MECH 519- Instrumentation and measurement, Spring 2008
Statistical analysis lab
Introduction
There are two distinguished models for describing the events in science and
engineering.
One is the deterministic model, in which the relationship among a dependent
variable and independent variables is strictly and accurately described by a governing
equation. In this type of model, the outcome is predictable and solely determined by
independent variables. The physical meaning of this type of models is that all possible
mechanism or issues about the relationship among the dependent and independent
variables are fully understood and fully considered.
Another model is the statistical or probabilistic model. In this model, the outcome
is not predictable so that the value of the dependent variable should be described by a
random variable. There are two main causes for this phenomenon:
(1) Some mechanism for governing the relationship among the dependent
variable and independent variables are not fully understood. When these
mechanisms are fully understood, the statistical or probabilistic model can be
replaced by the deterministic model. Weather forecast is a good example.
With more advanced technology, current weather forecast is more reliable.
(2) Some mechanisms are very hard to be fully controlled. For example, human
error is very hard to be fully controlled. For another example, the
microstructure of a material is very hard to be fully controlled. If the material
composition and the microstructure of material are fully controlled, the yield
strength of this material will be a constant. Actually, the yield strength of the
same brand material is not a constant due to the variation of composition and
the microstructure of the material.
The statistical analysis or probability theory is a good tool to deal with uncertainty
or randomness. People will use information based on probabilistic theory to make their
decision. However, proper interpretation of information, data or conclusion from
probabilistic theory is a must because statistical model can only provide imperfect and
incomplete information. .
Objectives
In this statistical analysis lab, the main goal is to apply the several basic concepts
in statistical theory discussed in class to assess measurement uncertainty. The objectives
of this statistical analysis lab are:
To calculate the mean and standard deviation of a set of data
To create the histogram
To determine the confidence intervals with given confidence level
To apply the 6 sigma principle to judge some data
To run simple linear regression and determine the uncertainty of the fitting line.
Notes: Submit the lab report in the format of a word file
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