Design of Experiments

Dr.P.B.BharateHead, Department of Statistics

Vice principal, Pratap College,Amalner

Outline of discussion

• Introduction• Experiment• Example• Models• Strategy of experimentation• Basic principles of design of experiments• Guidelines for the design of experiments

Introduction

System A system is a set of interacting or

interdependent components forming an integrated whole.

Ex Banking System, Reservation system. Social system

Process A Sequence of interdependent

and linked procedures which, at every stage, consume one or more resources (employee time, energy, machines, money) to convert inputs (data, material, parts, etc.) into outputs.

Ex. Chemical process.

Experiment• Observing a system or process helps us to understand how system and

process works.• To understand what happens to a process when we change certain factors

, we need to do more than observation.• To really understand cause and effect relationship in systems we must

deliberately change the input variables to the system and observe the output. i.e. we need to conduct experiment

• Observations on a system can lead to theories but experiments are required to prove the theories.

• Investigators perform experiments in all fields of inquiry. Each experimental run is a test.

• Experiment is a test or series of runs in which purposeful changes are made to the input variables of a process or system and output response is observed to identify the reasons for changes on out put response.

Objectives of Experiments

• Identify the input variables responsible for the observed changes in the response variable

• To develop a model relating the response variable with input variables.

• To use this model for process or system improvement or other decision making.

• Experimentation plays important role in science and engineering.

Manufacturing a car

• Productivity= Annual Revenue/ Annual cost• Factors that affect the demand of car as follows• Mileage of car• Convenience of driving• Aesthetic of the car• Selling price of the car• Size of the population• Income level of people• Number of competing brands• Location of consumers

• The objective of company is to identify the optimum level of production of car so as to increase the productivity

Example

• Comparison of two hardening processes i)oil quenching and ii) salt water quenching on an aluminum alloy

• Number of specimens or test coupons are subjected to two media and hardness is measured.

• Objective is to decide the best quenching medium.

Questions about the Experiment1. Are these two solutions the only quenching media of interest?2. Are there any other factors that might affect hardness that

should be investigated or controlled in this experiment(such as the temperature)?

3. How many coupons of alloy should be tested in each quenching solution?

4. How should the coupons be assigned to the quenching solution and in what order data should be collected?

5. What method of data analysis should be used?6. What difference in average observed hardness between the

two quenching solutions will be considered important?

Models

Mechanistic models• Deductive inference• From general to

particular• Follow directly from the

physical mechanism• Example• Oham’s law E=IR• Mathematical model

Empirical models• Inductive inference• From particular to general• Requires experimentation• Statistical model• We are concerned with

the turning the results of experiments into empirical models

Process or system

Inputs

Controlling factors

Un controling factors

outputsProcess

A process or system can be represented by the diagram

Strategy of Experimentation

• The general approach of planning and conducting the experiment is called the strategy of experimentation. Let us consider example of preparation of curd from milk. Some of the factors that influence the preparation of curd are as follows;

1. The temperature of the milk2. Quantity of curd culture added to milk3. PH value of the curd4. Fat of milk5. Pot used for curd6. Room temperature 7. Seasons winter , summer , monsoon8. Timing of the day morning , evening 9. The list can be extended.

Strategy of Experimentation

Best guess approachSelect an arbitrary combination of

factors and test it.No guarantee of best solution

One factor at a time approach(OFAT)

Varying each factor keeping other factors constant.

It fails to consider any interaction

Both approaches have drawbacks. Factorial design can give better solution in which we can test both the significance of main effects and interactions also.

Basic principles of design of experiments

• The statistical design of experiments refers to the process of planning

the experiments so that appropriate data will be collected and analyzed

by statistical methods, resulting in valid and objective conclusions.

• There are two aspects to any experimental problem i) design of the

experiment and ii) statistical analysis of the data.

• There are three basic principles of design of experiments

i) Randomisation ii) replication iii) blocking or local control

Randomization

• Allocation of the experimental material and the order of the runs of the

experiment performed are randomly determined.

• Statistical methods require that observations (or Errors) be independently

distributed random variables. Randomization make this assumption valid.

• Randomization average out effects of extraneous factors

• Randomization can be done by computer programs or random number

tables

Replication

• Replication means independent repeat run of each factor combination.

• Experimenter can obtain the estimate of experimental error . This estimate

of error is the basic unit of measurement for determining whether

observed differences in the data are really statistically significant.

• If sample mean is used to estimate the true mean, then

• variance of sample mean=(variance of the observations)/ no. of replications

• Increase in replications would give better estimates of mean.

Blocking

• It helps in improving the precision of the experiment

• It is used to reduce or eliminate the variability transmitted from

nuisance factors– factors that may influence the response variable

but in which we are not interested.

• Blocking means putting similar experimental material in one block.

And applying treatments in each block.

• Two batches of raw material for hardness testing experiment.

Guidelines for Designing an Experiments

1. Recognition of and statement of the problem

2. Selection of the response variable

3. Choice of factors, levels and ranges

4. Choice of experimental design

5. Performing the experiment

6. Statistical analysis of the data

7. Conclusions and recommendations

The first three points are related to pre experimental planning

Guidelines for Designing an Experiment

1. Recognition of and statement of the problemIt is necessary to develop all ideas about the objectives of the experiment . Team

approach is useful. Some of the reasons for running an experiment area)Factor screening- To find most influential factors having impact on response variable.b)Optimization- To find settings or levels of the important factors that result in desirable values of response variablec)Confirmation- To verify some theory or past experience. Testing effectiveness of new substitute materiald) Discovery - To find new materiale) Robustness- To find the conditions under which response variable seriously degrade

Guidelines for Designing an Experiment

2. Selection of the response variable

It should give required information. The measurement system capability is important.

3. Choice of factors, levels and rangesThe important factors having most influence are called design factors

or nuisance factors. These are classified as controllable, uncontrollable and noise factors . The levels of controllable factor are set by experimenter. It is important to minimize the variability transmitted by noise factors .

Cause –effect diagram , Fishbone diagram, process knowledge will be helpful in deciding levels.

Guidelines for Designing an Experiment

4. Choice of experimental design

It depends on the previous steps .There standard designs available. One can choose among them that best suits our experiment. Software are also available for deciding the design to be used. Model is also determined. it is the empirical relation between factors and response variable

5.Performing the experiment. Take utmost care to execute experiment as per plan. Any

mistake will lead to increase in error.

Guidelines for Designing an Experiment

6.Statistical analysis of the data

It assures that the Conclusions are objective.

Use graphical methods and Empirical model

7. Conclusions and recommendations

Draw practical conclusions and recommend the action.

Experimentation is a iterative procedure.

Conduct series of small experiments instead of comprehensive experiment

Best luck for better experimentation

Thank you