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CRITERIA THE ESTIMATION EXPEDIENCY OF CLASSIFICATION INFORMATION ON RELIABILITY OF THE EQUIPMENT AND DEVICES EPS
Farhadzadeh E.M., Muradaliyev A.Z., Abdullayeva S.A.
Azerbaijan Scientific-Research and Design-Prospecting Institute of Energetic AZ1012, Ave. H.Zardabi-94, e-mail:fem1939@rambler.ru
Abstract
Analysis of statistical data about refusals, maintenance service and repair of objects of electric systems, is an indispensable condition of a quantitative estimation of reliability of their work. The analysis assumes classification of data on a sort of attributes and their versions. Thus, the basic question there is a revealing significant version of attributes. The importance of an attribute established based on statistical criteria of check of hypotheses. The criteria based on boundary fiducially estimation of intervals are offered.
INTRODUCTION
Necessity and methodology of the analysis of reliability of work of the equipment and devices (objects) of electro power systems (EPS) according to about their deterioration, refusals, tests and restoration of a technical condition are regulated by corresponding Normative materials. Prominent feature of these data is dependence on the big number of attributes and their versions. This dependence carries data to a class multivariate. Multivariate character of data not considered at a quantitative estimation of parameters of reliability (PR) objects EPS.
1. Classification parameters of reliability of objects EPS
The variety of properties of reliability and describing these properties PR causes necessity of grouping PR on a way of calculation. As an example in table 1 formulas of calculation of the some PR power units (PU) TPS are resulted. Following designations are accepted: na - number of power units; moT,i - number of switching-off i-th PU; moT,£ - number of switching-off of all PU; Tp,i, -j- th realization of duration of the worker (p) conditions i-th PU; maB,i - number of emergency switching-off i- th PU; maB,£ - number of emergency switching-off of all PU; TaB,i,j - j-th duration of emergency switching-off i-th PU; m»n.,i - number of unsuccessful start-up i-th PU; mn i - number of start-up i- th PU; THn, i,j - duration j- th idle time after unsuccessful start-up i-th PU; mx.p.,i - number of switching-off in a cold reserve i-th PU; mx.p.aB,i - number of translations PU from a condition of cold reserve in an emergency condition; tn.p.,i - duration of idle time in scheduled repair i-th PU.
Let's distinguish PR, calculated as:
*
- an average arithmetic random variables. According to tabl.1 is t* and TaB ;
- relative size of total duration of a condition. As an example parameters P*, Pp, P* serve (see tabl.1.)
- probability of occurrence of event. In tabl.1 it- Q*B, Qn, and Q*
- specific number of events. In table 1 it is specific number of emergency switching-off PU (h*B)
and its versions (automatic switching-off PU, emergency switching-off PU by the personnel, manually, switching-off PU under the emergency application).
- function noted above individual parameters. In table 1 the factor of readiness K* and factor of technical use K*,, are resulted.
Table 1. Sample of parameters of reliability of power units 300 МWt TES
Condition Parameters of reliability Formula of calculation
Individual parameters
Finding PU in work Relative size of total duration of work PU within year, % P - p Щ tnoiii L ZTPi, j / п •8760 i=i j=\
Average duration of continuous work, cl T * = p пб mom,i пб L LTP-i, j / L mom, i i=1 j=1 i=1
Emergency останов PU Specific number of emergency switching-off (on 1000 cl. works) Ke = пб пб mOT 103Lmae, /LLTPi,j i=1 i=1 j=1
Specific number of switching-off under the emergency application; К.з. - Пб щ Пот = 103Lma3i, /LL*PiUJ i=1 i=1 j=1
Specific number of automatic switching-off at system failures Relative number of emergency switching-off Ко -Öl = 103Lmao,i /LL*PJJ i=1 i=1 j=1 пб пб = L mae,i / L mom,i i=1 i=1
Finding in emergency repair PU Average idle time in emergency repair, cl. Relative size of total duration of idle time in emergency repair, cl. T * - ae P: - пб mas,i пб L, L \ Tae i j / L, mae,i i=1 j=1 i=1 пб mae,i LLTa«i,j /п6 • 8760 i=1 J=1
Preservation of equipment PU Probability of refusal PU at start-up Probability of translation in a condition emergency repair from a condition of a cold reserve QHn пб пб =L mnnj/ L mni i=1 i=1 пб пб P. =L mрез,о. р J L m i=1 i=1
Cold reserve Relative size of total duration of a finding in a cold reserve P* рез пб m рез,! = 1 i,j /п6 • 8760 i=1 j=1
Scheduled repair Average duration of scheduled repair T * - п. р пб mn.P ,t пб - y y t /7 m 7 j 7 j n. P.i, j 7 j n. p.,i i=1 j=1 i=1
Complex parameters
Factor of readiness КГ - --P'/( P* + P* ) p V p ae s . = (P* + P* + P* ) V p ae рез s
Factor technical uses TT* КТ .И
2. Criteria of an estimation of character of a divergence M*,3 (taB) and MV,3 (t ^).
Following criteria recommended: Criterion K1. It is based on comparison of probability of empirical value of absolute size of a
relative deviation MV3 (taB) from MS3 (xaB) with critical (c) value of this probability equal
ak.
Calculations spent in following sequence:
1171 ill l\/. .. ........... ,
lV,3 ( aB ) llom Ms,3
defined:
r* s x -m «-*
the absolute size of a relative deviation MV3(taB) from ) under the formula
, ^ [(M (t as ) - M.3 (tas )]
SMV,3 (taB ) = -' , --(1)
M.3 (taB )
- tabulated data of [1] discrete values of statistical function fidudally distributions (s.f.f.d.) F*[8MV*(taB)] the required probability is defined av=1- FV[5MVV(taB)]. Here SMV*(taB) -counted on the basis of imitating modeling (**) possible values of absolute size of a relative
deviation MV,3 (taB ) from MS'3 (taB ) .
Note. Oudy^axbHue distributions for the first time have been entered into R.E.Fisherom's consideration in 30th years of the last century. These distributions characterize likelihood distributions of possible values of estimations of parameters of distribution of random variables. It specified that it is necessary to trust only statistical conclusions which basis is empirical data. A.N.Kolmogorov in 1942-year note, that fiducially probabilities and intervals are the most suitable at small number of supervision [2]. Transition from confidential intervals to fiducially is expedient at multivariate character of statistical data. Application to multivariate data of the mathematical device of functions of distribution of random variables of casual sample of general set can lead to erroneous recommendations. As it has noted been above the statistical data describing reliability of objects EPS concern to a class multivariate, and samples of these data on set version of an attribute (VA) - are not casual.
- if av does not exceed ak classification of set of statistical data on j- th versions i- th an attribute is inexpedient. In engineering calculations ak is accepted usually equal 0,05 or 0,1.
Lack of this criterion is necessity of the reference to the tables setting discrete values
fiducially distribution F [SM^t^)] allowing for set nv and SMV3 (t) roughly to define probability FV[SMV.3 (taB )].
Example 1. Let some data set is known about taB PU TPS capacity 300 MWt MV3(taB) = 72,4c.. Sample of realizations is received taB for one of PU and settlement size M* ^t^ ) = 51c. at nv=2. It is required to establish character of a divergence Mz 3 (taB ) and MV 3 (t aB). For the decision of this problem:
. ¡51 - 72,41
- it is calculated SM v (t ) = --— = 0,296
V'3 v aB / 4
- on tabl.1 [1] for nv=2 we find probability F* [SM V* (t aB )] s0,5
- as av=0,5. and aK=0,05<<av, classification of a data set about taB it is inexpedient. Criterion K2. It is based on comparison SMV3 (taB) and SMVK(taB) . According to the [1] size
SMV K (taB) corresponding aK=1- F [SM VK (taB )], it is calculated under the formula
SM V'K (taB ) = A/A/»V (2)
44
0,994 critical values SM V K (taB) approximating with accuracy for set ak and nv.
Here SMV (taB) - realization of possible absolute values of a relative deviation MV(taB) and
M V3 (taB); M
V(taB) - realizations of the possible values MV(taB) modeled on s.f.d. F, (taB )
for a preset value nv; A - constant factor.
The size defined ak. For aK=0,05 factor A=1,13, and for aK=0,1 - it is equal 0,95. Thus,
classification of a data set taB it is expedient, if SM* 3 (t ae) exceed SM * K (zae).
Example 2. We shall take advantage of data of an example 1. M v3(taB) = 72,4c. and
M V,3(taB) = 51c.; nv=2. Define critical value SM V*K(taB) = 1,13/72 = 0,80. Thus, as
SMv3(taB) << SMV ) classification of a data set with a significance value 0,05 is
inexpedient.
The considered example shows, that criterion K2 is simple enough. It is necessary to execute only two elementary calculations.
Criterion K3. It is based on comparison of experimental estimations Mv3(taB) and Mv3(taB) with boundary values fiducially intervals
M
V ,(l-aL ) (xae MV.aL(Xae )
Calculated on s.f.f.d. F [ÔM V K (xaB )]. Comparison carried out in following sequence:
MV,3 (^ae ) < M¡.S ^ae )
If
and M V.3 (xae ) < MVVak) (^ae ) Where MWat) ^ae ) = M 1.3 (x) '
1 -
A
n
That classification is expedient
If
MV.3 (^ae ) > M¡.3 ^ae )
and MV.3 (^ae ) > MV,ak (^ae )
Where MV*.^ (Tae ) = M¡.3 CO
That classification is expedient.
If the condition (3) is carried out,
and MV(l-aJ (^ae ) < M V.3 (Xae )
l + A
vn;
v y
and m¡.3 (x ae ) > mv.pt (^ae )
Where Mv .pfc (Xae ) = MV.3 (X)
1 +
Ay
VS7.
That classification is expedient
If the condition (6) is carried out,
and Mv.ai(Xae ) > MV.3 (Xae )
H /r ^ / \ ^^ f- X
and M¡.3 (Xae ) < M v .(1-pk ) (Xae )
Where M V.(1-^ ) (Xae ) = M V.3 (x) •
1 - A,
V 45
v y
(3)
(4)
(5)
(6)
(7)
(8)
(9) (10)
(11)
(12)
(13)
(14)
That classification is expedient
In all other cases, classification is inexpedient. Example 3. We shall address again to initial data of an example 1. As Ms 3 (xaB) > MV 3 (xaB), we
shall checkup conformity (4). For what it is calculated M** (i_a ) (xaB) .
MV*0, 95^) = 72,4 • (l - Vfy j = 14,4 c.
It is necessary to note, that for any ak=Pk the size of constant factor A can be calculated under the formula [1]
A=18,5a2 - 7,33a + 1,48 (15)
As Myg^^) > M**0 95(xaB), we shall check up a condition (10). For what we shall
calculate Mv>p (x^ ) . At ak=ßK=0,5
Mv,ßt Kb ) = 51-| 1 +
= 91, 9 c.
But as My 065 (xaB) > Mz 3 (t aB) classification is inexpedient.
Resulted calculations show, that, despite of a seeming bulkiness of criterion, calculation are small and simple. The opportunity concerns to advantages of this criterion to consider a mistake of the second sort. In the illustrative purposes in figure 1 the scheme of algorithm of application of criterion K3 is resulted the block.
2
1
Calculation ^ yes
M'v* (,- ajCO
4 no
r yes
I
3
MV,3(0<MI,3<XB)
Classification is expedient
Calculation
MV,Pk <Xb)
no
m;,3(tm)>M ;vPk)(o
yer
Classification is inexpedient
yes
Mv-,fraB)<MVßK (zj
no „ Calculation
Mv.«tCO
5 yes
C \ r "\
(T.J
Calculation MvH)W
9 no
no
no
6
7
Fig.1. The block the scheme of algorithm of application of criterion K3.
The analysis of the considered criteria allows establishing, that at the manual account VA it is necessary to consider as the basic criterion of check of expediency of classification of statistical data of some criterion K3. Criteria K2 and K1 should be considered as auxiliary mistakes for exception of the manual account.
Conclusion
1. It is necessary to distinguish five versions of ways of calculation of parameters of reliability of objects EPS on multivariate statistical data. These are the parameters calculated as average arithmetic random variables, parameters of relative duration of idle time, the parameters describing probability t frequency of occurrence of casual event, complex parameters.
2. Criteria check of hypotheses about the importance of versions of attributes for the parameters of reliability calculated as average arithmetic random variables recommended. As random variables modeled realizations of parameters of reliability considered, and as critical values boundary values fiducially intervals with the established factor of the importance entered.
References
1. Farhadzadeh E.M., Farzaliyev Y.Z., Muradaliyev A.Z. Comparison of parameters of average and individual reliability of the equipment of electro power systems. Electricity, №12, 2015.
2. Kolmogorov A.N. Definition of the center of dispersion and a measure of accuracy on the limited number of supervision. Proc. AS USSR. Series mathematical, 1942, №6, p.3-32
