USER MANUAL for PROGRAM "L9.EXE"(STATIC PROBLEMS)
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A PROGRAM FOR OPTIMIZING STATIC PROBLEMS
WITH 2-4 CONTROL FACTORS with 3-LEVELS EACH
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PART A For
a more detailed intro see Taguchi
Introduction
******
INTRODUCTION TO TAGUCHI METHOD
:
--------------------------------
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 :
[A] STATIC PROBLEMS :
Generally, a process to be optimized has several control factors which directly decide the target or desired value of the output. The optimization then involves determining the best control factor levels so that the output is at the the target value. Such a problem is called as a "STATIC PROBLEM".
This is best explained using a P-Diagram which is shown below ("P" stands
for Process or Product). Noise is shown to be present in the process but
should have no effect on the output! This is the primary aim of the Taguchi
experiments - to minimize variations in output eventhough noise is present
in the process. The process is then said to have become ROBUST.
There are 3 Signal-to-Noise ratios of common interest;
(I) SMALLER-THE-BETTER :
--------------------
n = -10 Log10 [ mean of sum of squares of measured data ]
This is usually chosen for all undesirable characteristics like " defects " etc for which the ideal value is zero. Also, when an ideal value is finite and its maximum or minimum value is defined (like maximum purity is 100% or maximum Tc is 92K or minimum time for making a telephone connection is 1 sec) then the difference between measured data and ideal value is expected to be as small as possible. The generic form of S/N ratio then becomes,
n = -10 Log10 [ mean of sum of sqaures of {measured - ideal} ]
(II) LARGER-THE-BETTER :
-------------------
n = -10 Log10 [mean of sum squares of reciprocal of measured data]
This case has been converted to SMALLER-THE-BETTER by taking the reciprocals of measured data and then taking the S/N ratio as in the smaller-the-better case.
(III) NOMINAL-THE-BEST :
------------------
square of mean
n = 10 Log10
-----------------
variance
This case arises when a specified value is MOST desired, meaning that neither a smaller nor a larger value is desirable.
Examples are;
(i) most parts in mechanical fittings have dimensions which are nominal-the-best type.
(ii)
Ratios of chemicals or mixtures are nominally the best type.
e.g. Aqua regia 1:3 of HNO3:HCL
Ratio of Sulphur, KNO3 and Carbon in gun powder
(iii) Uniformity
in deposition /growth /plating /etching thickness.
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
L9 Program files
******
THE PROGRAM FILES:
------------------
' The zipped file you receive will be L9ALL.zip
' It will contain
(1)
Executable Program in MS-DOS
-- L9.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 "L9.EXE"
' THE *.PAR AND *.DAT ARE INPUT FILES NEEDED BY "L9.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 SMALLER-THE-BETTER' OR LARGER-THE-BETTER OR NOMINAL-THE-BEST
' THEN DECIDE A filename.
' FOR SMALLER-THE-BETTER, CHOOSE MY FILE spld#.PAR' WHERE # = 2, 3 OR 4 (NUMBER OF CONTROL FACTORS)
' COPY spld#.par filename.par
' YOU MAY USE THIS COPY FOR FURTHER STEPS GIVEN BELOW[NOTE:REPEAT THE SAME FOR LARGER-THE-BETTER OR NOMINAL-THE-BEST]
(ii) Prepare the Parameter
file (as per instructions 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"
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. spldnz2.PAR or spldnz3.PAR
' TRY it sometime in FUTURE
DATA FILE STRUCTURE :
---------------------
I have provided (dummy) data for all the examples (so the
examples should run without difficulty).
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
num1 , real2
'num1 ==> number of measurements for each expt
'real2 ==> ideal value, if any, ELSE 0 (zero)
val(1), val(2), ... , val(num1) ' for expt#1
val(1), val(2), ... , val(num1) ' for expt#2
val(1), val(2), ... , val(num1) ' for expt#3
val(1), val(2), ... , val(num1) ' for expt#4
val(1), val(2), ... , val(num1) ' for expt#5
val(1), val(2), ... , val(num1) ' for expt#6
val(1), val(2), ... , val(num1) ' for expt#7
val(1), val(2), ... , val(num1) ' for expt#8
val(1), val(2), ... , val(num1) ' for expt#9
[blank lines]
[any other text for giving NOTES or COMMENTS]
HOW TO RUN L9.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 "L9.exe" will then use YOUR filename.PAR file
for control parameter details and filename.DAT as (dummy) data
and create 3 important files
for you,
(i) filename1.OUT
' THIS CONTAINS THE PARAMETER DETAILS' WHICH YOU HAVE GIVEN
' PLEASE CHECK THIS AND VERIFY THAT
' THE CONTROL PARAMETERS and LEVELS ARE correct
(ii) filename2.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) filename3.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
' EVERY ROW INDICATES AN 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 is existing
in filename.DAT file)
These files are
filename4.OUT ' DATAfilename5.OUT ' DATA SUMMARY
filename6.OUT ' FACTOR EFFECTS (ANOVA , % AND F )
filename7.OUT ' AT THE CONTAINS THE PREDICTED RESULTS
FOR OPTIMUM PARAMETER COMBINATIONSfilename9.OUT ' OPTIMUM SETTINGS OF PARAMETERS AND ANOVA SUMMARY
******
PART C
****** Click
here for the Default
Parameter files (to run with L9.exe) stat9ex.zip
HOW TO RUN THE PROGRAM " L9.EXE
"
---------------------------------
ONCE THE FILES filename.PAR AND filename.DAT ARE AVAILABLE, THE
PROGRAM " L9.EXE " CAN BE RUN BY ISSUING A COMMAND
L9 <CR> OR <ENTER>
THE FILES *4.OUT ONWARDS WILL CONTAIN THE RESULTS OF your EXPERIMENTS
ONLY AFTER
YOU HAVE real DATA IN filename.DAT
IMPORTANT :
PROGRAM L9.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 L9 <ENTER>
' AND THIS TIME GIVE A VALUE 0
Q2 ==> PARAMETER FILENAME
(WITHOUT EXTENSION .PAR)
TYPE spld4
or
TYPE SPLD4
' MS-DOS SYSTEM DOES NOT DIFFERENTIATE' UPPER OR LOWER CASE IN FILENAMES
' IF ANY PROBLEM, USE UPPER CASE
Q3 ==> DATA FILENAME ( PROMPT
WILL BE FOR spld4.DAT )
you may either
TYPE <ENTER>
or
TYPE spld4
Q4 ==>
' THE DISPLAY GIVES YOU FOUR CHOICES OF ANALYSIS
' TYPE 1 FOR S/N RATIO FOR SMALLER-THE-BETTER
' TYPE 2 FOR S/N RATIO FOR LARGER-THE-BETTER
' TYPE 3 FOR S/N RATIO FOR NOMINAL-THE-BEST
' TYPE
4 FOR S/N RATIO FOR MEAN OR AVERAGE
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
' 1,3,0 FOR 3-FACTOR EXPT
' 1,3,0,2 FOR 4-FACTOR EXPT
YOU MAY KEEP TYPING WHATEVER
COMBINATIONS YOU WANT TO FIND (ANY ONE OF 3^4 COMBINATIONS)
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) SMALLER-THE-BETTER :
--------------------
ALL FILENAMES START WITH A CHARACTER "s" (FOR SMALLER-THE-BETTER)(ii) LARGER-THE-BETTER :NEXT APPENDED STRING IS "pld" FOR PLD BASED EXPERIMENTS.
OPTIONAL STRING TO INDICATE NOISE PARAMETERS IS "nz" FOR NOISE
NEXT APPENDED IS THE 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) ARE
spld2.PAR and spld2.DAT
spld3.PAR and spld3.DAT
spld4.PAR and spld4.DAT
THE FILES WITH NOISE FACTORS ARE
spldnz2.PAR and spldnz2.DAT 'FOR NOISE FACTORS WITH 2-LEVELS
spldnz3.PAR and spldnz3.DAT 'FOR NOISE FACTORS WITH 3-LEVELS
STARTING CHARACTER IS "l" (lowercase character EL) AND REST IS SIMILAR(iii) NOMINAL-THE-BETTER :lpld2.PAR and lpld2.DAT
lpld3.PAR and lpld3.DAT
lpld4.PAR and lpld4.DAT
THE FILES WITH NOISE FACTORS ARE
lpldnz2.PAR and lpldnz2.DAT 'FOR NOISE FACTORS WITH 2-LEVELS
lpldnz3.PAR and lpldnz3.DAT 'FOR NOISE FACTORS WITH 3-LEVELS
STARTING CHARACTER IS "n" AND REST IS SIMILARnpld2.PAR and npld2.DAT
npld3.PAR and npld3.DAT
npld4.PAR and npld4.DAT
THE FILES WITH NOISE FACTORS ARE
npldnz2.PAR and npldnz2.DAT 'FOR NOISE FACTORS WITH 2-LEVELS
npldnz3.PAR and npldnz3.DAT 'FOR NOISE FACTORS WITH 3-LEVELS
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
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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