¿QUÉ
ES UN DISEÑO DE EXPERIMENTOS?
Es una
disciplina desarrollada específicamente para
el estudio, análisis y comprensión de
la variabilidad de los procesos y de
los datos.
Una
de las situaciones en las que hay más aplicación de la metodología estadística
es la que se refiere a la determinación de factores que causan variación, y la cuantificación del
efecto que cada uno de ellos tiene sobre esa variación. El estudio de la forma en que se combinan los
factores que afectan conjuntamente la variación. Es uno de los objetivos
principales del diseño de Experimento.
Un experimento se realiza por alguno de los siguientes motivos:
1. Determinar las
principales causas de variación en la respuesta.
2. Encontrar las
condiciones experimentales con las que se consigue un valor extremo en la
variable de interés o respuesta.
3. Comparar las
respuestas en diferentes niveles de observación de variables controladas.
4. Obtener un modelo
estadístico-matemático que permita hacer predicciones de respuestas futuras.
ETAPAS DE LA EXPERIMENTACIÓN
1. Reconocimiento
de un problema.
2. Formulación
del problema.
3. Especificación
de las variables a medir.
4. Acuerdo
sobre los factores y niveles a usar en el experimento.
5. Definición
del espacio de inferencia.
6. Selección
de las unidades experimentales.
7. Layout
del Diseño.
8. Desarrollo
del modelo estadístico.
9. Evaluación
preliminar del diseño.
10. Rediseño
del experimento.
11. Recolección
de datos.
12. Análisis
de los datos.
13. Conclusiones.
14. Implantación.
DEFINICIONES
Experimento: Un estudio en el
que el investigador tiene un alto grado de control sobre las fuentes de
variación importantes, se denomina experimento. Si se tiene poco control sobre
los factores, se habla de un estudio observacional.
Factores: Los fenómenos que
potencialmente causan variación, y que son controlados por el experimentador,
se denominan factores. También a veces se denominan tratamientos.
Niveles de un factor: Son los valores que
toma un factor. En general toman valores que se miden en escala categórica, aunque
a veces suelen ser medidos en escalas numéricas.
Combinación de tratamientos: Cada una de las combinaciones de niveles de todos los factores
involucrados en el experimento.
Corrida experimental: Cada una de las
fases en que se lleva a cabo el experimento. Cada corrida experimental
corresponde a una realización del experimento, bajo una determinada combinación
de tratamientos, y produce una observación.
Réplicas: Todas las corridas
experimentales que corresponden a una misma combinación de tratamientos. Son
repeticiones del experimento, bajo idénticas condiciones de los factores.
Objetivos: Lograr mayor precisión en la estimación de los efectos de los
factores y de sus interacciones, y estimar el error experimental.
Experimento balanceado: Es un experimento en que todos los niveles de
cada factor aparece el mismo número de veces. Si no se da esta situación, el
experimento es desbalanceado.
Diseño: La estructura constituida por los factores y los niveles que se les
asignan, en la experimentación. El diseño es la parte que controla el experimentador.
Respuesta: La variable objetivo, que se pretende optimizar, y que depende
potencialmente de los factores. La respuesta es lo que se mide como resultado
de la experimentación, no es controlada por el experimentador. Es una variable
medida en escala numérica.
Efecto principal: Un efecto principal es la variación en la
respuesta, atribuida al cambio en un factor determinado, a través de sus distintos
niveles.
Interacción: El efecto producido por la acción de un factor, influido por la
presencia de otro. Es un efecto combinado de dos o más factores. Si no existe
un efecto de interacción, se dice que los efectos de los factores son
aditivos.
Error experimental: La parte de la
variabilidad que no está explicada por los factores involucrados en el
experimento.
La siguiente figura muestra las generalidades del diseño experimental:
WHAT IS A DESIGN OF EXPERIMENTS?
It is an experiment designed that consists of a test or several tests in which changes are deliberately induced in the input variables of the System (Process) in order to enable the identification of the causes that cause the changes in the response.
It is a discipline developed specifically for the study, analysis and understanding of the variability of processes and data.
One of the situations in which there is more application of the statistical methodology is that which refers to the determination of factors that cause variation, and the quantification of the effect that each of them has on that variation. The study of how factors that jointly affect the variation are combined. It is one of the main objectives of the Experiment design.
An experiment is performed for any of the following reasons:
1. Determine the main causes of variation in the response.
2. Find the experimental conditions with which an extreme value is achieved in the variable of interest or response.
3. Compare the responses at different levels of observation of controlled variables.
4. Obtain a statistical-mathematical model that allows predictions of future responses.
STAGES OF EXPERIMENTATION
1. Recognition of a problem.
2. Formulation of the problem.
3. Specification of the variables to be measured.
4. Agreement on the factors and levels to be used in the experiment.
5. Definition of the inference space.
6. Selection of experimental units.
7. Layout of the Design.
8. Development of the statistical model.
9. Preliminary design evaluation.
10. Redesign of the experiment.
11. Data collection.
12. Data analysis.
13. Conclusions.
14. Implementation.
DEFINITIONS
Experiment: A study in which the researcher has a high degree of control over important sources of variation is called an experiment. If there is little control over the factors, there is talk of an observational study.
Factors: The phenomena that potentially cause variation, and that are controlled by the experimenter, are called factors. They are also sometimes called treatments.
Levels of a factor: These are the values that a factor takes. In general they take values that are measured on a categorical scale, although sometimes they are usually measured on numerical scales.
Combination of treatments: Each level combination of all the factors involved in the experiment.
Experimental run: Each of the phases in which the experiment is carried out. Each experimental run corresponds to one embodiment of the experiment, under a certain combination of treatments, and produces an observation.
Replicas: All experimental runs that correspond to the same combination of treatments. They are repetitions of the experiment, under identical conditions of the factors. Objectives: To achieve greater precision in the estimation of the effects of the factors and their interactions, and estimate the experimental error.
Balanced experiment: It is an experiment in which all levels of each factor appear the same number of times. If this situation does not occur, the experiment is unbalanced.
Design: The structure constituted by the factors and the levels assigned to them, in the experimentation. Design is the part that controls the experimenter.
Answer: The objective variable, which is intended to be optimized, and potentially depends on the factors. The answer is what is measured as a result of experimentation, it is not controlled by the experimenter. It is a variable measured in numerical scale.
Main effect: A main effect is the variation in the response, attributed to the change in a given factor, through its different levels.
Interaction: The effect produced by the action of one factor, influenced by the presence of another. It is a combined effect of two or more factors. If there is no interaction effect, the effects of the factors are said to be additive.
Experimental error: The part of the variability that is not explained by the factors involved in the experiment.
La siguiente figura muestra las generalidades del diseño experimental:
WHAT IS A DESIGN OF EXPERIMENTS?
It is an experiment designed that consists of a test or several tests in which changes are deliberately induced in the input variables of the System (Process) in order to enable the identification of the causes that cause the changes in the response.
It is a discipline developed specifically for the study, analysis and understanding of the variability of processes and data.
One of the situations in which there is more application of the statistical methodology is that which refers to the determination of factors that cause variation, and the quantification of the effect that each of them has on that variation. The study of how factors that jointly affect the variation are combined. It is one of the main objectives of the Experiment design.
An experiment is performed for any of the following reasons:
1. Determine the main causes of variation in the response.
2. Find the experimental conditions with which an extreme value is achieved in the variable of interest or response.
3. Compare the responses at different levels of observation of controlled variables.
4. Obtain a statistical-mathematical model that allows predictions of future responses.
STAGES OF EXPERIMENTATION
1. Recognition of a problem.
2. Formulation of the problem.
3. Specification of the variables to be measured.
4. Agreement on the factors and levels to be used in the experiment.
5. Definition of the inference space.
6. Selection of experimental units.
7. Layout of the Design.
8. Development of the statistical model.
9. Preliminary design evaluation.
10. Redesign of the experiment.
11. Data collection.
12. Data analysis.
13. Conclusions.
14. Implementation.
DEFINITIONS
Experiment: A study in which the researcher has a high degree of control over important sources of variation is called an experiment. If there is little control over the factors, there is talk of an observational study.
Factors: The phenomena that potentially cause variation, and that are controlled by the experimenter, are called factors. They are also sometimes called treatments.
Levels of a factor: These are the values that a factor takes. In general they take values that are measured on a categorical scale, although sometimes they are usually measured on numerical scales.
Combination of treatments: Each level combination of all the factors involved in the experiment.
Experimental run: Each of the phases in which the experiment is carried out. Each experimental run corresponds to one embodiment of the experiment, under a certain combination of treatments, and produces an observation.
Replicas: All experimental runs that correspond to the same combination of treatments. They are repetitions of the experiment, under identical conditions of the factors. Objectives: To achieve greater precision in the estimation of the effects of the factors and their interactions, and estimate the experimental error.
Balanced experiment: It is an experiment in which all levels of each factor appear the same number of times. If this situation does not occur, the experiment is unbalanced.
Design: The structure constituted by the factors and the levels assigned to them, in the experimentation. Design is the part that controls the experimenter.
Answer: The objective variable, which is intended to be optimized, and potentially depends on the factors. The answer is what is measured as a result of experimentation, it is not controlled by the experimenter. It is a variable measured in numerical scale.
Main effect: A main effect is the variation in the response, attributed to the change in a given factor, through its different levels.
Interaction: The effect produced by the action of one factor, influenced by the presence of another. It is a combined effect of two or more factors. If there is no interaction effect, the effects of the factors are said to be additive.
Experimental error: The part of the variability that is not explained by the factors involved in the experiment.
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