Transcript Example Hypothesis Tests - South Dakota School of Mines

IENG 486 - Lecture 09
Examples of Hypothesis Tests:
Anthropometric Data and Intro to
the Seven Tools of Ishikawa
7/20/2015
IENG 486: Statistical Quality & Process
Control
1
Assignment:
 Preparation:


Print Hypothesis Test Tables from Materials page
Have this available in class …or exam!
 Reading:

Chapter 5:

5.1 through 5.2, and 5.4 - only these portions are on Exam I
 HW 3:


CH 5: # 5, 26, 27
Review for Exam I
7/20/2015
IENG 486: Statistical Quality & Process Control
2
Grip Strength Data Results
 R-L Side, Equal Variance
Dominant Hand Means  Two-Sided Test at  = .05
 HA: There is a difference
Comparison:
2
 L = x1 = 129.4, S1 = 2788,  Test: Is | t | > t
0
.025, 52?
n1 = 34 people
 |1.91| > 2.021 - NO!
2
 R = x2 = 104.0, S2 = 1225,
 Keep the Null Hypothesis:
n2 = 20 people
 There is NOT a difference btwn
 Sp = 47.1, v = 52
L&R!
t0 
x1  x 2   0
Sp
7/20/2015
1
1

n1 n 2
(n1  1) S12  (n2  1) S 22
Sp 
n1  n2  2
IENG 486: Statistical Quality & Process Control
3
Grip Strength Data Results
 R-L Side, No
Assumptions Dom. Hand
Means Comparison:
2
 Two-Sided Test at  = .05

HA: There is a difference
 Test: Is | t0 | > t.025, 51?
L = x1 = 129.4, S1 = 2788,
 |2.12| > 2.021 - YES!
n1 = 34 people
 Reject the Null Hypothesis:
2
 R = x2 = 104.0, S2 = 1225,
 There IS a difference btwn
n2 = 20 people
L & R!
2
 v = 51
 S12 S 22 


 Why is this wimpy test
n n 
2 
 1
x1  x 2   0 v  2 2
significant when the other
2
2
t0 
 S1 
 S2 
wasn’t?




2
2
S1 S 2
n 


 1    n2 

ANS: Check the equal
n1 n 2
n1  1
n2  1
variance assumption!

7/20/2015
IENG 486: Statistical Quality & Process Control
4
Grip Strength Data Results
 Two-Sided Test at  = .10
 Unknown 0
 HA: There is a difference
Variances Comparison:
 Test: Is F0 > F.05, 33, 19?
2 = 2788
 S
1
n1 = 34, v1 = 33
2
 S2 = 1225
 n2 = 20, v2 = 19
2.276 > 2.07 - YES!
(if not, also check F1– /2, 33, 19)


 Reject the Null Hypothesis:

There IS a difference in variance!
At  = .05, this test is just barely
not significant
 (Should also have checked for
Normality with Normal Prob. Plot)

F0 
S12
S 22
7/20/2015
F1 ,v1 ,v2 
1
F ,v
2
,v1
IENG 486: Statistical Quality & Process Control
5
Statistical Quality Improvement
 Goal: Control and Reduction of Variation
 Causes of Variation:

Chance Causes / Common Causes



Assignable Causes / Special Causes



In Statistical Control
Natural variation / background noise
Out of Statistical Control
Things we can do something about - IF we act quickly!
Both can cause defects – because specifications
are often set regardless of process capabilities!
7/20/2015
IENG 486: Statistical Quality & Process Control
6
Ishikawa’s “Magnificent Seven” Tools
 The Seven Tools are:







Histogram / Stem & Leaf Diagram
Cause & Effect (Fishbone) Diagram
Defect Concentration Diagram
Check Sheet
Scatter (Plot) Diagram
Pareto Chart
Control Chart
- covered after exam!
 The tools were not invented by Ishikawa, but were very
successfully put into methodical use by him
 The first six are used before starting to use the seventh

They are also reused when needed to find an assignable cause
7/20/2015
IENG 486: Statistical Quality & Process Control
7
Ishikawa’s Tools: Histogram
A histogram is a bar chart that takes the shape
of the distribution of the data. The process for
creating a histogram depends on the purpose
for making the histogram.
One purpose of a histogram is to see the shape of a
distribution. To do this, we would like to have as
much data as possible, and use a fine resolution.
 A second purpose of a histogram is to observe the
frequency with which a class of problems occurs.
The resolution is controlled by the number of
problem classes. – see Pareto Chart slide!

7/20/2015
IENG 486: Statistical Quality & Process Control
8
Ishikawa’s Tools: Fishbone Diagram
Cause & Effect diagram constructed by
brainstorming
Identified problem at the “head”
 Connects potential causes along the spine
 Sub-causes are listed along the major “bones”

 Man
 Material
 Method
 Machine
 Environment
7/20/2015
IENG 486: Statistical Quality & Process Control
9
Cause & Effect Diagram, Cont.
 The purpose of the cause and effect diagram is to
obtain as many potential influencers of a process, so
that the problem solving can take a more directed
approach.
Man
Skill Level
Attention Level
Method
Low RPM
Travel Limits
Dusty
Environment
Bad Paint
Temperature
Humidity
Poor Conductor
Poor Mixing
Orifice Clogs
Poor Vendor
Worn Parts
Machine
7/20/2015
Material
IENG 486: Statistical Quality & Process Control
10
Ishikawa’s Tools: Defect Diagram
 A defect concentration diagram graphically records the frequency of a
defect with respect to product location.
 Obtain a digital photo or multi-view part print showing all product
faces.
 Operator tallies the number and location of defects as they occur
on the diagram.
7/20/2015
IENG 486: Statistical Quality & Process Control
11
Ishikawa’s Tools: Check Sheet
 Check sheets are used
to collect data (values
or pieces of
information) in a
consistent manner.
 List each of the
known / possible
problems
 Record each
occurrence
including timeorientation.
7/20/2015
Title
Header Info: Date, Time, Location, Operator, etc.
Times of Occurrence (periodic)
Types
of
Errors
Raw Data recorded here
Time of Occurrence Statistics
Type of
Error
Statistics
Overall
Statistics
Instructions, settings, comments, etc.
IENG 486: Statistical Quality & Process Control
12
Ishikawa’s Tools: Scatter Plot
 A scatter plot shows the relationship between any two variables of
interest:
 Plot one variable along the X-axis and the other along the Y-axis
Y
Y
X

Y
X
X
The presence of a relationship can be inferred or ruled out, but it
cannot determine if a cause and effect relationship exists
7/20/2015
IENG 486: Statistical Quality & Process Control
13
Ishikawa’s Tools: Pareto Chart
80% of any problem is
the result of 20% of the
potential causes
7/20/2015
60%
40
40%
20
20%
0
0%
Blisters
Defect Type
IENG 486: Statistical Quality & Process Control
14
Cumulative %
60
Wrong
Color
80%
Thick Coat
80
Thin Coat
100%
Tacky
100
Off-Color
120%
Abrasion
Frequency

120
Dirt/Dust
Histogram categories
are sorted by the
magnitude of the bar
 A line graph is overlaid,
and depicts the
cumulative proportion of
defects
 Quickly identifies where
to focus efforts
Pareto Chart for Paint Defects
Use of Ishikawa’s Tools
 Removing
special causes
of variation
 Preparation for:
 hypothesis
tests
 control
charts
 process
improvement
Statistical Quality Control and Improvement
Improving Process Capability and Performance
Continually Improve the System
Characterize Stable Process Capability
Head Off Shifts in Location, Spread
Time
Identify Special Causes - Bad (Remove)
Identify Special Causes - Good (Incorporate)
Reduce Variability
Center the Process
LSL
7/20/2015
0
USL
IENG 486: Statistical Quality & Process Control
15