Laboratory work 1 study of qualititive characteristics of technological processes
Aim: Providing of qualititive standards for the manufacturing process by obtained statistics
Contents
1. Analysis and initial introduction to PC statistical information about the values of performance indicators process (TP).
2. Preparation and evaluation of basic statistical characteristics of production performance systems values
3. Analysis of obtained results and defining of qualitative characteristics of Technological Process(TP).
4. Writing of results
1.1. Theoretical information (more detailed theoretical information for this LR you can find in the 3rd lecture).
Quality of TP is defined by elements of the technological system where this process occurs. At the same time, the quality of TP determines the efficiency of the whole technological system.
The quality change of TP could be connected with:
- change of elements of technological equipment as a result of the processes of aging and demolishing;
- change in the intensity of incoming or internal material flows in the system;
- violation of the functional relationships between the structural elements of the system;
- by external or internal disturbances, which were not considered while the organization of the system.
The TP management task is to choose the most rational from the set of possible states, from the nature of this tasks, execution of which is entrusted to the object. The solution of such problems is based on the obtained values adopted for this facility performance indicator. Transferring the system to a more organized state using managing is done by changing the values of the characteristics of the system.
To assess the effectiveness and management of selected TPs, the sets of quantitative indicators can be chosen (for example, the volume of output, quality, amount of spent resources, etc.), which characterize certain aspects of the functioning of the technological system. In its turn, these parameters depend on some technical, technological and economic characteristics of the production. For example, the following characteristics include accuracy and productivity of manufacturing equipment efficiency technologies used in the enterprise, the quality of management modes and parameters of manufacturing operations so on.
Thus, when analyzing the performance of TP, the analytic form of each of them can be expressed as a function of many variables, which are the special characteristics of TPs.
Additionally, we note that in the view of the impact of many factors on specific performance indicator, we can assume that the nature of change will be wearing random. Therefore, the study of such performance should be attributed to the exploration of random processes.
Suppose
that
for
the process, which is used in the enterprise, some indicators of its
quality
are selected.
We
denote
them
.
We
will assume that for the index
its nominal (planned) value
is
set,
that meets certain specified efficiency criteria. Since the change in
values of
is random, then its characteristics should be used statistical
evaluation of which will use: mathematical expectation
;
standard deviation
;
dispersion
,
and distribution law
of
index value
.
Further, to simplify the following characteristics will use
appropriate notation -
and
.
In practice, there assumed that for the well organized TP, the quality score value subordinate to the normal distribution law. For qualitative characteristics of TP the following criteria are used: stability, sustainability, reproducibility, accuracy, intention.
Stability of TP is its ability to retain the time value of all the above mentioned statistical estimates of its quality index and its distribution law.
Sustainability
TP - property
of the process to save
in
time
the
stability of statistical estimates
and
.
It
is
fair
that
the
stable
TP
is
sustainable.
But
not
always
vice
versa.
Reproducibilitive process is characterized by small changes in the values chosen for different time intervals.
Developing
of qualitative characteristics of TP using the above mentioned
criteria could be made with the help of statistical analysis of i
quantity of realizations
,
change of random function
of
performance indicator.
If
we analyze ensemble of
i’th
realizations
and
calculate
to
each
of
them
the
mathematical
expectation
,
standard
deviation
and
dispersion
and determine the type of the distribution law
of
values of index
,
then
we can determine the above
mentioned
criteria of
TPs.
Reproducibility
of
TP
could
be
determined
by
ergodic random process of changing the values
,
which
is conducted by analyzing the values of autocorrelation
function
.
Sustainability
of
TP
is
determined
by
the
values
and
of
function change random process
.
Also
with
the
help
of
and
we
can determine additional qualitative characteristics of TP:
intention
and accuracy.
The intention of TP is determined by the nature of change in values , and accuracy - .
Thus, if the result of statistical analysis of several samples indicator for every i’th of which we obtain values , , , and also determine the distribution law , then on the basis of the collected data, the following conclusions concerning the nature of TP, which was examined could be
:а)
if
the following conditions satisfy:
= const;
=
=
const;
obey the normal distribution law, then
TP is considered to be stable;
б) if the following conditions satisfy: = const; = = const then TP is considered to be sustainable;
в) if the following condition satisfy = = const then TP is considered to be accurate;
г) if = const then TP is considered to be intended.
Signs of reproducibility of TP we will establish due to the data of laboratory work #2.