Sec 47 Design And Analysis Of Experiment

DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

, knowledge, and resources. How well one succeeds will be a function of adherence

rve to confirm and modify these initial ideas. An iterative loop is established be

erimental “variability.”

s “plan, do, check, act.” Both statements illustrate the role of statistics as an i

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

statistics comes into formal play in two places: in helping design the experiments

nsidered course of action aimed at answering one or more carefully framed questio

tivity are too vast and varied to be left to a single individual.

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

ructed graphical displays of data quickly assist in data analysis.

illustrative examples. Many statistical software programs go far beyond the subje

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

o be qualitative, e.g., different machines, different operators, switch on or off.

different temperatures, then the factor temperature has four levels. In the case o

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

eatment combination” is the set of levels for all factors in a given experimental

gical entities, natural materials, fabricated products, etc. in known or unknown ways.

han between different portions. Observations

taken within a day are likely to be

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

use of certain tools called planned grouping, randomization, and replication.

influence . We say, “ (eta) is a function of x,” that is, η =f(x). Of course, observ

se. The errors (noise) attending a series of experiments have two primary componen

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

nd then repeating an experiment. Experimental error, the failure of agreement betw

odel, thus allowing the data to identify appropriate subsets of models for the exp

n of the roles of ε and η is formally recognized in an analysis of variance (ANO

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INTRODUCTION

batches, operators, machines, or days. These variables are commonly called “blocks,

ocks to accentuate the influences of the studied factors. Designs that make use of

of uncontrolled variables will balance out. It also improves the validity of esti

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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INTRODUCTION

ovides an opportunity for the effects of uncontrolled factors or factors unknown

to item measurements or to the variability occurring between adjacent items manu

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CLASSIFICATION OF EXPERIMENTAL DESIGNS

These designs have certain rational relationships to the purposes, needs, and phys

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COMPLETELY RANDOMIZED DESIGN : ONE FACTOR , k LEVELS

periment and there are k treatments (or levels of the factor) to be investigated.

e experiment. The advantages of the design are :

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COMPLETELY RANDOMIZED DESIGN : ONE FACTOR , k LEVELS

the case of a one-way classification analysis of variance, the most appropriate m

d the column headings were “Batch 1,” “Batch 2,” “Batch 3,” where the “batches” repr

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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COMPLETELY RANDOMIZED DESIGN : ONE FACTOR , k LEVELS

imenter, the data may be represented by the Fixed Effects Model (Model I), whereas

lso be interested in knowing about the “components of variance”; that is, the vari

ments.

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BLOCKED DESIGNS

of the studied factors are repeated each day or with a different operator, machin

ore using a block design data analysis.

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RANDOMIZED BLOCK DESIGN

divide the experiment into blocks, or planned homogeneous groups. When each such

s may also have an influence upon the response, then we might plan to observe all units at random within a given block.

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BALANCED INCOMPLETE BLOCK DESIGNS

t can be studied to three a day. The production manager is concerned that day-to-d

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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BALANCED INCOMPLETE BLOCK DESIGNS

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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LATIN SQUARE DESIGNS

r nonhomogeneity, i.e., two different blocking variables. Such designs were original

positions or operators and days. The studied variable, the experimental treatment

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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LATIN SQUARE DESIGNS

ur positions on the wear machine. A 4 X 4 Latin square will allow for both sources

3 X 3 to 7 X 7 are given in the table on next slide . Strictly speaking, every ti

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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LATIN SQUARE DESIGNS

at random, permute the rows at random, and assign the letters randomly to the tre

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YOUDEN SQUARE DESIGNS

by the fact that the number of rows, columns, and treatments must all be the same

of of of of of

treatments to be compared levels of one blocking variable (columns) levels of another blocking variable (rows) replications of each treatment times that two treatments occur in the same block

square, t = b and k = r.

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PLANNING INTERLABORATORY TESTS

of the true picture. It is always a difficult problem to decide whether or not o

of the materials to rank the laboratories. The data from the interlaboratory test

t is consistently high in its ability to measure the response will show a lower r

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PLANNING INTERLABORATORY TESTS

est is performed by several laboratories, the results are disappointing. The reaso

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PLANNING INTERLABORATORY TESTS

he program. The two materials should be similar in kind and in the value of the pr drawn through the median of all points in the x direction and a horizontal line

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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PLANNING INTERLABORATORY TESTS

e into four quadrants, and the first (and often revealing) step in the analysis is

upper right; if a laboratory is low on both samples, its point will lie in the lo

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NESTED ( COMPONENTS OF VARIANCE ) DESIGNS

nvestigations associated with interlaboratory comparisons, or the repeatability a

d” or “hierarchical” designs.

l elements are random variables.

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PLANNING THE SIZE OF THE EXPERIMENT

η

k

= η The corresponding averages y1, y2, …, yk computed from the recorded da

fied, existing tables or charts can be used to determine the necessary sample siz

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FACTORIAL EXPERIMENTS — GENERAL

ach of all possible combinations of levels that can be formed from the different

force, and the factorial experiment would consist of 20 trials. In this example, t

timated main effect is the difference between the average responses at the two le

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FACTORIAL EXPERIMENT WITH TWO FACTORS

at happens when other values of force and amperage are employed. Four values of f

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FACTORIAL EXPERIMENT WITH TWO FACTORS

ticeably higher resistivity values at amperage level 5 and the apparent changes i

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SPLIT - PLOT FACTORIAL EXPERIMENTS

r k to give a total of N = m1 X m2 X… X mk experimental trials.

alyst, that is, a 3 X 3 X 4 factorial design in N = 36 trials. To be a standard fa

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ACTORIAL EXPERIMENTS WITH k FACTORS ( EACH FACTOR AT

TWO LEVELS )

by a letter (or numeral) and then to denote the two levels (versions) of each fac

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EVOP : EVOLUTIONARY OPERATION

uce information about itself while simultaneously producing product to standards.

ate and temperature. The value of a dependent variable is the result of the settin

better operating conditions selected for any desired production rate. The response

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EVOP : EVOLUTIONARY OPERATION

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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EVOP : EVOLUTIONARY OPERATION

rease profit in an operating plant with minimum work and risk and without upsetti

ure on the process. Study cost, yield, and production records. ly the definitive text. ction management. Organize a team and hold training sessions. s that are likely to influence the most important response. steps according to a plan. (Cycle 2) and each succeeding cycle, estimate the effects. ificant, move to the indicated better operating conditions and start a new EVOP p en shown to be effective, change the ranges or select new variables P plan and adjust the ranges as necessary. he rate of gain is too slow, drop the current factors from the plan and run a new

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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EVOP : EVOLUTIONARY OPERATION

urers’ literature, patents, textbooks, and encyclopedias of technology. Do not negl

effect of past changes in equipment and conditions.

e use is the two-level complete factorial. There are important reasons to maintain

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EVOP : EVOLUTIONARY OPERATION

the average of the other four peripheral points. It is therefore a signal of curv actors. In the Taguchi literature the response would be termed “robust” to changes

Sec 47 DESIGN AND ANALYSIS OF EXPERIMENTS

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EVOP : EVOLUTIONARY OPERATION

ts, as can be seen by adding a constant to the five runs of Cycle 3, and recalcula

rate, percent impurity, or pounds of byproduct. A calculation sheet is made for ea

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BLOCKING THE 2 k FACTORIALS

e question is how to choose the trials to be run each day so as not to disturb th

action is constructed and labeled the block “generator.” Those runs carrying a plu

fect.

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BLOCKING THE 2 k FACTORIALS

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FRACTIONAL FACTORIAL EXPERIMENTS ( EACH FACTOR AT TWO LEVELS )

ed subset of all possible combinations. The analysis of fractional factorials is

therefore only 2kp- independent estimates are possible. In designing the fractional

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DESIGNING A FRACTIONAL FACTORIAL DESIGN

he column of signs associated with the highest order interaction. These signs are

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OTHER FRACTIONAL FACTORIALS

ny factors assumes great simplicity in the mathematical model for the response fu

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TAGUCHI OFF - LINE QUALITY CONTROL

se industrial environments experiments are run to identify the settings of both p

rtant to note that the word “design” takes differing connotations: product design,

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TAGUCHI OFF - LINE QUALITY CONTROL

hogonal arrays. The inner array consists of a statistical experimental design emp

noise statistics. No closure to the debate seems imminent. One thing is clear. The

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RESPONSE SURFACE DESIGNS

rch and development laboratories and sometimes on actual plant equipment itself. I

lled variables and a single response variable are studied. The data obtained are

rved (a second-order approximation).

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RESPONSE SURFACE DESIGNS

analyst with vivid insights into the nature of the responses and factors under in

ursued.

e with this approach is that a false optimum can be reached. Consider the followi

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RESPONSE SURFACE DESIGNS

ant yield. For example, there is an entire set of conditions of concentration and failed for a fairly simple reason.

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RESPONSE SURFACE DESIGNS

it deserves. This often leads to difficulties later on. In the present example the

o be done intelligently. The specific scale over which each factor is to be studie

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MIXTURE DESIGNS

ends on the proportions of the metallic elements present; gasoline is ordinarily a

trained to fall within narrow ranges, thus forming isolated mixture regions and r

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GROUP SCREENING DESIGNS

med, each containing several factors; the groups are tested; and individual factor

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