USER MANUAL for PROGRAM " L9DYN.EXE " (DYNAMIC)
===============================================+++++++++++++++++++++++++++++++++++++++++++++
A PROGRAM FOR OPTIMIZING DYNAMIC PROBLEMS
WITH 2-4 CONTROL FACTORS with 3-LEVELS EACH
+++++++++++++++++++++++++++++++++++++++++++++
******
PART A For
a more detailed intro see Taguchi
Introduction
******
INTRODUCTION TO TAGUCHI METHOD
(FOR DYNAMIC PROBLEMS):
------------------------------------------------------
Every experimenter has to plan and conduct experiments to obtain enough and relevant data so that he can infer the science behind the observed phenomenon. He can do so by,
(1) trial-and-error approach
:
--------------------------
By performing a series of experiments each of which gives him someunderstanding. This requires making measurements after every expt.so that analysis of observed data will allow him to decide what to do next - "Which parameters should be varied and by how much". Many a times such series does not progress much as negative results maydiscourage or will not allow a selection of parameters which oughtto be changed in the next expt. Therefore, such experimentation usually ends well before the number of experiments reach a double digit! The data is insufficient to draw any significant conclusions and the mainproblem (of understanding the science) still remains unsolved.
(2) Design of experiments
:
-----------------------
A well planned set of experiments
in which all parameters of interest are varied over a specified range is
a much better approach to obtain systematic data. Mathematically speaking
such a set of experiments is complete and ought to give desired results.
However, it does not easily lend itself to understanding of science behind
the phenomenon. The analysis is not very easy (though it is easy for the
mathematician/statistician) and thus effects of various parameters on the
observed data are not readily apparent. In many cases, particularly those
in which some optimisations are required, the method does not point to
the BEST settings of parameters. A classic example illustrating the drawback
of design of experiments is found in the planning of a world cup event,
say football. While all matches are well arranged with respect to the different
teams and different venues on different dates and yet the planning does
not care about the result of any match (win or lose)!!!! Obviously, such
a strategy is not desirable for conducting scientific experiments (except
for co-ordinating various institutions, people, equipment etc).
(3) Taguchi Method :
----------------
Dr. Taguchi of Nippon Telephones and Telegraph Company, Japan has developed a method based on " ORTHOGONAL ARRAY " experiments which gives much reduced " variance " for the experiment with " optimum settings " of control parameters. Thus the marriage of Design of Experiments with optimisation of control parameters to obtain BEST results is achieved in the Taguchi Method. "Orthogonal Arrays" (OA) provide a set of well balanced (minimum) experiments and Dr. Taguchi's Signal-to-Noise ratios (S/N), as objective functions for optimisation, help in data analysis and prediction of optimum results.
Taguchi Method treats
optimization problems in two categories,
[A] STATIC PROBLEMS :
[B] DYNAMIC PROBLEMS (TECHNOLOGY DEVELOPMENT) :
If the product to be optimized has a signal input that directly decides the output, the optimization involves determining the best control factor levels so that the "input signal / output" ratio is closest to the desired relationship. Such a problem is called as a "DYNAMIC PROBLEM".
This is best explained by a P-Diagram which is shown below. Again, the
primary aim of the Taguchi experiments - to minimize variations in output
eventhough noise is present in the process- is achieved by getting improved
Linearity in the input-output relationship.
In dynamic problems, we come across many applications where the output
is supposed to follow input signal in a predetermined manner. Generally,
a linear relationship between "input" "output" is desirable.
For
example : Accelerator peddle in cars,
volume control in audio amplifiers,
document copier (with magnification or reduction)
various types of moldings
etc.
There are 2 characteristics of common interest in "follow-the-leader" or "Transformations" type of applications,
(i) Slope of the I/O characteristics
and
(ii) Linearity
of the I/O characteristics
(minimum deviation from the best-fit straight line)
The
Signal-to-Noise ratio for these 2 characteristics have been defined as;
(I) SENSITIVITY {SLOPE}:
--------------------
The slope of I/O characteristics should be at the specified value (usually 1).
It is often treated as Larger-The-Better when the output is a desirable characteristics (as in the case of Sensors, where the slope indicates the sensitivity).
n = 10 Log10 [square of slope or beta of the I/O characteristics]
On the other hand, when the output is an undesired characteristics, it can be treated as Smaller-the-Better.
n = -10 Log10 [square of slope or beta of the I/O characteristics]
(II) LINEARITY (LARGER-THE-BETTER)
:
-------------------------------
Most dynamic characteristics are required to have direct proportionality between the input and output. These applications are therefore called as "TRANSFORMATIONS". The straight line relationship between I/O must be truly linear i.e. with as little deviations from the straight line as possible.
Square of slope or beta
n = 10 Log10 ----------------------------
variance
Variance in this case is the mean of the sum of squares of deviations of
measured data points from the best-fit straight line (linear regression).
L9 ORTHOGONAL
ARRAY :
------------------------------------
L9 ( 34 ) ORTHOGONAL ARRAY
-------------------------------------------------
Columns
EXPT
NO 1
2 3
4
-------------------------------------------------
1
1 1
1 1
2
1 2
2 2
3
1 3
3 3
4
2 1
2 3
5
2 2
3 1
6
2 3
1 2
7
3 1
3 2
8
3 2
1 3
9
3 3
2 1
-------------------------------------------------
LINEAR GRAPHS FOR L9
3,4
1 *--------------* 2
Interaction between any two factors can not
be studied
******
PART B Click
here for the Taguchi
L9DYN Program files
******
THE PROGRAM FILES:
------------------
' The zipped file you receive will be L9DYNALL.zip
' It will contain
(1)
Executable Program in MS-DOS
-- L9DYN.exe
(2)
Parameter files (for my examples) -- *.par
(3)
Data files (data for my examples) -- *.dat
(4)
output files (using my examples) --
*.out
' The program executable file is "L9DYN.EXE"
' THE *.PAR AND *.DAT ARE INPUT FILES NEEDED BY "L9DYN.EXE"
' AT RUN TIME THE PROGRAM CREATES THE RESULT FILES *.OUT
'
WHAT DO THE FILES
CONTAIN :
-------------------------------------------
*.PAR i.e. Parameter
file contains the details of the control factors
(or parameters) of the experiment.
*.DAT i.e. Data file
contains the measured data obtained in the
9 experiments of the (rows of) L9-Array.
*.OUT i.e.
Output files created at the run time
WHAT YOU HAVE TO DO :
---------------------
If you wish to perform TAGUCHI experiment of your own, then
take the following steps
(i) Select the S/N ratio
' Decide whether your expriment data should be used for(ii) Prepare the Parameter file (as per instructions below)' optimizing Sensitivity or Linearity (or both)
' THEN DECIDE A filename.
' CHOOSE MY FILE dyn9-#.PAR' WHERE # = 2, 3 OR 4 (NUMBER OF CONTROL FACTORS)
' COPY dyn9-#.par filename.par
' YOU MAY USE THIS COPY FOR FURTHER STEPS GIVEN BELOW
(iii) Prepare the Data file (as
per instructions below)
PARAMETER FILE STRUCTURE :
--------------------------
(i) Select a FILENAME for your PAR file
say it is filename.PAR
Now, you start preparing
your file --> filename.PAR
(ii) Your experiment title in the first line of filename.PAR
' simply overwrite on the existing' line in my example
' do not use "," (comma) in the title line
number of control factors
-- 2 or 3 or 4
Character to represent control factor #1 -- A
name of control factor #1 -- "namestringA"
[note:
FIRST 12 CHARACTERS WILL BE TAKEN. The quote signs are not required]
Levels of factor A -- 3
name of Level #1 of A -- "stringA1"
name of Level #2 of A -- "stringA2"
name of Level #3 of A -- "stringA3"
[note:
FIRST 6 CHARACTERS WILL BE TAKEN FOR THE LEVEL NAMES]
Character to represent control factor #2 -- B
name of control factor #2 -- "namestringB"
Levels of factor B -- 3
name of Level #1 of B -- "stringB1"
name of Level #2 of B -- "stringB2"
name of Level #3 of B -- "stringB3"
Character to represent control factor #3 -- C
name of control factor #3 -- "namestringC"
Levels of factor C -- 3
name of Level #1 of C -- "stringC1"
name of Level #2 of C -- "stringC2"
name of Level #3 of C -- "stringC3"
Character to represent control factor #4 -- D
name of control factor #4 -- "namestringD"
Levels of factor D -- 3
name of Level #1 of D -- "stringD1"
name of Level #2 of D -- "stringD2"
name of Level #3 of D -- "stringD3"
Character to represent signal factor -- M
Signal name -- "SignalNameString"
Levels of Signal M -- numM (say 5)
'SIGNAL LEVELS MUST BE BETWEEN
Signal Level values -- SignalVal(1)
-- SignalVal(2)
-- . . .
-- . . .
-- SignalVal(numM)
Keyword for noise factor -- NOISE
To indicate no noise factors
-- 0
next line also -- 0
(HOW TO INCLUDE NOISE?)
' I HAVE PROVIDED EXAMPLES FOR NOISE FACTORS
' FILENAMES *.PAR HAVING "NZ" IN THEM ARE WITH NOISE FACTORS
' e.g. dy9nz2.PAR for noise
factors with 2-levels each
'
dy9nz3.PAR for noise factors with 3-levels each
' TRY it sometime in FUTURE
DATA FILE STRUCTURE :
---------------------
I have provided (dummy) data for all the examples (so the
examples should run without difficulty,
filename is dyn9-4.DAT).
The data file structure
is given below,
[blank lines] 'Optional blank lines
"STRING QUALITY-NAME" 'Name of quality characteristics
[blank lines] 'Optional blank lines
"STRING QUALITY-UNITS" 'Units of measured data
[blank lines]
'Optional blank lines
nthsignal, 1stval, 2ndval . .
. nthval 'nthsignal ==> number of signal levels
'#thval ==> valueS of signal levels
num1 'number of measurements for each expt.
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#1
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#2
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#3
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#4
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#5
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#6
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#7
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#8
val(1,1stval), ... ,val(num1,1stval), val(1, 2ndval), ... , val(num1, 2ndval), val(1, nthval), ... , val(num1, nthval) ' for expt#9
[blank lines]
[any other text for giving NOTES or COMMENTS]
HOW TO RUN L9DYN.EXE
AND OUTPUT FILES THAT YOU GET AT RUN TIME :
-------------------------------------------------------------------
At the planning stage you need to first prepare your own
parameter file by modifying a copy of one of my parameter files.
Give a name to this copy as filename.par and overwrite your
parameter info line by line. Now the parameter file the filename.PAR
is ready for use. You may use the data file I have provided, by
copying it to filename.dat.
The program "L9DYN.exe" will then use YOUR filename.PAR file
for control parameter details and filename.DAT (that you can
obtain by copy command: msdos-prompt> copy dyn9-4.dat filename.DAT
This will create 3 important
files for you,
(i) filenameB1.OUT
{ B ==> Beta {maximize the slope) }
filenameL1.OUT
{ L ==> Linearity (minimize variance }
' THIS CONTAINS THE PARAMETER DETAILS' WHICH YOU HAVE GIVEN
' PLEASE CHECK THIS AND VERIFY THAT
' THE CONTROL PARAMETERS ARE correct
(ii) filenameB2.out
filenameL2.out
' THIS GIVES THE CHOSEN
' "ORTHOGONAL ARRAY" i.e. L9 ARRAY' THIS IS ALWAYS THE SAME
' so you need not check (or worry!)
' I have checked it ONCE for ALL.
(iii) filenameB3.out
filenameL3.out
' THIS GIVES THE all important EXPERIMENTER'S LOG
(iv) The program also creates other files
' USE THIS EXPERIMENTER'S LOG TO BEGIN THE EXPERIMENT'
' PERFORM ALL EXPERIMENTS AND
' NOTE DOWN ALL DATA
'
' MEASUREMENTS ARE not REQUIRED IN BETWEEN THE EXPERIMENTS.
' MEASUREMENTS CAN BE DONE AT THE END OF all EXPERIMENTS
(which are
relevant ONLY after REAL
data exists in filename.DAT file)
These files are
filenameB4.OUT ' DATA
LfilenameB5.OUT ' DATA SUMMARY
LfilenameB6.OUT ' FACTOR EFFECTS (ANOVA , % AND F )
LfilenameB7.OUT ' AT THE CONTAINS THE PREDICTED RESULTS
L FOR OPTIMUM PARAMETER COMBINATIONSfilenameB9.OUT ' OPTIMUM SETTINGS OF PARAMETERS AND ANOVA SUMMARY
L
******
PART C
****** Click
here for the Default
Parameter files (to run with L9DYN.exe) dyn9ex.zip
HOW TO RUN THE PROGRAM " L9DYN.EXE
"
------------------------------------
ONCE THE FILES filename.PAR AND filename.DAT ARE AVAILABLE, THE
PROGRAM " L9dyn.EXE " CAN BE RUN BY ISSUING A COMMAND
L9dyn <CR> OR <ENTER>
THE FILES
filenameB4.OUT
ONWARDS WILL CONTAIN THE RESULTS OF your EXPERIMENTS
L
IMPORTANT :
PROGRAM L9dyn.EXE during a run shows
the graphical plot of the factor effects.
[note: This
requires that the terminal be of VGA type]
At run-time, FOLLOWING QUERIES HAVE TO BE ANSWERED
Q1 ==> SEE THE PLOTS /or NOPLOT
TYPE 1 / 0
TRY BY TYPING A 1 ' IF YOUR SCREEN IS VGA , NO PROBLEM
' ELSE THE PROGRAM WILL CRASH ,' START AGAIN BY TYPING L9DYN <ENTER>
' AND THIS TIME GIVE A VALUE 0
Q2 ==> PARAMETER FILENAME
(WITHOUT EXTENSION .PAR)
TYPE dyn9-4
or
TYPE DYN9-4
' MS-DOS SYSTEM DOES NOT DIFFERENTIATEQ3 ==> DATA FILENAME ( PROMPT WILL BE FOR dyn9-4.DAT )' UPPER OR LOWER CASE IN FILENAMES
' IF ANY PROBLEM, USE UPPER CASE
you may either
TYPE <ENTER>
or
TYPE dyn9-4
Q4 ==>
' THE DISPLAY GIVES YOU TWO CHOICES OF ANALYSIS
' TYPE 3 FOR S/N RATIO FOR CONTINUOUS-CONTINUOUS FOR LINEARITY
' TYPE
4 FOR S/N RATIO FOR SLOPE OR BETA
PROGRAM WILL FLASH MANY VALUES ' JUST TO KEEP YOU ENTERTAINED
' PARTICULARLY ON A slow PC-AT
AND WILL HALT THE SCROLL TEMPORARILY
AFTER RESULTS
' YOU MAY WAIT FOR 5 sec.' LOOSE PATIENCE AND
' HIT THE <SPACEBAR> A FEW TIMES
' (NO HARM DONE)
ON SPECIFIC DEMAND FROM PROGRAM
TYPE A <CR> OR <ENTER>
' IMPLIES THAT THE SCREEN IS FROZEN' DISPLAY WILL NOT SCROLL
' TILL YOU HIT <CR> OR <ENTER>
' THIS IS PARTICULARLY SUITED TO
' "STARE" AT THE FACTOR-EFFECT PLOTS
ON <CR> OR <ENTER>
' IT WILL SHOW YOU ALL THE TABLES FOR 5 SEC.' EITHER USE "PAUSE" TO EXTEND THIS
' PERIOD OR USE <SPACEBAR> TO
' MOVE ON TO NEXT TABLE
FINALLY (AFTER TABLE 4.9)
IT WILL ASK YOU TO TYPE
NOMINAL COMBINATIONS
' IF ALL PARAMETERS ARE IN THEIR' MIDDLE LEVELS, THEN TYPE
' ONLY NUMBER CODES FOR THE
' PARAMETER LEVELS, SAY
' 2,2 FOR 2-FACTOR EXPTS.
' 2,2,2 FOR 3-FACTOR EXPTS.
' 2,2,2,2 FOR 4-FACTOR EXPTS
IT WILL THEN ASK FOR THE
OPTIMUM (OR NEW) COMBINATIONS
' TYPE THE COMBINATION DISPLAYED' AS OPTIMUM , SAY
' 1,3 FOR 3-FACTOR EXPT
' 1,3,1 FOR 3-FACTOR EXPT
' 1,3,1,2 FOR 4-FACTOR EXPT
YOU MAY KEEP TYPING WHATEVER
COMBINATIONS YOU WANT TO FIND
OR
END BY TYPING
' 0,0 FOR 2-FACTOR EXPT' 0,0,0 FOR 3-FACTOR EXPT
' 0,0,0,0 FOR 4-FACTOR EXPT
PROGRAM DISPLAYS THE FILENAMES
WHERE YOU MAY BE ABLE FIND THE
VARIOUS TABLES AND PREDICTED
RESULTS.
' YOU MAY PRINT ALL FILES BY STANDARD COMMAND' PRINT filename#.out where # = 1,2,..,9
NAMING
CONVENTION FOR MY EXAMPLE FILES:
WHEN YOU ARE MAKING A RUN FROM MY EXAMPLES, THE FOLLOWING CONVENTION
IS IMPLICIT IN THE FILENAMES
I HAVE USED,
(i) SLOPE OR LINEARITY
:
----------------------
ALL FILENAMES START WITH A CHARACTERS "dyn9" (FOR DYNAMIC - WITHOUT NOISE)OR "dy9" (FOR DYNAMIC - WITH NOISE)
NEXT APPENDED STRING IS "-#" (# INDICATES NUMBER OF CONTROL FACTORS)
OPTIONAL STRING TO INDICATE NOISE PARAMETERS IS "nz" FOR NOISE
NUMBER "2" FOR 2 CONTROL PARAMETERS
OR "3" FOR 3 CONTROL PARAMETERS
OR "4" FOR 4 CONTROL PARAMETERS
EXTENSIONS ARE ".PAR" FOR PARAMETER DETAILS
OR ".DAT" FOR MEASURED (OR DUMMY) DATA
THE FILES (WITHOUT NOISE FACTORS)
HAVE FILENAMES
"dyn9-2" FOR 2 CONTROL FACTORS,
"dyn9-3" FOR 3 CONTROL FACTORS
"dyn9-4" FOR 4 CONTROL FACTORS
(with extension .par or .dat)
THE FILES WITH NOISE FACTORS
HAVE FILENAMES
"dy9nz2" FOR NOISE FACTORS WITH 2-LEVELS EACH
"dy9nz3" FOR NOISE FACTORS WITH 3-LEVELS EACH
(with extension .par or .dat)
WHOAMI
Prof. Prakash R. Apte
Reliability Engineering (EE Dept)
Indian Institute of Technology
Powai, Mumbai - 400 076, India
FAX (off) : +91-22-572 3707 (EE office)
Phone (off) : +91-22-572 2545 ask op extn. 7872
Phone (home): +91-22-572 0426
e-mail: apte@ee.iitb.ac.in
web-page : http://www.ee.iitb.ac.in/~apte
***************************************************
W I S H Y O U A L L T H E S U C C E S S
W I T H T H E " T A G U C H I M E T H O D "
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last modifed on 22-Sep-2000 / 31-Aug-2000