Laboratory work 2

RESEARCH OF PROPERTY OF PRODUCIBILITY OF TECHNOLOGICAL PROCESS

Purpose of work: A lead through of statistical analysis of results of technological process is for establishment of his property of reducibility

Contents of work

1. Analysis and introduction in PEOM of initial statistical information, got at implementation LR1.

2. Leadthrough of autocorrelation analysis of initial data and construction the chart of autocorrelation function (CAF) of index of efficiency of technological process (TP).

3. Analysis of the got results of autocorrelation analysis and establishment of presence of sign of producibility of TP.

4. Registration of job performances.

2.1. Theoretical information (more thoroughly theoretical material for this LR is expounded in a theme 3 lecture employments). As a result of implementation of this LR it is necessary to define in TP the presence of property of producibility and to make decision in relation to a moment time of Tv, which this property will show up in. The sign of producibility belongs to the plural of high-quality estimations of TP, with most which students must were familiarize at implementation of LR1.

Property of producibility is characterized by the degree of closeness of results of estimations of select description of object, which is carried out during a select period by supervisions, taking into account a that circumstance, that research terms on this period can change under the action of different casual factors.

For the analysis of presence of the noted sign of TP it is again needed to take advantage of statistical information in relation to time-history of certain description of TP (as a rule, select index of efficiency of Y), that to work with sentinel rows - values of index of Y, which are fixed in certain moments of time of Ti supervision. The purpose of similar analysis is determination of moment of time of Tv, when the got estimations of index of Y can be considered objective and independent.

Before determination of property of reducibility often apply at the study of processes of object, which have the so-called “memory”.

This property shows up in that the values of similar parameters in some moment of burn-time object can depend on their values, what of them had in previous moment of time. If at a parameter found out such property, process, what this parameter characterizes, it is possible to classify as a “process with history” or “process with memory”.

Example.

Suppose that the study be an indicator of efficiency (PE) TS as the quality of products of this company. In the study, we are interested in TS, which is the connection between this indicator and performance characteristics of certain manufacturing operations of production. Note that the figure is multifactorial and depends not only on the quality of the process equipment, and training and performers, as raw materials from which these products are made, and so on. For this experiment, the last two factors will be classified as involuntary because the study of their value is not fixed. In this case it can be assumed that the change in quality of manufacturing operations for the parameter values ​​can be seen only with constant values ​​of uncontrolled parameters. For example, if the parameter values ​​as the incoming raw materials are not controlled, then with the change of their values ​​for new shipments of raw materials purchased quite possible is to change the values ​​of which can be seen as a reason to change the quality of the process equipment. Thus, it can be noted that for a party with some raw quality level of TP and his figure will have a "memory". This "memory" will exist until this batch of raw material is not over. Suppose that this happens in some time Tv. From this moment begins a new "memory" of our process and its selected index. The less the impact of uncontrollable factors on the characteristics of the process are controlled, the greater is the degree of reproducibility of the properties of this process.

That is, at time Te for which TP in the chosen feature will be recognized reproducible, can be considered the characteristics received quite objective and, importantly, independent of the influence of uncontrollable parameters. Fixing the display properties of reproducibility allows management to make the right decisions on the possible values ​​of the governing parameter changes (in this case - the quality of process equipment).

Thus, to study the properties of the reproducibility of the process, the initial data must have a time series (CR) recorded values ​​of PE studied in the previous RL. As the level of the Czech Republic will choose the value of PE studied in previous LR1 (data of one of the months of the company).

Suppose that the diagram of the Czech Republic (not completely) is shown in Figure 2.1. The figure shows the level of CR points that were given as the initial data in the variant LR1 time to time (weekdays), (​​1-month, 2-month, etc.). That is our problem by this time beat the Czech Republic is one working day.

Fig.2.1. Example time diagram dimensional interval time series PE Y

To establish the presence of signs of reproducibility TP use the method of autocorrelation analysis based on receipt and examination autocorrelation function (ACF) of a random process.

ACF is essentially a set of values ​​of the correlation coefficients between the values ​​underlying the Czech Republic and its the same, only shifted in time at some interval. This interval is called time shift or simply shift. ACF CR is defined as:

where: - multiple levels under baseline CR and CR-biased to a time shift ; , - expectation levels under baseline CR and the same CR Offset Shear ; - expectation of the product of the baseline levels and biased CR at time ; , - standard deviation levels under baseline and biased CR; - total levels of baseline CR; - number of time cycles, which is offset ,( ); , - at baseline, respectively, in CR times and .

On fig.2.2 schematically given type base CR (solid line) and the CR, which is shifted to offset (thick dashed line). On fig.2.3 are illustrative example graph ACF, which is called the correlogram. It clearly shows how often and with what delay parameter change affects these values ​​it.

Fig.2.2. Graphical representation of the base shear CR time shift

Fig.2.3. Graphical representation korelohramm ACF of the time series

At time Te for which the condition або ,

where - due to some limiting value close to 0, the result of research chosen PE Y can be considered statistically independent of uncontrollable factors, respectively - the process reproducible. Immediate objective performance LR2 is the definition of a point Te, in which we can assume TP reproducible.