3. Introduction
System
Process
A system is a set of interacting or
interdependent components
forming an integrated whole.
Ex
Banking System,
Reservation system.
Social system
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.
4. 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.
5. 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.
6. Manufacturing a car
• Productivity= Annual Revenue/ Annual cost
• Factors that affect the demand of car as follows
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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
7. 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.
8. Questions about the Experiment
1. 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?
9. Models
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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
10. Process or system
A process or system can
be represented by the
diagram
Inputs
Controlling
factors
Process
Un controling factors
outputs
11. 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 milk
2. Quantity of curd culture added to milk
3. PH value of the curd
4. Fat of milk
5. Pot used for curd
6. Room temperature
7. Seasons winter , summer , monsoon
8. Timing of the day morning , evening
9. The list can be extended.
12. Strategy of Experimentation
Best guess approach
Select 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.
13. 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
14. 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
15. 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.
16. 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.
17. 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
18. Guidelines for Designing an
Experiment
1. Recognition of and statement of the problem
It is necessary to develop all ideas about the objectives of the experiment .
Team approach is useful.
Some of the reasons for running an experiment are
a)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 variable
c)Confirmation- To verify some theory or past experience. Testing
effectiveness of new substitute material
d) Discovery To find new material
e) RobustnessTo find the conditions under which response variable
seriously degrade
19. 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 ranges
The 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.
20. 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.
21. 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
