mini tab 14 one day training 39403

Minitab 14 Quality Statistics

A person without data is merely expressing an opinion….

Created by Paul White - Aston Martin Six Sigma Department

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Introduction

Name

Department

Six Sigma / Minitab experience

Why are you here today?

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Training Topics

What is Six Sigma? Introduction to Minitab Version 14 Manipulation of data Basic statistics Graphs Quality tools Measurement System Analysis – R & R Control charts Normality testing Capability analysis Hypothesis Testing

What is Six Sigma?

‘The function of a statistician is to make predictions, and thus to provide a basis for action’ – W.E Deming

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6-Sigma99.99966% Good

6-Sigma99.99966% Good

• Seven articles lost per hour• 20,000 lost articles of mail per hour

3.8-Sigma99% Good3.8-Sigma99% Good

• Unsafe drinking water for almost 15 minutes each day

• Unsafe drinking water one minute every seven months

• 5,000 incorrect surgical operations per week

• 1.7 incorrect operations per week

• 1 missed putt per 9 holes of golf • 1 missed putt per 163 years

• 10,700 defects per million opportunities

• 3.4 defects per million opportunities

Is 99% Good Enough?

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Goals of Six Sigma

Reduce defects.

Improve process capability.

Improve customer satisfaction.

Increase shareholder value.

This ensures we are competitive, provides future security and opportunity for growth.

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100% Inspection – Does it work?

100% Inspection

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Finished files are the results of many years of sceintific studies combined with the experience of many years of

effort

F-Test

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How many did you see?

Have another look!

F-Test

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effort

F-Test

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Did anyone change their mind?

F-Test

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effort

F-Test

13

Did you spot anything else?

F-Test

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effort

F-Test

F-Test

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100% Inspection – Does it work?

100% Inspection

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DMAIC Improvement Model

Introduction to Minitab

‘Statisticians are people with tears wiped from their eyes’

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Introduction to Minitab

The 3 Minitab views - session folder, worksheet folder, project folder.

3 types of data entry– numbers, text and dates.

Importing text from other sources

Creating, opening and saving projects and worksheets.

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Session and Worksheet Folders

The 2 main windows in Minitab – The session folder & worksheet folder.

Session folder

Worksheet folder

Select different views using icons

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Project Folder

Multiple worksheets can be opened within the same project.

File /New / New worksheet

Multiple worksheets

Select project manager

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3 Types of data

Minitab stores numbers, text and dates.

Numbers – No symbol in column header, right aligned in cell

Text – T in column header, left aligned in cell

Date – D in column header, left aligned in cell

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Numeric Data Types

FAIL PASS

Electrical Circuit

TEMPERATURE

Thermometer

TimeTime

VariableAttribute

NO-GO GO

Caliper

QTY UNIT DESCRIPTION TOTAL

1 $10.00 $10.00

3 $1.50 $4.50

10 $10.00 $10.00

2 $5.00 $10.00

SHIPPING ORDER

Error

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Attribute vs Variable Data

Variable

Attribute

The Advantage of Variable Data

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Attribute vs Variable Data

Variable Data Available earlier in the process, before defects occur. Illustrates short term trends allowing immediate action. A small amount of data is required to draw conclusions

(minimum 30 individual readings).

Attribute Data Defect related, only after the fault has occurred. Only illustrates long term trends. A large amount of data is required to draw conclusions

(minimum 50 subgroups) Sometimes this is the only data available.

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Importing text from other sources

Easiest way is to copy & paste. However, an import function is available: File / other files / import special text.

Tip! Always title each column in the cell below the column reference number. this will make later analysis easier to interpret as the graphs will include your column description.

Select destination cell in Minitab and paste from clipboard

Select data from another source (such as Excel) and copy to clipboard.

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Saving projects and worksheets

Save projects to correct destination.

File / Save project as

Change default saving location

Rename with relevant filename and date

Manipulating Data

‘Facts are stubborn things, but statistics are more pliable’

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Manipulating Data

Erasing columns and rows

Stacking columns and rows

Transposing columns

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Erasing data

Erasing columns and rows

Select column and right click mouse

Delete cells

Tip! Undo function is available on the toolbar

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Stacking columns

Data / Stack / Stack Columns

Select columns to stack

Select stacked destination and subscripts

Click OK

Tip! Always store subscripts when stacking data, this will copy the column description to the adjacent data cell. This makes future analysis easier, to discriminate between data sets.

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Transposing data

Data / Transpose columns

Switch the data pattern from columns to rows.

Select columns to transpose

Select destination option

Tip! If your data is already in Excel you can use the ‘paste special’ function to transpose from columns to rows and vice versa! Use Minitab & Excel interchangeably to conduct data analysis.

Click OK

Basic Statistics

‘Statistics should be used the way a drunk uses a lamp post, more for support than enlightenment ’

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Basic Statistics

Descriptive statistics

Inferential statistics

Graphical summary

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Descriptive Statistics

Stat / Basic statistics / display descriptive statistics.

Stat /Basic statistics / Display descriptive statistics

Select variables, click OK

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Descriptive Statistics

Descriptive statistics describe the sample we have gathered, tells us what is.

Session window output

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Measures of Average

Mean:Calculated average. Sum of all individual values, divided by the number of samples.

Mode: Most frequently occurring value.

Median: The middle number when the values are sequentially arranged.

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Mean =

Mean

5, 5, 4, 2, 1,1, 4, 5, 3, 2.

Measures of Average

3.2

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5, 5, 4, 2, 1,1, 4, 5, 3, 2.

Measures of Average

Mode =

Mode

5

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Median =

Median

5, 5, 4, 2, 1,1, 4, 5, 3, 2.

Measures of Average

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1, 1, 2, 2, 3, 4, 4, 5, 5, 5.

Median = 3.5

3+4 2 = 3.5

Median

Measures of Average

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Mean =3.2Mode =5Median =3.5

5, 5, 4, 2, 1,1, 4, 5, 3, 2.

Measures of Average

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Graphical Summary

Stat / Basic statistics / Graphical summary.

Stat / Basic Statistics / Graphical Summary

Select variable

Click OK

Tip! Note the confidence level of 95% in the option window. This applies to the inferential statistics that will be displayed in the graphical summary.

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Graphical Summary

Descriptive statistics describe the sample we have gathered, tells us what is. Inferential statistics allows us to “infer” about the population, tells us what

“probably is”. Inferences are never definite, only stated with a degree of confidence.

Normality test



10.810.410.09.6

Median

Mean

10.1510.1010.0510.009.959.90

1st Quartile 9.800

Median 10.0253rd Quartile 10.240Maximum 10.839

9.922 10.105

9.915 10.126

0.268 0.400

A-Squared 0.19

P-Value 0.902

Mean 10.014StDev 0.321Variance 0.103

Skewness -0.003050Kurtosis -0.106782N 50

Minimum 9.310

Anderson-Darling Normality Test

95% Confidence I nterval for Mean

95% Confidence I nterval for Median

95% Confidence I nterval for StDev95% Confidence I ntervals

Summary for Tool 1

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High Standard DeviationHigh Variability

Low Standard DeviationLow Variability

Standard Deviation

Standard Deviation refers to the collective deviation of the entire data set

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6.1465.5 6.5 7

xx

x

x

x

5.26

xbar = 6.146

6.965.9 6.47

xbar = 6.146

-0.8860.814

-0.246

0.324

-0.006

5.26,6.96,5.90,6.47,6.14.

r = 6.96 – 5.26 = 1.70

r = 1.70

Standard Deviation

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Calculating standard deviation is best shown in table format: (xbar = 6.146)

Data x - xbar (x – xbar)2

5.26

6.96

5.90

6.47

6.14

-0.886 0.7849960.814

-0.246

0.324

-0.006

0.662596

0.060516

0.104976

0.000036

= 1.61312S = (x – X)2

n - 1√_

Standard Deviation

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S = (x – X)2

n - 1√_

S = 1.613124√

S = 0.40328√S = 0.635 (to 3 s.f.)

We can now use the formula:

Standard Deviation

Tip! The square of the standard deviation is the variance.

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The distribution of area as a percentage:

-3s -2s -1s X +1s +2s +3s

68.26%

95.44%

99.73%

0.135%

0.135%

Normal Distribution

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Graphical Summary

Descriptive statistics describe the sample we have gathered, tells us what is. Inferential statistics allows us to “infer” about the population, tells us what

“probably is”. Inferences are never definite, only stated with a degree of confidence.

Normality test



10.810.410.09.6

Median

Mean

10.1510.1010.0510.009.959.90

1st Quartile 9.800

Median 10.0253rd Quartile 10.240Maximum 10.839

9.922 10.105

9.915 10.126

0.268 0.400

A-Squared 0.19

P-Value 0.902

Mean 10.014StDev 0.321Variance 0.103

Skewness -0.003050Kurtosis -0.106782N 50

Minimum 9.310


95% Confidence I nterval for Mean

95% Confidence I nterval for Median

95% Confidence I nterval for StDev95% Confidence I ntervals

Summary for Tool 1

Graphs

‘A picture tells a 1,000 words’

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Graphs

Time series plot

Histogram

Boxplot

Editing graphs

Update graphs in real time

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Time Series Plot

Graph / Time series plot

Graph / Time Series Plot

Select simple option

Tip! Minitab 14 allows multiple time series plots on one chart if required!

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Time Series Plot

Graph / Time series plot

Select variable to plot

Select time scale

Select stamp

Select stamp column

Click OK

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Time Series Plot

Time series plot displays the trend over time

Date

Tool 1

19/0

2/20

06

14/0

2/20

06

09/0

2/20

06

04/0

2/20

06

30/0

1/20

06

25/0

1/20

06

20/0

1/20

06

15/0

1/20

06

10/0

1/20

06

05/0

1/20

06

01/0

1/20

06

11.0

10.5

10.0

9.5

Time Series Plot of Tool 1

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Histogram

Graph / Histogram.

Graph / Histogram

Select simple option

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Histogram

Graph / Histogram.

Select variable to graph

Click OK

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Histogram

A histogram shows the distribution of the data.

Tool 1

Frequency

10.810.610.410.210.09.89.69.4

16

14

12

10

8

6

4

2

0

Histogram of Tool 1

Tip! When copying graphs into other file formats, such as the 6 Panel template. Use edit / paste special and paste the graph as a picture to reduce the file size.

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Boxplot

Graph / Boxplot

Graph / Boxplot

Select Multiple Y’s - Simple Option

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Boxplot

Graph / Boxplot

Select variables

Click OK

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Data

Tool 3Tool 2Tool 1

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13

12

11

10

9

8

7

6

Boxplot of Tool 1, Tool 2, Tool 3

Boxplot

A boxplot is a ‘birds eye view’ of a histogram.

Whisker

Inter quartile range – middle 50%

Median

Tip! A boxplot is a very good tool to compare multiple distributions.

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Editing Graphs

Minitab 14 allows advanced graphical editing features.

Double click graph on area to be edited (as per Excel approach)

Use options box to edit graphical features

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Editing Graphs

Minitab 14 allows advanced graphical editing features.Data

Tool 3Tool 2Tool 1

14

13

12

11

10

9

8

7

6

Boxplot of Tool 1, Tool 2, Tool 3

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Update Graphs in Real Time

Minitab 14 allows graphs to be updated as the data source changes.

A green cross indicates that the graph reflects the data source

If the data source changes, a yellow circle indicates that the graph does

not reflect the data source.

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Graphs can be updated automatically or upon request.

Right click graph and select update graph now

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A green cross indicates that the graph has been updated.

Tip! The update graph function can be used on all graphs in the graph menu (except stem & leaf) and all control charts!

Quality Tools

‘Statistics may be defined as a body of methods for making wise decisions in the face of uncertainty ’ – W.A.Wallis

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Quality Tools

Pareto chart

Cause and Effect Diagram

Multi-Vari Chart

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Quality Tools

Stat / Quality Tools / Pareto chart

Select columns for labels and frequencies

Click OK

Stat / Quality Tools / Pareto Chart

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Quality Tools

Pareto charts are based on the 80 / 20 rule. Used to prioritise focus.

Cumulative frequency

Faults

Results

Tip! Pareto charts should also be produced using COPQ for each defect.

Count 19 17 15100 39 25 23 22 21 20 20Percent 5.9 5.3 4.731.2 12.1 7.8 7.2 6.9 6.5 6.2 6.2Cum % 90.0 95.3 100.031.2 43.3 51.1 58.3 65.1 71.7 77.9 84.1

Count

Perc

ent

Characteristic

Oth

er

Fas

cia

- P

oor

Fit

Glo

veb

ox

poor

fit

Pai

nt D

efec

t -

LH d

oor

Fla

t bat

tery

Rea

r bum

per

poor

fit

Wat

er le

ak R

r D

oor

Cam

ber

adju

stm

ent

Win

d n

oise

Frt

Door

Air V

ent Poor

Fit

Wid

get

350

300

250

200

150

100

50

0

100

80

60

40

20

0

Pareto Chart of Characteristic

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Cause & Effect Diagram

Conduct team brainstorm Stat / Quality tools / Cause & Effect Diagram

Stat / Quality Tools / C&E Diagram

Enter causes in columns or text

Click OK

Tip! Use 5 why analysis to drill down to root cause. Minitab 14 allows multiple sub branches to be entered in the option box.

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Cause & Effect Diagram

Use C&E to understand relationship between inputs and outputs.

Tip! The Six Sigma team should score the relationship between inputs & outputs using the C&E matrix to prioritise team focus.

DistortionPanel

Environment

Measurements

Methods

Material

Machines

Personnel

Poor training

Material Handling

New Labour

Shims missing

Location peg damage

Wear on tool

Damaged panels

Panel dimensions

Burr on panel

Standardised Work

Stock Rotation

Build sequence

procedureNo measurement

No gauge R&R

Gauge calibration

Poor lighting

Temperature

Humidity

BIW Door Panel

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Multi-Vari Chart

Graphical analysis of means for different factors. Stat / Quality tools / Multi-Vari Chart

Stat / Quality Tools / Multi-Vari Charts

Enter response variable (y) and factor levels (x)

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Multi-Vari Chart

Stat / Quality tools / Multi-Vari Chart

Mean values displayed for each factor level

Multi-Vari charts can be used during a screening DOE to reduce KPIV’s to the ‘critical few’.

Displays main effects and interactions.

Tool Number

Torq

ue

321

56

55

54

53

52

51

50

49

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Atlas CopcoBosch

Supplier

Multi-Vari Chart for Torque by Supplier - Tool Number

Measurement Systems Analysis

‘When you can measure what you are talking about and express it in numbers, you know something about it. But, when you cannot express it in numbers, your knowledge is of the meagre and unsatisfactory kind’ – Lord Kelvin

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Measurement Systems Analysis

MSA Overview

Attribute Gauge R&R

Variable Gauge R&R

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The purpose of Measurement System Analysis (MSA) is to ensure the information collected is a true representation of what is occurring in the process.

MSA is the evaluation of measurement system variation in comparison to process variation.

Measurement System Analysis

MSA validation is required before commencing data collection.

Process Variation

Measurement System Variation

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R & R – Repeatability and reproducibility.

Repeatability refers to the inherent variability of the measurement system.

Same operatorSame partSame condition

Repeatability is the ‘within’ variation.

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Reproducibility refers to the variation that occurs when different conditions are used to take the measurement.

Different operatorDifferent partsDifferent conditions

Reproducibility is the ‘between’ variation.

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Reproducibility refers to the variation that occurs when different conditions are used to take the measurement.

Different operatorDifferent partsDifferent conditions

Reproducibility is the ‘between’ variation.

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Data Types

FAIL PASS

Electrical Circuit

TEMPERATURE

Thermometer

TimeTime

VariableAttribute

NO-GO GO

Caliper

QTY UNIT DESCRIPTION TOTAL

1 $10.00 $10.00

3 $1.50 $4.50

10 $10.00 $10.00

2 $5.00 $10.00

SHIPPING ORDER

Error

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Attribute Gauge R & R Exercise

Scenario The process to stamp dots on a domino is highly variable. RFT data is required to evaluate process performance. Measurement system must be validated first.

Study Method 2 operators 2 measurements per operator 7 samples

N.B Only 7 samples used due to time constraints. A minimum of 30 samples required for Six Sigma projects.

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Measurement Procedure No. 1

Visually inspect all dominoes to identify samples with dots smaller than the master sample.

Any non-conformance is considered a reject. Colour is of no consequence.

You have been allocated 15 seconds to inspect each sample.

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Is the measurement system repeatable and reproducible?

What can be done to improve the measurement system?

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Measurement Procedure No. 2

Inspect all dominoes with the gauge provided. Ensure there are no spots smaller than the master sample. Any non-conformance is considered a reject. Colour is of no consequence.

You have been allocated 30 seconds to inspect each sample.

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Stat / Quality Tools / Attribute Agreement Analysis

Select data, samples and appraisers

Stat / Quality Tools / Attribute Agreement Analysis Enter study

information

Click OK

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Attribute Gauge R & R Output

Attribute Gage R&R StudyAttribute Gage R&R Study for Result

Within AppraiserAssessment Agreement

Appraiser # Inspected # Matched Percent (%) 95.0% CI Eric 7 7 100.0 ( 65.2, 100.0)John 7 7 100.0 ( 65.2, 100.0)

# Matched: Appraiser agrees with him/herself across trials.

Between AppraisersAssessment Agreement

# Inspected # Matched Percent (%) 95.0% CI 7 7 100.0 ( 65.2, 100.0)

# Matched: All appraisers' assessments agree with each other.

Graphical Output Session Window

Graph displays actual % result and 95% confidence interval Session window displays detailed results

Appraiser

Pe

rce

nt

J ohnEric

100

80

60

40

20

0

95.0% CIPercent

Date of study: 13/10/2006Reported by: Paul WhiteName of product: BIW Panel Distortion

Assessment Agreement

Within Appraisers

Tip! A Kappa statistic is available to determine correlation within & between appraisers.

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Attribute Gauge R & R Summary

A ‘typical’ Attribute Gauge R&R Study includes: 1 to 3 operators (measurement takers) 30 samples 2 to 3 trials (measurements) of each sample by each operator Samples that are typical of the process (pass & fail)

An acceptable study is where 100% agreement between each operator and the Master Attribute has been achieved (if a Master Attribute is included).

Analysis of the results from a failed study can identify where improvements need to be made: Operator training Standardised inspection process Measurement Procedure

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Variable Gauge R & R

R&R studies are conducted to ensure the data collected is a true representation of what is occurring in the process.

The purpose of variable gauge R&R studies are to calculate the amount of measurement system variation in comparison to the process variation and the process tolerance.

A ‘typical’ variable gauge R&R Study includes: 1 to 3 operators (measurement takers) 10 samples 2 to 3 trials (measurements) of each sample by each

operator Samples that are typical of the process (in spec & out of

spec)

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ScenarioScenarioGandalf’s Castle has been under siege from the Orcs for several days

and he seems to be losing the battle. The main problem is that Gandalf’s long range weapons – the catapults

– keep missing the Orcs who are sheltering behind a ridge 200m away. They keep shooting either too long or too short.

Gandalf wants to improve the accuracy of his catapults.But, before he can improve the accuracy Gandalf must ensure he can

measure the distance repeatedly & reproducibly.

ExerciseConduct variable r&r study on catapult shot length.10 shots (or samples), 2 operators, 2 measurements per operatorRecord results on flip chart.

Variable Gauge R & R Exercise

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Stat / Quality Tools / Gage Study / Gage R&R Study (Crossed)


Tip! A Nested Gage R&R Study is available for a destructive measurement study.

91



Enter part no. Operator & Measurement Data

Tip! Always enter the process tolerance via the options box. It is imperative to compare measurement system variation against the process variation & the process tolerance.

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Gage R&R Study – ANOVA Method

Gage name: Tin Foil

Reported by: Paul White

Date of study: 16th February 2006

Tolerance: 0 +/-0.05

%Contribution

Source Variance (of Variance)

Total Gage R&R 19.62 1.59

Repeatability 17.73 1.44

Reproducibility 1.89 0.15

Part-to-Part 1212.92 98.41

Total Variation 1232.55 100.00

StdDev Study Var %Study Var

Source (SD) (5.15*SD) (%SV)

Total Gage R&R 4.4299 22.814 12.62

Repeatability 4.2110 21.687 11.99

Reproducibility 1.3752 7.082 3.92

Part-to-Part 34.8270 179.359 99.20

Total Variation 35.1076 180.804 100.00

Number of distinct categories = 11

Variable R & R Pass Criteria

% Study Variation must be < 30%

% Contribution must be < 9%

Distinct categories must be >=5

Tip! Gauge calibration does not negate the requirement to conduct an MSA. Calibration confirms the gauge is accurate, MSA ensures the whole measurement system is repeatable and reproducible.

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Variable R&R – Pass Criteria % Contribution% Contribution

Measurement Measurement System Variation as a percentage of Total Observed Process Variation (Variance)

% Study Variation % Study Variation

MMeasurement System Standard Deviation as a percentage of Total Observed Process Standard Deviation (using Standard Deviation)

% Tolerance % Tolerance

MMeasurement Error as a percentage of Tolerance

Number of Distinct Categories Number of Distinct Categories

Less Less than 5 indicates Attribute conditions

% Contribution % Study Variation (Process Control)

% Tolerance (Product Control) # of Distinct Categories

It is desirable to have ALL indicators Green

RR

YY

GG < 1% Good

2-9% Acceptable

> 9% Unacceptable RR

YY

GG < 10% Good

11-30% Acceptable


YY

GG < 10% Good

11-30% Acceptable


YY

GG > 10 Good

5-10 Acceptable

< 5 Unacceptable

94

Per

cent

Part-to-PartReprodRepeatGage R&R

100

50

0

% Contribution

% Study Var

Sam

ple

Ran

ge

30

15

0

_R=5.3

UCL=17.32

LCL=0

1 2

Sam

ple

Mea

n

200

100

0

__X=99.5UCL=109.4LCL=89.5

1 2

Part54321

200

100

0

Operator21

200

100

0

Part

Ave

rage

54321

200

100

0

1

2

Operator

Gage name: VernierDate of study: 13/06/2006

Reported by: Paul WhiteTolerance: N/A

Components of Variation

R Chart by Operator

Xbar Chart by Operator

Measurement by Part

Measurement by Operator

Operator * Part Interaction

Gage R&R (ANOVA) for Measurement

Variable R & R Diagnostic Graphs

Review the diagnostic graphs to identify sources of measurement system variation.

Overall health of Measurement System

Repeatability

Reproducibility

Repeatability & gauge linearity

Reproducibility across operators

Reproducibility across parts

95

Catapult MSA

Analyse MSA data collected from catapult

Discuss results with team

Present findings to class

96

Variable Gauge R & R Summary

A ‘typical’ Variable Gauge R&R Study includes: 1 to 3 operators (measurement takers) 10 samples 2 to 3 trials (measurements) of each sample by each operator Samples that are typical of the process.

An acceptable study is where the total gauge R&R is less than 30% of the process spread or tolerance.

Distinct categories must be > = 5.

Analysis of the results from a failed study can identify where improvements need to be made: Standardised inspection process Operator training Measurement Procedure

97

Summary – MSA

At conclusion of the MSA, the Six Sigma team should know:

The measurement system is capable of gathering data that accurately reflects variation in the process.

If there is measurement error, how big it is and a method of accounting for it.

Measurement increments are small enough to show variation.

Sources of measurement error have been identified

Control Charts

‘Statistics is not a discipline like physics, chemistry or biology where we study a subject to solve problems in the same subject. We study statistics with the main aim of solving problems in other disciplines." - C.R. Rao

99

Control Charts

Introduction to Control Charts

Control Limits

In Control

Out of Control

Attribute control charts

Variable control charts

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Control Charts

A control chart is a run chart with upper and lower control limits (not specification limits).

Control charts are used to detect and monitor process variation over time.

Distinguishes between special and common cause.

Data must be collected in ‘real time’.

It is important to record the ‘voice of the process’. Ensure all process events / changes are logged.

Can be used as a reference point to evaluate the impact of process changes.

Serves as a tool for ongoing control.

101

Control Limits

1

2

3

4

5

7

8

9

Average +/- 3 S.D

99.73%

Upper Control Limit

Lower Control Limit

Control limits are calculated from the data from the process.

Control limits are not specification limits!

102

In Control

A process is in control when all of the values are randomly spread between the control limits.

To be in control means the process is consistent.

1

2

3

4

5

7

8

9

1

2

3

4

5

7

8

9

103

Out of Control

A process is out of control when one value exceeds the control limits.

This is special cause variation.

1

2

3

4

5

7

8

9

1

2

3

4

5

7

8

9

104

Out of Control

A process is out of control when 9 readings fall on one side of the process average but inside the control limits.

This out of control condition indicates a process shift.

1

2

3

4

5

7

8

9

1

2

3

4

5

7

8

9

105

Out of Control

A process is out of control when 6 readings in a row, display a continuous trend in an upward or downward direction.

This out of control condition indicates process drift / wear.

1

2

3

4

5

7

8

9

1

2

3

4

5

7

8

9

5566

SPC charts require ‘real time’ data collection.

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Out of Control Rules

Tools / Options / Control Charts / Define Tests

Tip! Minitab uses Nelson’s Test for Special Cause as they improved on the Western Electric Rules by aligning the probabilities of false alarm rates.

Tests for special cause

Tools / Options/ Control Charts / Define Tests

107

Start

Is data Attribute or Variable?

Attribute Variable

Defects or Defective?

Is the subgroup

sample size contstant?

Is theamount of

opportunities for defect contstant?

p-chart np-chart u-chart c-chart

Is the subgroup sample size

greater than 10?

Is the subgroup sample size

greater than 1

Individual & Moving Range

- I & MR

Average & Range - Xbar &

R

Average & Standard Deviation - Xbar & S

Yes

No

No

Yes

Yes

NoNoYes

Attribute Variable

Defective Defects

Control Chart Selection

Tip! There are other control charts available for special situations. A Cusum chart can be used when trying to detect small fluctuations in a process.

108

P Chart

Stat / Control Charts / Attribute Charts / P-Chart

Select column with defective amounts

Tip! Use the scale options to display the date on the chart x-axis.

Select column with subgroup sample sizes in. I.e. Daily or weekly volume

Select OK

Stat / Control Charts / Attribute Charts/ P-Chart

109

P Chart

A P Chart displays the proportion defective.

Tip! The P Chart is based on the Binomial distribution – pass or fail.

Date

Pro

port

ion

09/0

2/20

06

07/0

2/20

06

05/0

2/20

06

03/0

2/20

06

01/0

2/20

06

30/0

1/20

06

28/0

1/20

06

26/0

1/20

06

24/0

1/20

06

22/0

1/20

060.4

0.3

0.2

0.1

0.0

_P=0.1097

UCL=0.2338

LCL=0

1

P Chart of No of cars with Defective Vent

Tests performed with unequal sample sizes

110

U Chart

Stat / Control Charts / Attribute Charts / U-Chart

Click OK

Select column with defects data

Select column with subgroup sample sizes in. I.e. Daily or weekly volume

Stat / Control Chart / Attribute Charts / U Chart

111

U Chart

A U Chart displays the no of defects per unit.

Tip! The U Chart is based on the Poisson distribution – how many defects per item.

Date

Sam

ple

Count

Per

Unit

09/0

2/20

06

07/0

2/20

06

05/0

2/20

06

03/0

2/20

06

01/0

2/20

06

30/0

1/20

06

28/0

1/20

06

26/0

1/20

06

24/0

1/20

06

22/0

1/20

060.6

0.5

0.4

0.3

0.2

0.1

0.0

_U=0.1300

UCL=0.2732

LCL=0

1

U Chart of No of Air Vents Defects

Tests performed with unequal sample sizes

Unequal subgroup sample sizes will create castellated control limits

112

Variable Control Charts

Accuracy describes

Centering

Precision describesSpread

113

Individual & Moving Range Chart

Stat / Control Chart / Variables for Individuals / I&MR

Tip! Always title your chart using the Labels option box. All charts should have a title to aid reader interpretation.

Select column with measurement data

Click OK

Stat / Control Chart/ Variables for Individuals / I&MR

114

Individual & Moving Range Chart

I & MR chart shows the trend of individual data readings over time.

Tip! I & MR charts should be used to control process parameters (something that does not leave with the vehicle) I.e. Oven temperature, humidity, etc.

Displays the trend over time of individual readings. This part of the chart shows the accuracy of the process .

Displays the difference between consecutive readings. This part of the chart shows the precision of the process .

Date

Indiv

idual V

alu

e

15/02/200610/02/200605/02/200631/01/200626/01/200621/01/200616/01/200611/01/200606/01/200601/01/2006

11.0

10.5

10.0

9.5

9.0

_X=10.014

UCL=11.039

LCL=8.988

Date

Movin

g R

ange

15/02/200610/02/200605/02/200631/01/200626/01/200621/01/200616/01/200611/01/200606/01/200601/01/2006

1.2

0.9

0.6

0.3

0.0

__MR=0.386

UCL=1.260

LCL=0

I-MR Chart of Tool 1

115

Average & Range Chart

Stat / Control Chart / Variables for Sub-Groups / Xbar & R

Select column with measurement data

Click OK

Select subgroup size

Stat / Control Chart/ Variables for Sub-Groups / Xbar & R

116

Average & Range Chart

Xbar & R chart shows the average reading per subgroup over time.

Displays the trend over time of the subgroup average readings. This part of the chart shows the accuracy of the process .

Displays the range for each subgroup. I.e. Difference between the highest & lowest reading within each subgroup. This part of the chart shows the precision of the process .

Tip! Xbar & R charts should be used to control process characteristics (something that leaves with the vehicle) I.e. Gap condition on a door, thickness of paint, wheel alignment etc.

Sample

Sam

ple

Mean

10987654321

10.50

10.25

10.00

9.75

9.50

__X=10.014

UCL=10.458

LCL=9.569

Sample

Sam

ple

Range

10987654321

1.6

1.2

0.8

0.4

0.0

_R=0.770

UCL=1.629

LCL=0

Xbar-R Chart of Tool 1

117

Control Charts Summary

A control chart is a run chart with upper and lower control limits (not specification limits).

Control charts are used to detect and monitor process variation over time.

Distinguishes between special and common cause.

It is important to record the ‘voice of the process’. Ensure all process events / changes are logged.

Can be used as a reference point to evaluate the impact of process changes.

Serves as a tool for ongoing control.

Normality Test

‘Are statisticians normal?’

119

LSL Target USL

Normal Distribution

Normal Distribution

Data distribution characterized by a smooth, bell-shaped curve.

120

The distribution of area as a percentage:

-3s -2s -1s X +1s +2s +3s

68.26%

95.44%

99.73%

0.135%

0.135%

Normal Distribution

121

Normality Test

Stat / Basic statistics / Graphical summary.

Stat / Basic Statistics / Graphical Summary

Select variable

Click OK

Tip! Note the confidence level of 95% in the option window. This applies to the inferential statistics that will be displayed in the graphical summary.

122

Normality Test

Normality test

P-Value > 0.05 indicates a normal distribution

10.810.410.09.6

Median

Mean

10.1510.1010.0510.009.959.90

1st Quartile 9.800Median 10.0253rd Quartile 10.240Maximum 10.839

9.922 10.105

9.915 10.126

0.268 0.400

A-Squared 0.19P-Value 0.902

Mean 10.014StDev 0.321Variance 0.103Skewness -0.003050Kurtosis -0.106782N 50

Minimum 9.310


95% Confidence Interval for Mean

95% Confidence Interval for Median

95% Confidence Interval for StDev95% Confidence I ntervals

Summary for Tool 1

It is imperative to conduct a normality test when assessing variable data. The normal distribution is described by the mean and standard deviation (the

kurtosis & skewness provide additional info. about the shape of the curve). Control charts, process capability, 2 sample t-test and many other statistical

procedures are based on the normal distribution.

123

Typical Distributions

The shape has a bell shape.It is symmetric.

The shape has two humps.It is bimodal.

The shape has a long tail.It is not symmetric.

The shape is flat. There are one or more outliers.

124

Normality Test

Always conduct a normality test on variable data before conducting any statistical procedures.

I.e. Process capability, hypothesis testing etc.

Process Capability

‘A knowledge of statistics is like a knowledge of foreign languages or of algebra; it may prove of use at any time under any circumstances’

126

Process Capability

What is Process Capability?

Attribute Process Capability.

Variable Process Capability.

Sigma as a measure of capability.

127

Process Capability

Capability analysis is a measure of how well a process is meeting the expectations of the customer.

It provides a current performance baseline for the process.

It can be used as a reference point to evaluate the impact of process changes.

It can be displayed by several indices dependent on the data type.

128

VARIABLE DATA

Cp

Pp Ppk

Cpk

ATTRIBUTE DATA DPMODPUDPO

Capability Indices

129

Attribute Process Capability

50 readings are required to calculate attribute process capability.

Determine if failure mode is defective or a defect. Defective: Item is pass or fail. Defects: Item has multiple defects.

If item is defective use: Defects Per Million Opportunities (DPMO).

If defects per item are being assessed, use: Defects Per Unit (DPU).

130

DPMO

DPMO = Total number of defects

Total units Opportunities per unit 1,000,000

DPMO = 1,000,000D

N O

Calculate DPMO to identify baseline process capability. Unit (N) Defect (D) Opportunity (O) DPMO

DPMO ‘levels the playing field’ between different complexity processes.

I.e. The supplier of a bolt may only have 2 opportunities for failure whilst the supplier of the in-car entertainment system will have multiple opportunities due to a highly complex process.

131

DPMO in Minitab

Six Sigma / Product Report

Select Six Sigma / Product Report

Enter defects, units & opportunities

132

DPMO in Minitab

DPMO Metric

Six Sigma / Product Report

DPMO graphical

representation

It is imperative that the opportunities for failure are kept constant in the measure and the improve phases to validate the before and after condition. I.e. We are comparing ‘apples with apples’.

Short-Term Sigma

133

Always assess for a stable process and a normal distribution before calculating variable capability indices.

• Normal Data: Cp / Cpk Pp / Ppk

•Non-Normal Data: Why is data non-normal? If non-normality is to be expected, conduct a box-cox transformation.

Variable Capability Analysis

Cp / Cpk & Pp / Ppk indices are based on the normal distribution. Therefore, it is imperative to assess for stability & normality before calculating capability.

134

Variable process capability is the ability of a process output to ‘fit’ between the maximum and minimum specification limits which have been defined by the customer/engineer.


43 5 6 743 5 6 7

Can this distribution from a process output fit between the specification limits of 5 1?

135

LSL USL

Tolerance Process spread

LSL USL

Mean

Capability is an assessment of: process spread as a ratio of the process tolerance. – Cp / Pp

Cpk / Ppk is the location of the process mean with respect to both process specification limits.


136

Cp =

Cp =

Cp =

Cp =

Cp =

LSL USL

1

3

2

0.5

1

Cp Examples

137

Cpkl = 1

LSL USL X

Cpkl = 5

X

Cpkl = 1X

Cpkl = 0.5 X

Cpkl = 3

X

Cpku = 1

Cpku= 1

Cpku = 3

Cpku= 0.5

Cpku = -1

Cpk Examples

138

nominal

Cp = 3.70UpperSpecification Limit

LowerSpecification

Limit

+3s-3s

Cp Example

139

nominal

UpperSpecificationLimit

LowerSpecificati

onLimit

Once

Cp Example

How many times does the total process spread (+/- 3 standard deviations) fit inside the total tolerance?

140

nominal


LowerSpecificati

onLimit

Cp Example

OnceTwice


141

nominal


LowerSpecificati

onLimit

Cp Example


OnceTwice3 times

142

nominal


LowerSpecificati

onLimit

Cp Example

OnceTwice3 timesAnd 0.7


143

nominal


LowerSpecificati

onLimit

Cp Example

Cp = 3.70

144

nominal


LowerSpecificati

onLimit

Cpk Lower Example

Once

How many times does half the total process spread (3 standard deviations) fit between the mean and the lower specification limit?

145

nominal


LowerSpecificati

onLimit

Cpk Lower Example

Twice


146

nominal


LowerSpecificati

onLimit

Cpk Lower Example

3 Times


147

nominal


LowerSpecificati

onLimit

Cpk Lower Example

4 Times


148

nominal


LowerSpecificati

onLimit

Cpk Lower Example

5 Times


149

nominal


LowerSpecificati

onLimit

Cpk Lower Example

Cp = 3.70Cpkl = 5.00

150

nominal


LowerSpecificati

onLimit

Cpk Upper Example

How many times does half the total process spread (3 standard deviations) fit between the mean and the upper specification limit?

Once

151

nominal


LowerSpecificati

onLimit

Cpk Upper Example

Twice


152

nominal


LowerSpecificati

onLimit

Cpk Upper Example

And 0.4


153

nominal


LowerSpecificati

onLimit

Cp / Cpk Indices

Cp = 3.70Cpku = 2.4

154

Manually calculate Cp / Cpk

Group Exercise

Cpk U = U.S.L. - Process Average

3 x SD

Cpk L =

3 x SD

Process Average - L.S.L.

Cp = Tolerance

6 x SD

• USL = 12• LSL = 8• Mean = 10.5• SD = 0.33

155

Draw Process Capability

Use pencil & paper to draw the following distribution.

Mean = 10.5LSL = 8 USL =12

1 Standard Deviation = 0.33

8 109 11 12 137

156

#1 #2

#3 #4

Relate Cp / Cpk to Archers Target

157

Normal Capability Analysis in Minitab

Stat / Quality Tools / Normal Capability Analysis

Select Stat / Quality Tools /

Capability Analysis /

Normal

Remember! It is imperative that stability and normality tests are conducted before calculating Cpk / Ppk indices.

158


Stat / Quality Tools / Capability Analysis / Normal

Select Column to

assess

Enter subgroup

size

Enter upper & lower spec.

limits

Click OK

159

12.011.410.810.29.69.08.4

LSL USL

LSL 8Target *USL 12Sample Mean 10.0137Sample N 50StDev(Within) 0.331209StDev(Overall) 0.322772

Process Data

Cp 2.01CPL 2.03CPU 2.00Cpk 2.00

Pp 2.07PPL 2.08PPU 2.05Ppk 2.05Cpm *

Overall Capability

Potential (Within) Capability

PPM < LSL 0.00PPM > USL 0.00PPM Total 0.00

Observed PerformancePPM < LSL 0.00PPM > USL 0.00PPM Total 0.00

Exp. Within PerformancePPM < LSL 0.00PPM > USL 0.00PPM Total 0.00

Exp. Overall Performance

WithinOverall

Process Capability of Tool 1


Stat / Quality Tools / Capability Analysis / Normal

Short Term Capability

Long Term Capability

For a process to be deemed ‘capable’, the Cpk must be >= 1.67 & the Ppk >= 1.33.

160

For example:

Cpk of 1 = Sigma value of 3

Cpk of 0.5 = Sigma value of 1.5

By converting DPMO and Cpk to a Sigma value we can compare performance between attribute and variable processes.

The higher the Sigma value, the better the process.

To convert Cpk to Sigma we merely multiply the Cpk value by 3 to get the Sigma value.

Cpk conversion to Sigma

161

}Sigma is a universal measure of process performance.

Advantage of using Sigma

VARIABLE DATA

Cp

Pp Ppk

Cpk

ATTRIBUTE DATA DPMODPUDPO

Hypothesis Testing

‘Statistics is never having to say you are right’

163

Hypothesis Testing

Hypothesis Testing Overview

Hypothesis Testing - Proportions

Hypothesis Testing – Variances

Hypothesis Testing - Means

164

Hypothesis Testing Overview

Provides objective solutions to questions which are traditionally answered subjectively.

Can be used to determine a difference in proportions, means and variances (standard deviation).

Graphical analysis indicates a potential difference. Hypothesis testing infers a statistically significant difference

(with a degree of confidence).

A hypothesis test should always be conducted in the improve phase to validate the improvements to the baseline process capability.

165

Variable orAttribute Data?

1 or 2 Factor?

1 or >1 Levels?

Contingency Table

HO : FA Independent FBHA : FA Dependent FB

Stat>Tables>Chi2 Test

Attribute2

Factor

1 Factor

2-Proportion Test

Stat>Basic Stat>2-Proportion

2 Samples2 levels to test for

each 2 levels

1-Proportion Test

Stat>Basic Stat>1-Proportion

1 Sample1 levelto test

Is data normal?

1, 2 or >2levels?

Test formean or sigma?

1-Sample t Test

Stat>Basic Stat>1-Sample t

Chi2 Test

Stat>BasicStat>Display Desc>Graphical Summary(if target sigma falls

between CI, then fail toreject HO )

F Test

Stat>ANOVA>Homogeneity of

Variance

2-Sample t Test

Stat>Basic Stat>2-Sample t

(if sigmas are equal, usepooled std dev to compare.

If sigmas are unequalcompare means using

unpooled std dev)

1 level

2 levels

Test formeans

Test forsigmas

Bartlett's Test

Stat>ANOVA>Homogeneity of VarianceIf sigmas are NOT equal, proceed with caution or use

Welch's Test, which is not available in M initab

More than2 levels

1-Way ANOVA(assumes equality of

variances)

Stat>ANOVA>1-Way(then select stacked or

unstacked data)

Test for means

Data Normal

HO: 1 = t

HA: 1 t

t = target

Levene's Test

Stat>ANOVA>Homogeneity of Variance

If HO is rejected, then you cango no further

Datanot

Normal

1, 2 or morelevels?

Test medianor sigma?

1 level

Chi2 Test

Stat>BasicStat>Display Desc>Graphical Summary(if target sigma falls

between CI, then fail toreject HO )

HO: 1 = t

HA: 1 t

t = target

Test for sigmas

1-Sample Wilcoxon or1-Sample Sign

Stat>Non-parametric>and either 1-Sample

Sign or 1-SampleWilcoxon

TestMedians

2 ormorelevels

M ann-Whitney Test

Stat>Non-parametric>M ann-Whitney

M ood's M edian Test(used with outliers)

Stat>Non-parametric>M ood's test

Kruskal-Wallis Test(assumes outliers)

Stat>Non-parametric>Kruskal-Wallis

2 ormorelevels

HO: M1 = M2

= M3 ...

HA: M i Mj for i j

(or at least one is different)

HO: M1 = M2

= M3 ...

HA: Mi Mj for i j


HO: M1 = Mt

HA: M1 Mt

t = target

HO: M1 = M2

HA: M1 M2

H O : 1 = 2

= 3 ...

H A : i j for i j

(o r a t least one is d iffe ren t)

HO: 1 = t

HA: 1 t

t = target

HO: 1 = 2

= 3 ...

HA: i j for i j


HO: 1 = 2

HA: 1 2

HO: 1 = 2

= 3 ...

HA: i j for i j


HO: P1 = Pt

HA: P1 Pt

t = target

HO: P1 = P2

HA: P1 P2

2 levels only

If P > 0.05, then fail to reject H O If P < 0.05, then reject H O Ensure the correct sam ple size is taken.

1, 2 or moreFactors?

Variable

2 levels or> 2 levels?

Fail to reject H O

Courtesy of Jeff Railton and Andy Battyof Seagate Technology.Revised: June 23, 1999

(Hypothesis Roadmap E.vsd)

ST ART >>>

2 or more Factors

1Factor

HO : Data is normalHA : Data is not normal

Stat>Basic Stat>Normality Test orStat>Basic Stat>Descriptive Statistics

(graphical summary)

HO: 1 = 2

HA: 1 2

ANOVA orMultiple Regression

Is DataDependent?

No,Data is drawnindependently

from twopopulations

Paired t Test

Stat>Basic Stat>Paired t

HO: 1 = 2

HA: 1 2

Yes,Data isPaired

Test formean or sigma?

Test forsigmas

Test formeans

Hypothesis Testing Roadmap

166

Hypothesis Testing – Proportions

Stat / Basic Statistics / 2 Proportions


Enter trials (sample size) & events (defects)

in the option box

Click OK

167

Hypothesis Testing – Proportions


P-Value < 0.05 indicates a significant difference

Either accept, or fail to accept the null hypothesis. It is assumed there is no difference unless proven otherwise. I.e. Innocent until proven guilty!

168


Stat / Basic Statistics / 2 Variances


Always conduct a normality test before conducting a hypothesis test on variable data.

Enter variables to

compare

Click OK

169



Standard deviation & confidence

interval

95% Bonferroni Confidence Intervals for StDevs

Tool 2

Tool 1

2.01.51.00.5

Data

Tool 2

Tool 1

1413121110987

Test Statistic 0.04P-Value 0.000

Test Statistic 57.07P-Value 0.000

F-Test

Levene's Test

Test for Equal Variances for Tool 1, Tool 2

P-Value < 0.05 indicates a significant difference

Use the F-Test statistic for normal data and Levene’s Test statistic for non-normal data.

170

Hypothesis Testing – Means

Stat / Basic Statistics / 2 Sample t

Stat / Basic Statistics /

2 Sample t

Always conduct a normality and 2 variances test before conducting a 2 Sample T test. However, if the sample sizes are equal, the requirement to conduct a 2 variances test is not applicable.

Enter variables to

compare

Select equal variances if applicable

Click OK

Select boxplot

171

Hypothesis Testing – Means

Stat / Basic Statistics / 2 Sample t

P-Value >= 0.05 infers that the

means are from the same

population

If the P is low, the null must go!

172

Summary

What is Six Sigma? Introduction to Minitab Version 14 Manipulation of data Basic statistics Graphs Quality tools Measurement System Analysis – R & R Control charts Normality testing Capability analysis Hypothesis Testing

173

Questions and Answers

Created by Paul White - Aston Martin Six Sigma DepartmentSources:Ford Six Sigma Black Belt Training Material 2006Ford Six Sigma Green Belt Training Material Version 5.0Jaguar SPC Training Material 2004

mini tab 14 one day training 39403

Documents

years of effortf

years of sceintific

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ftestfinished files

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