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Abstract

Continuous improvement (CI) unceasingly strives to improve the performance of production and service firms. The learning curve (LC) provides1988 Department of Industrial Engineering and a means to observe and track that improvement. At present, however, the concepts of CI are abstract and imprecise and the rationale underpinning the LC is obscure. For managers to improve processes effectively, they need a more scientific theory of CI and the LC. This paper begins to develop such a theory. Our approach is based on learning cycles, that is, in each period management takes an action to improve the process, observes the results, and thereby learns how to improve the process further over time. This analysis suggests a differential equation that not only characterizes continuous improvement but also reveals how learning might occur in the learning curve. This differential equation might help management to evaluate the effectiveness of various procedures and to improve and enhance industrial processes more quickly.
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Toward a Theory of Continuous Improvement and the Learning Curve
Author(s): Willard I. Zangwill and Paul B. Kantor
Source:
Management Science,
Vol. 44, No. 7, (Jul., 1998), pp. 910-920
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/2634506
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Toward
a
Theory
of
Continuous
Improvement
and
the
Learning
Curve
Willard
I.
Zangwill
*
Paul
B.
Kantor
Graduate School
of Business,
1101 East
58th
Street, University of Chicago, Chicago,
Illinois 60637
Tantalus, Inc.
and
RUTCOR, Rutgers University, New Brunswick, New Jersey 08903
C
ontinuous
improvement (CI) unceasingly
strives to
improve
the
performance
of
production
tand
service firms. The
learning
curve
(LC) provides
a means
to
observe and track that
improvement. At present, however, the concepts of CI
are
abstract and imprecise and the
ra-
tionale
underpinning
the
LC
is
obscure.
For
managers
to
improve processes effectively, they
need
a more
scientific theory
of CI and the LC.
This paper begins
to
develop such
a
theory. Our
approach
is based on
learning cycles,
that
is,
in
each
period management
takes an
action
to
improve
the
process,
observes the
results,
and
thereby
learns
how
to
improve
the
process further
over
time.
This
analysis suggests
a
differential
equation
that
not
only
characterizes continuous
improvement but
also
reveals
how
learning might occur
in
the learning curve. This differential
equation might help management
to evaluate the effectiveness of
various
procedures
and to
improve
and
enhance industrial
processes
more
quickly.
(Continuous Improvement; Improvement; Learning; Learning Cycle; Learning Curve; Learning Theory;
Man-
agement Effectiveness; Quality;
Total
Quality Management;
Value
Added; Deming; Lotka; Volterra)
1. Introduction
Continuous improvement (CI)
is
an
array
of
powerful
techniques that has produced substantial
improvements
in numerous companies and organizations.
CI provides
perhaps
the
most central
and
universal
component
of
TQM (total quality management) which
itself has
helped many companies achieve high quality
and pro-
ductivity. Despite the clear effectiveness
of CI, however,
no scientific theory exists to guide its application
or to
systematically improve
the
concepts
of CI themselves.
This paper attempts to begin development
of such a
theory.
The
approach presented may
assist manage-
ment
to
enhance
industrial
processes
more quickly be-
cause
it
reorients
the
fundamental
paradigm
used
to
achieve improvement.
Right
at
the start this paper connects
the concept of
continuous
improvement
with the
concept
of the learn-
ing curve (LC).
This
makes sense because
in
the
indus-
trial context CI and the LC are
different, yet
are
sym-
biotic. The LC forecasts how fast
future
costs will
drop
as
more of an item is
produced.
But it does not
suggest
how to reduce
costs nor how
to
reduce
them faster. CI,
on
the
other
hand,
identifies what improvement
to
make, and how
to do that better and
faster.
In
this sense,
CI removes some
of the obscurity behind the
LC and
can help management
improve the
LC's rate of learning.
The theory this
paper develops for
CI is then equally
applicable to
the LC.
This paper also
exposes and attacks
a serious problem
with
the
LC.
At
present, to
determine
the
amount
of
learning (process
improvement)
management generally
uses
the total cost
method.
That
is,
management
exam-
ines the total cost
in
one period compared
with the total
cost
in
the next
period. But
that
approach,
as we
will
see,
often
produces
significant
statistical errors. This paper
suggests
that
a
superior approach
may
be to
monitor
the
amount
of
cost reduction
directly.
The
direct
method
does
not
compare
total
costs,
but
only
examines the few
aspects
of the
process
that
have
been changed.
Because
the
direct method
generally
substantially reduces
the
(rather large) error
of
the present
method,
it
often sig-
nificantly improves
the value of both the
LC and CI.
0025-1909 / 98/4407/ 0910$05.00
Copyright
X)
1998,
Institute for
Operations
Research
910 MANAGEMENT SCIENCE/VOl. 44,
No. 7,
July
1998
and the Management Sciences
ZANGWILL
AND
KANTOR
Toward
a
Theory
of Continuous
Improvement
and
the
Learning
Curve
To analyze and
understand the improvement
process
this
paper employs the
fundamental notion of the
learning
cycle. Specifically,
in each
period management attempts
various strategies to
make improvements. At the end
of
the period management
observes how effective these
strat-
egies were.
That
information is then
employed
to
develop
better strategies for the
next period. In one learning
cycle,
for
example, management
might change the software pa-
rameters
on a
machine, see
if
production improves,
and if
so, change
the software
parameters
on
all similar ma-
chines.
Learning cycles
and their
inherent
feedback and
adaptation capabilities seem fundamental to
maintaining
rapid, long term
improvement.
This paper presents five
postulates that seem to un-
derlie certain types of industrial
learning
and
that
give
rise
to a
differential equation
that
seems
to describe
that
learning. The differential
equation introduces to the
LC
and
CI literature the
Lotka-Volterra approach of pred-
ators
and
prey. Here the
prey
are
the errors, wastes,
and
other inefficiencies that
impair
the
operations
of the
pro-
cess. The
predators
are
management,
because
they
are
attempting
to eradicate the
inefficiencies
in
order
im-
prove
the
system.
The
predictor-prey
approach
often
produces interest-
ing results,
and it does
so
in
our case also because the
differential
equation
naturally produces
three
types
of
solutions.
Two are well-known
learning
curves:
the ex-
ponential
and the
power
law. The third
solution,
how-
ever,
is new
in
this arena and
might
be a
new
type
of
learning
curve. The new solution can be more funda-
mental
than the
others,
as
(1)
it
seems to
depict
the com-
plete
elimination of
unnecessary work,
and
(2)
the other
two
solution
forms can be built
up
from
this new form.
First,
the
paper
reviews
CI,
a
battery
of
procedures
known to boost
efficiency,
often
dramatically.
Next the
LC is examined as a historical
antecedent
that
provides
a
quantitative
basis for CI.
Finally,
the
paper
develops
the differential
equation
and
explore
its
implications.
2.
Historical Review
Continuous
Improvement
The
management
approach
called "continuous
im-
provement"
raises
the
efficiency
of
many processes
and
systems
and is
closely
integrated
with total
quality
man-
agement, just-in-time,
and kaizen
(largely equivalent
to
CI). Imai (1991) states that
".
. .
kaizen can increase
productivity by 30, 60, or even 100 percent or more
without major capital investment." Harmon and Peter-
son
(1990)
echo this view and ". . .
expect improve-
ment
of 50 to 90 percent and more." Schonberger (1986)
cites
improvement by
factors of
5, 10,
or
even 20
in
man-
ufacturing cycle
time.
Two Origins of Continuous Improvement: Toyota
and Statistical
Reasoning.
CI
traces its
origins
to
two
major historical trends, both dating from about 1950.
The first occurred
at
Toyota, where Tiichi Ohno and
Shigeo Shingo
conceived the
just-in-time (JIT) produc-
tion
system (also
called
kanban, Japanese production,
lean
production) and catalyzed
a
production revolution
of
a
magnitude
similar to that of
Henry
Ford a
genera-
tion earlier.
JIT pioneered
the
disciplined
and
organized
methodology
that
produced the impressive efficiency
gains just cited. As one example of how this is accom-
plished, Toyota employees conduct systematic analyses
to
improve
the
way
that
they
do
their jobs,
and
they
do
this
every
week
(Adler 1991).
The second trend underpinning CI is the quality
movement and statistical
reasoning,
conceived
in
the
1920s
by
Shewhart. Its
contemporary
renaissance is
of-
ten traced
to
W. Edwards
Deming's
1950
lectures to
Jap-
anese
executives, during
which
he
highlighted
the im-
portance
of data collection and of Shewhart's Plan-Do-
Check-Act
(PDCA) cycle (a
statement
in
the
learning
cycle approach
taken in
this
paper).
The
Legacy
of
Cost Analysis: The Learning Curve
The
historical
predecessor
of our
analysis
of
CI is
the
learning curve,
which monitors and
forecasts
improve-
ment
by
a
quantitative approach.
We take
the
viewpoint
that what drives
continuous
improvement
is
some sort
of
underlying learning.
The
LC
contributes
a
simple
mathematical
relationship
between some metric
(per-
formance
measure)-such
as the
cost, quality,
or
cycle
time
of
producing
an
item-and
a
firm's
experience
in
producing
that item.
The
resulting
curve
of
the metric
very
often follows some standard
form,
often
a
power
law. This form of
mathematical
description (unlike
what will
be
developed below)
has
no
parameters
ex-
plicitly representing
the
policies
and
procedures
of
management.
MANAGEMENT
SCIENCE/
Vol. 44, No. 7,
July
1998 911
ZANGWILL AND
KANTOR
Toward a
Theory of Continuous Improvement
and the
Learning
Curve
Let
C(q)
be the
cost (or
other
metric)
of
manufactur-
ing the qth item
in a
series
and
C(1) be the cost of
pro-
ducing
the first one. Then for
p,
the
parameter
of learn-
ing, the classical power law becomes
C(q)
=
C(l)q-P.
(1)
Time
(t) is often substituted
for the
quantity
pro-
duced (q).
The LC has been widely employed
in
nearly
all in-
dustries (see
Dutton and Thomas 1982
and
Dutton et
al.
1984). Its typical
use is to forecast the cost of
producing
the item
in
the future. Because the LC is so
important,
attempts have been made
to
place
the
learning curve
on
theoretical foundations.' While these analyses propose
reasons why the empirically observed learning curve
might occur, they do not suggest practical procedures
by
which
management might systematically
accelerate
the learning. Mishina (1987) punctuates this point
by
noting
that
the causes of
learning
are
not clear and that
"black boxes" seem to lurk behind the curve.
The result is
a
"dumb"
learning
curve
that
simply
records
learning,
where the
learning just
happens,
driven
by
an unknown "natural economic
phenome-
non."
Indeed,
traditional LC
theory provides
no
orga-
nized
way
for
management
to
improve
the
slope
of the
LC so that
learning (improvement
in
cost or
other met-
ric)
occurs
faster.
Adding Learning Cycles
to the
Learning
Curve
What is
missing
from the traditional
LC
theory
and
would
help
make the
learning
occur faster
are the con-
cepts
of
CI and in
particular
the notion of the
learning
cycle.
Under
the
learning cycle,
as
noted,
in
each
period
management attempts strategies
to decrease
the
costs
(or
other
metric)
and if the
strategy
is successful
adopts
it. The
example
cited about
improvement
at
Toyota
il-
'An
excellent review
of
the
learning
curve
is given by
Muth
(1986),
who also suggests his own model based on
the statistical theory of
extremes. Other work reviewed in Kantor
and Zangwill (1991)
in-
cludes Roberts' (1983) and Sahal's (1942) probabilistic
models, Vene-
zia's (1985) optimization model, and Levy's
(1965) component-based
model. More recently, Argote
et al.
(1990)
stressed
the
role of forget-
ting in learning, while Camm et al. (1993)
noted that forgetting might
be explained by variations
in
production
rate. Adler and Clark
(1991),
for
data
from
an
electronics
equipment
firm, identify engineering
changes and work force training as important
inputs to learning.
lustrates how that firm applies this learning cycle con-
cept weekly.
To apply the learning cycle notion to the LC requires
that management determine whether the strategies it
uses in a period (cycle) really help to reduce the cost.
The "obvious" way to determine this information is to
subtract the total cost of
making
the item
at
the end of
the period from the total cost at the end of the previous
period.
The
amount
of
improvement
is thus
AC(q)
=
C(q)
-
C(q
-
1). (2)
3. Problems
with
Identifying the
Improvement
Although calculating Equation (2) appears straightfor-
ward,
it is
not,
because as Bohn
(1991) stresses,
the usual
cost
data
are
extremely noisy.2
To
illustrate, suppose
the
cost
in
a
period
is 100 with
an
error of
?+10 (standard
deviation of 10). Let the cost
in
the next period be 95
with an error of ?10.
Using
basic
subtraction,
the
re-
sulting
cost
improvement
is 5.
That
result, however,
generally
is not correct.
First consider the
common case where the distribu-
tions of the errors are normal
and
independent.
Then
the
improvement
is 5
?
14.
Here, although
the initial
error was about 10
percent,
after the subtraction to cal-
culate the
improvement,
the error has ballooned to 280
percent.
Next
consider a most
auspicious
case when
the
errors have
a
correlation
of
0.5.
The error is still
a
sizable
?10, meaning
that the
amount
of
improvement
would
have
a
200-percent
error.
Moreover,
these
examples
are
not anomalies. An
extremely large
error will
nearly
al-
ways
result because the subtraction involves two
large
numbers
that
are similar
in
value.
When it is measured
as a
difference,
the value of the real
improvement
is
almost
anyone's guess.
The
large
error
in
the traditional
approach
makes
it
difficult
to
identify statistically significant relationships
among
variables-a
problem
that
may help explain
why
there has been
little
progress
in
determining
an
underlying understanding
of CI
and LC.
2
For particular techniques to
analyze the data see Box and
Tiao "In-
tervention Analysis with Applications
to Economic
and Environmen-
tal Problems,"
J.
American Statistical
Association, 70 (1975), 70-79.
912 MANAGEMENT SCIENCE/Vol. 44, No. 7,
July
1998
ZANGWILL AND KANTOR
Toward a Theory of Continuous Improvement
and
the Learning Curve
Analysis of Errors
To analyze the cause of the errors, note that the total
cost (or other metric)
of
producing an item is actually
the sum of the costs of numerous small activities, say
a,,
.
..,
an,
each with its own random variation. These
small activities
might
be:
entering
sales
data, billing,
contacting clients, training, telephoning,
heat
etc. As-
suming
n
=
100
activities,
the total cost
in
the
period
t
-
1
(using time instead of cumulative quantity made)
can be
written
C(t
-
1)
=
a,
+
a2+ a3
+
+
aloo
Suppose
that
during period
t
management attempts
to
reduce
the cost
of
some
activities.
Let
bi
denote the
cost
of those
particular
activities
at the end of the
period.
If
management
works on two activities
during
the
period,
the
cost
of
activity
i
=
1,
2 is cut from
ai
to
bi.
Since
management
does not
work on
any
of the other activi-
ties,
their costs should be
unchanged except
for
random
disturbances.
Let those
costs
at the end of
period
t
be
designated
a*,
... , a
0o. The total cost in
period
t
is
thus
C(t) = b, + b2 + a3* + + a*00
Calculating
the
improvement, AC,
from
Equation (2),
AC(t)
=
C(t)
-
C(t
-
1)
=
[a,
+
a2
+
a3
+
* * *
+
a100]
-[b,
+ b2 + a3*
+
+ a*o].
(3)
Using
the
approach
of
subtracting
total costs
(Equation
(2))
the
improvement
calculated includes
the
errors of
200
cost estimates.
Some observers
have
suggested
that the error
might
be reduced
by taking
a
long
series of
observations. But
that
approach
does not
help
because
it
takes too much
time
to obtain
the
data, perhaps quite
a
few
learning
cycles.
Our
goal
is to obtain information
quickly
so
we
can
rapidly
learn how
to
make better
improvements.
To
overcome some
of
these
error
difficulties,
we
pro-
pose
to
measure the amount of cost
improvement by
looking only
at
the activities
improved.
In the above
example,
since
only
two of the
100 activities
were
changed,
we can calculate the
improvement using
the
equation
AC(t)
=
(a,
-
b1)
+
(a2
-
b2). (4)
Since this equation has the errors of only four terms to
contend with, the error is substantially reduced.3
Example Of Obtaining Data
But how can we obtain the data needed for Equation
(4)? To illustrate this, suppose for action 1 management
moves machine A next to machine B, eliminating the
need to forklift the material from A to B. Say manage-
ment estimates
the
cost of
the
forklifting as $2. Moving
machine A next to B then should cut $2 from the cost
of
making
the item.
Consequently,
the
quantity
a,
-
b
=
$2.
As
a
second
action
during the period, suppose
man-
agement revises the software
on their
enterprise
re-
source
planning system. Suppose
that
reduces
the
scrap
and
defect rates, thereby cutting $7 from the cost
of
making the item. Hence a2
-
b2=
$7.
Whenever several individual
improvements
are
made, their sum is assumed be to the total improvement
made.
Recasting Equation (4)
AC(t)
=
a,
-
b,
+ a2- b2= $8, (5)
for a cost reduction of
$8.
While
this
$8
value
undoubtedly
has
some
error,
it is
likely
to
be
a
small fraction of
the
error
produced
by
subtracting
the
total
costs
as in
Equation (3).
This is
because
the
errors
of
only
a
very
few terms accumulate
in
Equation (5),
but
Equation (3)
bears the error of
200
terms
(assuming
100
small
activities).
This
approach
of
looking directly
at
the actions
im-
proved
makes certain
assumptions.
For
instance,
the
improvements
made should not
interact,
and
also
the
improvements
made should not cause
any
decreased
effectiveness in other
parts
of the
process.
In
practice,
these
assumptions
should be checked
by inspection
and
careful
monitoring,
and when
necessary
some or
all of
the additional terms
in
Equation (3) might
have to
be
included.
Also,
the cost
improvement
of
an
activity
should
be
easily
obtained.
In
general
that
can
be done
by measuring
the relevant
operational
factors before
and after the
change,
for
instance,
the reductions
in
time, scrap, rework, labor,
machine
time,
and
so
on. In
most cases
obtaining
the amount
of
improvement
3In
fact,
if
activities 1
and 2 were
improved by
different
methods,
we
would
look at each difference
separately.
MANAGEMENT SCIENCE/ Vol. 44,
No.
7, July 1998
913
ZANGWILL AND
KANTOR
Toward a
Theory of Continuous Improvement
and the
Learning Curve
directly is easy and inexpensive and
requires minimal
data collection
(Hands-On, How-To,
Kaizen and JIT
1992). Unless the situation is highly
unusual, only a few
of the terms
in
Equation (3)
will
be needed.
4.
Psychological Learning
Theory
Since
learning
and
improvement-the
central
issues
here-are human
endeavors, psychological
learning
theory may
be relevant to the model to be
developed.
Newell and Rosenbloom
(1981)
noted that the
power
law of
learning (Equation (2)) empirically
fit a
number
of
psychological learning
situations.
They
also
suggest,
however,
the
importance
of the
exponential,
where
for
a
parameter r, the exponential law has
the form
M(q)
=
M(O)
exp(-rq).
(6)
(Here
we
use
M(q)
to
unmistakably depict
a
general
metric,
not
necessarily cost.)
The
exponential's use
in
human
learning is strongly
justified
from a
theoretical
viewpoint.
Mazur
and
Hastie
(1978) comment,
"For more
than
two decades
psychol-
ogists
have relied on
exponential equations
more
than
any
others . .
."
and "reliance on the
exponential
has
not declined.
.
."
Exponential
Laws and Industrial
Improvement
The
exponential
law is also well-known
in
industrial
learning
situations.
Levy's (1965)
LC
model uses the ex-
ponential,
as does the
analysis by
Schneiderman
(1988).
Muth
(1986)
has also
noted
departures
from
the
power
law and
cites several other forms that have
appeared
in
the literature.
A
particularly interesting application
of the
exponen-
tial law was
made
at
Analog
Devices
(see
Schneiderman
1988
and
Stata
1989)
when
they
discovered that
many
of their
important
business
processes
followed
an
ex-
ponential (or
half-life
law,
as
they
called
it).
Such
pro-
cesses included on time
delivery, outgoing
defect
levels,
lead
time, manufacturing cycle time, process
defect
level, yield,
and time
to market.
Management
then used
these half-life curves
to
promote
the elimination of
problems
and
to enhance the rate of
improvement.
Relative to the industrial
and the
psychological
learn-
ing theory literature,
the classical
power
law, Equation
(2),
and the
exponential, Equation (6),
seem
to
be the
two curves
in
most
widespread
use.
5. The
Differential
Equation
Postulates
The
differential equation is founded
upon five postu-
lates.
POSTULATE Ia.
For any given metric,
M,
and
process,
the
process
can be
operated
so
that it achieves its
optimum
performance
level, denoted by Z*, as
measured by that metric.
Also, (Ib):
management
can estimate Z*.
Given
any
process
and the
available
equipment,
la-
bor, and other
resources,
we
postulate
that
management
can estimate an
optimal way (ideal,
best)
to
operate
the
process. The value of
the metric when
the process is
operating
at an
optimum
is denoted
as
Z*.
Depending
upon
the
metric
Z
might,
for
example,
depict
the
fastest
time to make the
product,
or the
lowest
cost.
The Optimal
Value
Z*
Has Different
Definitions
Like its sister
term, "quality," the
optimal value Z* is
difficult to define
precisely. Depending
on the
applica-
tion, management can estimate
Z*
by
extrapolation or
in
a
variety
of
ways (Zangwill 1993), such as:
1.
Benchmark.
Management
can
study
the
perfor-
mance of similar
systems
or
processes
at
the best firms
in
the world.
Management then sets
the
goal,
Z
*,
so
that
the
system
would then be
operating
at least as well as
the best such
process.
2.
Technological
Entitlement. The
system
may
be eval-
uated
by engineers
to
determine its
performance
if
it
were
operating optimally,
with no
wastes, defects,
or
problems
of
any
kind.
Management
then establishes this
performance
level
as the
goal
to strive
for,
Z*. This def-
inition
for
Z*
has been
widely
utilized at firms like
Al-
coa
(Zangwill
1993).
EXAMPLE.
To
illustrate the entitlement
approach
for
determining
Z*,
consider a
process
for
handling
a sales
order,
and let the metric
be
cycle
time.
Suppose
the
pro-
cess takes three
weeks, during
which there are three ma-
jor steps:
the order itself must be checked for
accuracy,
the customer's credit must be
checked,
and an order
must be
placed
for the material
required
to make the
item.
During
this
process
the order must be transferred
to each of
the
three different offices
that
do the
respec-
tive
steps (see
figure 1).
In
this case
Z*,
the minimum
cycle
time for this
pro-
cess,
is determined
by
the "real" work.
If,
for
example,
914 MANAGEMENT SCIENCE/
Vol.
44, No. 7, July 1998
ZANGWILL AND KANTOR
Toward a Theory of Continuous Improvement and the Learning Curve
Figure
1
Processing
a
Sales
Order
CHECK
CHECK
ORDER
ORDER
CREDIT
MATERIAL
(1/2HR) (1/2HR)
(1/2HR)
THREE
WEEKS
each of the
steps takes
about a half
hour of someone's
time,
Z* is 1.5 hours. During
the
rest
of the time (three
weeks,
less 1.5 hours), the
sales
order
is being sent
from
office to office
or sits
on
someone's
desk (or
in
the
mem-
ory
of
some computer).
These latter activities
are ex-
amples of
NVA, or waste,
when no productive
work
is
being
done
while the
sales
order
ages.
In an
ideal
pro-
cess
they
would
not
exist.
Reaching
the Performance
Goal
With
some
training,
management
can
usually
decide
upon
the
optimal point,
Z*. Moreover,
it
is usually
not
necessary
to
know Z* accurately, because
the actual
op-
eration of the
system
is usually so
far
away
from
Z*
that
a
sizable
error
in
Z* has little
managerial import.
For
instance,
in
the above example,
it makes little difference
if Z
*
is 1.5
hours
or
3 hours,
since what
must be
attacked
is
the
cycle
time of three
weeks. As the
system operates
closer to
Z*, management
can revise
the
estimate
of Z*.
The usual
challenge
facing management
is not
how to
estimate
Z*,
but
how
to
improve
the
system
so
that it
operates
close
to
performance
level Z*.
POSTULATE
II.
Other things being
equal, for any
metric
M(q),
the rate
of improvement
is
proportional
to the
nonvalue-added
(NVA)
component of
the
metric, N(q).
Spe-
cifically,
M(q)
=
(other
factors )
x
N(q)
Further, specify
the NVA as
N(q)
=
M(q)
-
Z*.
(7)
In
common
parlance
NVA
is
frequently
construed as
any
work that
does not
contribute
value to the final cus-
tomer.
For
mathematical precision,
however,
we define
NVA
as in
Equation 7,
so
that NVA is
any
"work" not
required
by
the
ideal
operating
process
Z*. In
particular,
if
M(q)
is the
current
performance
level,
then
M(q)
-
Z*
represents
the
amount
of
metric
that remains to be
removed before the process will
operate optimally. In
actual practice the common usage
of NVA and our def-
inition are almost identical. Typically,
NVA includes re-
work, waiting, changes, delays, erroneous
information,
defects, wastes, preparation time,
transportation, idle
time,
and
inspection. Also,
NVA
would
be the work
in
making any
items not
sold.
Postulate
II can thus be in-
terpreted as follows:
If
M(q)
-
Z* is large, there are
many opportunities to improve,
so the rate of improve-
ment should be large. Conversely,
if M(q)
-
Z is small,
there are few opportunities
and the rate of improvement
should be
small.
POSTULATE
III.
The rate
of improvement
is proportional
to the
effectiveness of management
in
a
Volterra-Lotkaform.
In
the 1920s Lotka and, separately,
Volterra (see Mur-
ray 1989) suggested
an
equation
describing populations
of
predators
and
prey.
As a
simple instance,
wolves
prey
on
moose. Over
a
wide
range
of
conditions,
the
rate of elimination of moose over time
(-
dS
/ dt)
will
be
proportional
to:
(1) the
number
of
moose
S(t),
as the
opportunities
for
each wolf
are
proportional
to
the number of
moose;
(2) the
number of wolves
W(t),
as
the moose
popu-
lation
will decline in
proportion
to
how
many
wolves
are preying upon them.
This
analysis
led Lotka
and
Volterra
to the
multipli-
cative relationship:
dS / dt
=
-aW(t)S(t).
In
the
present context,
the
"prey"
is
the nonvalue added
component
of the
metric, N(q)
=
M(q)
-
Z*. That
rep-
resents the
errors,
extra
work and waste that
manage-
ment
wants
to
get
rid
of. The
"predator" is
the
man-
agement,
or
more
precisely
the
effectiveness of manage-
ment's
effort
to
improve
the
process.
Let
E(q)
denote
that
effectiveness
of
management
in
making improvements
after
q
items are made.
Consequently,
we
may
rewrite
the Lotka and Volterra
observations4
as
the rate of
improvement
in
the
metric is
propor-
tional to
4 See also Fine
and Porteus
(1989), who express
improvement
as a
random variable
that is a fraction of the
amount left to
improve.
MANAGEMENT
SCIENCE/ Vol.
44, No. 7, July
1998
915
ZANGWILL
AND KANTOR
Toward
a
Theory of Continuous
Improvement and the Learning Curve
(i) the effectiveness of
management, E(q), and
(ii) the
amount of
metric left to
eliminate, N(q).
6.
The
Continuous Improvement
Equation
The postulates
combine
to
produce
our
continuous
im-
provement
differential
equation.
Assuming
that low
values of
the metric
are
"better,"
and
noting
that Z* is
a
constant,
-
dN
/ dq
=
rate of
improvement
in
the metric.
(8)
Following
Postulate III, we then
have for
c
a
coefficient
of
proportionality:
dN/dq
=
-cE(q)N(q).
(9)
To
measure
improvement
in
any practical
applica-
tion, express
Equation (9)
in
finite differences:
/N/
Aq
=
-cE(q)N(q).
(10)
These
forms,
Equation (9)
and also
Equation
(10),
are
the
"continuous
improvement
differential
(or
finite dif-
ference) equation"
(CIDE).
7.
Monitoring
the Effectiveness
of
CI
In
applying
the CIDE to actual
operations,
the
quantity
Z*, being
the ideal
performance
of the
process,
would
be
estimated
early
in the
project. M(q)
would also
be
known,
since that
is
the value of the
metric, say
cost,
after
q items
are
processed.
Further,
c
would
be
set to
the scale of the
data,
so without
loss
of
generality
we
can set c
=
1.
To
apply
the
CIDE, thus,
we need
only
determine the rate at which
the
metric
improves, /M
/
Aq,
as that will
provide
the
effectiveness
of
manage-
ment:
E(q).
Specifically,
E(q)
AMM/
(/qN(q)).
(11)
During any period
of
interest, Aq
is the number of items
processed.
(If
we are
examining
how
the
metric
im-
proves
from the time the
36th
item
is
made
until the
39th
item
is
made,
then
/\q
=
3.)
Next we must estimate
AM,
or how much the metric
changed
during
that
interval. As
discussed,
direct ob-
servation is generally preferable to inference from some
change
in
a
grand total. With that done, E(q) is then
known.
In
general, suppose that during different intervals of
time a firm implements different CI techniques, such as
SPC, moving
the
machine, improving maintenance,
training, etc. Then for any specific CI technique imple-
mented, E(q) expresses the corresponding effectiveness
of
CI.
That
information lets us identify which improve-
ment efforts
or
techniques
are
more powerful.
Practical Importance of the CIDE
Using the metric M(q) alone does
not
easily provide
information
about
the effectiveness
of
an
improvement
technique. But the CIDE does, because
it
normalizes the
improvement to account for the amount of metric left,
N(q)
=
M(q)
-
Z.
For
example, suppose SPC
is
implemented
on a
spe-
cific machine and
$3 per
unit
is
saved,
so AM1
=
$3.
Suppose
that
later,
after more
products
are
processed,
a
new
incentive
system
motivates the workers to save
$2
per item,
so
L\M2
=
$2.
Since $3
is
larger
than
$2,
it
appears
that
installing SPC has
a
bigger impact
than
the
new
incentive system, and
that
SPC ought
to be de-
ployed through
the entire
operation
before the incentive
system
is. But that
might
not
be
correct.
The absolute
amount of savings
must
be
adjusted
for
the
amount
of
NVA
left, N(q).
In
particular, suppose,
Ni(q)
=
$6
and
N2(q)
-
$3.
Then
from
the
CIDE,
since
$2
/
$3 is greater
than
$3
/
$6,
the incentive
system
is
ac-
tually
more effective.
What
is
relevant here is the fraction of NVA
cut,
not
the
absolute
amount
cut. Without
use
of
the
CIDE,
man-
agement might erroneously replicate
a method that
had
been
effective
only
because
it was
applied
to
a
situation
with a
sizable
value
of
N(t).
The CIDE
automatically
adjusts
for the NVA
left and thereby produces
an
ap-
propriately
scaled
measure
of
impact,
the
percentage
of
NVA
cut.
8.
Autonomous Solutions of the
CIDE
So
far the CIDE has been
given
in
general
form. We now
show that for
simple dependencies
of
the
E(q),
effec-
tiveness
of
management,
on the current level
of
N(q),
the CIDE can be solved
explicitly.
916
MANAGEMENT SCIENCE/ Vol. 44, No. 7, July
1998
ZANGWILL
AND KANTOR
Toward a
Theory
of
Continuous
Improvement
and the
Learning
Curve
To
motivate
that
expression,
note that
E(q) might
de-
pend
upon
the amount of
known NVA
in
the
process:
N(q)
=
M(q)
-
Z*. On the one
hand,
when there is
a
compelling need to
improve,
such as
a
tight
deadline,
management
might
increase its effort
toward
the
end.
In this
case,
as
M(q)
-
Z*
gets
small, E(q)
increases.
On
the other
hand,
without
special
pressure,
as
the
optimum
point
Z*
is
approached
and little
possible
im-
provement
remains,
management
might
shift its atten-
tion
away
from this
project
to
other
more immediate
needs.
In
this
case,
as
M(q)
-
Z*
gets
small, E(q)
de-
creases.
Postulate IV subsumes both of these
possibili-
ties.
POSTULATE
IV.
The
effectiveness
of
the
CI
effort depends
upon
the
amount
of improvement
remaining,
according
to a
power
law.
Specifically, for
a
parameter, K,
and
coefficient
K,
E(q)
=
KN(q)K.
(12)
Equation
(12) represents
ways
in
which
management
can
change
the level of
effort
(effectiveness)
it
puts
into
this
activity
as
improvement
is
accomplished.
In
partic-
ular,
N(q)
=
M(q)
-
Z* is
decreasing
as
improvements
are
being
made.
If
the
parameter
K
>
0,
the
effectiveness
of
management
is
decreasing,
while K
<
0
represents
increasing
effectiveness,
and K
=
0
is
constant effective-
ness
of
management.
9.
Explicit Solutions
of
the CIDE
Plugging Equation
(12)
into the
CIDE
Equation
(10)
we
obtain
dM/dq
=
-cK(M(q)
-
Z*)K+l.
(13)
Solutions
Depending
on
the
parameter,
three solutions
to
Equa-
tion
(13)
result
(Kantor
and
Zangwill
1996).
If K
>
0,
the
solution is
a
power
law,
which,
as
in
Equation
(1),
is the classical
form
of
production
learning.
Restoring
the
full
value of the
metric, M(q),
the
general
form is:
M(q)
=
(M(1)
-
Z*)(1
+
qoff)P(q
+
qoff)-P
+ Z*.
When the offset
parameter
qoff,
which shifts the
origin,
is set
to
zero,
the classical
law
results:
M(q)
=
(M(1)
-
Z*)q-P
+
Z*, q
?
1.
(14)
This
law
is often written
with Z
*
=
0.
If K
=
0,
the solution is an
exponential law.
M(q)
=
(M(O)
-
Z*)
exp(-rq)
+ Z*.
(15)
Setting
K
< 0
generates
a
new
class
of
solutions,
which go to
Z* at a finite amount
of production qmax.
We call
this class the
finiteform, since it seems to
rep-
resent
specific categories of NVA
being (totally) elimi-
nated
from
the process in a finite
period of time.
M(q)
=
(M(O)
-
Z*)(1
-
q/qmax)d
+
Z*
for
q
<
qmax
=
Z*
forq
2
qmax.
(16)
Empirical Evidence
Certainly, the
power
law
and the
exponential are well-
known
to reflect
learning. More
important, empirical
testing
confirmed
that the
new
form, the finite, also
seems to
reflect industrial
learning. Specifically, the
three
forms were
tested on
published data series from
the
quality
progress literature.
The data series sub-
sumed
metrics
as
diverse as "cost
per keystroke" (for
data
entry)
and
"errors
per
invoice," and included
var-
ious cycle time
measures.
For
the
21 data series ana-
lyzed,
the finite form fit
the data best
in
9 cases, and the
power
and
exponential
forms were
each best
in
6 cases.
In
sum,
all
three forms
were
empirically
validated
and
were
roughly equally good
in
fitting
the
learning
and
improvement
data
(See
Kantor and
Zangwill 1996).
The
empirical
evidence for the three forms can be inter-
preted
as
preliminary support
for the
CIDE
Equation
(8)
and
for
Equation (13).
10.
Interpretation
of the Three
Families of
Solutions
Since
all
three solution forms
of
the CIDE seem
useful,
let us
examine them
in
more detail.
Power Law and
Exponential
Forms of
Learning
In
the
LC literature the
classical
form
is the
power law,
Equation
(14). However,
as
mentioned,
other
equation
forms have
also
appeared
in the
literature,
most
notably
the
exponential
form, Equation
(15).
Managerial
Application
of
the
Exponential
From
a
managerial viewpoint,
the
exponential
is
a
very
attractive choice because it is
memoryless.
The other
forms are
more cumbersome because
they require
MANAGEMENT
SCIENCE/ Vol. 44, No.
7, July 1998
917
ZANGWILL AND KANTOR
Toward a Theory of Continuous Improvement and the Learning Curve
specification of
a
starting point, a shift
q0ff,
or an
ending
point qmax. To apply the exponential
management
needs
merely to articulate the goal of
achieving
a
given per-
centage improvement per unit time. Hewlett-Packard
states goals this way. At Analog
Devices,
Schneiderman
(1988) introduced the exponential,
and it
is discussed
as part
of
that
firm'
strategy by Stata
(1989).
Motorola also
employs
the
exponential
in
forming
goals (Smith
and
Zangwill 1988).
The
proprietary
data
we obtained from Motorola,
while not
conclusive,
in-
dicate
that
exponential improvement
was
holding
for
several factors-of-2
improvement.
As a means
for
man-
agement
to
establish improvement
goals,
the
exponen-
tial
seems
the form of choice.
Finite Forms
The finite form (Equation (16)) has
not previously ap-
peared
in
either
the
learning curve
or
CI literature.
With
the exponential
or
power models NVA vanishes
only
asymptotically.
The finite
form,
however, goes
to
zero
in finite experience or time, and this
seems
to
happen
in
practice.
In
manufacturing,
for
example,
a
just-in-
time
system might
eliminate certain
inventory storage.
Metric
components
associated
with the
storage,
such
as
cost,
time
of
storage,
or
defects
occurring during
stor-
age, then totally disappear. Thus
the finite form
seems
to describe the
elimination of
some
step
in
the work
process.
11.
Hierarchy of
Solution
Curves
The
three forms
are
not
just
solutions
to the CIDE.
They
also seem to form
a
hierarchy
describing
the removal of
NVA when viewed at different scales of
detail.
To
ex-
plore
this we introduce Postulate
V.
POSTULATE
V.
Additive
Decomposition
of
Metric.
The
metric
M(q) of
a
process
can
be
decomposed
into
submetrics
Mi(q),
which are metrics
for steps of
the
process,
and whose
sum is
the
metric
M(q).
M(q)
=
,
Mi(q).
(17)
This
interpretation holds,
with
appropriate
amend-
ment,
for the
key
metrics
of
cycle
time, quality,
and
cost.
For
example,
if
M(q) represents
total
cycle
time to
com-
plete
a
process,
Mi(q)
is the time to
complete
the ith
step
on the
critical
path
for
that
process.
If
M(q) represents
total defect events
(quality), it is the sum of all
defect
events occurring in all
activities of the production pro-
cess, and
Mi
is the
number
of
defects contributed by the
ith
activity.
If
M(q)
is the cost to make
an
item, then the
terms
Mi
(q)
represent the cost of the numerous activities
in the process. For
multiplicative metrics, such as the
yield in wafer
production, the logarithmic transform
leads to additivity.
Exponentials Sum
to Power Law
Utilizing
Postulate
V,
the
exponential
and
the
power
law become
intimately related. The power
law
of
im-
provement
can
be
represented by
a
sum of
exponentials,
or
in
the
limit,
as
the
integral
of
exponentials.
(1?
q.in )P(q
+
qmin )-P
0
1
= (1
+
qnin)p
f
17()
e-rqmin rPe-rqdr.
(18)
Equation (18) suggests
that,
at least
in
principle,
the
to-
tal
metric M(q)
could
improve
as
a
power law,
while
the
component parts of that
metric,
Mi(q),
improve
as
exponentials (see Kantor and
Zangwill 1991).
Finite Forms
Approximate Exponential Forms
It is also true is that the
exponential
can
be
approxi-
mated
as
a
sum of finite forms
(Kantor
and
Zangwill
1996).
The
exponential
can
be written as:
e-rq
=
q
(1 -
q/qmax)d
+
1)
d
d+1
-rqmaxdqmax
Xqmaxr
e
~mxq~.(19)
The
Hierarchy of
Improvement Curves
The three functional forms
appear
to
compose
a hier-
archy. Sums
of the finite form can well
approximate
the
exponential form,
and sums of
exponentials
can well
approximate
a
power
law.
However,
the
reverse is
not
true,
as
such
sums would
require negative coefficients,
which seems to make no sense.
Since
the finite form can
generate
the
other
two,
but not
conversely,
the finite
form
seems
the most
fundamental.
As mentioned,
each
finite
term can be
interpreted
as
the elimination of
a
category
of NVA.
Consequently,
it
might
be that both the
power
law and
the
exponential
are
observed
at
high
levels of
aggregation
when the
un-
derlying reality
is that
many
small contributions to
the
metric are eliminated
entirely.
918 MANAGEMENT SCIENCE/
Vol.
44, No.
7, July 1998
ZANGWILL AND KANTOR
Toward a Theory of Continuous Improvement
and the Learning
Curve
Perspective on the Three Forms
As Feller (1940) noted, the power law is something
of a
catchall, because
it
provides
a
good fit for
a variety of
curves.
When a
power
law
is
observed,
we cannot ig-
nore the possibility that, in reality, the data
are the sum
of other forms.
This
could
largely explain
the dominant
role of the power law in the learning curve
literature,
where cost data are sums of hundreds or thousands
of
separate
series of
data.
Specifically,
even
if
the total met-
ric, M(q), appears
to
follow
a
power law,
the detailed
source metrics,
Mi(q),
might not. They
might be finite
forms, depicting quantities
of metric
being
eliminated.
13. Summary
Lack of
a
quantitative theory for the learning
curve and
for
the concepts of continuous improvement
has
inhib-
ited their development and their application.
We sug-
gest
that a
powerful
method to
produce
improvement /
learning is repeated use of the learning cycle.
During
each learning cycle, management
can observe what
techniques are producing greater improvement
and
thus
can
learn how to improve processes
faster and
faster.
The traditional
way to
obtain data for the
learning
cycle
would be to
subtract
the total cost
(or
other
metric)
in one
period
from
the
total
cost
in
the
previous
period.
That technique, however,
can
introduce
sizable
errors,
and we
propose
that it
is
often
possible
to reduce that
error
by measuring
the individual
improvements
di-
rectly.
The
notion
of the
learning cycle
allows us
to propose
the
beginnings
of a
theory
of continuous
improvement /
learning.
This
theory
is based on
a
five
postulates
and
leads to a differential
equation describing
the
learning.
This equation
then leads us to three forms of the learn-
ing curve:
the
power law,
the
exponential,
and the finite.
With
regard
to
the
coexistence of
power
law
and ex-
ponential
forms of
learning,
the differential
equation
shows that these
may belong
to the same
family
as
a
new
law
of
learning,
the
finite form. In
industrial
situ-
ations,
the
power
and
exponential
laws
might
be
sums
of finite
forms, suggesting
that
the
finite
law
may
be
more basic.
It is
hoped
that this
theory
will be tested
through
di-
rect measurement
of
the elimination
of NVA.
Other
tests
might
examine whether
complex systems
are
gov-
erned
by
the
finite
form at the level
of
small
component
processes, by exponential forms at intermediate levels
of
aggregation,
and
by power
laws
at
the
highest aggre-
gation levels.5
5 This work has been supported in part by the National Science Foun-
dation program in Decision, Risk, and Management Sciences grant
SES8821096
to
Tantalus,
Inc. The
authors wish
to thank Paul
Noakes,
Vice
President of Motorola, Inc., for
his
help
in
obtaining
data for
this
project. Professors Harry Roberts
and
Gary Eppen, Graduate
School
of
Business, University
of
Chicago,
contributed valuable advice.
Moula Cherikh and Xiaomei
Xu, of Tantalus, Inc., performed
com-
puter analyses. We acknowledge the thoughtful
and
persistent efforts
of the editors and referees.
References
Adler, P. S. and K. B. Clark, "Behind
the Learning Curve: A Sketch of
the Learning Process," Management
Sci., 37, 3 (1991), 267-281.
,
"NUMMI,
Circa
1988,"
Department
of
Industrial Engineering
and Engineering Management,
report, Stanford University, Stan-
ford, CA, June,
1991.
Argote, L., S. Beckman, and
D. Epple, "The Persistence and Transfer
of Learning in Industrial
Settings," Technical Report, Carnegie
Mellon
University,
Pittsburgh, PA, 1990.
Bohn, R., "Noise
and
Learning
in Semiconductor Manufacturing,"
University of California report,
San Diego CA, March, 1991.
Camm, J. D.,
T.
R. Gulledge,
and N.
K.
Womer, "Forgetting:
A
Pro-
duction Line
Representation,"
presented
at TIMS
/
ORSA Na-
tional Meeting, Chicago, IL,
May (1993).
Dutton, J.
M. and
A.
Thomas,
"Progress Functions
and Production
Dynamics," report, (Graduate
School of Business Administration,
New
York
University,
New
York, May, 1982).
,
and
J.
E.
Butler,
"The
History
of
Progress
Functions as a
Managerial Technology,"
Business History Rev., 58,
2
(1984),
204-
233.
Feller, W.,
"On the
Logistic
Law of
Growth and
Its
Empirical
Verifi-
cations
in
Biology," Acta Biotheoret.,
5 (1940), 51-66.
Fine,
C. H. and E.
L.
Porteus,
"Dynamic
Process
Improvement," Oper.
Res., 37,
4
(1989), 580-591.
"Hands-On, How-To,
Kaizen and
JIT," Workshop,
Kaizen
Programs,
University
of
Dayton, Dayton,
OH,
July 13-16,
1992.
Harmon,
R.
L.
and
L. D.
Peterson, Reinventing
the
Factory,
Free
Press,
New
York,
1990.
Imai, M.,
in
(Kaizen
Institute of
America,
701
Dragon, Austin, TX).
Kantor,
P. B. and W. I.
Zangwill,
"Theory
of the
Learning
Rate
Budget," Management Sci.,
March
(1991),
315-330.
and
,
"Studies of
a
Theory
of
Continuous
Improvement,"
report, Rutgers University,
New
Brunswick, NJ,
1996.
Levy,
F.
K., "Adaptation
in
the
Production
Process," Management
Sci.,
11, 6 (1965),
B136-B154.
Mazur, J.
E. and R.
Hastie,
"Learning
as Accumulations:
A
Reexami-
nation of the
Learning
Curve," Psychological Bulletin, 85, 6 (1978),
1256-1274.
MANAGEMENT SCIENCE/ Vol. 44, No. 7, July 1998
919
ZANGWILL
AND
KANTOR
Toward
a
Theory of Continuous
Improvement
and
the
Learning
Curve
Mishina, K., "Behind the Flying Fortress Learning Curve," report, Har-
vard Business School, Cambridge, MA, 1987.
Murray, J. D., Mathematical Biology, Springer-Verlag, Berlin 1989.
Muth, J. F., "Search Theory
and
the Manufacturing Progress Func-
tion," Management Sci., 32, 8 (1986), 948-962.
Newell,
A. and
P. S. Rosenbloom, "Mechanisms of Skill
Acquisition
and
the
Law
of Practice," Report, Department of Computer Sci-
ence, Carnegie-Mellon University, Pittsburgh, PA, 1981.
Roberts, P.,
"A
Theory
of the
Learning Process," J. Operational
Res.
Society,
34
(1983),
71-79.
Sahal, D.,
"A
Theory
of
Progress Functions,"
International Institute
of
Management, Berlin, Germany, 1942.
Schneiderman,
A.
M., "Setting Quality Goals," Quality Progress, April
(1988),
51-57.
Schonberger, R. J.,
World
Class Manufacturing, Free
Press,
New
York,
1986.
Smith, B. and W.
Zangwill,
"Total
Customer Satisfaction: The Moto-
rola
System," Report,
Graduate School of
Business, University
of
Chicago, Chicago, IL,
1988.
Stata,
R., "Organizational
Learning-The Key
to
Management
Inno-
vation," Sloan
Management Rev., 30,
3
(1989), 63-74.
Venezia, I., "On the Statistical
Origins
of
the
Learning Curve," Euro-
pean
J.
Oper. Res.,
19
(1985), 191-200.
Wright,
T.
P., "Factors
Affecting
the Cost
of
Airplanes,"
J.
Aeronautical
Sci.,
3
(1936),
122-128.
Zangwill, W. I., "The
Limits of Japanese
Production Theory," Inter-
faces, 22, 5 (1992), 14-25.
,
Lightning Strategies for
Innovation,
Lexington,
Division of
Simon
and Schuster, New
York, 1993.
Accepted
by Ralph
Katz;
received November
1993.
This
paper
has
been with the
author
24 months
for
4
revisions.
920
MANAGEMENT
SCIENCE/Vol.
44,
No.
7,
July
1998
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