[link - powerpoint slides]

The Scientific Method and

Quality Improvement

OCMA 2006

tom.sutton@mohawkcollege.ca

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