Laboratory work 3 choice for characteristic for technical process management
Purpose: Rationale for the characteristics of the process that can be used to improve the results
Contents of
1. Analysis and introduction to the PC original experimental data.
2. Conducting linear correlation analysis of initial data
3. Analysis of the results and forming conclusions.
4. Execution results.
1.1. Theoretical information (more theoretical material for this hr forth in Articles 5 lectures).
Quality management in technological systems (TS) is determined on the one hand, by choosing the best management decisions, on the other hand, the possibility of their effective implementation. Improving the quality of governance should lead to a reduction of losses in the performance of enterprise resource processes that are involved in it.
The
organization of management TS appropriateness of any management
decision should be assessed by changing the values of some
selected criteria. This criterion should have corresponding
performance indicators. This figure should be the nature of the
physical variable that adequately reflects the nature of performance
criteria, is a quantitative measure and is a function of the basic
characteristics and parameters of the object. Given the complexity of
such objects as TS, their versatility, a large number of their
characteristics, values change which has impact on the value of
the naturally assume that in the mathematical sense is a function of
many variables. Note that these variables are not equivalent in terms
of management efficiency values. Management by some variables are
quite costly, others - not provides tangible effect in the change of
values, others create the effect of management only through a large
period of time, and so on. Given the strong desire to achieve
management results very quickly and with low cost resources selection
process parameter control becomes a very complex task. For the
solution, there are certain mathematical techniques - both
theoretical and experimental. By theoretical methods (methods that do
not require pre-assembled experimental material) include methods of
peer reviews. Experimental methods require basically experimental
data obtained from a real object or the object-analogue. Such methods
include the elements of the theory sensitivities of variance or
correlation analysis. It is through the latter method in this LW
problem will be solved in the general election set
process parameters (PP) those that can be effectively used as a
control.
Description of the method of correlation analysis
In
situations where you do not know whether there is a correlation
between some characteristics of the process that is investigated,
applying the method of correlation analysis. Correlation analysis of
physical quantities enables statistically assess the degree of
interaction between the process parameters and to determine the
effectiveness of this communication. In our case, using the method of
correlation analysis will help determine how significant is the
relationship between the selected performance indicators of
performance F criteria PP and some parameters of the TS with the
total set
.
The concept of correlation coefficient
In solving the problem of finding the presence of correlation between the parameters TP and its evaluation index these physical quantities are classified as accidental. Then the functional relationship between them, which are found are stochastic (random) character.
Suppose
that an experiment for finding and evaluate the relationship of some
physical quantities X and Y (and the value X is classified as an
independent, or a factor, and the value Y - as the dependent variable
or response). In preparation for the experiment value of factor X are
scaled to n values
in the range of change of its values
.
The experimental part of the study is as follows.
For each of the planned values of the independent variable X is made a certain number m of experiments on the measurement values Y, that we have - fold repetition of the experiment with the same initial conditions. As a result of accumulated values are. The obtained experimental data can add to your table view is presented Table. 3.1. It: - the number determined for the experimental fixed values of the variable, and - the number of experiments to measure the values of a variable with the same value). Add that for different values of measurements need not be the same.
Тable. 3.1
Table of results of the correlation experiment
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Initial
values
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... |
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Number of experiment |
Results
of experiments on the measurement values
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1 |
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... |
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2 |
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... |
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... |
... |
... |
... |
... |
... |
... |
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... |
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independent
variable
for each series of experiments
dependent
variable
For
all obtained in each i-th
series of experiments (the initial condition
)
values
are determined by their average value
.
Then, according to an experiment conducted graphic
.
An example of such a schedule submitted to Fig.3.1 (not shown in the
figure point spread
for
each fixed value
,
and show only their average value
).
Fig.3.1. The principle of constructing experimental regression line
Constructed graph is called the regression line relationship variables and . This chart illustrates the relationship between law random variables X and Y with some approximation.
The
smaller spread of values
around the regression line, the greater is the statistical
relationship between X and Y. If numbers
are located as close as possible to the appropriate values
,
we can conclude the existence of a strong statistical relationship
between X and Y, which can be approximated graphically regression
line and submit in the form analytical expression.
The degree of communication correlation between X and Y is defined by the values of the correlation coefficient:
,
where
M[х·у] - mathematical expectation of the product of pairs of
values (xi;
yі,j)
results of experiments; M[х] і М[у] – accordance mathematical
expectation values хi
and
yі,j,
results of experiments,
і
- mean-square deviation values X і Y.
Correlation coefficient ranges from -1 to 1:
-1
≤
≤ 1.
When
=
1 believe that the values X і Y are
absolute
correlated,
ie values
,
the experiences equal value
,
who are on the regression line.
When
= 1 there is a positive correlation, ie, increasing values of X
meets Y values increase.
When = -1 there is a negative correlation, ie, increasing X corresponding decrease in Y. The correlation between X and Y is strong if = 0,7 ÷ 1; average, when = 0,3 ÷ 0,7, and weak, if < 0,3.
Value = 0 of X and Y can have two cases:
1) they do not correlate;
2) the law of non-linear regression.