
- Logistic
- Approximates the normal curve
- Gamma
- Always skewed to right
Hypothesis Testing Terms
- H0
- Null: no difference exists
- Ha
- Alternative: a difference exists
- p-value rule
- p below alpha, reject H0
- Fail to reject
- Not proof H0 true
- Alpha
- Type I error risk
- Beta
- Type II error risk
- Power
- 1 - beta
- Beta 0.20
- Power of 0.80
- Delta
- Smallest difference worth detecting
- Sample size inputs
- Alpha, beta, delta
- Random sampling
- Required, or inference fails
Correlation + Regression
- Scatter diagram
- Shows relationship, never causation
- r range
- -1 through 1
- r near 0
- No relationship at all
- r at 1
- Every point on line
- Pearson
- Usual correlation calculation
- Regression
- Predicts y from x
- Chi-squared goodness-of-fit
- Tests data for normality
- Beyond 3 sigma
- Under 1% of data
Chart Data Split
Variable: X-bar, I-MR. Attribute: p, np, u, c
p, np: defective unitsu, c: defect countsnp, c: constant size
Control vs Capability
In control
- Low variation
- Control limits from data
- Says nothing about spec
Capable
- Low variation too
- Centered on requirement
- Measured by Cpk
Steady vs steady and right
Control Chart Picker
- Continuous, subgroups under 8→X-bar & R(Mean plus range)
- Continuous, subgroups over 8→X-bar & S(Sigma easily calculated)
- Continuous, no sensible subgroups→I-MR(Individual points)
- Data slow or costly→I-MR(Cannot wait for subgroups)
- Discrete, percent defective→p chart(Sample size varies)
- Discrete, percent, constant size→np chart(Counts nonconforming units)
- Defect counts, size varies→u chart(Defects per unit)
- Defect counts, constant size→c chart(Defects per sample)
Capability + Control Limits
- Sigma level
- Center to nearest specification limit
- Sigma level formula
- (USL - median) / sigma
- Take which value
- The smaller of two
- Cpk
- sigma level / 3
- Cpk 1.33
- Equals sigma level 4
- Cpk 2.0
- Equals sigma level 6
- UCL
- 3 sigma above center
- LCL
- 3 sigma below center
- Zone C
- Nearest the center line
- Zone A
- Outermost, beside control limits
Common vs Special Cause
Common cause
- Built into process
- Expected variation
- Fix the system
Special cause
- Outside normal expectation
- Bad headset, new hire
- Investigate the event
Process noise vs outside event
Out-of-Control Tests
- Test 1
- One point beyond limitsAct now
- Test 2
- Nine in a row, one side
- Test 3
- Six points trending steadily
- Test 4
- Fourteen points alternating direction
- Test 5
- Two of three in A
- Test 6
- Four of five in B
- Test 7
- Fifteen in a row, C
- Test 8
- Eight in a row, skipping C
Common Traps
Sigma level vs priority
Sigma flags worst variation ≠ Cost sets the priority
FTY vs RTY
FTY hides rework ≠ RTY charges rework
Control vs spec limits
Control limits from data ≠ Spec limits from customer
Correlation vs causation
Scatter shows relationship ≠ It never proves cause
Failing to reject
Not proof H0 true ≠ Only insufficient evidence
p charts vs u charts
p tracks defective units ≠ u tracks defect counts
DMAIC vs DMADV
DMAIC improves existing ≠ DMADV designs new
Alpha vs beta
Alpha rejects true null ≠ Beta keeps false null
Cpk vs sigma level
Cpk is sigma / 3 ≠ Cpk 1.33 equals 4
Last Minute
- 1.DPMO = defects / opportunities x 1,000,000
- 2.RTY subtracts scrap and rework
- 3.Multiply step yields for overall
- 4.Cpk = sigma level / 3
- 5.Cpk 1.33 equals sigma level 4
- 6.Control limits sit 3 sigma out
- 7.Subgroups under 8: X-bar & R
- 8.Subgroups over 8: X-bar & S
- 9.No subgroups: use I-MR chart
- 10.p and np track defective units
- 11.u and c track defect counts
- 12.np and c need constant size
- 13.p below alpha means reject H0
- 14.Power = 1 - beta
- 15.Seven muda plus talent, ideas, capital
- 16.5S ends with Sustain
- 17.Charter is the Define output
- 18.Fishbone: People Process Materials Procedure
- 19.Exam: 100 questions, 2 hours
- 20.Pass needs 280 of 400
- 21.Open book: bring your manual
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