Quality and Productivity
Production Output ($ created)
Productivity =
Production Input ($ consumed)
Materials + Direct Labor + Indirect Labor + Capital + Service
Scrap Rework Inspection Machine Warranty
Scrap Rework Inspection Machine Warranty
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Productivity vs. Quality in
Automobile Assembly
US/NA
NIC
Labor hours / vehicle
50 J/J
J/NA
EU
40
30
20
0 20 40 60 80 100 120 140 160 180
Assembly Defects per 100 Vehicles
Womack, James P., Daniel T. Jones, and Daniel Roos. “The Machine that Changed the World:
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The Story of Lean Production.” New York, NY: HarperCollins, 1991, pp. 93.

Statistical Process Control
(Shewhart) Control Charts
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X Charts (“X bar Chart”)
Periodical Random Samples xi of n items
1.
x1 + x2 + .... + xn
x=
2.
n
σ
Assume µ, σ are known ⇒σx =
3.
n
UCL = µ + 3 ⋅ σ x LCL = µ − 3 ⋅ σ x
4.
Plot x ' s
5.
Is Process out of Control ?
6.
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Tests For Control
4/5 in B 6 in row 15 in C UCL
A
B
C
µ
C
B
A LCL
2/3 in A 9 below 14 alt.
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IF µ and σ are unknown
Use Average of Sample Means x for µ
Instead of σ:
If n ≤ 10 (typically)
Use Average Sample Range R
or
UCL = x + A2 ⋅ R , LCL = x − A2 ⋅ R
Use Average Standard Deviation of Samples s
UCL = x + A3 ⋅ s , LCL = x − A3 ⋅ s
IF n > 10
3⋅ s 3⋅ s
UCL = x + LCL = x −
,
c4 ⋅ n c4 ⋅ n
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R and s Charts
Measure Process Variability
Same Idea as X Chart
Control Limits for R-chart
UCL = D4 * R, LCL = D3 * R
Control Limits for s-chart
UCL = B4 * s, LCL = B3 * s
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Parameter Values
To estimate
For X Chart For R Chart For s Chart
σ
R-based s-based
n A2 A3 D3 D4 B3 B4 C4
2 1.880 2.659 0 3.267 0 3.267 0.7979
3 1.023 1.954 0 2.575 0 2.568 0.8862
4 0.729 1.628 0 2.282 0 2.266 0.9213
5 0.577 1.427 0 2.115 0 2.089 0.9400
6 0.483 1.287 0 2.004 0.03 1.970 0.9515
7 0.419 1.182 0.076 1.924 0.118 1.882 0.9594
8 0.373 1.099 0.136 1.864 0.185 1.815 0.9650
9 0.337 1.032 0.184 1.816 0.239 1.761 0.9693
10 0.308 0.975 0.223 1.777 0.284 1.716 0.9727
15 0.223 0.789 0.348 1.652 0.428 1.572 0.9823
20 0.180 0.680 0.414 1.586 0.510 1.490 0.9869
25 0.153 0.606 0.459 1.541 0.565 1.435 0.9896
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X vs. R and s Charts
Spreading of Variance
Wandering of Mean
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6 Sigma
“From 99.73 %
To 99.99966 %”
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Companies Implementing
Six Sigma
Motorola DuPont
Texas Instruments American Express
ABB BBA
AlliedSignal Ford
GE Dow Chemical
Bombardier Johnson Controls
Nokia Noranda
Toshiba
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Machine Capability Index
Specification Width Specification Width
σ
σ
2σ
2σ
6σ
6σ
Specification Width Specification Width
cp = =1 cp = =2
Process Width [6σ ] Process Width [6σ ]
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6-Sigma and Learning
Specification Width
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Baldridge Award Winners
Year M a n u f a c t r u r in g S e r v ic e s S m a ll B u s in e s s e s
• • •
2000 D a n a C o rp o ra tio n O p e ra tio n s M g m t. I n te rn a tio n a l L o s A la m o s N a tio n a l B a n k
• K A R LEE C om p.
• • •
1999 S T M ic ro e le c tro n ic s BI S u n n y F resh F o o d s
• R itz -C a rlto n H o te ls
•
B o e in g A irlift & T a n k e r
1998 • T e x a s N a m e p la te s
• S o la r T u rb in e s ,
• • •
1997 3 M D e n ta l P ro d u c ts M e rrill L y n c h C re d it X e ro x B u s in e s s S e rv ic e s
• S o le c tro n
• • •
1996 A D A C L a b o ra to rie s D a n a C o m m e rc ia l C re d it C o rp . T rid e n t P re c is io n
•
1995 A rm s tro n g W o rld In d .
• C o rn in g In c , T e le c o m m .
• •
1994 A T & T C o n su m e r C o m m . S e rv . W a in w rig h t I n d u s tr ie s
• G T E D ire c to rie s C o rp .
• • •
1993 E a s tm a n C h e m ic a l A m e s R u b b e r C o rp .
• • •
1992 A T & T N e tw o rk S y s te m s A T & T U n iv e rs a l C a rd S e rv ic e s G ra n ite R o c k C o m p a n y
•
(N o w L u c e n t) R itz -C a rlto n H o te ls
• T I (D e fe n s e S y s te m s )
• • •
1991 S o le c tro n C o rp . M a rlo w In d u s trie s
• Z y te c C o rp .
• • •
1990 C a d illa c M o to r C a r F e d e ra l E x p re ss W a lla c e C o .
• IB M R o c h e s te r
• • •
1989 M illik e n & C o m p a n y
• X e ro x (B u s in e s s P ro d u c ts &
S y s te m s )
• • •
1988 M o to ro la G lo b e M e ta llu rg ic a l
• W e s tin g h o u s e E le x tric
(N u c le a r F u e l)
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Research On Quality Award
Winners
Hendricks & Singhal
Management Science, 43, 9, Sep 1997
107% (mean) 48% (median) higher
Operating Income
64% (24%) higher Change in Sales
Management Science, 47, 3, Mar 2000
36% to 46% better Stock Performance
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Overview of Approaches
Crosby: General Road Map for Mgmt.
Juran: Conceptual Model for Costs of
Quality
Deming: SPC - Application for Shop
Taguchi: Finding the right Specs
6-Sigma: Narrowing down on Specs
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Approach to Q-Improvement
Map Customer Needs to Product Specs
1.
Optimize Design Parameters (Taguchi)
2.
Get Consistent Inputs (weeks)
3.
Get in Control (SPC) (months)
4.
Get Capable (Kaizen) (year, ongoing)
5.
If not capable, then radical
6.
Improvement
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What it takes
Understanding of Process
Understanding of Customer
Culture of Trust
Quality Incentives
Standardized Methods
Education & Training
Support Systems
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