Design of Experiments

UNIT – II

DESIGN OF EXPERIMENTS

Introduction

Experiments are a natural part of the engineering and scientific decision - making process. In a designed experiment the engineer makes deliberate or purposeful changes in the controllable variables of the system or process, observes the resulting system output data, and then makes an inference or decision about which variables are responsible for the observed changes in output performance. Designed experiments play a very important role in engineering design and development and in the improvement of manufacturing processes. Generally when products and processes are designed and developed with designed experiments, they enjoy better performance, higher reliability and lower overall costs. Designed experiments also play a crucial role in reducing the lead time for engineering design and development activities.

An experiment is just a test or series of tests. Experiments are performed in all engineering and scientific disciplines and are an important part of the way, we learn about how systems and processes work. The validity of the conclusions that are drawn from an experiment depends, to a large extent, on how the experiment was conducted. Therefore, the design of the experiment plays a major role in the eventual solution of the problem that initially motivated the experiment.

Experimental units: The objects upon which the measurements are taken are called experimental units. The design of an experiment implies one time problem after selecting the factor combinations (treatments) to be employed in an experiment. One must decide how the treatments should be assigned to the experimental units.

Basic principles in the Design of Experiment.

There are three basic principles of an experimental design. They are

(1) Randomization

(2) Replication

(3) Local control (error control)

1. Randomization

A set of objects is said to be randomized, when they are arranged in random order.

The most frequently used assumption is the one which relates the observations (units) are independent. We can judge the assumption by insisting on random assignment of treatment to the experimental units. This randomization makes the test valid by making it appropriate to analyse the data as though the assumption of independent errors are true. Here, randomization permits us to proceed as though independence is a fact but does not guarantee independence. No amount of randomization will completely eliminate the errors but still randomization is the best technique designed to attain the desired result.

Randomization is like insurance. It is always a good idea and even sometimes better, than we expect.

2. Replication

The independent execution of an experiment more than once is called replication.

Replication is necessary to increase the accuracy of estimates of the treatment effects. It also provides an estimate of the error variance which is a function of the differences among observations from experimental units, under identical treatments. As the number of replication increases, the error is reduced. But, it cannot be increased indefinitely as it increases cost of the experiments. Also, due to limited resources, too many replications cannot be used. Sensitivity of statistical methods for drawing inference also depends on the number of replications. xo od bolavijom

3. Local control

To provide adequate control of extraneous variables, another essential principle used in the experimental design is the local control. This includes techniques such as grouping, blocking and balancing of the experimental units, used in the experimental design. By grouping, we mean combining sets of homogeneous plots into groups, so that different manures may be used in different groups. The number of plots in different groups need not necessarily be the same. By blocking, we mean assigning the same number of plots in different blocks. The plots in the same block may be assumed to be relatively homogeneous. We use as many manures as the number of plots, in a block, in a random manner. By balancing, we mean adjusting the procedures of grouping, blocking and assigning the manures in such a manner that a balanced configuration is obtained. (fonos 10115) lonnoo Isso I (E)

Complete Block Designs

There are three such designs. They are

(1) Completely Randomized Design

(2) Randomized Block Design

(3) Latin Square Design