Multifactor design of experiments software
Encyclopedia
Software that is used for designing factorial experiments plays an important role in scientific experiments generally and represents a route to the implementation of design of experiments
procedures that derive from statistical
and combinatoric
theory. In fact, in September 2009, at the International Industrial Statistics in Action Conference at Newcastle University in England, statisticians from SmithKline Beecham Pharmaceuticals put up a poster saying that easy-to-use design of experiments (DOE) software (product name omitted here to maintain article neutrality) must be made available to all experimenters to foster use of DOE.
. He was described by Anders Hald
as "a genius who almost single-handedly created the foundations for modern statistical science." Fisher initiated the principles of design of experiments
and elaborated on his studies of "analysis of variance
". He also concurrently furthered his studies of the statistics of small samples.
Perhaps even more important, Fisher began his systematic approach of the analysis of real data as the springboard for the development of new statistical methods. He began to pay particular attention to the labour involved in the necessary computations performed by hand, and developed methods that were as practical as they were founded in rigour. In 1925, this work culminated in the publication of his first book, Statistical Methods for Research Workers
. This went into many editions and translations in later years, and became a standard reference work for scientists in many disciplines. In 1935, this was followed by The Design of Experiments, which also became a standard.
Before Fisher's multi-factor DOE breakthrough, the common experimentation method was conducted using OFAT (one-factor-at-a-time) experimentation. It is a sea-going gentleman named James Lind
who today is often attributed as a one-factor-at-a-time experimenter who discovered a cure for scurvy in 1747.
One-factor-at-a-time (OFAT) experimentation reached its zenith with the work of Thomas Edison’s
“trial and error” methods. OFAT was and remained the basis of scientific experimental design until agricultural needs to furnish growing city populations with food together with concurrent diminishing farm living necessitated something better.
Agricultural science
advancements served to meet the combination of larger city populations and fewer farms. But for crop scientists to meet widely differing geographical growing climates and needs, it became important to differentiate local growing conditions. For local crops to be used as a guide to feeding entire populations, it became more essential to economically extend crop sample testing to overall populations. As statistical methods advanced (primarily the efficacy of designed experiments instead of one-factor-at-a-time experimentation), representative factorial design of experiments began ensuring that inferences and conclusions could profitably extend experimental sampling to the population as a whole. However, a major problem existed in determining the extent to which a crop sample chosen was truly representative. Factorial DOE began revealing methods to estimate and correct for any random trending within the sample and also in the data collection procedures trend estimation
.
During World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding up industrial development for the Allied forces. These designs can be quite compact, involving as few as two levels of each factor and only a fraction of all the combinations, and yet they are quite powerful for screening purposes. After the war, a statistician at Imperial Chemical, George Box, described how to generate response surfaces
for process optimization. From this point forward, DOE took hold in the chemical process industry, where factors such as time, temperature, pressure, concentration, flow rate and agitation are easily manipulated. Later, Box co-authored a textbook that formed the basis for the original version of DOE software by Stat-Ease,Inc., called Design-Ease®.
Design of experiments results, when discovered accurately with DOE software, strengthen the capability to discern truths about sample populations being tested: see Sampling (statistics)
. Statisticians describe stronger multi-factorial DOE methods as being more “robust
”: see Experimental design.
As design of experiments software advancements gave rise to solving complex factorial statistical equations, statisticians began in earnest to design experiments with more than one factor (multifactorial components) being tested at a time. Simply stated, computerized multi-component design of experiments began supplanting one-factor-at-a-time experiments. Computer software designed specifically for designed experiments became a commercial reality in the 1980s—available from various leading software companies such as the aforementioned Design-Ease, JMP
and Minitab
.
Notable benefits when using design of experiments software include avoiding laborious hand calculations when:
Today, factorial DOE software is a notable tool that engineers, scientists, geneticists, biologists, and virtually all other experimenters and creators, ranging from agriculturists to zoologists, rely upon. DOE software is most applicable to controlled, multi-factor experiments in which the experimenter is interested in the effect of some process or intervention on objects such as crops, jet engines, demographics, marketing techniques, materials, adhesives, and so on. Design of experiments software is therefore a valuable tool with broad applications for all natural, engineering, and social sciences.
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
procedures that derive from statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and combinatoric
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
theory. In fact, in September 2009, at the International Industrial Statistics in Action Conference at Newcastle University in England, statisticians from SmithKline Beecham Pharmaceuticals put up a poster saying that easy-to-use design of experiments (DOE) software (product name omitted here to maintain article neutrality) must be made available to all experimenters to foster use of DOE.
Background
The term "design of experiments" (DOE) derives from early statistical work performed by Sir Ronald FisherRonald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
. He was described by Anders Hald
Anders Hald
Anders Hald was a Danish statistician who made contributions to the history of statistics.He was a professor at the University of Copenhagen from 1960 to 1982.- Bibliography :...
as "a genius who almost single-handedly created the foundations for modern statistical science." Fisher initiated the principles of design of experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
and elaborated on his studies of "analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
". He also concurrently furthered his studies of the statistics of small samples.
Perhaps even more important, Fisher began his systematic approach of the analysis of real data as the springboard for the development of new statistical methods. He began to pay particular attention to the labour involved in the necessary computations performed by hand, and developed methods that were as practical as they were founded in rigour. In 1925, this work culminated in the publication of his first book, Statistical Methods for Research Workers
Statistical Methods for Research Workers
Statistical Methods for Research Workers is a classic 1925 book on statistics by the statistician R.A. Fisher. It is considered by some to be one of the 20th century's most influential books on statistical methods. According to ,...
. This went into many editions and translations in later years, and became a standard reference work for scientists in many disciplines. In 1935, this was followed by The Design of Experiments, which also became a standard.
Before Fisher's multi-factor DOE breakthrough, the common experimentation method was conducted using OFAT (one-factor-at-a-time) experimentation. It is a sea-going gentleman named James Lind
James Lind
James Lind FRSE FRCPE was a Scottish physician. He was a pioneer of naval hygiene in the Royal Navy. By conducting the first ever clinical trial, he developed the theory that citrus fruits cured scurvy...
who today is often attributed as a one-factor-at-a-time experimenter who discovered a cure for scurvy in 1747.
One-factor-at-a-time (OFAT) experimentation reached its zenith with the work of Thomas Edison’s
Thomas Edison
Thomas Alva Edison was an American inventor and businessman. He developed many devices that greatly influenced life around the world, including the phonograph, the motion picture camera, and a long-lasting, practical electric light bulb. In addition, he created the world’s first industrial...
“trial and error” methods. OFAT was and remained the basis of scientific experimental design until agricultural needs to furnish growing city populations with food together with concurrent diminishing farm living necessitated something better.
Agricultural science
Agricultural science
Agricultural science is a broad multidisciplinary field that encompasses the parts of exact, natural, economic and social sciences that are used in the practice and understanding of agriculture. -Agriculture and agricultural science:The two terms are often confused...
advancements served to meet the combination of larger city populations and fewer farms. But for crop scientists to meet widely differing geographical growing climates and needs, it became important to differentiate local growing conditions. For local crops to be used as a guide to feeding entire populations, it became more essential to economically extend crop sample testing to overall populations. As statistical methods advanced (primarily the efficacy of designed experiments instead of one-factor-at-a-time experimentation), representative factorial design of experiments began ensuring that inferences and conclusions could profitably extend experimental sampling to the population as a whole. However, a major problem existed in determining the extent to which a crop sample chosen was truly representative. Factorial DOE began revealing methods to estimate and correct for any random trending within the sample and also in the data collection procedures trend estimation
Trend estimation
Trend estimation is a statistical technique to aid interpretation of data. When a series of measurements of a process are treated as a time series, trend estimation can be used to make and justify statements about tendencies in the data...
.
Use of software
Factorial experimental design software drastically simplifies previously laborious hand calculations needed before the use of computers.During World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding up industrial development for the Allied forces. These designs can be quite compact, involving as few as two levels of each factor and only a fraction of all the combinations, and yet they are quite powerful for screening purposes. After the war, a statistician at Imperial Chemical, George Box, described how to generate response surfaces
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
for process optimization. From this point forward, DOE took hold in the chemical process industry, where factors such as time, temperature, pressure, concentration, flow rate and agitation are easily manipulated. Later, Box co-authored a textbook that formed the basis for the original version of DOE software by Stat-Ease,Inc., called Design-Ease®.
Design of experiments results, when discovered accurately with DOE software, strengthen the capability to discern truths about sample populations being tested: see Sampling (statistics)
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
. Statisticians describe stronger multi-factorial DOE methods as being more “robust
Robust statistics
Robust statistics provides an alternative approach to classical statistical methods. The motivation is to produce estimators that are not unduly affected by small departures from model assumptions.- Introduction :...
”: see Experimental design.
As design of experiments software advancements gave rise to solving complex factorial statistical equations, statisticians began in earnest to design experiments with more than one factor (multifactorial components) being tested at a time. Simply stated, computerized multi-component design of experiments began supplanting one-factor-at-a-time experiments. Computer software designed specifically for designed experiments became a commercial reality in the 1980s—available from various leading software companies such as the aforementioned Design-Ease, JMP
JMP (statistical software)
JMP is a computer program that was first developed by John Sall and others to perform simple and complex statistical analyses.It dynamically links statistics with graphics to interactively explore, understand, and visualize data...
and Minitab
Minitab
Minitab is a statistics package. It was developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in 1972...
.
Notable benefits when using design of experiments software include avoiding laborious hand calculations when:
- Identifying key factors for process or product improvements.
- Setting up and analyzing general factorialFactorial experimentIn statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be...
, two-level factorial, fractional factoria (up to 31 variables) and Plackett–Burman designs (up to 31 variables). - Performing numerical optimizations.
- Screening for critical factors and their interactionInteractionInteraction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect...
s. - Analyzing process factors or mixture components.
- Combining mixture and process variables in designs.
- Rotating 3D plots to visualize response surfacesResponse surface methodologyIn statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
. - Exploring 2D contours with a computer mouse, setting flags along the way to identify coordinates and predict responses.
- Precisely locating where all specified requirements meet using numerical optimization functions within DOE software .
- Finding the most desirable factor settings for multiple responses simultaneously.
Today, factorial DOE software is a notable tool that engineers, scientists, geneticists, biologists, and virtually all other experimenters and creators, ranging from agriculturists to zoologists, rely upon. DOE software is most applicable to controlled, multi-factor experiments in which the experimenter is interested in the effect of some process or intervention on objects such as crops, jet engines, demographics, marketing techniques, materials, adhesives, and so on. Design of experiments software is therefore a valuable tool with broad applications for all natural, engineering, and social sciences.
External links
- Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd Edition
- Design and Analysis of Experiments, 7th Edition
- DOE Simplified: Practical Tools for Effective Experimentation, 2nd Edition
- RSM Simplified: Optimizing Processes Using Response Surface Methods for Design of Experiments
- Warning Signs in Experimental Design and Interpretation
- NIST Eng. Stats Section 5 Process Improvement