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Stat 435
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Stat 435/835 Statistical Methods for Process Improvement
Course Overview
Stefan Steiner, [email protected]
Background
Capstone statistics course No new statistical methods introduced But, we use what you have previously learnt
Numerical and graphical data summaries (Stat 231)
Linear regression (Stat 231 [+331]) Design of experiments (Stat 332 [+430]) Analysis of Variance (Stat 332)
Practice appropriate application Develop statistical thought process
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Course Learning Objectives
Learn about the Statistical Engineering algorithm, strategies and approaches for solving chronic excess variation problems think strategically about how to achieve cost-effective
variation reduction reduce variation by following a step-by-step algorithm learn how to use appropriate statistical plans and tools
to achieve the goal of Statistical Engineering
Understand sources of variation and their role in process improvement
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Course Learning Objectives (cont.)
Learn how to better use empirical methods; that is, learn effective and efficient ways to plan, execute and analyze the results of a process investigation
Apply the methodology to Watfactory, a virtual manufacturing process, to aid in learning Tell me, I will forget Show me, I may remember Involve me and I will understand
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Textbook
This course covers the material in textbook Statistical Engineering: An algorithm for reducing variation in manufacturing processes published by Quality Press 2005
You are expected to read the textbox on your own Download electronic version and/or Borrow text for the term from me
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Watfactory
The course (though not the textbook) is designed around a virtual process called Watfactory
Watfactory is a web based virtual process to produce camshafts demo later
Watfactory website www.student.math.uwaterloo.ca/~watfacto/login.htm
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Watfactory Project
You will be divided into teams and assigned different versions of Watfactory to improve
Watfactory projects involve: nine weekly written progress reports two class presentation on your progress two management reviews of another team
See course outline and the report and presentations guidelines for more information
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Videos
You are also expected to watch the series of the videos on your own time A suggested schedule is given in the written
course outline
The videos cover all the material from the textbook as well as the Watfactory virtual process
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MINITAB Statistical Software
General purpose statistical software Most commonly used package in the quality
improvement area Very easy to use
data window looks like a spreadsheet pull down menus to access numerical analysis and
graphs better than Excel for statistics/graphics
Used throughout these course notes and in the corresponding book
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Course Topics (Book Chapters in Brackets) Introduction Overview and Goals (1-3, 5) Watfactory The Statistical Engineering Algorithm (4) Problem Selection and Definition (6) Measurement System Analysis (7) Choosing a Variation Reduction Approach (3, 8) Finding a Dominant Cause using the Method of Elimination and
Families of Variation (9) Tools for Finding a Dominant Cause (10-12) Verification of the Dominant Cause (13) Revisiting the Choice of Variation Reduction Approach (14) Determining the Feasibility of an Approach (15-20) Implementation and Holding the Gains (21) Wrap Up and Conclusions
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Introduction
Problems are only opportunities in work clothes
Henry J. Kaiser
Variation Definition
Variation is both deviation of output from target changing value of output from part to part
V6 piston diameters target diameter = 101.591 mm measured diameters for 3 consecutive pistons:
101.593, 101.589, 101.597
Chap
. 1: I
ntro
duct
ion
2
Consequences of Variation
Excess output variation leads to Poor performance Scrap and/or rework Low customer satisfaction Extra costs
sProcess improvement
3
Chap
. 1: I
ntro
duct
ion
Reducing Variation
We can improve the process by Better centering to target Reducing variation among the parts
Reducing variation among parts is usually harder than moving the process center
4
Chap
. 1: I
ntro
duct
ion
Truck Pull
Chap
. 1: I
ntro
duct
ion
5
Pull is a critical alignment characteristic Target pull: 0.23 Newton-meters Almost all trucks in last 2 months were
within specs -0.12 to 0.58 Nm Goal: reduce pull variation about the target
Engine Block Leaks
6
Chap
. 1: I
ntro
duct
ion
Cast iron engine blocks were tested for leaks
Current scrap rate was 2-3% Goal: reduce leak rate to less than 1%
Camshaft Lobe Runout
7
Chap
. 1: I
ntro
duct
ion
Camshaft lobe geometry is critical Base circle run-out is a positive measure
of the max. deviation from an ideal circle Goal: reduce average run-out Issue: physical lower limit of zero
Sand Core Strength
Breakage of sand cores occurred in handling Goal: increase average core strength Issue: cores that were too strong led to
casting defects
8
Chap
. 1: I
ntro
duct
ion
Crankshaft Main Diameter
Excessive main diameter variation Histogram suggests process off target Goal: move average diameter to target Issue: asymmetric costs
9
Chap
. 1: I
ntro
duct
ion
-5 0 5
0
1
2
3
4
5
6
7
1front
Perc
ent
Paint Film Build Vehicle paint appearance is critical Film build lower specification is 15 thou Goal: reduce film build variation Issue: reducing variation would allow decrease
in average film build and cost savings
10
Chap
. 1: I
ntro
duct
ion
Refrigerator Frost Build
11
Chap
. 1: I
ntro
duct
ion
Customer complaints about frost build up in frost free fridges
Goal: eliminate frost build up Issues:
difficult to measure frost except during customer usage
causes found to be in usage environment
Describing Processes
If I had to reduce my message to management to just a few words, Id say it all had to do with reducing variation
W. Edward Deming, 1900-1993
Process A series of actions which are carried out
in order to achieve a particular result. (Collins Dictionary ) Manufacturing processes
e.g. production of automobiles or automobile parts Service processes
e.g. credit applications, customer returns, Math faculty admissions
Measurement processes e.g. gauges, operators, etc. produce measurements
2
Chap
. 2: D
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Process Map
Each time the (e.g. exhaust manifold) process operates it creates a unit/part/realization
Chap
. 2: D
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oces
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3
Melting
Core Making
Molding
Pouring Shakeout Machining
Melting
Core Making
Molding
Pouring Shakeout Machining
Process Outputs and Inputs
Outputs: characteristics of the realizations of interest to the customers characteristics related to performance or ease
of assembly, e.g. strength of casting, dimensions, etc.
Inputs: features of the process itself e.g. operators, pouring temperature,
properties of the sand, etc. Inputs and Outputs can be
continuous, binary, ordinal, etc.
Chap
. 2: D
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4
Critical to Quality (CTQ)
Every manufactured product has 1+ critical to quality (CTQ) output characteristics e.g. piston head diameter, credit application
decision Often we can make the process better if
we reduce variation in the CTQ(s). CTQs typically have a target value and
specification limits e.g. 595 5 microns from nominal for piston
head diameter 5
Chap
. 2: D
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ses
Output Distribution
We are interested in the distribution of output values from the process
We can summarize the output distribution graphically by histogram numerically by the center (average), standard
deviation, min, max, etc. A histogram shows the distribution of the
output values, the bar heights give the relative frequency for each range of output values
Chap
. 2: D
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6
Describing Variation Truck alignment (pull): target 0.23, specs -0.12 to 0.58, well centered good process
7
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. 2: D
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Types of Problems Excessive variation Poor targeting
Chap
. 2: D
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8
3210-1-2-3
30
20
10
0
deviation
Freq
uenc
y
840
30
20
10
0
deviation
Freq
uenc
y
76543210
40
30
20
10
0
out-of-round
Freq
uenc
y
Defect rate too high
Combination
Types of Problems
Chronic versus sporadic problems chronic problems are persistent and resist solution sporadic problems are urgent and short-lived
(firefighting) Problems with a continuous output
characteristic e.g. time, length, etc. excessive variation (high scrap and/or rework) poor targeting of the process center
Problems with a binary output characteristic, e.g. pass/fail, defective/not defective defect rate too high
Chap
. 2: D
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9
Measure of Variation (StDev)
We quantify variability (across units) as where is output for ith part and is the average
Stdev is expressed in the same measurement units as the process output
For bell shaped histograms almost all values will fall within
10
21stdev
1
niiy y
n
y
3average stdevr
Chap
. 2: D
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iy 1,2,...,i n
Fixed and Varying Process Inputs A fixed input changes only when we deliberately
change it, e.g. control plan iron pouring temperature target value process or product design changes
A varying input naturally changes from part to part or time to time, e.g. core dimensions change from casting to casting operators change each shift raw material characteristics change each batch environmental conditions
Chap
. 2: D
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11
Causes (of Variation) Variation in the output(s) as the process
runs must have a cause! Only varying (not fixed) inputs can be
causes of this output variation Some causes have a large (or dominant)
effect others have little or no effect Denote output (y), fixed inputs (z) and
varying inputs (x), then we might model 12 1 2 1 2, ,..., , ,...Y f x x z z
Chap
. 2: D
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What is a Cause?
Can the product design (process design) be a large cause of output variation?
Chap
. 2: D
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13
cause
outp
ut
Scatterplot of output vs cause
cause
outp
ut
Scatterplot of output vs cause
Dominant Cause of Variation We shall assume (to start) that for every
problem, there is a SINGLE DOMINANT CAUSE Pareto Principle applied to causes see the next page
Secondary causes can be identified, but the tools and strategies used in the search for a cause work best if there is a single dominant cause
The assumption is more likely to hold with a focused problem
e.g. one with a single failure mode
Chap
. 2: D
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14
Pareto Principle
First proposed by Vilfredo Pareto in 1906 80% of Italian land owned by 20% of the people 80/20 rule
Since then principle has been shown to be widely applicable
Here we apply it to causes of variation Most of the output variation can be explained
by just one or a few causes (varying inputs) Vital few, trivial many 15
Chap
. 2: D
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Model for Single Cause
Suppose where x represents a single cause
Then, assuming independence between the cause x and all other causes, we have
Chap
. 2: D
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16
Y f x R
2 2Rstdev Y stdev due to x V
Effect of Square Root Sum of Squares Formula
17 1.00.90.80.70.60.50.40.30.20.10.0
1009080706050403020100
standard deviation(due to cause) / standard deviation(total)
Perc
entr
educ
tion
inov
eral
lvar
iatio
n
22(output) (due to cause) due to all other causessd sd sd Ch
ap. 2
: Des
crib
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Proc
esse
s
Dominant Cause Continuous Output
18
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. 2: D
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Continuous cause Discrete cause
Dominant Cause with Binary Output (Ggood, Bbad)
19
Input value
G GGG B BBBCh
ap. 2
: Des
crib
ing
Proc
esse
s
G
G
G
G
B
BB
B
B
G
G
G
G
G
B
B
BB
Input 1
Inp
ut
2
G
Interaction and Correlation
There is an interaction between 2+ inputs if the effect on the output of changing either input depends on the level of the other input
Interaction is not to be confused with correlation between two inputs a correlation exists between two inputs if they
vary together in some way, e.g. when input1 is low, input2 also tends to be low
note two inputs can be correlated whether they have an effect on the output or not
Chap
. 2: D
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20
Cause and Output Relationship
In the search for a dominant cause we look for a strong correlation between a varying input and the output, such as
We assume that reducing the variation in a dominant cause will reduce variation in the output
However, correlation does not guarantee this! Verify assumption later
Chap
. 2: D
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21
Variation Reduction Steps
To reduce variation Juran suggests two steps Diagnostic journey find the cause(s) of
the variation Focus on varying inputs (xs)
Remedial journey find a solution To improve we must change something Focus on fixed inputs (zs)
22
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. 2: D
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Solutions
To change the long term output variation (i.e. solve the problem) we will need to change one or more fixed inputs!
Change to a fixed input might help if it reduces the variation in the dominant cause changes the relationship between a dominant
cause and the output moves the process output center
Chap
. 2: D
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23
Seven Variation
Reduction Approaches
A fool can learn from his own experiences;
the wise learn from the experience of others
Democritus, 460-370 B.C.
The Seven Variation Reduction Approaches Fix the Obvious Based on Knowledge of a
Dominant Cause Desensitize the Process to Variation in a
Dominant Cause Feedforward Control Based on a Dominant Cause Feedback Control Make Process Robust to Noise 100% Inspection Change the Process Center
Cha
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: Var
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App
roac
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2
Fix the Obvious Based on Dominant Cause Reduce variation in the dominant cause
Existing Process Improved Process
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: Var
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App
roac
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3input
outp
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input
outp
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Truck Pull In the early phases of improving the truck
alignment process, the team looked at right caster stratified by alignment gauge
As the trucks enter the gauges haphazardly the dominant cause is the gauges
An obvious solution was to recalibrate the gauges (and monitor them over time)
Cha
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: Var
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App
roac
hes
4
30252015
4.8
4.3
3.8
day
avg
right
cast
er
Hubcap Damage
Customers complained of wheel trim and hubcap damage
A dominant cause of the broken retaining legs was found to be a combination of cold weather and contact with curbs.
An obvious solution was to replace the inherently brittle existing ABS hubcap with a new design made of mineral reinforced polypropylene
Cha
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App
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5
Desensitization
Desensitize a process to variation in a dominant cause
Existing Process Improved Process
Cha
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: Var
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App
roac
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6input
outp
ut
input
outp
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Engine Block Porosity Problem: cast iron engine block subsurface porosity Dominant cause: iron pouring temperature. Low
temp. occurred during (un)planned stoppages Using an experiment the team explored the effect of
a new core wash
Solution: change the block core wash to reduce the effect of the iron temperature variation
Cha
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App
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hes
7
alternateregular
400
300
200
100
0
wash
poro
sity
Feedforward Control Monitor the dominant cause and predict the
future behavior of the output If the prediction is far enough from the target,
adjust the process Existing Process Improved Process
Cha
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: Var
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App
roac
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8
input
outp
ut
input
outp
ut
Truck Alignment (Pull) Pull is an important characteristic as it indicates
how well a truck will track on a standard highway Variation in truck frame geometry is a dom. cause
of variation in the key alignment characteristic left caster that affects pull
Solution: Adjustment for each alignment assembly measure geometry from bar coded label on each frame predict left caster and pull using a predictive equation drill cam to adjust predicted pull closer to target
Cha
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: Var
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App
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9
Feedback Control
Monitor the output characteristic and predict future behavior from current and past observations
If the prediction is far enough from the target, make an adjustment to the process
Existing Process Improved Process
Cha
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: Var
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App
roac
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10
Target
time
outp
ut
Target
time
outp
ut
V6 Piston Diameter Excess piston diameter variation was a problem Stratifying the process by streams found structural
variation in the diameters
Solution: Informal feedback controller (one on each stream) Every 15 minutes select and measure two pistons If their average is outside the range 2.7 to 10.7 (target is
6.7 microns) adjust the process center to compensate
Cha
p. 3
: Var
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App
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11
Make the Process Robust
Change fixed inputs to reduce the effects of unidentified causes.
Cha
p. 3
: Var
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App
roac
hes
12original processimproved process
control input settings
outp
ut
Paint Thickness Door paint thickness variation was a problem Dominate variability acted vehicle-to-vehicle An investigation to find the cause failed An investigation to search for more robust settings
was conducted An experiment involving five fixed inputs was conducted Each experimental run consisted of painting five
consecutive cars Performance measure was the log standard deviation of
thickness over the five cars Solution: Change the process settings
high Zone X voltage, high conductivity, low temperature
Cha
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100% Inspection
Reduce the variability by identifying and then scraping or reworking all parts that have values of the output beyond selected inspection limits
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roac
hes
140123456789
10
output
Perc
ent
UpperInspectionLimit
LowerInspectionLimit
Blocked Exhaust Manifolds
Blocked exhaust manifold ports are very rare, but result in catastrophic failure of the engine
A blocked port is relatively difficult to detect since it is not visible
Search for a cause is difficult because blocked ports are so rare Ten year search was fruitless
Automatic 100% inspection of all manifolds using ultrasound was expensive, but outweighed the potential cost of a blocked port reaching the customer
Cha
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Change the Process Centre
Adjust process center to move it closer to the target
Existing Process Improved Process
Cha
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App
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16output
Perc
ent
Process Target
output
Perc
ent
Process Target
Battery Seal Leaky battery seals resulted in rework and
customer complaints Low tensile seal strength was the cause of leaks The problem was reformulated to increase the
tensile strength of the seal
An experiment looked at the effect of temp., melt time and elevator speed on the tensile strength
Solution: Low melt temp. increases seal strength
Cha
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: Var
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App
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17
speedtemptime
highlowhighlowhighlow
440
420
400
380
360
seal
stre
ngt
The Seven Variation Reduction Approaches
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App
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18
Process Output
control
Feedback Control
Process Output???
Making a Process Robust
Process
Output Inspection
Process
Change the Process Center
Process
control
Feed-forward ControlDominant
Cause Output
ProcessDominantCause
Desensitize Process
Output
Process Output
Fix the Obvious by ReducingVariation in a Dominant Cause
Statistical Engineering: An Algorithm for Reducing Variation in Manufacturing
Processes
Begin with the end in mind
Stephen Covey
Statistical Engineering
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A union of engineering and statistics applied to chronic manufacturing problems Statistical methods are needed to plan
investigations and to analyze the collected data
Engineering methods are needed to help plan the investigations, interpret the results and to act on the acquired information
INCREASED PROCESS KNOWLEDGE pp
OPPORTUNITIES FOR PROCESS IMPROVEMENTS
2
The Key is Knowledge
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There is no substitute for knowledge W. Edwards Deming
The greatest obstacle to discovery is not ignorance it is the illusion of knowledge
Daniel Boorstin
By increasing knowledge of how and why a process behaves as it does, we will discover cost effective changes to the process that will reduce variation
3
Goal of Algorithm
Quickly find a low cost solution to a chronic problem
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StatEng Algorithm Uses engineering knowledge and statistical
methods to reduce variation Statistical methods are needed to plan
investigations and to analyze the collected data
Engineering knowledge is needed to help plan the investigations, interpret the results and to act on the acquired information
Requirements for success A high volume manufacturing process A clearly defined chronic process problem A small team of dedicated problem solvers Management support and understanding
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StatEng Algorithm
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Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
6
Competing Algorithms
Shainin Red X Strategy Six Sigma (DMAIC, Breakthrough
Cookbook) Taguchis Parameter and Tolerance Design Demings PDSA Cycle
Statistical Engineering is more focused and prescriptive
Statistical Engineering reflects the iterative nature of real problem solving.
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Structured Problem Solving
A systematic approach to Problem Solving / Variation Reduction is good because it: Prevents jumping to incorrect solutions Is a good communication tool Encourages teamwork Is teachable Is manageable
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Define Problem and Check Measurement Stages
Part of other algorithms, but
Benefits of establishing a problem baseline can be enormous Allows us to know if the problem should be priority
and later whether we have solved problem Effects design of future investigations
The measurement system is critical Provides our only view of the process Checking the measurement system starts the search
for a dominant cause Often (in our experience) a source of trouble
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Third Stage
10
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Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Choosing a Variation Reduction Approach Stage
Begin with the end in mind Stephen Covey 7 approaches to reduce variation
Fix the Obvious Based on a Dominant Cause Desensitize the Process to Dominant Cause Variation Feedforward Control Based on a Dominant Cause Feedback Control Make Process Robust to Noise 100% Inspection Change the Process Center
Choice of approach effects how we proceed
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Fourth Stage
12
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Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Finding Dominant Cause Stage
Focus on varying inputs Use families of causes and method of
elimination (more on this later) Based (mostly) on sequence of observational
studies Often the most time consuming stage Not always needed, but usually worth it
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Assessing Feasibility and Implementation Stages How to assess feasibility or implement is
different for each of the 7 approaches. e.g. not all solutions require knowledge of a
dominant cause Use designed experiments on fixed inputs
to assess possible process changes
Note: we delay the use of (expensive) designed experiments until the assessing feasibility stage of the algorithm
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StatEng Algorithm Keys Structured (Stage by Stage) Algorithm
prevents jumping to incorrect solutions is a good communication tool encourages teamwork is teachable and manageable
Selecting a working (tentative) solution approach early on to drive what we do next
Seven possible variation reduction approaches Fix the Obvious (or Reformulate) Using a Dominant Cause Desensitize the Process to Variation in a Dominant Cause Feedforward Control Feedback Control Make Process Robust 100% Inspection Change the Process Center
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StatEng Algorithm Keys (cont.)
An important consideration in the algorithm is whether or not to search for a dominant cause. looking for a dominant cause is strongly
recommend! Separating the search for a dominant cause
from the search for a solution Specific tools and strategies are associated
with the various stages in the algorithm A series of investigations is (normally) required
to find a solution
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Process Investigations
A series of investigations are required within the StatEng algorithm
Problem definition Measurement system analysis Searching for a dominant cause Verification of the dominant cause Determining if a proposed approach is
feasible Testing a proposed solution
Cha
p 4:
Sta
tistic
al
Eng
inee
ring
Alg
orith
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17
QPDAC (Question, Plan, Data,
Analysis and Conclusion) Framework
There is no substitute for knowledge
W. Edward Deming, 1900-1996
Observational/Experimental Plans Observational plan: observe the current process
in action does not interfere with existing process may measure inputs/outputs not usually measured usually low cost (relative to experimental plan)
Experimental plan: deliberately manipulate the values of one or more inputs (fixed or varying) usually high cost logistical challenges may need to contain produced parts as they may be of
suspect quality
Stat
Eng
Alg
orith
m
2
QPDAC Statistical Method
For each investigation, we propose the QPDAC (Chap. 5) framework
Specify a clear Question(s) that tells us what we want to know about the process
Develop a Plan that specifies how we will collect data to try to answer the question
Collect the Data according to the Plan Perform Analysis to summarize the data Draw Conclusions from the investigation to
(try to) answer the question
Stat
Eng
Alg
orith
m
3
Issues in Process Studies We want to infer how the process will
operate in the future from data collected over a short period of time
It's tough to make predictions, especially about the future Yogi Berra
How we collect the data and its quality are crucial
Process consistency is needed to make reasonable predictions
Stat
Eng
Alg
orith
m
4
Key Decisions in the Plan of an Empirical Investigation
What are the parts and population available for the investigation? i.e. over what time frame will we conduct the investigation? defines the study population
How will we select units to be included in the sample? includes the choice of the number of parts defines the sampling protocol
What inputs and outputs will we measure or deliberately change on the selected parts?
Stat
Eng
Alg
orith
m
study population
time0
sample
target populationstudy population
time0
sample
target population
5
Choosing the Problem
Our plans miscarry because they have no aim. When you dont know what harbor youre aiming for,
no wind is the right wind.Lucuis Annaeus Seneca, 5 BC-65 AD
First Stage of the Algorithm
Chap
. 6a:
Cho
osin
g a
Focu
sed
Prob
lem
2
Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Projects
Management should choose projects/problems based on customer and/or business requirements
(use Pareto Principle, 80/20 rule) greatest $ return lowest cost of problem solving likelihood of success availability of trained and knowledgeable people
Need management input/decisions to prioritize DO NOT start a large number of projects
simultaneously!
Chap
. 6a:
Cho
osin
g a
Focu
sed
Prob
lem
3
Problem Definition Statistical Engineering requires a focused problem
general problems may not have a single dominant cause One project can generate several Statistical Engineering
problem solving efforts Example leaking engine blocks
Project: Reduce scrap rate due to casting defects in machined engine blocks
Problems: Eliminate three different failure modes (center, cylinder bore and rear intake wall) that caused leaks
Focusing may require studies, new measurement systems, redefinition of the problem(s).
Chap
. 6a:
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osin
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sed
Prob
lem
4
Link Between Projects, Problems and Investigations
Translate management defined projects into specific problems
Use StatEng algorithm to guide choice of investigation different at each stage
Use QPDAC framework to help plan, conduct and analyze each individual investigation
Chap
. 6a:
Cho
osin
g a
Focu
sed
Prob
lem
5
Project
Problem A Problem B
Question A1Baseline
Apply StatEngAlgorithm Question A3
...Question A2Measurement
...
Connecting Rods Project to Problem
Managements goal was to reduce the rod scrap rate from 3.2% to less than 1.5% would be easier to address a more specific
problem defined in terms of a binary output (scrap or not),
we prefer a continuous output
Chap
. 6a:
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osin
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sed
Prob
lem
6
Rod Scrap by Day
Scrap rate fairly stable over time
Chap
. 6b:
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blem
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7
Connecting Rod Scrap Locations
Grinding (68%) was the dominant location for scrap detection looking more closely (not shown here), 90% of the scrap at grind
was due to undersized rods Rod thickness was selected to define the baseline
if thickness variation can be reduced so that undersized rods are eliminated, scrap reduction is approximately 3.2% x 0 .68 x 0.9 = 1.96%, so overall scrap rate will be approximately 1.25 % (Goal met)
Chap
. 6a:
Cho
osin
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Focu
sed
Prob
lem
8
grind
bore
broach
assemb
lyOth
ers
85 24 14 6 264.9 18.3 10.7 4.6 1.564.9 83.2 93.9 98.5 100.0
0
50
100
0
20
40
60
80
100
DefectCount
PercentCum %
Perc
ent
Cou
nt
Key Elements of Focusing a Project to One or More Problems
Identify and address the most important failure modes
Replace a binary or discrete output by a continuous one, if possible
Define the problem in terms of an output that can be measured locally and quickly (e.g. refrigerator frost buildup)
Choose the problem goal to meet the management project goal
Chap
. 6a:
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osin
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Focu
sed
Prob
lem
9
Process Certification Process certification is a desirable prerequisite to
Statistical Engineering FIX THE OBVIOUS!
ensure basic good process management follow standard operating procedures as written include safety, training, housekeeping, maintenance need to have a defined process before improvements
can be made Elements covered by Quality system standards
such as ISO 9000/QS 9000 Statistical control (i.e. a stable process as defined
by a control chart) is not required for Statistical Engineering to work
Chap
. 6a:
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osin
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sed
Prob
lem
10
Selecting an Output To define the problem we need to select an output
characteristic (or more than one) that can be used to summarize the size and nature of the problem
Select a critical process output continuous characteristic (dimension, time, ...) discrete characteristic (defect count, scrap, ...)
We can summarize the output using a performance measure, e.g. mean, standard deviation, histogram, run chart,
capability ratio, ... scrap/rework rate, run chart, cost, ...
Chap
. 6a:
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osin
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Prob
lem
11
Quantifying the Baseline
If you know a thing only qualitatively, you know it no more than vaguely. If you know it quantitatively - grasping some numerical measure that distinguishes it from an infinite number of other possibilities you
are beginning to know it deeply. Carl Sagan, 1932-1996
First Stage of the Algorithm
Chap
. 6b:
Pro
blem
Ba
selin
e
2
Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement and Validate Solutionand Hold the Gains
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
refo
rmul
ate
Assess Feasibility and PlanImplementation of Approach
Change Process (or Sub-process) Center
Determining the Problem Baseline To complete the first stage of the StatEng algorithm,
we must establish the problem baseline, i.e. quantify the size of the current problem
The baseline performance is used to set goals [when is the project completed?] track progress help in the search for a dominant cause!
used to plan investigations used to help in the analysis of the results of
investigations
validate success of a solution
Chap
. 6b:
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blem
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3
Problem Baseline Investigation We conduct a study (i.e. sample and measure parts from
the process) to determine the problem baseline The specific goals of this baseline investigation are to
estimate/determine the distribution of output values process center and
process standard deviation, etc. full extent of variation (FEoV) in the output nature of the process variation over time (time family
of output variation) The time family of the output variation provides strong
clues about the nature of the dominant cause (the dominant cause must act in the same time family as the output variation)
Chap
. 6b:
Pro
blem
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4
Time Families of Variation Some outputs (causes) change a lot from one part to
the next, others change more slowly over time. e.g. raw material properties usually change slowly whereas piston dimension is different from part to
part What is slow and fast depends on your perspective
and specific process e.g. plant environment (daily/seasonal changes),
operators (change each shift) There are many time families
part to part, hour to hour, shift to shift, day to day, week to week, etc.
Chap
. 6b:
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blem
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5
Time Family Example Problem: Excessive scrap due to diameter variation in a
piston manufacturing process. To assess the time families part to part and hour to
hour suppose we measure diameter on three consecutive pistons once per hour for 12 hours output varies slowly output varies quickly
Chap
. 6b:
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blem
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Time Families Example
Chap
. 6b:
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blem
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7
output varies slowly output varies quickly
Uses of Time Family Knowledge
Knowing the output time family is extremely useful for planning, it helps us select an appropriate time frame (i.e. study
population) for future observational investigations
define a run for future experimental investigations
Output time family also allows us to eliminate varying inputs that act in other time families as suspect dominant causes
Chap
. 6b:
Pro
blem
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8
Establishing the Baseline Goal: assess process performance (center and
variation), and output time families Investigation should
capture effect of all major sources of variation e.g. different machines, raw material, operators, etc.
consist of 100s (continuous output) or 1000s of parts (binary output)
use a systematic sampling plan designed to allow us to assess a variety of time families
Appropriate time frame for baseline data is key longer is better, but is more expensive how long is long enough?
Chap
. 6b:
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blem
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selin
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9
Connecting Rod Baseline Select 20 consecutive rods twice haphazardly
each day for five days, total of 200 rods Measure the thickness of each rod at each of the
four positions total of 800 thickness measurements
Questions are five days enough? How can we tell/check? are 800 measurements enough? why are the two batches of 20 consecutive rod
chosen haphazardly from within each days production?
Chap
. 6b:
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blem
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10
Row/Column Format Baseline Data
Each row represents a different rod and position
Each column gives the values for a different input
MINITAB worksheet Most convenient format
for data analysis Not the default way to
store data in Excel
Chap
. 6b:
Pro
blem
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selin
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11
Rod Baseline Results Numerical Summaries, thickness = deviation (in thousands of an inch) from nominal (0.9 inches) mean: 34.6 standard deviation: 11, min and max: 2, 59
Histogram with specification limits 10 and 60
Chap
. 6b:
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blem
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12
thickness
Freq
uenc
y
5648403224168
70
60
50
40
30
20
10
0
10 60
Histogram of thickness
MINITAB Histogram
Graph , Adding reference lines for specification limits
Chap
. 6b:
Pro
blem
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selin
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13
Setting the Problem Goal
Want to eliminate undersized rods process well centered already, so need to reduce
thickness variation Specification range is 10 to 60 thou Set goal to reduce thickness standard deviation to less than
Corresponds to a ~25% reduction from the baseline standard deviation of 11
Chap
. 6b:
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blem
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14
60 108.3
6
Stratifying the Output We can learn a lot about the process and the
nature of the dominant cause by stratifying the output in a number of ways by time family, e.g. by day, batch, etc. by location family, e.g. position
To graphically compare the distribution of output (or input) values stratified into subprocesses use an individual values plot with groups (plot on left
on next slide), or a box plot with groups (plot on right on next
slide) if the number of observations is large
Chap
. 6b:
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blem
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15
Rod Baseline Comparing Different Positions
Position 3 lower on average Would the undersized rods (scrap) problem be
solved if we could increase the average thickness at position 3?
Chap
. 6b:
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blem
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selin
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16
MINITAB Individual Values Plot Graph /sW
Chap
. 6b:
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blem
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17
MINITAB Boxplot (With Groups) Graph
Chap
. 6b:
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blem
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18
Box (and Whiskers) Plot shows a five number summary of the distribution
min, max, median, 25th and 75th percentiles a summary of a histogram turned on its side outlying observations are shown with a separate symbol
(rule for outlier vs. min or max varies with software)
Chap
. 6b:
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blem
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19
thic
knes
s
60
50
40
30
20
10
0
Boxplot of thickness
median
75th percentile
25th percentile
max
minoutliers
Rod Baseline Day to Day Pattern
Chap
. 6b:
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blem
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selin
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20
We see little output variation from day to day, i.e. the variation in thickness is large and roughly the same in each of the five days
Rod Baseline Time Pattern
Chap
. 6b:
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blem
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21
Little variation from batch to batch 20 consecutive parts give the FEoV
helps us choose time frame for future investigations tremendous clue about the dominant cause
Rod Baseline Time Series Plot
Chap
. 6b:
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blem
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e
22
Multivari Chart
The proposed sampling plan for a baseline investigation is systematic
As a result, the elapsed time between parts follows a consistent pattern but is not the same for all parts
The standard time series plot is not ideal. A multivari chart is designed for this sort of data We look at multivari investigations later when
searching for the dominant cause
Chap
. 6b:
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blem
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selin
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23
Rod Baseline Multivari Charts
Chap
. 6b:
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blem
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MINITAB Instructions Multivari
Chap
. 6b:
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blem
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Multivari Dialog Box For a multivari chart always using the option
Display individual data values Note that the factor used to define horizontal
axis is the last factor in the list
Chap
. 6b:
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blem
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26
Rod Baseline Conclusions An estimate of the long term rod thickness variation
(standard deviation, denoted ) is 11 To meet the goal we need to reduce the output
variation to around 8 Full extent of output variation (FEoV) is 2 to 59 Output varies in the part to part family Subsequent investigations conducted over a short
time interval should result in the output FEoV Dominant cause must act in the part to part and
position to position families Can almost solve the problem by increasing the
average thickness at position three by around 10 units
Chap
. 6b:
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blem
Ba
selin
e
27
yV
Baseline Over Too Short a Time Suppose we see the following hypothetical
pattern of output by day
Large day to day effect it is hard to tell what will happen tomorrow we need to collect data over many more days to
be sure that the baseline variation represents the long term behavior of the process
Chap
. 6b:
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blem
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54321
60
50
40
30
20
10
day
thic
knes
s
Watfactory
An Online Virtual Manufacturing Environment
Tell me and I will forget. Show me and I may remember.
Involve me and I will understand. Chinese Proverb
Watfactory (Camshaft) Manufacturing Process Watfactory is designed to model a
manufacturing process that produces automotive camshafts
Consider a single output, denoted y300 The target for y300 is zero (measured from
nominal) and specification limits are -10 to 10
Wat
fact
ory
2
Watfactory Process Map
There are three types of process characteristics one output (y), can be measured at y100, y200, y300 60 varying inputs (xs), change as the process runs 30 fixed inputs (zs), normally constant, but changeable
Machine 1
Machine 2
Machine 3
Stream 1Machine B
Stream 2Machine B
Step 200Step 300
Varying Inputsx16, ..., x25
Fixed Inputsz1, ..., z6
y300
Final Output
y200
Step 200Output
Assembly
Step 100
Varying InputsMachine #: x31
x32, ..., x45
y100
Step 100Output
Component A
Component E
Component D
Component C
Component B
Components
Varying Inputsx1, x2, x3
Varying Inputsx4, x5, x6
Varying Inputsx7, x8, x9
Varying Inputsx10, x11, x12
Varying Inputsx13, x14, x15
Varying InputsStream #: x46x47, ..., x53
Welding
Stream 2Machine A
Stream 1Machine A
Varying Inputsx26, ..., x30
Fixed Inputsz7, ..., z12
Fixed InputsCan be Set by Machine
z13, ..., z18
Step 150
Assembly
Welding Heat Treatment
Step 250
Varying InputsStream #: x46x54, ..., x60
z25, ..., z30
Fixed InputsCan be Set by Stream
z19, ..., z24
Machine 1
Machine 2
Machine 3
Stream 1Machine B
Stream 2Machine B
Step 200Step 300
Varying Inputsx16, ..., x25
Fixed Inputsz1, ..., z6
y300
Final Output
y200
Step 200Output
Assembly
Step 100
Varying InputsMachine #: x31
x32, ..., x45
y100
Step 100Output
Component A
Component E
Component D
Component C
Component B
Components
Varying Inputsx1, x2, x3
Varying Inputsx4, x5, x6
Varying Inputsx7, x8, x9
Varying Inputsx10, x11, x12
Varying Inputsx13, x14, x15
Varying InputsStream #: x46x47, ..., x53
Welding
Stream 2Machine A
Stream 1Machine A
Varying Inputsx26, ..., x30
Fixed Inputsz7, ..., z12
Fixed InputsCan be Set by Machine
z13, ..., z18
Step 150
Assembly
Welding Heat Treatment
Step 250
Varying InputsStream #: x46x54, ..., x60
z25, ..., z30
Fixed InputsCan be Set by Stream
z19, ..., z24
Wat
fact
ory
3
Watfactory Process Game Management has determined that the final
output (y300 - straightness measured in microns from nominal) exhibits too much variation Your teams goal is to find a cost effective way to
reduce the variation in y300 so that (virtually) all camshafts are within the specification limits You have a budget of $10,000 to find a solution Your team will follow the Statistical Engineering
algorithm (covered in the textbook and associated videos) and conduct a series of process investigations looking for a way to reduce variation in y300
Wat
fact
ory
4
More Process Information Process runs 3 shifts, 5 days a week, 1 part per minute i.e. 1440 camshafts are produced per day
Varying Inputs (x1, , x60) Type (continuous/categorical) Process step in which they act (assembly, welding,
heat treatment) History (pattern of variation over time) e.g. x25 is the operator in the assembly step, x42 the cooling temperature in the welding operation x50 the heating time in the heat treatment step
Fixed inputs (z1, , z30) Current level, possible range e.g. z22 is coil length in the heat treatment step
Wat
fact
ory
5
Varying Inputs Information
Wat
fact
ory
Varying Input
Description Type (# levels)
Observed Range
Varying Input
Description Type (# levels)
Observed Range
x1 dimension A continuous unknown x31 machine # categorical (3) 1, 2, 3 x2 diameter A continuous unknown x32 squeeze time continuous unknown x3 hardness A continuous -2.2, 7.2 x33 feed rate continuous unknown x4 dimension B continuous unknown x34 temperature continuous -17, 29.6 x5 diameter B continuous -17.1, 22.2 x35 dimension 1 continuous unknown x6 hardness B continuous -14.3, 18.5 x36 electrode force continuous unknown x7 dimension C continuous unknown x37 humidity continuous unknown x8 diameter C continuous -20, 26.6 x38 dimension 2 continuous 0.2, 10.4 x9 hardness C continuous unknown x39 mandrel position continuous -1.5, 12.1
x10 dimension D continuous unknown x40 weld time continuous unknown x11 diameter D continuous unknown x41 load time continuous -1.6, 9.4 x12 hardness D continuous -7.5, 19.6 x42 cooling temp. continuous unknown x13 dimension E continuous unknown x43 spacing continuous unknown x14 diameter E continuous unknown x44 operator categorical (5) 1, 2, , 5 x15 hardness E continuous -12.6, 21.2 x45 fixture categorical (12) 1, , 12 x16 temperature continuous unknown x46 stream # categorical (2) 1, 2 x17 fixture categorical (5) 1, 2, , 5 x47 power density continuous unknown x18 humidity continuous -3.0, 12.2 x48 induction level continuous -20, 26.2 x19 ball size continuous unknown x49 frequency continuous -14.5, 29.5 x20 orientation categorical (3) 1, 2, 3 x50 heating time continuous 0.9, 8.4 x21 position continuous unknown x51 operator categorical (4) 1, 2, 3, 4 x22 pressure continuous -10.3, 22.4 x52 depth continuous unknown x23 force continuous unknown x53 coupling degree continuous unknown x24 offset continuous -2.5, 6.9 x54 surface area continuous -14, 21 x25 operator categorical (3) 1, 2, 3 x55 coil categorical (8) 1, , 8 x26 temperature continuous -10.6, 15 x56 current continuous unknown x27 fixture categorical (5) 1, 2, , 5 x57 hold time continuous unknown x28 operator categorical (4) 1, 2, 3, 4 x58 air gap continuous unknown x29 power continuous unknown x59 inductance continuous -8.8, 13.4 x30 static continuous unknown x60 quench temp. continuous -4.3, 8.8
6
Input Time Family Information
Wat
fact
ory
7
Watfactory Login Web site: www.student.math.uwaterloo.ca/~watfacto/login.htm Login ID and Password are given at registration (each
team has access to a different copy of the process) A guest login (to a different version of the process) is
also available
Wat
fact
ory
8
Team Home Page Gives summary information on virtual date remaining funds y300 specification limits links to more information
You can request data from previous
studies change your password see investigation/solution
history
Wat
fact
ory
9
Available Empirical Investigations Observational: prospective, retrospective Experiments: with varying inputs, fixed inputs or both Offline experiments: e.g. component swap Solutions: process changes
Wat
fact
ory
10
Conducting Investigations For each investigation you need to specify Type of investigation
(observation/experimental,) What input(s): x1, , x60 (if any) and/or
output(s): y100, y200, y300 to measure How many parts and which parts (camshafts) to
measure For experimental plans you also need to specify
which fixed inputs (z1, z30) and/or varying inputs (x1, , x60) to control to which levels and when
Wat
fact
ory
11
Investigation Costs There is a cost (in $ and time) for each investigation. Cost influences: Type of investigation Prospective/observational studies are cheaper Number of parts
Which inputs/outputs are selected. Cost/part measuring each input and output, e.g. $1/part for y300 tracing parts through the process, i.e. matching inputs
and/or outputs measured at different processing steps The cost for each investigation you conduct is recorded! Costs can be determined before running an investigation
Wat
fact
ory
12
Prospective Measurement Costs
Wat
fact
ory
Process Step
Varying Input
Measurement Costs Per
Part
Process Step
Varying Input
Measurement Costs Per
Part x1 3 x31 2 x2 2 x32 1 x3 5 x33 1 x4 2 x34 1 x5 3 x35 2 x6 5 x36 2 x7 1 x37 1 x8 1 x38 1 x9 5 x39 1
x10 1 x40 1 x11 3 x41 4 x12 5 x42 2 x13 3 x43 2 x14 2 x44 1
Components
x15 5
200
x45 1 x16 1 250, 300 x46 1 x17 1 x47 1 x18 2 x48 2 x19 1 x49 2 x20 1 x50 2 x21 1 x51 1 x22 2 x52 1 x23 6
250
x53 1 x24 1 x54 2
100
x25 1 x55 1 x26 1 x56 2 x27 1 x57 12 x28 1 x58 1 x29 5 x59 1
150
x30 2
300
x60 2
13
Tracing Costs (per part) Tracing costs are applicable when inputs and/or
outputs are measured at different process steps. This cost accounts for the additional expense of
tracing parts through the manufacturing process. Tracing costs are in addition to the standard
measurement costs for any input or
14
Wat
fact
ory
Output Based Tracing Costs Per Part Upstream
Output Downstream
Output Cost
y100 y200 12 y100 y300 22 y200 y300 10
Input Based Tracing Costs Per Part Inputs Cost Links to Output
Components (x1, , x15) 6 y100 Step 100 (x16, , x25) 3 y100 Step 150 (x26, x30) 6 y200 Step 200 (x31, , x45) 3 y200 Step 250 (x46, , x53) 6 y300 Step 300 (x54, , x60) 3 y300
Investigation Time Virtual time elapses when you conduct
investigations in Watfactory Time elapsed depends on your choice of study
population time elapsed is rounded up to nearest shift minimum investigation time is 1 shift
Your team home page shows your current virtual time in terms of weeks, days and shifts since the start
15
Wat
fact
ory
Other Investigations There are also special investigation costs and time
associated with the other types of investigations such as measurement assessment retrospective assembly versus components component swap experiments with varying inputs, fixed inputs or both
We cover these costs and time elapsed later when the investigation is needed 16
Wat
fact
ory
Possible Solutions Goal is to reduce variation in y300 a solution requires a process change
Possible solutions include changing 1+ fixed input (z1,z30) adding 100% inspection reducing varying input variation (x1,,x60) adding a feedback controller adding a feedforward controller
Solution cost (per part) depends on the type of solution selected
Wat
fact
ory
17
Hints and Suggestions Use the StatEng algorithm To find a solution look for a dominant cause(s) of output
variation use a series of studies focus on fixed inputs that act in the same
processing step as the dominant cause(s) Use only process knowledge obtained
inside Watfactory (realistic, but not real)
Wat
fact
ory
18
Organization of Data and Results You will conduct a series of empirical investigation in
Watfactory Often the plan for the next investigation will best be
determined using knowledge gained from previous investigations As a result, it is helpful to stay organized Suggestions Create a new Minitab project with a sensible name
for each investigation Summarize the plan and conclusions from each
investigation in a single document
Wat
fact
ory
19
Watfactory Project Reports
Summarize progress in 9 written reports Each report describes 1+ investigation plan investigation collect the data in Watfactory conduct an analysis to draw conclusions write a short report that summarizes your rationale
for choices made in the plan and gives a summary of your conclusions
Use the QPDAC (Question, Plan, Data, Analysis and Conclusion) framework to organize each report
20
Wat
fact
ory
Available Watfactory Videos Baseline/prospective investigation Measurement system assessment
Assembly/disassembly and component swap investigations Retrospective investigations Experimental (with varying and/or fixed
inputs) investigations Possible solutions
Wat
fact
ory
21
1st Watfactory Investigation Establishing the Baseline
, 4 BC AD 65
Prerequisites
Watched videos and read textbook for Chapters 1-6 Chapter 6 covers the baseline investigation
Wat
fact
ory
Base
line
2
Current Algorithm Stage
Wat
fact
ory
Base
line
3
Define Focused Problem
Check the Measurement System
Find and Verify a DominantCause of Variation
Implement Approach
Choose Working Variation Reduction Approach
Fix the ObviousDesensitize Process
Feedforward Control
Feedback ControlMake Process Robust
100% Inspection
Validate Solutionand Hold the Gains
refo
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Assess Feasibility of Approach
Change Process (or Sub-process) Center
Baseline Goals
Complete the first stage of the Statistical Engineering algorithm by Estimating the process variability, i.e. , and
center Determining the full extent of variation (FEoV) in
the output Determining the time pattern in the output
variation, e.g. does the output vary a lot from part to part, hour to hour, shift to shift, day to day,
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Investigation Plan
Select a plan to address the baseline goals Decide what inputs/outputs to measure Choose the study population period of time when you collect data
Select a sampling protocol and sample size
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Investigation Cost and Time
Costs See prospective investigation costs in the
Watfactory introduction video or Watfactory diagnostic journey written summary Recall measurement and tracing costs
Elapsed Time Depends on study population Should not be more than 1 week (at least for first
baseline investigation)
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Baseline Investigation Selection
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Random Sampling Example
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Systematic Sampling Example
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