X Sifting 2 X Sifting MultiVari Analysis Classes and Causes Hypothesis Testing NND P1 Hypothesis Testing ND P1 Intro to Hypothesis Testing Inferential Statistics ID: 559769
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Slide1
Analyze Phase
“
X
”
SiftingSlide2
2
“
X” Sifting
Multi-Vari Analysis
Classes and Causes
Hypothesis Testing NND P1
Hypothesis Testing ND P1
Intro to Hypothesis Testing
Inferential Statistics
“
X” Sifting
Welcome to Analyze
Hypothesis Testing ND P2
Wrap Up & Action Items
Hypothesis Testing NND P2Slide3
3
Multi-Vari Studies
In the Define Phase we used Process Mapping to identify all the possible
“
X’s” on the horizon. In the Measure Phase we used the X-Y Matrix, FMEA and Process Map to narrow our investigation to the
probable “X’s”.
X
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X
The quantity of Xs
when we apply
leverage (The vital
few)
The quantity of Xs
when we apply
leverage (The vital
few)
X
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The quantity of Xs
when we apply
leverage (The vital
few)
The quantity of X’
s
remaining after
DMAIC
The many Xs
when we first start
(The trivial many)
The many X’
s
when we first start
(The trivial many)
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The quantity of Xs
after we think
about Y=
f(X
) + e
The quantity of Xs
after we think
about Y=
f(X
) + e
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The quantity of Xs
after we think
about Y=
f(X
) + e
The quantity of X’
s
keep reducing as
you work the projectSlide4
4
Multi-Vari Definition
Multi-Vari Studies
– a tool that graphically displays patterns of variation. Multi-Vari Studies are used to identify possible X’s
or families of variation. These families of variation can hide within a subgroup, between subgroups, or over time.
The Multi-Vari Chart helps in screening factors by using graphical techniques to logically subgroup discrete X’s (Independent Variables) plotted against a continuous Y (Dependent). By looking at the pattern of the graphed points, conclusions are drawn from about the largest family of variation.
Multi-Vari Chart can also be used to assess capability, stability and graphical relationships between X’s and Y’s.Slide5
5
Purpose
The use of a
Multi-Vari Chart
illustrates analysis of variance data graphically.
A picture can be worth a thousand words… or numbers.Multi-Vari Charts are useful in visualizing two-way interactions.Multi-Vari Charts reveal information such as:Effect of work shift on Y’s.
Impact of specific machinery or material on Y’s.Effect of noise factors on Y’s, etc.Slide6
6
Multi-Vari ExampleSlide7
7
Method
Sampling Plans should encompass all three types of variation: Within, Between and Temporal.
1. Create Sampling Plan
2. Gather Passive Date
3. Graph Data
4. Check to see if Variation is Exposed
5. Interpret Results
Gather
Passive
DataGraphData
IsVariation
Exposed
InterpretResults
Create Sampling Plan
No
YesSlide8
8
Sources of Variation
Within Unit or
Positional
Within piece variation related to the geometry of the part.Variation across a single unit containing many individual parts; such as a wafer containing many computer processors.
Location in a batch process such as plating.Between Unit or CyclicalVariation among consecutive pieces.
Variation among groups of pieces.Variation among consecutive batches.Temporal or over time Shift-to-Shift
Day-to-DayWeek-to-WeekSlide9
9
Machine Layout & Variables
Die
Release
Ambient
Temp
Injection Pressure Per Cavity
Master Injection Pressure
Fluid Level
% Oxygen
#2
#3
#4
#1
Distance to Tank
Die
TempSlide10
10
Sampling Plan
Cavity #1
Die Cycle #1
Monday
Wednesday
Friday
Die Cycle #2
Die Cycle #3
Cavity #2
Cavity #3
Cavity #4
Die Cycle #1
Die Cycle #2
Die Cycle #3
Die Cycle #1
Die Cycle #2
Die Cycle #3Slide11
11
Within-Unit Encoding
Within Unit
Die Cycle #1
Monday
Wednesday
Friday
Die Cycle #2
Die Cycle #3
Die Cycle #1
Die Cycle #2
Die Cycle #3
Die Cycle #1
Die Cycle #2
Die Cycle #3
Cavity #1
Cavity #2
Cavity #3
Cavity #4Slide12
12
Between-Unit Encoding
Unit to Unit
Cavity #1
Die Cycle #1
Monday
Wednesday
Friday
Die Cycle #2
Die Cycle #3
Cavity #2
Cavity #3
Cavity #4
Die Cycle #1
Die Cycle #2
Die Cycle #3
Die Cycle #1
Die Cycle #2
Die Cycle #3Slide13
13
Temporal Encoding
Temporal
Cavity #1
Die Cycle #1
Monday
Wednesday
Friday
Die Cycle #2
Die Cycle #3
Cavity #2
Cavity #3
Cavity #4
Die Cycle #1
Die Cycle #2
Die Cycle #3
Die Cycle #1
Die Cycle #2
Die Cycle #3Slide14
14
Using Multi-Vari to Narrow X’
s
List potential X’
s and assign them to one of the families of variation.
This information can be pulled from the X-Y Matrix of the Measure Phase.If an X spans one or more families assign %’s to the supposed split.Slide15
15
Using Multi-Vari to Narrow X’
s
Graph the data from the process in Multi-Vari form.
Identify the largest family of variation.
Establish statistical significance through the appropriate statistical testing.Focus further effort on the X’s associated with the family of largest variation.
Remember the goal is not only to figure out what it is but also what it is not!Slide16
16
Data WorksheetSlide17
17
Run Multi-VariSlide18
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Identify The Largest Family of VariationSlide19
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Root Cause Analysis
Focus further effort on the X’
s associated with the family of greatest variation.
Die Cycle to Die Cycle – Something is Changing!Slide20
20
Call Center Example
A company with two call centers wants to compare two methods of handling calls at each location at different times of the day.
One method involves a team to resolve customer issues, and the other method requires a single subject-matter expert to handle the call alone.
Output (Y)Call Time
Input (X)Call Center (GA,NV)Time of Day (10:00, 13:00, 17:00)
Method (Expert, Team)Slide21
21
Call Center Example
Which is causing the greatest variation…
Time? Method
? Location? Slide22
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Call Center Example
Is the largest source of variation more or less obvious?Slide23
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Call Center ExampleSlide24
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Call Center ExampleSlide25
25
Multi-Vari Exercise
Exercise objective:
To practice Six Sigma techniques learned to date in your teams.
Open file named
“MVA Cell Media.MTW”.
Perform Capability Analysis; use the column labeled volume. There is only an upper specification limit of 500 ml. ?Are the data Normal? _______Is the process Capable? _______
What is the issue that needs work in terms of Six Sigma terminology?Shift Mean? _______Reduce variation? _______Combination of Mean and variation? _______
Change specifications? _______Slide26
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MVA Solution
Check for Normality…
Is that normal?Slide27
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MVA Solution
Another method to check Normality is…Slide28
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MVA SolutionSlide29
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MVA Solution
REDUCE VARIATION!! - then shift MeanSlide30
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MVA Solution
Perform a Multi-Vari AnalysisSlide31
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MVA Solution
What is the largest source of variation?Slide32
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Data Collection Sheet
The data used in the Multi-Vari Analysis must be balanced for MINITAB
TM
to generate the graphic properly.
The injection molding data collection sheet was created as follows:3 time periods4 widgets per die cycle
3 units per time periodSlide33
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Data Collection SheetSlide34
34
Classes of Distributions
Multi-Vari is a tool to help screen X’
s by visualizing three primary sources of variation. Later we will perform Hypothesis Tests based on our findings.
At this point we will review classes and causes of distributions that can also help us screen X’
s to perform Hypothesis Tests.
Normal Distribution
Non-normality – 4 Primary Classifications Skewness Multiple Modes
Kurtosis GranularitySlide35
35
The Normal (Z) Distribution
Characteristics of Normal Distribution (Gaussian curve) are:
It is considered to be the most important distribution in statistics.
The total area under the curve is equal to 1.
The distribution is mounded and symmetric; it extends indefinitely in both directions approaching but never touching the horizontal axis.All processes will exhibit a Normal curve shape if you have pure random variation (white noise).
The Z distribution has a Mean of 0 and a Standard Deviation of 1.The Mean divides the area in half, 50% on one side and 50% on
the other side.The Mean, Median and Mode are at the same data point.
+6
-1
-3
-4
-5
-6
-2
+4
+3
+2
+1
+5Slide36
36
Normal Distribution
Why do we care?
ONLY IF we need accurate estimates of Mean and Standard Deviation.
Our theoretical distribution should MOST accurately represent our sample distribution in order to make accurate inferences about our population.Slide37
37
Non-Normal Distributions
1 Skewed
2 Kurtosis
3 Multi-Modal
4 GranularitySlide38
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Skewness Classification
Potential Causes of Skewness
1-1
Natural Limits
1-2 Artificial Limits (Sorting)
1-3 Mixtures1-4 Non-Linear Relationships
1-5 Interactions1-6 Non-Random Patterns Across Time
Right Skew
Left Skew
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0
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20
30
40
50
60
Frequency
10
15
20
0
10
20
30
40
FrequencySlide39
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Mixed Distributions 1-3
Mixed Distributions
occur when data comes from multiple sources that are supposed to be the same yet are not.
Sample A
Sample B
Combined
Machine A
Operator A
Payment Method A
Interviewer A
Machine B
Operator B
Payment Method B
Interviewer B
+
=Slide40
40
1-4 Non-Linear Relationships
Non-Linear Relationships
occur when the X and Y scales are different for a given change in X.
Marginal Distribution
of X
1
0
0
5
0
0
1
0
5
0
X
Y
Marginal Distribution
of YSlide41
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1-5 Interactions
Interactions
occur when two inputs interact with each other to have a larger impact on Y than either would by themselves.
With Fire
No Fire
35
30
25
Interaction Plot for Process Output
Room Temperature
Spray
No Spray
Aerosol Hairspray
On
OffSlide42
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1-6 Time Relationships / Patterns
The distribution is dependent on time.
Often seen when tooling requires
“
warming up
”
, tool wear, chemical bath depletions, ambient temperature effect on tooling.
Time
10
20
30
40
50
20
25
30
Marginal Distribution
of YSlide43
43
Non-Normal Right (Positive) Skewed
Moment coefficient of Skewness will be close to zero for symmetric distributions, negative for left Skewed and positive for right Skewed.Slide44
44
Kurtosis
Kurtosis
refers to the shape of the tails.
Leptokurtic
Platykurtic
Different combinations of distributions causes the resulting overall shapes.
Leptokurtic
Peaked with Long-Tails
Platykurtic
Flat with Short-TailsSlide45
45
Platykurtic
Multiple Means shifting over time produces a plateau of the data as the shift exhibits this shift.
Causes:
2-1. Mixtures: (Combined Data from Multiple Processes)
Multiple Set-Ups
Multiple Batches
Multiple Machines
Tool Wear (over time)
2-2 Sorting or Selecting:Scrapping product that falls outside the spec limits2-3 Trends or Patterns:
Lack of Independence in the data (example: tool wear, chemical bath)2-4 Non Linear RelationshipsChemical SystemsSlide46
46
Leptokurtic
Causes:
2-1. Mixtures: (Combined Data from Multiple Processes)
Multiple Set-Ups
Multiple Batches
Multiple Machines
Tool Wear (over time)
2-2 Sorting or Selecting:Scrapping product that falls outside the spec limits2-3 Trends or Patterns:Lack of Independence in the data (example: tool wear, chemical bath)2-4 Non Linear Relationships
Chemical Systems
Distributions overlaying each other that have very different variance can cause a Leptokurtic distribution.Slide47
47
Multiple Modes 3
Reasons for
Multiple Modes
:
3-1 Mixtures of distributions (most likely) 3-2 Lack of independence – trends or patterns
3-3 Catastrophic failures (example: testing voltage on a motor and the motor shorts out so we get a zero reading)
Now that
’
s my kind of mode!!Slide48
48
Bimodal Distributions
2 Different Distributions
2 different machines
2 different operators
2 different administratorsSlide49
49
Extreme Bi-Modal (Outliers)Slide50
50
Bi-Modal – Multiple OutliersSlide51
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Granular 4
Granular data is easy to see in a Dot Plot.
Use Caution!
It looks
“Normal” but it is only symmetric and not Continuous.
Causes:4-1 Measurement system resolution (Gage R&R)4-2 Categorical (step-type function) dataSlide52
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Normal Example
Notice the contrast to the previous page!Slide53
53
Conclusions Regarding Distributions
Non-normal Distributions are not BAD!!!
Non-normal Distributions can give more Root Cause information than Normal data (the nature of why…)
Understanding what the data is telling us is KEY!!!
What do you want to know ???
Find the key….Slide54
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Summary
At this point you should be able to:
Perform a Multi-Vari Analysis
Create and interpret a Multi-Vari Graph
Identify when a Multi-Vari Analysis is applicableInterpret how Skewed data looksExplain how data distributions become Non-normal when they are really Normal