“The International Congress of Mathematicians (ICM) is an event of unique significance to the mathematical community around the world. It is held once every four years. The venue for the Congress is chosen, from the bids received for it, by the International Mathematical Union. India has won the bid for holding the ICM in 2010. This is the first time the event is to happen in India, and only the third time in Asia (after Kyoto - 1990 and Beijing - 2002). With the concurrence of IMU it has been decided to hold ICM 2010 at Hyderabad during the period 19th to 27th August, 2010.This congress will be held at the Hyderabad International Convention Centre (HICC). A web page for the ICM 2010 is located at http://www.icm2010.org.in” |
Speaker: Professor Aloke Dey, Indian Statistical Institute, New Delhi
Title : Design of Factorial Experiments Time(s): 3:00 p.m., February 5, 7, 12, and 13, 2008 Venue : Ramanujan Hall, Department of Mathematics, IIT Bombay |
About the Speaker: Aloke Dey, formerly Professor and currently an INSA Senior Scientist at the Indian Statistical Institute, New Delhi, has made significant contributions in the area of Design of experiments and related combinatorics. He is an author/coauthor of four books and nearly 125 research papers which have appeared in leading Statistical journals. He is also a former Editor of Sankhya. |
Abstract: Factorial experiments form an extremely useful class of experiments with applications in many diverse fields. In a typical factorial experiment, there is an output variable that is hypothesized to depend on a number of input variables, called factors. Each factor has at least two settings, these settings being termed as levels. A combination of the levels of all the factors is called a treatment combination and one experiments with all possible (or, a suitable subset) of these treatment combinations. If the number of levels of each of the factors involved is the same, we say that the experiment is a symmetric one; otherwise, the experiment is called an asymmetric or mixed factorial experiment. In a factorial experiment, one is interested in making inferences on effects of individual factors, called the main effects as also their interrelationship, called interactions. In this series of talks, the main features of design and analysis of factorial experiments will be discussed. To begin with, a complete characterization of (parametric) treatment contrasts belonging to the factorial effects (i.e., the main effects and interactions) using tensor product of matrices is given. Next, the concept of confounding is introduced and a method of constructing confounded designs is described. A general theory of block designs for factorial experiments is developed and some important notions like orthogonal factorial structure and balance are introduced. In an arbitrary factorial experiment, the number of treatment combinations increases rapidly with increase in the number of factors and/or the number of levels. In such a scenario, it is impracticable in most practical situations to experiment with a complete factorial and one has to experiment with a suitable subset of the treatment combinations. Such an experimental strategy is called fractional replication. Fractional factorial plans are of substantial recent interest due to their wide applicability, particularly in industrial experimentation and quality control work. We describe the essential features of a fractional factorial plan. Such plans are then related to orthogonal arrays. Some methods of construction of symmetric orthogonal arrays are also described. |