the Estimation of mutual agency it is indicative qualities and is certain key figure of merit
Main objective of it, an element of a technique of statistical management difficult processes is identification of key figures of merit of the subprocesses which martempering will allow to combine mathematical expectations of distributions of figures of merit of exits of a difficult process with their rating values and it is simultaneously essential to reduce a variation of the personal computer of exits of the difficult
Process.
This purpose is attained by means of the algorithm represented in drawing 2.4.11ервым a stage is allocation, groups IIK distribution, which (the greatest impact on distribution parametres makes on mathematical expectation or a dispersion), the investigated personal computer of an exit difficult industrial engineers cheskogo process and.
Drawing 2.4. The circuit design of determination of dependence between the personal computer and definitions key show ліс l I qualities
In the capacity of criterion of sampling подіруппіл the personal computer, making the greatest impact, is offered [I] relation of an average quadratic deviation (or mathematical expectation) and regression factor і th personal computer of subprocess to standard quadratic deviations (or to mathematical expectation)
The personal computer of a difficult techno of logic process ^ the given relation will be called Further factor of the contribution of the personal computer. The given factor which is paying off for mathematical expectation and a dispersion as;
Мхійі + bt Mh
* 1 00 %;
(11.12)
ft „= - *100 %. ДІ. 1 Ї)
Sh
The subgroup of the personal computer which is characterised by the maximum factor of the contribution, makes the greatest impact on spread of the personal computer difficult technological prodessa.
Such estimation becomes possible at the expense of the properties manifested by functions at the expense of properties of dispersions and mathematical expectations at convolution of distributions of the personal computer of subprocesses in distribution of the personal computer difficult tehnologichsskogo jіроцесеа.
According to [26,85] if dependence of the personal computer of an exit of difficult process () and
Subprocesses entering into it (l;) it is possible to write down as:
And
+ (AND, 14)
i-j
That mathematical expectation of the personal computer of exits of difficult process will pay off as:
p
Md. = (j, М1 (+ Vd - (11.15)
1 = 1
Mj - mathematical expectation of the personal computer of an exit of a difficult process, Mh. - matemat icheskoe expectation of the personal computer of//th figure of merit.
From the formula directly follows, THAT the more Сйі/УХ (+ і), the more its agency Еіа M. Accordingly a measure of the contribution of the personal computer g ' th subprocess in mathematical expectation of the personal computer slozhnoju a process can
PgMh; + Ьі
To be the relation—!—.
Mg
Accordingly a dispersion of the personal computer an exit combine from a process will pay off proceeding from the formula:
P ' AND
oj - V Jar - =У (11.16)
1=0 to; t=i і 1 j-> at g-> About, II. J 7)
I st? (And, ETH] - д3о ^) \prig - »-1.
Where (1118)
And from (11.17) dependence is visible: the above value jg (thz, the
Their agency on analogous with the instance set forth above with mathematical expectation is stronger, a measure of the contribution of the personal computer of//th subprocess in spread of values of the personal computer of an exit of a difficult process can be
The relation------,
Measure of measurement of not casual magnitudes jg, is the factor of the regression, the matching subprocesses, counted as [89]:
«f =
(11.19)
Where - a covariance between 7th personal computer of subprocess and the personal computer difficult
Process and z, and in - number of pairs data for h. And h.
However application of factor of the regression counted by formula (11.15), is is possible only for linear functions. Dli adequate sampling of the subprocess, making the greatest impact in case function of dependence of matching personal computers has nonlinear character, it is necessary to lead it by some transformations to a linear aspect. In table 2.5 most often meeting aspects of nonlinear functions, and also matching transformations of factors of a regression n the regression contribution are resulted.
Table 2.5.
Transformation of factor of the contribution depending on a regression aspect
Pranetsekis function to linear NDTSIU
Conducting of the first stage allows to reduce essentially quantity of the personal computer, interconnections between which are necessary for studying for determination of the key personal computer. It is obvious, that in most cases the personal computers having the greatest factor of the contribution will refer to to the subprocesses, had more close to exits of difficult process.
Further it is necessary to instal key figures of merit (handheld computer), and the greatest extent influencing zga exits of a difficult process. On the personal computer which are final in chosen іруппе the personal computer, directly influences three groups of factors:
1. The personal computers which are exits of other subprocesses;
2. Control actions of the given personal computer;
3. Disturbing affectings.
With the account j oe about, that personal computers of control actions are independent of the personal computer of exits of other processes by magnitudes the formula II. 16) subprocess it can be spread out as follows:
Where / - number 11К directly previous investigated 7 personal computers, and — a serial number of the personal computer of control action for 7th personal computer, g - the random quantity symbolising the saved up contribution of disturbing affectings.
If in (11.19) in appropriate way to spread out personal computer dispersions
The previous subprocesses to be gained following expression:
Where g — a serial number of the personal computer of an entry of the difficult process influencing 7th personal computer, aw - a serial number of the personal computer of the subprocess previous of 7 personal computers.
Similarly with use (IL15) the mathematical expectation is displayed:
Thus, finally the basic characteristics of distribution of the personal computer ljubosh subprocess depend on matching personal computers of entries of a difficult process., FROM all personal computers of control actions previous GEK and the saved up contribution of disturbing affectings. Hence, the problem of statistical management is reduced by a difficult process to allocation of the handheld computer which are referring to or to entries of a difficult process, or to control actions of subprocesses making it,
The handheld computer of a difficult process is installed by consecutive application of factor of the contribution to all the personal computer of exits of subprocesses of an investigated subgroup of the personal computer. Then the factor of a gain of the personal computer by difference scaling between factors of the contribution of the personal computer of an exit of subprocess in the final personal computer of group of the personal computer and factor of contributions of the personal computer previous it pays off. For the personal computer of entries of a difficult process the gain factor is equal to contribution factor. Calculation of factor of a gain is made for the personal computer of exits of subprocesses but the formula:
(IL22)
Where / “matching level in hierarchy of the personal computer, previous level of hierarchy of a parametre / - a serial number of a parametre of level D directly connected with xh g - a serial number of a parametre of level/-/, directly connected with xlf.
After revealing of the personal computer with the greatest factor of a gain it is necessary to count values of factor of the contribution for its personal computer
Control actions [II]. This becomes for necessity definition to reveal disturbing affectings dli the observed personal computer,
Disturbing affectings are connected with those parametres of a difficult process with which cannot be operated or if management of them is connected with the big expenses [$1,90]. Besides, disturbing affectings can be called not considered personal computers or giaimodejstviem between them and the investigated personal computer. Scaling of level of disturbing affectings is expedient for spending at inequality performance:
T Ї I?
4 tfQ.u < WB. Ї, (IL23)
3 = 1 E =]
Scaling are made by means of use of factor of level ynmushchajushchih affectings (KZl) and for mathematical expectation
Pay off as:
(IL24)
Values To,
A little bit more difficult also are made by means of the formula:
[$ «• [й|сг ^ + 2 KJl7l] + [* = 1 a^o-nT | 4 2 i’rj 0г2), there is a high probability of that some personal computers or interconnections between them, essentially influencing pases investigated group of the personal computer, are not revealed. In this case it is necessary to revise process on revealing of such personal computers or interconnections between them. As a result of definition of the personal computer with the greatest factor of a gain two alternatives ' are possible 1. The greatest factor of a gain is characteristic for the personal computer of an exit of subprocess p this case it is necessary to count the contribution. The personal computer of its control actions, one of which is key figure of merit of a difficult process; 2. The greatest factor of a gain is characteristic for the personal computer of an entry of Difficult process, in this case - it is key Figure of merit difficult that but logic process, Thus, model of statistical management of the difficult Technological processes it is possible to represent in the form of sequence of elements making it (drawing 2,6). 1
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