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Continuous Improvement
Ideas
Seven Statistical Tools
Check sheet Pareto chart Cause and effect diagram Histogram Scatter plot Stratification Graphs (control charts)
Problem
75 defective springs in a week’s production Check sheet with defect type Display on a Pareto chart Identify the important problem Focus on the “vital few” not the
“trivial many”
Pareto ChartCount
Perc
ent
Defect type
Count8.0 5.3 4.0
Cum % 56.0 82.7 90.7 96.0 100.0
42 20 6 4 3Percent 56.0 26.7
80706050403020100
100
80
60
40
20
0
Pareto Chart of Defect type
Cracks
Environment
Measurements
Methods
Material
Machines
People
Type B
Type A
Oven Temp
QuenchTemp
CarbonContent
Guage
Inspector
Cause-and-Effect Diagram
Histogram of Crack Size
Size
Perc
ent
6543210
40
30
20
10
0
Histogram of Size
Size
Perc
ent
40
30
20
10
0
6543210
40
30
20
10
0
A
B
Panel variable: Type
Histogram of Size of Crack versus Type
Hardening Temperature
Cra
ck S
ize
767472706866646260
160
150
140
130
120
Scatterplot of Crack Size versus Temperature
Type A Cracks
Ideas
DESIGN
Experiment for three factors
Steel Temp Carbon Oil Temp
Low Low Low
High Low Low
Low High Low
High High Low
Low Low High
High Low High
Low High High
High High High
Ideas
DESIGN
RUN
Ideas
DESIGN
RUN
ANALYZE
Carbon
% C
rack
free
1-1
74
73
72
71
70
69
Oil TOil T
% C
rack
free
1-1
90
85
80
75
70
65
60
55
Steel T-11
Main Effects Plot for % Crackfree Interaction Plot for % Crackfree
Ideas
DESIGN
RUN
ANALYZE
Ideas
DESIGN
RUN
ANALYZE
More Ideas
KNOWLEDGE
What is Six Sigma?
Process Capability
16141210864
LSL USLProcess Capability
99% Quality Level
• 20,000 lost mail articles per hour
• Unsafe drinking water 15 minutes /day
• 5000 incorrect surgical operations per week
• 2 short or long landings at major airports/day
• 200,000 wrong drug prescriptions per year
• No electricity for 7 hours per month
Sigma Quality Level
pp
m d
efe
cts
7654321
1000000.00
100000.00
10000.00
1000.00
100.00
10.00
1.00
0.10
0.01
Scatterplot of ppm vs Sigma
Average company
Best in Class
Domestic airline flightFatality rate (0.43ppm)
Six Sigma Capability
16141210864
LSL USL
Process Capability
Six Sigma
Define
Measure
Analyze
Improve
Control
Six Sigma Black Belt
Define• Project scope• Metrics• Problem statement
Six Sigma Black Belt
Measure• Process analysis• Probability and statistics• Collecting and summarizing data• Properties and applications of
prob. Distributions• Measurement systems• Analyzing process capability
Six Sigma Black Belt Analyze• Exploratory data analysisA. Sources of variationB. Regression, analyze residuals• Hypothesis testingA. Interval estimatesB. Tests for means, variances and proportionsC. Paired comparisonsD. ANOVAE. Contingency tables
Six Sigma Black Belt Improve• Design of experimentsA. Design principlesB. One factor experimentsC. Full factorial experimentsD. Fractional factorial experimentsE. Robustness conceptsF. Mixture experiments• Response surface methodologyA. Steepest ascentB. Higher order experiments• Evolutionary Operation (EVOP)
Six Sigma Black Belt Control• Statistical Process ControlA. Application of control chartsB. Analysis of control charts• Advanced SPCA. Short run SPCB. EWMA, CUSUM• Lean tools for control• Measurement system analysis• Design for Six SigmaA. Quality Function DeploymentB. Robust designC. Failure mode and effects analysis
Six Sigma Black Belt Improve• Design of experimentsA. Design principlesB. One factor experimentsC. Full factorial experimentsD. Fractional factorial experimentsE. Robustness conceptsF. Mixture experiments• Response surface methodologyA. Steepest ascentB. Higher order experiments• Evolutionary Operation (EVOP)
Design of Experiments
Popcorn Experiment
Brand Time Power Taste Bullets
Low Low Low 74 32
High Low Low 75 35
Low High Low 71 16
High High Low 80 13
Low Low High 81 7
High Low High 77 8
Low High High 42 6
High High High 32 3
Analysis
1
-1
1
-11-1
Power
Time
Brand
32
7781
42
80
7574
71
Cube Plot (data means) for Taste
PowerPower
Me
an
1-1
80
70
60
50
40
Time-11
Interaction Plot (data means) for Taste
The Helicopter Experiment
Design an experiment to study the factors that may affect flight time.
Measure distance from target as well
Helicopter Factors
Factor - +
Paper type Regular Bond
Wing length 3.00” 4.75”
Body length 3.00” 4.75”
Body width 2.00” 1.25”
Paper clip No Yes
References
Paper by George Box www.statease.com www.minitab.com www.asq.org www.isixsigma.com