USER MANUAL for PROGRAM "L18.EXE"(STATIC PROBLEMS)
=================================================

+++++++++++++++++++++++++++++++++++++++++++
A PROGRAM  FOR  OPTIMIZING STATIC PROBLEMS
WITH 5-7 CONTROL FACTORS with 3-LEVELS EACH
AND  only  1 CONTROL FACTOR  with  2-LEVELS
+++++++++++++++++++++++++++++++++++++++++++

******
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 the 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.

L18   ORTHOGONAL   ARRAY :
----------------------------------------------

L18  ( 21 X 37 )  ORTHOGONAL  ARRAY

----------------------------------------------------
Columns
EXPT NO     1    2        3    4    5    6    7    8
----------------------------------------------------
1            1    1        1    1    1    1    1    1
2            1    1        2    2    2    2    2    2
3            1    1        3    3    3    3    3    3
4            1    2        1    1    2    2    3    3
5            1    2        2    2    3    3    1    1
6            1    2        3    3    1    1    2    2
7            1    3        1    2    1    3    2    3
8            1    3        2    3    2    1    3    1
9            1    3        3    1    3    2    1    2

10            2    1        1    3    3    2    2    1
11            2    1        2    1    1    3    3    2
12            2    1        3    2    2    1    1    3
13            2    2        1    2    3    1    3    2
14            2    2        2    3    1    2    1    3
15            2    2        3    1    2    3    2    1
16            2    3        1    3    2    3    1    2
17            2    3        2    1    3    1    2    3
18            2    3        3    2    1    2    3    1
-----------------------------------------------------

LINEAR  GRAPH  FOR  L18

1              2                3          4          5          6          7          8
*---------*                   *          *          *          *          *          *
can study                 Interaction between any two columns (from 3 - to - 8)  is
interaction               confounded with the remaining columns and can not be studied
1 X 2

Note: Interaction between columns 1 and 2 is orthogonal to
all columns and hence can be estimated without sacrificing
any column. The interaction can be estimated from the 2-way
table of columns 1 and 2.

Columns 1 and 2 can be combined to form a 6-level column.

******
PART B  Click here for the Taguchi L18 Program files
******

THE PROGRAM FILES:
------------------

'   The zipped file you receive will be L18ALL.zip

' It will contain

(1) Executable Program in MS-DOS         --   L18.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  "L18.EXE"

' THE *.PAR AND *.DAT ARE INPUT FILES NEEDED BY "L18.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
18 experiments of the (rows of) L18-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 # = 5, 6, 7 or 8  (NUMBER OF CONTROL FACTORS)

' COPY spld8.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 -- 5  or 6  or  7  or  8

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 -- 2

[note: ONLY ONE 2-LEVEL FACTOR IS ALLOWED.
IT CAN BE DECLARED AS THE FIRST CONTROL FACTOR.
'IF THERE IS NO 2-LEVEL FACTOR,
'THEN THE FIRST FACTOR CAN HAVE 3-LEVELS,
'IN WHICH CASE, MAXIMUM NUMBER OF FACTORS WILL BE 7]

name of Level #1 of A -- "stringA1"

name of Level #2 of A -- "stringA2"

[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 control factor #5 -- E

name of control factor #5 -- "namestringE"

Levels of factor E -- 3

name of Level #1 of E -- "stringE1"

name of Level #2 of E -- "stringE2"

name of Level #3 of E -- "stringE3"

Character to represent control factor #6 -- F

name of control factor #6 -- "namestringF"

Levels of factor F -- 3

name of Level #1 of F -- "stringF1"

name of Level #2 of F -- "stringF2"

name of Level #3 of F -- "stringF3"

Character to represent control factor #7 -- G

name of control factor #7 -- "namestringG"

Levels of factor G -- 3

name of Level #1 of G -- "stringG1"

name of Level #2 of G -- "stringG2"

name of Level #3 of G -- "stringG3"

Character to represent control factor #8 -- H

name of control factor #8 -- "namestringH"

Levels of factor H -- 3

name of Level #1 of H -- "stringH1"

name of Level #2 of H -- "stringH2"

name of Level #3 of H -- "stringH3"

Keyword for noise factor -- NOISE

To indicate END OF DATA -- 0
next line also -- 0

(I HAVE NOT INCLUDED NOISE)

(I WILL INCLUDE NOISE 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

val(1), val(2), ... , val(num1) ' for expt#10

val(1), val(2), ... , val(num1) ' for expt#11

val(1), val(2), ... , val(num1) ' for expt#12

val(1), val(2), ... , val(num1) ' for expt#13

val(1), val(2), ... , val(num1) ' for expt#14

val(1), val(2), ... , val(num1) ' for expt#15

val(1), val(2), ... , val(num1) ' for expt#16

val(1), val(2), ... , val(num1) ' for expt#17

val(1), val(2), ... , val(num1) ' for expt#18

[blank lines]

[any other text for giving NOTES or COMMENTS]

HOW TO RUN L18.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 "L18.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 ARE correct

(ii) filename2.out

' THIS GIVES THE CHOSEN

' "ORTHOGONAL ARRAY" i.e. L18 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

' 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

(iv) The program also creates other files

(which are relevant ONLY after REAL data is existing in filename.DAT file)

These files are

filename4.OUT ' DATA

filename5.OUT ' DATA SUMMARY

filename6.OUT ' FACTOR EFFECTS (ANOVA , % AND F )

filename7.OUT ' AT THE CONTAINS THE PREDICTED RESULTS
FOR OPTIMUM PARAMETER COMBINATIONS

filename9.OUT ' OPTIMUM SETTINGS OF PARAMETERS AND ANOVA SUMMARY

******
PART C
******   Click here for the Default Parameter files (to run with L18.exe)  stat18ex.zip

HOW TO RUN THE PROGRAM " L18.EXE "
---------------------------------

ONCE THE FILES filename.PAR AND filename.DAT ARE AVAILABLE, THE

PROGRAM " L18.EXE " CAN BE RUN BY ISSUING A COMMAND

L18 <CR> OR <ENTER>

THE FILES *4.OUT ONWARDS WILL CONTAIN THE RESULTS OF your EXPERIMENTS

IMPORTANT :

PROGRAM L18.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 L18 <ENTER>

' AND THIS TIME GIVE A VALUE 0

Q2 ==> PARAMETER FILENAME (WITHOUT EXTENSION .PAR)

TYPE spld8
or
TYPE SPLD8

' 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 spld8

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

' 2,2,2,2,2 FOR 5-FACTOR EXPTS.

' 2,2,2,2,2,2 FOR 6-FACTOR EXPTS.

' 2,2,2,2,2,2,2 FOR 7-FACTOR EXPTS

' 2,2,2,2,2,2,2,2 FOR 8-FACTOR EXPTS

IT WILL THEN ASK FOR THE

OPTIMUM (OR NEW) COMBINATIONS

' TYPE THE COMBINATION DISPLAYED

' AS OPTIMUM , SAY

' 1,3,2,1,1 FOR 5-FACTOR EXPT

' 1,3,2,1,1,3 FOR 6-FACTOR EXPT

' 1,3,2,1,1,3,2 FOR 7-FACTOR EXPT

' 1,3,2,1,1,3,2,1 FOR 8-FACTOR EXPT

YOU MAY KEEP TYPING WHATEVER

COMBINATIONS YOU WANT TO FIND (ANY ONE OF 3^8 COMBINATIONS)

OR

END BY TYPING

' 0,0,0,0,0 FOR 5-FACTOR EXPT

' 0,0,0,0,0,0 FOR 6-FACTOR EXPT

' 0,0,0,0,0,0,0 FOR 7-FACTOR EXPT

' 0,0,0,0,0,0,0,0 FOR 8-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)

NEXT APPENDED STRING IS "pld" FOR PLD BASED EXPERIMENTS.

OPTIONAL STRING TO INDICATE NOISE PARAMETERS IS "nz" FOR NOISE

NEXT APPENDED IS THE NUMBER "5" FOR 5 CONTROL PARAMETERS

OR "6" FOR 6 CONTROL PARAMETERS

OR "7" FOR 7 CONTROL PARAMETERS

OR "8" FOR 8 CONTROL PARAMETERS

EXTENSIONS ARE ".PAR" FOR PARAMETER DETAILS

OR ".DAT" FOR MEASURED (OR DUMMY) DATA

THE FILES (WITHOUT NOISE FACTORS) ARE

spld5.PAR and spld5.DAT

spld6.PAR and spld6.DAT

spld7.PAR and spld7.DAT

spld8.PAR and spld8.DAT

(ii) LARGER-THE-BETTER :
-------------------

STARTING CHARACTER IS "l" (lowercase character EL) AND REST IS SIMILAR

THE FILES (WITHOUT NOISE FACTORS) ARE

lpld5.PAR and lpld5.DAT

lpld6.PAR and lpld6.DAT

lpld7.PAR and lpld7.DAT

lpld8.PAR and lpld8.DAT

(iii) NOMINAL-THE-BETTER :
-------------------

STARTING CHARACTER IS "n" AND REST IS SIMILAR

THE FILES (WITHOUT NOISE FACTORS) ARE

npld5.PAR and npld5.DAT

npld6.PAR and npld6.DAT

npld7.PAR and npld7.DAT

npld8.PAR and npld8.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 "

***************************************************

Go back to Apte's web-page

Go back to Taguchi Page

last modifed on 22-Sep-2000 / 31-Aug-2000