ALTPLAN
Microcomputer
Software
for
Developing
and Evaluating
Accelerated
Life Test Plans
Karen L. Jensenf
Department 0 Statistics
Iowa State University
November 1985
References.
CONTENTS
Introduction.
General overview of accelerated
life testing.
PurposeofALTPLAN
Getting started.
Preparation
of input values.
Hardwarerequirements
Starting
the program
Programorganjzation'
'
Diagrams of the structure
of the program.
Brief
description
of MAIN menu options.
Description
of program options.
Quit-donewithALTPLAN
Input (or change) specifications
of testing
situation.
Develop accelerated
life
test plans.
Evaluate
accelerated
life
test plans.
Sample session with ALTPLAN
Getting started.
Enteringinputvalues
Developingplans
Evaluatingtheplans
Exiting
from the program.
Remarks about the sample session.
1
1
4
4
4
5
5
l7
9
11
11
..12
16
19
22
22
22
28
36
38
39
Appendix
A.
DESCRIPTION OF TYPES OF ACCELERATEDLIFE TESTS
41
B.
INITIAL
43
c.
SUMMARY
OF PROGRAM
LIMITATIONS
D.
AREAS FOR POSSIBLE IMPROVEMENT
E.
STATISTICAL REFERENCESAND COMPUTATIONALFORMULAS.
INSTALLATION OF ALTPLAN
44
47
Computational
formulas.
47
i
distribution.
1.
INTRODUCTION
General
overview
An accelerated
tion
life
about the
For example,
percentile
test
time
stress
to
which
signed
to
operate
of
time
that
to failure
or
is
is
It
is
exposed
for
have a long lifetime
ditions,
it
may be impossible
at these
In order
the
length
of the
experiment
lating
is
at higher
called
type
of
extrapolation
mean that
intends
stress
design
and fewer
by the
end of
the
level
test.
If
level
when operated
make these
test
can be
stress
conditions.
de-
any other
to the
length
of
product
is
or
design
stress
during
about the
time
without
accelerated"
cona test
to
fail-
increasing
by running
is then
This
is
As in
tI
Inference
failure
product
material
inferences
to
a
some type of
enough failures
to make inferences
to
or
under
product
to estimate
of
a limit
the
or
the time
of stress.
is often
informa-
the
made by extrapo-
type
of extrapolation
in stress.
extrapolation
few failures
bution
material
levels.
in time.
to estimate
the
a life
extrapolation
Another
is
test,
back to the
and that
to observe
conditions
obtain
test
assumed that
the
a life
to
life
to
there
to
of some material
related
situation,
available
is
a particular
expected
performed
performed
may run an accelerated
under
experimental
testing
distribution
product
it
life
an experiment
distribution.
material
type
is
a researcher
of this
of the
of accelerated
the
than
test,
that
The limit
are
may be necessary
on available
observed
at
lOOPth percentile
lOOP% of the
one would
units
low stress
1
life
for
the
testing
test
may
If
one
conditions.
of the time
at a certain
need to
the estimate.
time
in
extrapolate
to
failure
stress
in
distrilevel
time
to
fail
make
With
a fixed
in stress
is
length
that
required
is
are
necessarily
of time
required
inversely
increased.
dangerous,
it
is
designing
a test
low the
researcher
the
amount of
related
-if
important
to
of
balance
these
balance
test
amount of extrapolation
extrapolation
one is
each type
Various
to
testing,
and the
Since
plan.
for
plans
the risks
in
decreased,
extrapolation
types
of
time
the
is
other
is
potentially
extrapolation
have been developed1
for
that
a particular
in
that
testing
alsitu-
ation.
In
developing
these
test
plans,
some simplifying
assumptions
are
made:
.there
is a single
.there
is
accelerating
a linear
relationship
and an appropriate
.the
time
to
the Weibull
To specify
for
the
transformation
failure
log
of the stress
distribution
a particular
follows
testing
of
time
an appropriate
2
the
design
stress
the
linear
relationship
variable,
a particular
situation,
transformation
value
stress
may still
the percentile
of the
the number of units
1 See, for
failure
and
form such
one must provide
for
the
stress
as
values
and the
highest
between
log
time
variable,
stress
to
value
failure
example,
Meeker
for
which
and trans-
hold,
time
to
failure
distribution
that
estimated,
4.
to
variables:
1.
3.
between the
or the Lognormal.
following
formed
stress
available
(1984)
for
the test,
and Meeker and Hahn (1985)
2 -
is
to
be
1.
5
the
assumed form of the time
6
guesses
stress
7
values
guess value
8
for
the
of time
is
these
values,
specified
the particular
Since
types
life
test
variance
ified
3.
plans
of
test
test
plans
stress
plans
design
time
(the
and highest
to
failure
censoring
dis-
time).
may be developed.
at which
units
units
are
to these
may be developed,
The following
affects
the
experiment
if
which
the
occur
at certain
Robustness
idea
of
of
are criteria
the
size
tests
of
these
are
estimate
of the
at a desired
number
that
of
in the
the
of experimental
The expected
specifications
for
test
levels
variance
accuracy
The basic
at the
for
A test
tested
and
levels
comparisons
comparing
must
accel-
plans:
The resulting
2
possible
allocation
several
of failure
spread parameter
available
by_the
be made between plans.
erated
the
and
length
distribution,
(Pn and PH' respectively),
tt'ibution,
Given
plan
of the probabilities
to failure
level
failures
of the percentile:
sample necessary
at
each
based may be inaccurate
to departures
of
planning
the
testing
to obtain
spec-
of confidence
level
numbers are too small,
stress
this
the
of
stress
in
assumptions
and failures
the
upon
may not
levels
from the
assumed input
an accelerated
situation
may be compared in various
-3
test
and use these
ways
-
life
values
is
to
to
take
develop
the
test
Purpose of ALTPLAN
ALTPLAN is
evaluation
a computer
program
of accelerated
life
of several
paring
will
these
possible
plans
generate
the
and Hahn (1985)
alternative
2.
types
of
and will
is
test
plans
according
that
useful
plans
plans
also
the
means of
criteria
development
by Meeker
the user
to
the
evaluating
mentioned
presented
allow
the
ALTPLAN allows
and provides
to
in
developand com-
above.
(1984)
and
ALTPLAN
and Meeker
modify
plans
or
above)
are given
specify
plans
GETTING STARTED
2.1
Preparation
The values
to
of
of the
input
following
ALTPLAN (default
The
type
values
of
variables
values
(described
are given
transformation
as in-
in parentheses):
to
applied
original
stress
values
(Linear).
2.
The design
stress
value
assumed life-stress
(Standardized
3.
0.000,
of the time to
failure
4.
The total
number of units
5.
The assumed form of the time to
6.
Guess values
7.
The value
8.
the
of the
stress
time
for
the
which
spread parameter
(1.000)
-
test
to
the
hold
is
to be
(1000).
distribution
probabilities,
-4
be expected
distribution
failure
(1.000)
The censoring
at which
(0.10).
available
failure
value
1.000)
at the
but ion
design
stress
can still
estimated
for
highest
relationship
values:
The percentile
and the
in the
(NONE).
PD and PH (NONE).
time
to
failure
distri-
1.
key.
Hardware
requirements
ALTPLAN may be run on an IBM PC, AT or
and a minimum of
256K RAM.
XT with
ALTPLAN requires
and an 8087 Math Coprocessor
at
least
DOS 2.1
An 8D-column printer
one disk
(or
later
drive
version)
is recommended,
but
not necessary.
Starting
the program
Before
procedure
for
Place
starting
is off,
If
the computer
is
turn
already
reset
from menus
program
The user
will
<CONTROL><ALT> <DEL> simul-
running
ALTPLAN by typing:
the
1 will
the
appear
directions
a menu-driven
operation
given
program,
by making
may make a selection
most cases,
follow
press
begin
to the
2 <ENTER> may be known to
guide
instructions.
it on.
in figure
ALTPLAN is
number corresponding
In
an installatiop,
ALTPLAN
screen
controls
B for
time,
the machine.
Use ALTPLAN by following
user
first
A.
on,
When the A> prompt appears,
each screen
this
in drive
the computer
and the title
the
See appendix
If
to
for
the program
A>
4
program
ALTPLAN diskette
taneously
3.
the
must be completed.
Instructions
2
runni~g
the
option
and then
a
terminology
5
bottom
meaning
series
pressing
as <RETURN>.
used in
the
by typing
menu has a default
some users
at
The
of
the
choices
the
the
(D)
that
of
single
<ENTER>2
option
terminology
IBM documentation.
which
in
AlTPlAN
"icrocolputer SoftNare
for
Developing and EvaluatirlY
Accelerated Life Test Plans
Version 1.0 -Novelber 1985
Press ENTERto continue
Figure 1:
may be selected
a program
ways option
5
If
the
by simply
Title
pressing
segment and move back
number 1.
a printer
is
up in
is the
on paper
command.
To obtain
time,
press
begin
everything
to
default
may be obtained
a copy of
<CONTROL><PRTSC> simultaneously.
appears
To stop
<CO~7ROL><PRTSC> again
-
on the
this
leave
is
al-
option.
the
<SHIFT> <PRTSC> simultaneously.
that
-6
The option
the menu structure
output
at a particular
printing
<ENTER>.
In many cases it
available,
IBM PC print-screen
screen
screen,
printing,
using
screen
To
press
press
3.
3.1
PROGRAM ORGANIZATION
Diagrams
Figure
of the structure
2:
Diagram of the
Figure
3:
of the program
structure
Diagram
of the
7
of the entire
Input
Module
program
Figure 4:
Figure 5:
Diagram of the Plan Development Module
Diagram
of the Plan Evaluation
8 -
Module
3.2
Brief
description
of MAIN menu options
The MAIN menu (shown in
figure
6) is the
routines
on the
main
user
Each option
may choose
menu options
specific
central
menu has
activities.
Brief
starting
point
a submenu with
descriptions
for
all
which
of
the
follow
ALTPLAN
I1AIN I1ENU
1.
2.
3.
4.
Quit -done with ALTPLAN
Input (or change)specifications of testing situatiorl
Developacceleratedlife test plans
Evaluateacceleratedlife test plans
Enter numberof selection
\.
;
Figure 6:
1.
QUIT -DONE
With
this
Main menu
WITH ALTPLAN
option
the
iting,
the user
will
values
and test
plans
user
may exit
be given
-9
from the
a chance to
-
program
save the
Before
current
exinput
3.
ly.
tion.
2
INPUT (OR CHANGE) SPECIFICATIONS OF THE TESTING SITUATION
With
this
define
option
the
them in
ously
the
testing
through
these
saved in a disk
may enter
situation.
the
by ALTPLAN.
of plans,
user
Values
keyboard
If
plans
there
If
of the
by reading
a file
are
any plans
currently
they
variables
may be entered
or
and their
file.
values
that
by typing
created
corresponding
input
are not saved,
they
in
previthe
values
list
may be
are discarded.
DEVELOP ACCELERATEDLIFE TEST PLANS
In this
section
of the
of
plans.
Ten types
test
The user
or
There
ticular
4
may modify
completely
plan
program the user
plans
is
of
any plan
specify
also
plans
this
generated
includes
section
display
sensitivity
of
automatical-
has been previously
stress
in
types
values
this
devel-
and allocations
section
to
of
delete
par-
from consideration.
are
each plan.
the
several
may be generated
that
an option
EVALUATE ACCELERATED LIFE
As plans
plans
may develop
TEST PLANS
in
the variance
More information
of the program:
the
the DEVELOP section,
of the
estimate
for
evaluation
a sample
characteristics
of each type
size
of plans,
of plan
10 -
to the
a display
of
of the percentile
the
for
may be generated
calculation,
and an analysis
assumed failure
in
detailed
of
distribu-
the
4
DESCRIPTION OF PROGRAM
OPTIONS
4.1
Quit
-done
The screen
with
in figure
ALTPLAN
7 will
be displayed
when this
option
is
chosen
QUIT -DONE WITHALTPLAN
Decide Nhat to do with current inputs and plans
1.
2.
Before exiting, save specifications and test plans
Do nDt save specifications and test plans ID)
Enter number of selection or <ENTER>
for default ID)
,/
Figure 7:
.Selection
of
the
(but
1 will
testing
not
deleted)
asked for
a file
Selection
2 will
allow
the user
situation
with
to save the
and all
this
name under
allow
Quit menu
plans
testing
which
the user
gram
11 -
current
that
have
situation.
specifications
been developed
The user
will
be
to save the data.
to
immediately
exit
from the
pro-
specifications.
Input
(or
change)
Specifications
developed
of the
or
specifications
testing
situation
evaluated.
Most of
need not
be changed before
plans
the
to
time
have default
of testing
failure
distribution
values,
so they
situation
must be entered
the
inputs
have
default
can be developed.
and the
plans
are
values
that
The assumed form of
failure
must be entered
before
probabilities
do not
any plans
may be de-
before
veloped
Whenever
situation,
any changes
the plans
be directly
are
made in
developed
compared to
under
the plans
The user
has
of the
testing
in a disk
before
the
list
may be read back into
the
program
There
file
are
two
MAIN menu is
plans,
chosen.
as is the
in figure
possible
are plans
method of
input
inputs
gives
user
could
of
testing
situation
saving
the
cannot
under
the
new
plans
and the
they were
developed
is cleared.
If
this
saved,
data
time.
when the
no plans
program
the
under which
appear
are
testing
be developed
at another
menu that
similar
to
to
first,
in the
as above,
and must
to
enter
type
the user
the
could
currently
and plans.
Selecting
the
of plans
there
will
option
situation
case when the
main menu is
there
If
which
of
INPUT option
currently
has just
in
on the
the
been started,
list
of
the
menu
8 appears
The second
the
menus that
specifications
the former
the
specifications
the
the
in
Thus,
input
values
option
list
appear
but
adds another
of plans,
also
for
the
of changing
-12
(from
variables
all
the user
choose whether
the menu in figure
by keyboard
when INPUT is
chosen
question.
on
If
must choose the
to save
the
cur-
9 is presented.
either
menu) will
allow
The menu in figure
the values
or
just
10
some of the
quence.
INPUT (OR CHANGE)
SPECIFICATIONSOF TESTINGSITUATION
"ethDd Df input?
1.
2.
Enter input by keyboard (D!
Enter input from file
Enter numberof selection or <ENTER;for default ID)
>
Figure 8:
values
user
Option
1 (ALL) will
Option
2
Selecting
a file
to
The user
will
ALTPLAN, that
sible
enter
containing
file
take
(SOME) leads
to choose particular
Initial
the user
to
variables
input
input
be asked
input
the
menu in
from a file
the
the entire
figure
11,
input
se-
allowing
the
to enter
specifications
for
through
There
names.
-13
allow
and test
name of
is to be retrieved.
~1ill
-
the
the user
plans
file,
is no facility
to retrieve
from diskette.
previously
for
saved
listing
by
pos-
INPUT (DR CHANGE)SPECIFICATIONSOF TESTIN6SITUATION
"ethod
of input?
I Save current plans? (if
any)
1. Enter input by keyboard -first,
save current plans
2. Enter input by keyboard -do not save plans ID)
3. Enter input from file
-first,save
currerlt plans
4. Enter input fro. file
-do not save plans
Ente! nulber of selection
or <ENTER>for
)
Figure 9:
Input
14
menu
default
ID)
ENTERI NPUTBY ~:EYBOARD
1.
2.
ChangeALL of the input values ID}
ChangeSO"Eof the input values
Enter numberof selection or <ENTER)
for default IDJ
":'
Figure 10:
An input
-15
-
submenu
CHOOSE
THE VALUESYOUWISH TO "ODIFY
1. Modifyno lore values (D)
2. Life/stress relationship
3. Stress values andtheir input/output forlls)
4. Percentile to be estimated
5. Salple size
6. Distribution of ti.e-to-failure
7. _Failure probabilities
B. Value of spreadparaaeter9.
Censoringtile
Enter number of selection
)
Figure
4.3
Develop
When the user
accelerated
selects
11:
life
this
or (ENTER;.for
An input
test
default
(DJ
submenu
plans
option
on the
MAIN menu, the menu in
figure
12 appears.
.Selection
1 simply
tines
and back to the
Selection
2 leads
generate
various
to
3 allows
developed
allows
in
and modify
the user
to
the user
out of
the plan
figure
13,
development
rou-
MAIN menu
the
types
menu are described
.Selection
takes
menu in
of plans.
The types
an appendix
the
user
it.
modify
to
take
In the
the
-16
to this
first
stress
allowing
of plans
the
user
listed
to
in this
guide.
a plan
that
step,
the
values
has
already
menu in
in various
figure
ways
been
14
Once
DEVELOP
ACCELERATED
LIFE TESTPLANS
1.
Exit -returrl
2.
3.
4.
5.
6enerateplans autolatically
Kodify a plan
Specify a plan
Delete plants)
to the "AIN lenu (DJ
Enter number of selection
or <ENTER>for
default
(DJ
)
Figure 12:
all
necessary
the
user
is
modifications
given
the
the modifications
the
list
another
have
option
of
are completed,
of plans
The user
is
menu
been made to
modifying
stress
the allocations.
the plan
then
the
is
given
evaluated
the option
levels,
After
and added to
of modifying
plan
.Selection
4 allows
and allocation
first
Plan development
(Step
1),
the user
completely
specify
the
stress
values
the
stress
values
of a plan.
The user
must specify
and then
the allocation
(Step
Selection
5 allows
The user
is
the
presented
choose the plans
to
user
to
with
a
to delete.
-17
delete
list
of
2).
some of
all
the
current
current
plans
plans
and may
GENERATE
PLANSAUTOKATICALLY
1.
2.
3.
5.
7.
Exit -return to DEVELOP
lenu !D)
Generate aJJ plans, then return to plan menu
StatisticaJJy Optilum pJan4.
3 leveJ Best Standard plan
Best Co.promise plans6.
Equal ExpectedNumberFailing pJan
4:2:1 Allocatiorl plans
Enter numberof selection or ':ENTER).
for default !D)
,I
Figure
13:
Menu for
automatic
18 -
generation
of plans
MODIFYA PLAN
Step 1:
1.
2.
3.
4.
Modify stress values
"ake no changesto stress levels (D)
Add a stress level
Delete a stress level
Changea stress value
Enter numberof selection or (ENTER}for default ID)
)
Figure
4.4
Evaluate
When option
14
accelerated
4 on the
life
1 simply
.Selection
2 leads
plan.
the sample size
at
user
mula.
to
plan,
the option
After
test
returns
a specified
the particular
level
modification
the user
to
necessary
to have a specified
of
calculates,
confidence.
then the menu in
shown that
gives
necessary
the option
of performing
this
changes
a particular
amount of accufirst
16 appears,
chooses
giving
used in the sample
are
completed,
sample size.
calculation
19
15 appears.
for
The user
figure
the values
any necessary
figure
the main menu
which
of changing
the
the menu in
a routine
level
menu
plans
MAIN menu is chosen,
.Selection
racy
Stress
The user
for
another
size
a
display
is
then
plan.
the
for-
is
given
EVALUATEACCELERATED
LIFE TESTPLANS
1.
2.
3.
4.
Exit -return to "AIN lenu !D)
Calculate necessarysalple size
Seedetailed display of test plans
Perforl sensitivity analyses
Enter numberof selection or (ENTER)for default ID)
)
Figure 15:
Selection
3 allows
teristics
of particular
hIes
the
2 and 10 in
following
for
the user
the
stress
ii)
proportional
iii)
number of units
iv)
failure
v)
expected
erated
value
see detailed
plans.
paper
The display
of Meeker
menu
displays
follows
of the
the
and Hahn (1985)
charac-
form of taand includes
level:
in original
and standardized
units,
allocation,
allocated,
probability,
and
number failing.
4 allows
plans
to
each stress
i)
Selection
Plan evaluation
to the
the user
to
analyze
the
guesses made about the
20
sensitivity
time
to
of
failure
the
gen-
distri-
plans.
CALCULATENECESSARY
SAKPLESIZE
Makedesired changesin current default values
1.
2.
3.
"ake no (lore) changes ID)
Value of the spread paraleter
Percent error in estilate of percentile4.
Probability of staying within percent error
Enter nulber of selection or <ENTER>
for default (DI
>
Figure 16:
bution.
to
Version
the
If
lated
of
assumed distribution
is
automatically
the
distribution
distribution
under
calculated
is
analogously.
the
if
guess values
generated
variance
to the
variance
of the
available
21
variances
is
in
the
of
R(WLfLL)
of
failure
of
the
list
is
a plan
calcu-
generated
under
of a plan
distribution
assumed distribution
The analysis
sensitivity
of
and evaluated
Lognormal
the
plan
is Weibull,
assumption
the
of
A ratio
of the
assumption
R(LW/WW) is
to
ratio
formula
an analysis
the distribution.
the
evaluated
plans
ALTPLAN offers
each
a Weibull
defined
used in the sample size
for
R(WLfLL)
normal
and
1.0
assumed form of
calculated
under
Values
a Log-
generated
assumption.
is Lognormal
sensitivity
probabilities
of
is
not
and
input.
(e.g.
5.
SAMPLE SESSION WITH ALTPLAN
5.1
Getting
Consider
the
Hahn
pared,
started
adhesive-bonded
(1985)
the
power
Following
values
of
the
the
element
list
variables
of
example
input
that
discussed
values
specify
that
the
by Meeker
must be pre-
testiag
situation
are as follows:
Model of life/stress
relationship
Highest stress valueDesign stress value
Percentile
to be estimated
Sample size
Assumed form of time to failure
distribution
Failure
probabilities:
PD
Arrhenius
120 degrees
50 degrees
.10
300 units
Weibull
.001
.900
Value of spread parameter PH
Censoring time
The program is
2 is
testing
started
chosen
Figures
input
17 through
specifying
failure
not
in
menu to
instructions
given
enter
the
input
routine
above and op-
specifications
of
the
of censoring
either
values
their
for
of
adhesive-bonded
power
shown are those
for
probabilities,
The routines
entry
main
to the
21 show examples
the
Screens
tion,
183 days
situation.
Entering
ues
1.000
according
on the
C
C
original
entry
problem
The val-
are
of sample size,
given
as
distribu-
and spread parameter.
entry
time
element
screens.
of
the
require
desired
explanation.
units
stress
Stress
temperature)
22
value
form(s)
and for
values
may be given
or
standardized
in
The current (default) lodel for life/stress
relationst:ip is
LINEAR
CHOOSE
MODELFORLIFE/STRESSRELATIONSHIP
1. Linear:
2. -Inverse power law:
3. Arrhenius:
X= T
X = login
X = -1 ! (T + 2731
Enter numberof selectiori or <ENTER}
for defaul t !D)
) 3
Figure 17:
units,
est
where standardized
stress
sively
input
tailed
is
with
of
stress
to
values,
values
displays.
design
(see formula
standardized
standardized
lead
1.000
Entering
and/or
Since
units
in
the
all
three
options
for
stress
values.
Figure
18
choice
when entering
in the
program until
input
it
is
life/stress
stress
is
0.000
in appendix).
or
see
user
and standardized
The user
stress
will
form(s)
values
always
original
possibilities
for
input
changed in the
holds
routine.
in
for
in
de-
values
in
mentioned
The user
choice
input
units
and detailed
options.
and the
units
be shown stress
the
shows these
23
in
high-
may work exclu-
may choose to use original
displays,
values
model
above
output
of
makes this
all
routines
The current (default) choice of fortis)
value input and output is:
INPUT: std
OUTPUT:std
for stress
CHOOSE
STRESSVALUEFOR" FOR INPUT ANDDETAILEDOUTPUT
!std=standardized units, Driginal=Driginal
1. -INPUT:std
2. INPUT:std
3. INPUT:original
unitsj
OUTPUT:std
OUTPUT:original and std
OUTPUT:original and std
Enter numberof selection or ':ENTER>
for default ID)
> 2
Figure 18:
If
0.000
option
1 is
and the
highest
or 3 is chosen,
valt'es
the
way of
failure
testing
the test.
tionship
the
is
second
step
time
the
is
(1984).
choice
of whether
for
is
stress
stress
automatically
changed,
to
is
set
enter
of changing
probabilities
censoring
After
the user
automatically
effects
The failure
Meeker
design
stress
probabilities
between
foTm(s)
values
automatically
to 1.000.
design
set
If
to
option
2
and highest
stress
the option
of hav-
units
When censoring
ing
chosen,
the
in original
Entering
the
time
adjusted.
the
length
are adjusted
and the
adjustments
to use the
is given
adjusted
values.
-24
This
of time
according
failure
probabilities
are made,
the user
values
or
return
is
a simple
available
to
the
for
rela-
given
is
given
by
the
to the unadjusted
Current stress values
design stress:
highest stress:
0.0000
1.0000
Type in new value or press ENTERto keep current value
desiQ"stress:
50
highest stress:
120
Figure 19:
Figure
22 shows the
display
Entering
of the
25
stress
input
'values
values.
The current percentile to be estilated is 0.10000
Type in new value or press ENTERto keep current vilue
Percentile to be estilated:
Figure 20:
Entering
the percentile
26
to be estimated
The current cerlsoring tile
is
1.0000
Type in new value or press ENTERto keep current va]ue
Censoring tile:
183
Figure 21:
Entering
the
27 -
censoring
time
After
I
5F'ECIFICATION5
OF THE TESTIN6SITUATION
Life/stress
relatiorlship:
:
Distribution of
tile to failure:
ARRHENIUS:
WElBULL
I
I
Stress values
:
Design:
Highest:
Failure probabilities
50.0000:
120.0000:
Percentile
to be esti.at~d-
At design stress:
At highest stress:
:
:
0.10000
0.00100
0.90000
Valueof
spreadparaleter:
1.0000
I
I
Sallple size
:
300
Censoringtille
183.0000
Press ENTERto continue
Figure
5.3
Developing
input
Taking
It
to
the
veloped.
of
it
"generate
plans
at the
V(P) for
tistically
The
have been entered,
to
variance
interest
ratio
of
causes
plans
input
values
of
the
the
set
gives
stress.
particular
possible
of plans
in
the value
maximum likelihood
design
is
automatically"
the
The column headed "V(P)"
ymptotic
of
values
all
Display
plans
option
generate
22:
to
develop
plans.
and then the
option
figure
of n/o2
estimator
to
the value
times
of the
The column headed
plan
23 to be de-
of
t'Ratio"
the
as-
percentile
gives
V(P) for
the
the
sta-
optimum plan
Of
specJ.
the process
1
yap
"
an
of entering
option
stress
is
now chosen.
values
28
Figure
Figures
24 and
26 shows a display
25 show
of the
requested.
ACCELERATED
LIFE TESTPLANSASSU~IN6A WEIBULL DISTRIBUTION
P=().10000 PD=O.OO100 PH=O,
90000
Plan i Type:
Nulber: Code:
1
2
or
,)
4
5
b
1
B
9
10
Stress levels:
low
"iddle
High:
20PT 0.682
38S
0.571
38C10 0.b63
3BC20 0.b38
3BEE 0.b73
3FT100 0.609
3FT90 0.548
3FT80 0.487
3FT70 0.42b
3FTbO 0~365
0.706
0.333
0.621
0.531
0.651
0.571
0.571
0.571
0.571
0.571
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.786
0.831
0.819
0.837
0.804
0.774
0.744
0.713
0.699'
Allocation:
"iddle
High:
low
Precision
VIP) Ratio
0.294 120.
0.333 138.
0.279 125.
0.269 130.
0.121 154.
0.143 146.
0.143 150.
0.143 159.
0.143 172.
0.143 186.
0.333
0.100
0.200
0.228
0.286
0.286
0.286
0.28b
0.286
1.000
1.148
1.043
1.08b
1.283
1.216
1.248
1.324
1.431
1.554
Press ENTER
to continue
Figure 23:
plan
with
tering
the stress
the allocation
The display
It
in
of the 3FTI00
plan
specified
3,
4,
plan
plans
27 shows the process
completely
when the
"delete
specified
plans
of enplan.
option
generated
plans,
(plan
plan
code M3FTI00) , and the
11 with
12 with
plan
type
by typing
30 shows the
new list
29
type
code USER)
those
numbers
of plans
a modified
is
automatically
accomplished
Figure
current
28 shows the
29 appears
above (plan
and 5 is
the question.
figure
of
Figure
entered.
and figure
shows the
sian
2,
values
Display
Deleting
in
ver-
plans
response
to
SPECIFYA PLAN
Step 1:
Specify stress values
Enter the nulber of levels of stress you wish to
have in this test plan or press ENTER
to have 3 levels
Nulber of levels:
Figure 24:
4
Entering
the number of stress
30
levels
ENTERTHE STRESSVALUES
Enter 4 stress values in standardized fori:
(You lay enter these values in any order
Stress values:
.8.Q
Figure 25:
.7
Specifying
31
stress
values
ABBRcVIATEDDISPLAYOF PLANNU"BER12
ASSUMED
WEIBULLDISTRIBUTION,
P=O.10000 PD=Q.OO100
PH=O.90000
Press ENTERto contirlue
Figure
26:
Display
of the plan
32 -
being
spec.ified
SPECIFYA F'LAN
Step 2:
Specify the allocation
Enter the allocations you wish to have at each stress
level in response to the prompts below.
For each level you Nill be shownthe stress value and
the initial allocation of zero. Type in the allocatiori
as a nulber betweerlzero and one.
If you just type ENTER
the allocation of zero will stay.
Stress level
1
Standardized stress
value = 0.700
Allocation = 0.000
Stress level 2
Standardized stress value = 0.800
Newallocation:
.2
Allocatiorl = 0.000
NewallDcatiDn:
Figure
.5
27:
Entering
33 -
the
allocation
ABBREVIATED
DISPLAYOF PLANNU"BER12
ASSUMED
WEIBULLDISTRIBUTION,
P=O.lOOOOPD=O.OOIOO
PH=O.90000
Stress:
level:
nulber :
-50.0000
1
2
3
4
Stress in :
: Proportion
original:
Standardized:of test ur,its
units:
stress:
allocated
96.0087
103.6736
111.6636
120.0000
0.000
0.700
0.800
0.900
1.000
0.50
0.20
0.20
0.10
The plan has nowbeen spe~ified.
It will be evaluated and addedto the set
of plans already gerlerated.
Press ENTER
to continue
Figure 28:
The completed
34
plan
ACCELERATED
LIFE TESTPLANSASSU"IN6A NEIBULLDISTRIBUTION
P=O.10000 PD=O.OOlOO PH=O.90000
Plan: Type:
Nulber: Code:
1
2
3
4
5
6
7
8
9
10
11
12
Stress levels:
low "iddle High:
20PT 0.682
3BS
0.571 0.786
3BC10 0.663 0.831
3BC20 0.638 0.819
3BEE 0.673 0.837
3FTI00 0.609 0.804
3FT90 0.548 0.774
3FT80 0.487 0.744
3FT70 0~426 0.713
3FT60 0.365 0.699
"3FT1000.500 0.804
USER 0.700 12 lore)
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
low
Allocation:
Precision
"iddle High: VIP) Ratio
0.706
0.333 0.333
0.621 0.100
0.531 0.200
0.651 0.228
0.571 0.286
0.571 0.286
0.571 0.286
0.571 0.286
0.571 0.286
0.571 0.286
0.500 12 lore)
0.294
0.333
0.279
0.269
0.121
0.143
0.143
0.143
0.143
0.143
0.143
0.100
Enter the nulbers of the plans you Nish to delete!
separated by spaces: 234 5
Figure 29:
Before
35
plans
are deleted
120.
138.
125.
130.
154.
146.
150.
159.
172.
186.
163.
178.
1.000
1.148
1.043
1.086
1.283
1.218
1.248
1.324
1.431
1.554
1.361
1.482
ACCELERATED
LIFE TESTPLANSASSU"IN6 A WEIBULL DISTRIBUTION
P=O.10000 PD=O.OOlOO PH=O.90000
Press ENTERto continue
After
Figure 30:
5.4
Evaluating
The plans
the
pIa:\'
generated
and figure
are deleted
the plans
developed
" evaluate
plans
plans"
in the previous
option
when the
section
may be evaluated
on the main menu
sample
32 shows the detailed
size
calculation
display
36
of plan
Figure
is
6
by choosing
31 shows the
requested
for
dis-
plan
6
SA"PLESIZE DETER"INATION
Percentile to be estilated
Value of the spread paraleter
Percent error in estilate of percentile
Probability of staying within percent error
Distribution of tile to failure
PD=O.OOlOO
Test plan used:
REQUIRED
TOTALSA"PLESIZE:
0.10000
1.0000
100.00
0.9500
WEIBULL
PH=0.90000
1169
Press ENTERto continue
Figure 31:
Sample size
37
determination
DETAILEDDISPLAYOF PLANNUKBERb
ASSU"EDWEIBULLDISTRIBUTION,
P=O.10000PD=O.OO100
PH=O.90000
Stress:
in original:
units:
: Proportion: Nulber of :
: Expected
Standardized:
of
: test units: Probability: numberof
stress:
test units: illocated : of failure :test units
:
: allocated:
50.0000
89.2952
104.0235
120.0000
0.000
0.609
0.804
1.000
:
--0.00100
0.57
171
0.29
85
0.14
42
: failing
18
33
37
0.11
0.40
0.90
Press ENTERto continue
Figure
Exiting
user
wil]
Detailed
display
of a plan
from the program
may request
saved before
32:
exiting
be asked for
that
the
from the
plans
program
a filename
38
developed
during
As shown in
this
figure
session
33,
be
the user
Figure
5.6
Remarks about the sample
This
sample session
ious
options
tion
have not
the
Saving
33:
program
is
a short
concerning
data
been shown.
by making the
the plans
and input
values
session
example of how ALTPLAN may be used.
entry,
plan
These options
appropriate
39
development,
and plan
may be explored
menu selections.
while
Varevaluarunning
ACKNOWLEDGEMENT
Program
by Dr.
code
William
for
generation
Q. Meeker.
and express
my appreciation
he provided
to me during
and evaluation
I would
for
this
like
to
of
acknowledge
the technical
project
40 -
test
support
plans
this
was provided
contribution
and encouragement
Appendix
A
DESCRIPTION OF TYPES OF ACCELERATEDLIFE TESTS
The ~ ~
statistically
ance of the estimate
.The
1 ~
~
levels
with
lowest
stress
optimum plan
the
of the percentile
standard
equal
(20PT) minimizes
plan
(3BS) has 3 equally
allocations.
value
is
Subject
to
chosen to minimize
this
spaced stress
restriction,
the variance
the
of the esti-
mate of the percentile
.The
~
compromise plans
tion
of
the
test
units
which
is
(3BC1O and 3BC20) put a specified
(.10
stress
level,
stress
levels
Subject
stress
levels
are chosen
and .20,
respectively)
chosen as halfway
to
these
at
between
the
to minimize
the
variance
the middle
low and high
the
restrictions,
propor-
low and high
of
the
estimate
of the percentile
The ~
equal
compromise
expected
plan
each stress
except
level,
the
number
that
failing
the
plan
allocations
(3BEE) is
are
like
chosen
expected number of units
a best
so that
failing
at
is
the
middle
and
same.
.The
els
high
optimized
with
~:~:1
a 4:2:1
stress
allocation
plan
allocation
levels,
of
test
respectively.
to minimize
the variance
tile,
the
stress
middle
units
to
the
of the
as close
41
estimate
as possible
stress
low,
The low and middle
are chosen
with
(3FTIOO) has three
test
stresses
of
the percen-
to
halfway
be-
justed
tween the
low and high
probability
of
percentile
that
.The
adjusted
are obtained
failure
~:~:.!
from
the
to 0.90,
stress
value
in
.The
.The
the
0.80,
modified
values
plans
as possible
(i.e.,
type
have plan
42
be at
least
4:2:1
plan
0.60
times
3FT80,
the
twice
the
by
3FT70,
reducing
stress
to
between
halfway
restrictj.on
code beginning
described
low
of
the
low
level
is
ad-
that
with
above.
code USER.
3FT60)
the
the value
The middle
type
that
PM ~ 2~~P).
(3FT90,
one of the plans
plans
stress
again to the
(any plan
by modifying
user-specified
0.70,
optimum plan.
subject
to the restriction
plans
optimized
be as close
stress
obtained
at the middle
allocation
value
high
subject
is to be estimated
stress
to
stresses
the
low and
PM ?: 2"'"P.
M) are those
3.
5.
6.
Appendix
INITIAL
This
version
two special
see the
the "device"
configuration
Put DOS 2.1
section
(or
screen
control.
In order
must be on the diskette
described
information,
1.
extended
files
The procedure
system.
INSTALLATION OF ALTPLAN
of ALTPLAN uses
the program,
B
below
will
used to
accomplish
on "Configuration
this.
version)
boot
the
For more
commands,
particularly
manual
command, in the DOS reference
a later
to run
diskette
in Drive
A and boot
the
system.
2.
Put an empty diskette
in Drive
Format the diskette
in Drive
format
A>
4.
C~1PY a file
from
the
A>
B.
B with
the command:
b:/s
DOS diskette
with
copy a:ansi.sys
b:
Remove the DOS diskette
and place
the
the
command:
ALTPLAN diskette
in
Drive
A
Copy the ALTPLAN files
onto
the
new diskette
A>
copy a:ALTPLAN.EXE b:
A>
copy a:config.sys
The CONFIG.SYS file
consists
with
the commands:
b:
of one line:
DEVICE=ANSI.SYS
7.
Now the
boot
the
new ALTPLAN diskette
the
section
system
and to
in this
(the
one in drive
run ALTPLAN.
guide
on starting
-43
-
Follow
B) can be used to
the
the program
instructions
in
Appendix
C
SUMMARYOF PROGRAM
LIMITATIONS
ALTPLAN will
levels
of
errors
if
stress
up to
for
the user
Available
power
allow
models
50 plans
each plan.
attempts
of
to
be developed
The program
to develop
life/stress
will
more than
with
up to
terminate
with
SO plans
relationship
are
failure
are Weibull
Inverse
Linear,
law and Arrhenius
.Available
distributions
of time
to
and Lognor-
mal
Limitations
on input
Variable
values
follow:
default
PD
PH
Percentile
(P)
minimum
maximum
NONE
.00001
NONE
.00001
< 1.000
.10
.00001
< 1.000
p
1000
1
1,000,000
spread parameter
1
> 0
1,000,000
censoring
1
> 0
1,000,000
sample size
Stress
10
time
values:
standardized
units
original
units
Linear model
Inverse power
Arrhenius
-10.00
-1,000,000
law
> 0
> -273
10.00
1,000,000
1,000,000
1,000,000
NOTE:
Errors
within
the
may occur
given
limits.
in plan
If
evaluation
a message such
may be the problem.
-45
even when PD and PH are
-
as "EPLAN ERROR" or
1.
3.
6.
Appendix D
AREAS FOR POSSIBLE IMPROVEMENT
Sensitivity
sensitivity
analysis:
to
misspecified
failure
prob-
abilities.
2.
Help screens
put an option
on each menu for
for
of
HELP with
the other
menu options
Evaluate
by the
plans
first
entry
4.
Add an initial
5.
Develop
a batch
provide
an option
a vector
percentiles
-determine
the
plan
in the vector
module for
version
to
testing
of
the
reduce
the
at a single
program
for
number
of
stress
condition
experienced
users
menu selections
or
that
must be made
Provide
lar
7.
for
the
output
of a data
ccllection
sheet for
plan
Provide
a listing
of
files
saved
46
previously
by ALTPLAN.
a particu-
1.
ing,"
Appendix
E
STATISTICAL REFERENCESAND COMPUTATIONALFORMULAS
REFERENCES
Meeker,
Plans
W. Q
for
Weioull
and Lognormal
Technometrics
2.
Meeker,
Life
IIA Comparison
(1984).
26,
-Some
Accelerated
Distributions
G. J.
Practical
for
Quality
Cornell
(1985).
How To Plan An Accelerated
Guidelines.
and Samuel S.
Shapiro.
Control.
COMPUTATIONALFORMULAS
1.
Transformations
x = T
Linear
Inverse
power
x = log(T)
law
x = -1
Arrhenius
where
x = transformed
T = stress
Test
and Type I Censor-
Statistical
ed by John A
Life
157-171.
W. Q. and Hahn,
Test
of
/
(T + 273)
stress
value
47
in original
units
Techniques,
American
editSociety
2.
Standardization
z =
(X -X~)
/
-~
-X
H
)
D
Z = standardized
where
3.
(X
stress
value
x = transformed
stress
value
XD = transformed
design
stress
XH = transformed
highest
stress
value
value
Variance ratio
R = V(P) / v
where V(P) = Variance
of the estimate
percentile
v = Variance
for
the plan under
of the estimate
percentile
for
of the
the
lOOPth
consideration
of the
lOOPth
statistically
optimum plan
See Meeker
the
(1984)
percentile
portional
to
for
formulae
to compute
be estimated,
the
allocation.
-48
-
stress
V(P)
as a function
levels,
and the
of
pro-
5.
4
Alternative
parameterization
The testing
for
input
dardized
Let
situation
to ALTPLAN.
(log)
t(z)
has been
tion-scale
An alternate
censoring
= F(z;O,l)
specified
time,
a,
Then ~
-1
terms
of PD and PH
parameterization
and the
be the standardized
distribution
in
uses a stan-
standardized
cdf
(p) denotes
of
tlle
the
100Pth quantile
Then,
PD = t(a)
PH = +(a-b)
determination
where Z = ZCI-IX/2)
a = value
of the spread parameter
v = Variance
r = percent
of the
error
estimate
/ 100
49 -
b
assumed loca-
of the distribution.
Sample size
slope,
of the percentile