CN101930503A - Method for computing importance in maintaining components of equipment - Google Patents

Abstract

The invention discloses a method for computing importance in maintaining components of equipment, comprising the following steps: utilizing variables to express a component set in a device system; establishing a state possibility distribution set of basic variables corresponding to the components; composing the multiple components into one assembly according to the series-parallel connection structural relationship; sequentially computing a conditional probability distribution set of all implicit variables, a posterior state distribution set of the variables of the device system, a posterior state distribution set of the variables of the device and the importance in maintaining each variable in the basic variable set; sequencing the importance in maintaining all the basic variables from high to low; and determining the most important maintaining components. The invention solves the problem of mutual separation between the reliability and the structural relevance of the existing method, simplifies the computation steps, improves the computation efficiency, can effectively recognize the key component of the device system, guides the monitoring and the maintaining of the key component, effectively improves the maintenance efficiency and reduces the maintenance cost.

Description

A kind of method for computing importance in maintaining components of equipment

Technical field

The invention belongs to plant maintenance and ensure the field, be specifically related to a kind of importance degree computing method of giving maintenance importance degree classification information for part of appliance.

Background technology

Fast development along with device design technology, equipment manufacturing technology and infotech, it is integrated, intelligent that legacy equipment moves towards gradually, inner structure and relevance are huge day by day and complicated, cause device systems to present great uncertainty at the distributions of its parts, the aspects such as incidence relation between parts.The maintenance personal is difficult to definite real failure cause, and takes effective maintenance measures, has brought great challenge for the plant maintenance safeguard work.

The importance degree analysis is important research contents in the reliability theory, and it can be used for, and fiduciary level is distributed, the fields such as optimal design of system.System's importance degree is meant that when a certain ingredient lost efficacy in the system, it can not satisfy the influence degree that regulation requires to total system.Importance degree is that a kind of quantity of each unit significance level in the reflection system embodies.The calculating of importance degree is come out each unit of system under certain physical significance, so the calculating of importance degree is one of important component part of system reliability quantitative test exactly by the big minispread of its importance.

Facts have proved that each ingredient influences difference to what thrashing produced in the system: some ingredient inefficacy can cause system crash, and some ingredient lost efficacy then can not produce serious consequence.Set up system's importance degree computing method, effective recognition system weak link, the work of guidance system optimal design, with the reliability index of less human and material resources raising original system.

Since at first proposing to come the contribution of quantization means ingredient to system performance with importance degree in 1969, Chinese scholars has been carried out a large amount of research to system's importance analysis from Birnbaum.Existing system importance degree computing method mainly comprise reliability importance computing method and structure importance computing method two big classes.

The hypothetical target device systems is a two condition monotone system S, and it has following feature: (a) equipment S is made up of n parts, i.e. C={C ₁, C ₂..., C _i..., C _n, C wherein _iRepresent i parts; (b) equipment S and parts C _iAll has only two states, i.e. duty 0 and malfunction 1; (c) reliability function of equipment S is represented with R (S), and the reliability function of parts is with gathering R={R (C ₁), R (C ₂) ..., R (C _i) ..., R (C _n) expression, wherein R (C _i) expression i parts reliability function; (d) the structural relation E=[E of each parts among the equipment S _Ij], 1≤i.j≤n represents, wherein E _Ij=1 expression has a directed edge from parts C _iPoint to parts C _j(e) lifting of any one part reliability can not reduce the reliability of entire equipment, promptly as P (C _i=0)＞P (C _i=0) time, P (S|P (C _i=0))＞P (S|P (C _i=0)).Two type systematic importance degree computing method are as follows respectively:

Reliability importance is the degree that causes the system reliability variation from the variation of the angle analysis ingredient reliability of reliability, and its computing method as the formula (1).The physical significance of reliability importance is, when the variation of same numerical value takes place in the reliability of different parts, and the degree difference that equipment S reliability changes.

$I{\left(R\right)}_{C_i}^S=\frac{\∂R\left(S\right)}{\∂R\left(C_i\right)}---\left(1\right)$

Wherein,

Expression parts C _iReliability importance with respect to equipment S.

At the incidence relation that exists between each ingredient in the system, Meng has proposed the structure importance notion and has been used for describing ingredient in the residing status of system relationship structure, and its computing method as the formula (2).The physical significance of structure importance is, as parts C _iWhen serviceable condition is changed to malfunction,, this unit status accounts for the ratio that other unit status variable is gathered feasible value sum because changing the equipment S fault that causes separately.

$I{\left(S\right)}_{C_i}^S=\frac{1}{2^{n-1}}\×\underset{c^{\′}}{\mathrm{\Σ}}(\mathrm{\Φ}(C_i=0,C^{\′})-\mathrm{\Φ}(C_i=1,C^{\′}))---\left(2\right)$

Wherein,

Expression parts C _iStructure importance with respect to equipment S; C '={ C ₁..., C _I-1, C _I+1..., C _nRepresent except parts C _iOutside the state variable set of all parts; All feasible state variable distributions of c ' expression C ' add up to 2 ^N-1Ф () is a structure function, represents when all parts are in a certain state, and the virtual condition of device systems, Ф ()=1 indication equipment S is in serviceable condition.

But existing method still has the following disadvantages: (a) the reliability importance computing method need be set up reliability function R (S) for device systems, are difficult to accurately make up this function when incidence relation between parts is complicated; (b) the angle calculation parts importance degree of structure importance computing method slave unit structure needs to calculate the minimal cut set that respectively comprises each parts, will be difficult to finish when equipment scale is huge; (c) reliability of part of appliance and architectural characteristic are two inseparable factors, and above-mentioned importance analysis is isolated and considered this two factors, is difficult to weigh the significance level of part of appliance comprehensively; (d) the system optimization task of main equipment oriented design phase of above-mentioned importance analysis is difficult to provide support for the physical device maintenance process.

Summary of the invention

In order to overcome the demand that prior art can not adapt to large-scale and complicated device, the deficiency that is difficult to weigh equipment and is difficult to provide support comprehensively for maintenance process, the invention provides a kind of towards safeguarding the method for computing importance in maintaining components of equipment that ensures, the critical component of effective identification equipment system instructs monitoring and maintenance to critical component fast.

The technical solution adopted for the present invention to solve the technical problems is: reliability and the significance level of structural relation calculating unit in maintenance process of taking all factors into consideration parts.At first, utilize existing parts and reliability information to identify the probability distribution over states of basic variable and basic variable; Secondly, go out to imply variable and conditional probability distribution thereof according to the device structure relation recognition; Then, when utilizing Bayes' theorem calculating basic variable to be in different conditions, the posteriority distributions of the implicit variable of device systems; Finally, adopt maintenance importance degree computing formula to calculate the maintenance importance degree of each basic variable, and ordering.The physical significance of maintenance importance degree is, it is parts cause the equipment integral fault under current reliability state a mathematical expectation, promptly when device systems need keep in repair, the parts of repair and replacement importance degree maximum brought maximum lifting can for the reliability of entire equipment.Concrete steps are as follows:

1, according to the component set C={C that comprises among the device systems S ₁, C ₂..., C _i..., C _n, C wherein _iRepresent i parts, n represents all number of components in the system, with each parts C _iUse variable X _iExpression, i=1 ..., n when the parts operate as normal, is 0 to the value of dependent variable, when unit failure, is 1 to the value of dependent variable, as the formula (3), and called after basic variable set X={X ₁, X ₂..., X _i..., X _n, X wherein _iI variable in the set of expression basic variable is because C _iWith X _iCorresponding one by one, the basic variable sum also is n;

I=1 wherein ..., n (3)

2, each part reliability function set R={R (C that provides according to the device design document ₁), R (C ₂) ..., R (C _i) ..., R (C _n), set up the probability distribution over states of the basic variable of each parts correspondence and gather P={P (X ₁=0), P (X ₂=0) ..., P (X _i=0) ..., P (X _n=0) }, as the formula (4), P (X wherein _i=0) probability distribution over states of i basic variable of expression;

P (X _i=0)=R (C _i), i=1 wherein ..., n (4)

3, the modular construction relational matrix E=[E that provides according to the device design document _Ij], 1≤i.j≤n presses the series parallel structure relation with a plurality of parts in the equipment and forms an assembly, uses variable Y _kExpression when the assembly operate as normal, is 0 to the value of dependent variable, when component faults, is 1 to the value of dependent variable, and the implicit variable of called after, with π (Y _k) the implicit variable Y of expression _kThe variable that is comprised, these variablees are the reflections that constitute the parts of this assembly, if C ₄Be certain assembly Y ₃Ingredient, then

By constantly parts and assembly being made up by the connection in series-parallel relation, final formation implied variable set Y={Y ₁, Y ₂..., Y _k..., Y _m, Y wherein _kThe implicit variable of representing k assembly correspondence, Y _mThe implicit variable of expression entire equipment system component correspondence, m represents the sum of all implicit variablees in the system;

4, the modular construction relational matrix E that provides according to the device design document determines { π (Y ₁), π (Y ₂) ..., π (Y _k) ..., π (Y _m) in institute comprised actual connection in series-parallel relation between variable, and the conditional probability distribution of calculating all implicit variablees is based on this gathered CP={P (Y ₁| π (Y ₁)), P (Y ₂| π (Y ₂)) ..., P (Y _k| π (Y _k)) ..., P (Y _m| π (Y _m)), P (Y wherein _k| π (Y _k)) conditional probability distribution of expression k implicit variable;

Wherein, the conditional probability distribution computing method of implicit variable are specific as follows: as π (Y _k) when middle variable is cascaded structure, Y _kConditional probability distribution as the formula (5); As π (Y _k) in variable be that parallel-connection structure is Y _kConditional probability distribution as the formula (6);

5, carry out reasoning according to Bayesian formula and conditional probability distribution set CP, calculate basic variable X respectively _i=0, (i=1 ..., in the time of n), the posteriority distributions of device systems variable set { P (Y _m=0|X ₁=0) ..., P (Y _m=0|X _i=0) ..., P (Y _m=0|X _n=0) }, as the formula (7), P (Y wherein _m=0|X _iWhen=0) i parts of expression normally move, the probability of the normal operation of device systems;

P (Y _m=0|X _i=0)=P (Y _m=0| π (X _i)) * P (π (X _i) | X _i=0), and wherein (i=1 ..., n) (7)

6, carry out reasoning according to Bayesian formula and conditional probability distribution set CP, calculate basic variable X respectively _i=1, (i=1 ..., in the time of n), the posteriority distributions of equipment variables set { P (Y _m=0|X ₁=1) ..., P (Y _m=0|X _i=1) ..., P (Y _m=0|X _n=1) }, as the formula (8), P (Y wherein _m=0|X _iWhen=1) representing i unit failure, the probability of the normal operation of device systems;

P (Y _m=0|X _i=1)=P (Y _m=0| π (X _i)) * P (π (X _i) | X _i=1), and wherein (i=1 ..., n) (8)

7, calculate each variable X in the basic variable set respectively by the mode of formula (9) _i, (i=1 ..., maintenance importance degree n)

(i=1 ..., n);

$I{\left(W\right)}_{X_i}^{Y_m}=(P(Y_m=0|X_i=0)-P(Y_m=0|X_i=1))\×(1-P(X_i=0))---\left(9\right)$

8, the maintenance importance degree to all basic variables sorts from high to low, determines most important Awaiting Parts in the equipment.

The invention has the beneficial effects as follows: because based on device structure and reliability information, towards safeguarding support mission, a kind of maintenance importance degree computing method that can comprehensively weigh part reliability and structural relationship have been proposed, solved the problem that reliability and structural relationship are isolated mutually in the existing system importance degree computing method, simplify calculation procedure simultaneously, improved counting yield, effectively the critical component of identification equipment system, instruct monitoring and maintenance to critical component, effectively improve maintenance efficiency, reduce maintenance cost.

The present invention is further described below in conjunction with drawings and Examples.

Description of drawings

Fig. 1 is the process flow diagram of a kind of method for computing importance in maintaining components of equipment of the present invention.

Fig. 2 is the device structure graph of a relation among the embodiment 1.

Fig. 3 discerns the process flow diagram that implies variable according to component set and structural relation figure.

Fig. 4 is the device structure graph of a relation among the embodiment 2.

Fig. 5 is the implicit identification variables order among the embodiment 2.

Embodiment

Embodiment 1:

Below in conjunction with the drawings and specific embodiments the present invention is done further detailed description.

With reference to Fig. 1, a kind of importance in maintaining components of equipment of the present invention calculation side comprises the steps:

Step 1, according to the component set C that comprises among the device systems S, each parts in the component set are represented that with the variable among the basic variable set X its concrete mode is as follows:

According to part of appliance structural relation figure among the embodiment shown in Figure 21, equipment S is by 5 parts C={C as can be known ₁, C ₂, C ₃, C ₄, C ₅Form.Therefore, these 5 parts are represented with corresponding basic variable respectively, and determined the feasible value of basic variable, constitute basic variable set X={X according to the mode of formula (3) ₁, X ₂, X ₃, X ₄, X ₅.

Step 2 according to each part reliability function set R that the device design document provides, is set up the probability distribution over states set P of the basic variable of each parts correspondence, and its concrete mode is as follows:

According to parts reliability function R={R (C among the embodiment 1 ₁)=0.88, R (C ₂)=0.91, R (C ₃)=0.84, R (C ₄)=0.95, R (C ₅)=0.88} sets up the (X with the probability distribution over states of the corresponding basic variable of parts set P={P according to the mode of formula (4) ₁=0)=0.88, P (X ₂=0)=0.93, P (X ₃=0)=0.84, P (X ₄=0)=0.95, P (X ₅=0)=0.88}.

Step 3, modular construction relational matrix E according to the device design document provides presses the series parallel structure relation with a plurality of parts in the equipment and forms an assembly, and constantly parts and assembly is made up by the connection in series-parallel relation, final foundation implied variable set Y, and its concrete mode is as follows:

According to part of appliance structural relation figure among the embodiment shown in Figure 21, its structural relation matrix as the formula (10).

$E=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\\ 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0\end{array}\right]---\left(10\right)$

With reference to Fig. 3, implicit identification variables flow process comprises the steps:

Step 301, all parts { C in the judgment device structure ₁, C ₂, C ₃, C ₄, C ₅Do not exist parallel connection to concern execution in step 304;

Step 304, all parts { C in the judgment device structure ₁, C ₂, C ₃, C ₄, C ₅Be in the same cascaded structure execution in step 305;

Step 305 is with all the parts { C in this cascaded structure ₁, C ₂, C ₃, C ₄, C ₅Deletion;

Step 306 is directly set up an implicit variable Y ₁Replace above-mentioned parts, i.e. π (Y ₁)={ X ₁, X ₂, X ₃, X ₄, X ₅, circulation execution in step 301;

Step 301 according to new device structure, has only a variable Y in the device structure ₁, judge not have parallel-connection structure, execution in step 304;

Step 304 according to new device structure, has only a variable Y in the device structure ₁, judge not have cascaded structure, finish, i.e. Y={Y ₁, Y ₁Be equipment variables;

Step 4 according to the modular construction relational matrix that the device design document provides, is determined π (Y _k) in the connection in series-parallel relation of variable, calculate the conditional probability distribution set CP of all implicit variablees based on this, its concrete mode is as follows:

Therefore, by formula (10) π (Y as can be known ₁)={ X ₁, X ₂, X ₃, X ₄, X ₅In variable be cascaded structure, directly calculate implicit variable Y by formula (5) ₁Conditional probability distribution as the formula (11), CP={P (Y ₁| π (Y ₁))

Step 5 is carried out reasoning according to Bayesian formula and conditional probability distribution set CP, calculates basic variable X respectively _i=0, (i=1 ..., in the time of n), the posteriority distributions P (Y of equipment variables _m=0|X _i=0), (i=1 ..., n), its concrete mode is as follows:

According to formula (7), P (Y ₁=0|X _i=0) can write following form, as the formula (12).

P(Y ₁＝0|X _i＝0)

＝P(Y ₁＝0|X ₁＝0，...，X _i＝0，...，X _n＝0)×P(X ₁＝0)×...×P(X _i＝0)×...×P(X _n＝0)

+P(Y ₁＝0|X ₁＝1，...，X _i＝0，...，X _n＝0)×P(X ₁＝1)×...×P(X _i＝0)×...×P(X _n＝0)

.

. (12)

.

+P(Y ₁＝0|X ₁＝0，...，X _i＝0，...，X _n＝1)×P(X ₁＝0)×...×P(X _i＝0)×...×P(X _n＝1)

.

.

.

+ P (Y ₁=0|X ₁=1 ..., X _i=0 ..., X _n=1) * P (X ₁=1) * ... * P (X _i=0) * ... * P (X _n=1) will imply variable conditional probability distribution CP={P (Y again ₁| π (Y ₁)) bring formula (12) into, can get formula (13).

$P(Y_1=0|X_i=0)=P(Y_1=0|X_1=0,...,X_i=0,...,X_n=0,)\×\underset{j}{\overset{1,...i-1,i+1,...,n}{\mathrm{\Π}}}P(X_j=0)---\left(13\right)$

At last, can calculate based on the equipment variables posterior probability of different parts set { P (Y according to formula (13) ₁=0|X ₁=0), P (Y ₁=0|X ₂=0), P (Y ₁=0|X ₃=0), P (Y ₁=0|X ₄=0), P (Y ₁=0|X ₅=0) }, as shown in table 1.

Table 1

Step 6 is carried out reasoning according to Bayesian formula and conditional probability distribution set CP, calculates basic variable X respectively _i=1, (i=1 ..., in the time of n), the posteriority distributions P (Y of equipment variables _m=0|X _i=1), (i=1 ..., n), its concrete mode is as follows:

According to formula (8), P (Y ₁=0|X _i=1) can write following form, as the formula (14).

P(Y ₁＝0|X _i＝1)

＝P(Y ₁＝0|X ₁＝0，...，X _i＝1，...，X _n＝0)×P(X ₁＝0)×...×P(X _i＝1)×...×P(X _n＝0)

+P(Y ₁＝0|X ₁＝1，...，X _i＝1，...，X _n＝0)×P(X ₁＝1)×...×P(X _i＝1)×...×P(X _n＝0)

.

. (14)

.

+P(Y ₁＝0|X ₁＝0，...，X _i＝1，...，X _n＝1)×P(X ₁＝0)×...×P(X _i＝1)×...×P(X _n＝1)

.

.

.

+P(Y ₁＝0|X ₁＝1，...，X _i＝1，...，X _n＝1)×P(X ₁＝1)×...×P(X _i＝1)×...×P(X _n＝1)

To imply variable conditional probability distribution CP={P (Y again ₁| π (Y ₁)) bring formula (14) into, can get formula (15).

P(Y ₁＝0|X _i＝1)＝0 (15)

At last, can calculate based on the equipment variables posterior probability of different basic variables set { P (Y according to formula (15) ₁=0|X ₁=1), P (Y ₁=0|X ₂=1), P (Y ₁=0|X ₃=1), P (Y ₁=0|X ₄=1), P (Y ₁=0|X ₅=1) }, as shown in table 1.

Step 7 is calculated the maintenance importance degree of each variable in the basic variable set respectively

Its concrete mode is as follows:

Respectively with basic variable X _iP (X _i=0), P (Y ₁=0|X _i=0), P (Y ₁=0|X _i=1) etc. information is brought formula (9) into, can calculate the maintenance importance degree set of basic variable in the basic variable set

As shown in table 1.

Step 8 sorts from high to low to the maintenance importance degree of all basic variables, determines most important Awaiting Parts in the equipment, and its concrete mode is as follows:

Will

In the ordering from big to small of each value, as shown in table 1, finally determine parts C ₃For needing most the parts of maintenance in the current device.

In addition,,, calculated the reliability importance and the structure importance of each parts respectively according to formula (1) and formula (2) for same embodiment 1 shown in Figure 2 for the physical significance of further Verify Repair importance degree, as shown in table 1.

Embodiment 2:

With reference to Fig. 1, a kind of importance in maintaining components of equipment of the present invention calculation side comprises the steps:

Step 1, according to the component set C that comprises among the device systems S, each parts in the component set are represented that with the variable among the basic variable set X its concrete mode is as follows:

According to part of appliance structural relation figure among the embodiment shown in Figure 42, equipment S is by 10 parts C={C as can be known ₁, C ₂, C ₃, C ₄, C ₅, C ₆, C ₇, C ₈, C ₉, C ₁₀Form.Therefore, these 10 parts are represented with corresponding basic variable respectively, and determined the feasible value of basic variable, constitute basic variable set X={X according to the mode of formula (3) ₁, X ₂, X ₃, X ₄, X ₅, X ₆, X ₇, X ₈, X ₉, X ₁₀.

Step 2 according to each part reliability function set R that the device design document provides, is set up the probability distribution over states set P of the basic variable of each parts correspondence, and its concrete mode is as follows:

According to parts reliability function among the embodiment 2

Set up (X according to the mode of formula (4) with the probability distribution over states of the corresponding basic variable of parts set P={P ₁=0)=0.99, P (X ₂=0)=0.93, P (X ₃=0)=0.87, P (X ₄=0)=0.8, P (X ₅=0)=0.9, P (X ₆=0)=0.85, P (X ₇=0)=0.75, P (X ₈=0)=0.88.P(X ₉＝0)＝0.86，P(X ₁₀＝0)＝0.8}

Step 3, modular construction relational matrix E according to the device design document provides presses the series parallel structure relation with a plurality of parts in the equipment and forms an assembly, and constantly parts and assembly is made up by the connection in series-parallel relation, final foundation implied variable set Y, and its concrete mode is as follows:

According to part of appliance structural relation figure among the embodiment shown in Figure 42, its structural relation matrix as the formula (16).

$E=\left[\begin{array}{cccccccccc}0& 1& 0& 0& 1& 0& 1& 0& 0& 0\\ 0& 0& 1& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]---\left(16\right)$

With reference to Fig. 3, implicit identification variables flow process comprises the steps:

Step 301, parts C in the judgment device structure ₃And C ₄Between have relation in parallel, execution in step 302;

Step 302 is with all the parts { C in this parallel-connection structure ₃, C ₄Deletion;

Step 303 is directly set up an implicit variable Y ₁Replace above-mentioned parts, i.e. π (Y ₁)={ X ₃, X ₄, circulation execution in step 301;

Step 301, parts C in the judgment device structure ₉And C ₁₀Between have relation in parallel, execution in step 302;

Step 302 is with all the parts { C in this parallel-connection structure ₉, C ₁₀Deletion;

Step 303 is directly set up an implicit variable Y ₂Replace above-mentioned parts, i.e. π (Y ₂)={ X ₉, X ₁₀, circulation execution in step 301;

Step 301 according to new device structure, is judged not have parallel-connection structure, execution in step 304;

Step 304, variable C in the judgment device structure ₂And Y ₁Between have series relationship, execution in step 305;

Step 305 is with all the parts { C in this cascaded structure ₂, Y ₁Deletion;

Step 306 is directly set up an implicit variable Y ₃Replace above-mentioned parts, i.e. π (Y ₃)={ X ₂, Y ₁, circulation execution in step 301;

Step 301 according to new device structure, is judged not have parallel-connection structure, execution in step 304;

Step 304, variable C in the judgment device structure ₅And C ₆Between have series relationship, execution in step 305;

Step 305 is with all the parts { C in this cascaded structure ₅, C ₆Deletion;

Step 306 is directly set up an implicit variable Y ₄Replace above-mentioned parts, i.e. π (Y ₄)={ X ₅, X ₆, circulation execution in step 301;

Step 301 according to new device structure, is judged not have parallel-connection structure, execution in step 304;

Step 304, variable C in the judgment device structure ₇And C ₈Between have series relationship, execution in step 305;

Step 305 is with all the parts { C in this cascaded structure ₇, C ₈Deletion;

Step 306 is directly set up an implicit variable Y ₅Replace above-mentioned parts, i.e. π (Y ₅)={ X ₇, X ₈, circulation execution in step 301;

Step 301, variable Y in the judgment device structure ₃, Y ₄And Y ₅Between have relation in parallel, execution in step 302;

Step 302 is with all the parts { Y in this parallel-connection structure ₃, Y ₄, Y ₅Deletion;

Step 303 is directly set up an implicit variable Y ₆Replace above-mentioned parts, i.e. π (Y ₆)={ Y ₃, Y ₄, Y ₅, circulation execution in step 301;

Step 301 according to new device structure, is judged not have parallel-connection structure, execution in step 304;

Step 304, variable C in the judgment device structure ₁, Y ₆And Y ₂Between have series relationship, execution in step 305;

Step 305 is with all the parts { C in this cascaded structure ₁, Y ₆, Y ₂Deletion;

Step 306 is directly set up an implicit variable Y ₇Replace above-mentioned parts, i.e. π (Y ₇)={ X ₁, Y ₆, Y ₂, circulation execution in step 301;

Step 301 according to new device structure, has only a variable Y in the device structure ₇, judge not have parallel-connection structure, execution in step 304;

Step 304 according to new device structure, has only a variable Y in the device structure ₇, judge not have cascaded structure, finish.

Finally, obtain implicit variable set Y={Y ₁, Y ₂, Y ₃, Y ₄, Y ₅, Y ₆, Y ₇, Y wherein ₇Be the device systems variable, as shown in Figure 5.

Step 4 according to the modular construction relational matrix that the device design document provides, is determined π (Y _k) in the connection in series-parallel relation of variable, calculate the conditional probability distribution set CP of all implicit variablees based on this, its concrete mode is as follows:

Therefore, by formula (14) π (Y as can be known ₁)={ X ₃, X ₄In variable be parallel-connection structure, directly calculate implicit variable Y by formula (6) ₁Conditional probability distribution as the formula (17).

Therefore, by formula (14) π (Y as can be known ₂)={ X ₉, X ₁₀In variable be parallel-connection structure, directly calculate implicit variable Y by formula (6) ₂Conditional probability distribution as the formula (18).

Therefore, by formula (14) π (Y as can be known ₃)={ X ₂, Y ₁In variable be cascaded structure, directly calculate implicit variable Y by formula (5) ₃Conditional probability distribution as the formula (19).

Therefore, by formula (14) π (Y as can be known ₄)={ X ₅, X ₆In variable be cascaded structure, directly calculate implicit variable Y by formula (5) ₄Conditional probability distribution as the formula (20).

Therefore, by formula (14) π (Y as can be known ₅)={ X ₇, X ₈In variable be cascaded structure, directly calculate implicit variable Y by formula (5) ₅Conditional probability distribution as the formula (21).

Therefore, by formula (14) π (Y as can be known ₆)={ Y ₃, Y ₄, Y ₅In variable be parallel-connection structure, directly calculate implicit variable Y by formula (6) ₆Conditional probability distribution as the formula (22).

Therefore, by formula (14) π (Y as can be known ₇)={ X ₁, Y ₆, Y ₂In variable be cascaded structure, directly calculate implicit variable Y by formula (5) ₇Conditional probability distribution as the formula (23).

Finally, obtain the conditional probability distribution set CP={P (Y of all implicit variablees ₁| π (Y ₁)), P (Y ₂| π (Y ₂)), P (Y ₃| π (Y ₃)), P (Y ₄| π (Y ₄)), P (Y ₅| π (Y ₅)), P (Y ₆| π (Y ₆)),

。

P(Y ₇|π(Y ₇))}

Step 5 is carried out reasoning according to Bayesian formula and conditional probability distribution set CP, calculates basic variable X respectively _i=0, (i=1 ..., in the time of n), the posteriority distributions P (Y of equipment variables _m=0|X _i=0), (i=1 ..., n), its concrete mode is as follows:

According to formula (7), P (Y ₇=0|X _i=0) can write following form, as the formula (24).

P(Y ₇＝0|X _i＝0)＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁，Y ₆，Y ₂|X _i＝0)

＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁|X _i＝0)×P(Y ₆|X _i＝0)×P(Y ₂|X _i＝0)

＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁|X _i＝0)

×P(Y ₆|Y ₃，Y ₄，Y ₅)×P(Y ₃|X _i＝0)×P(Y ₄|X _i＝0)×P(Y ₅|X _i＝0)

×P(Y ₂|X ₉，Y ₁₀)×P(X ₉|X _i＝0)×P(X ₁₀|X _i＝0)

(24)

＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁|X _i＝0)×P(Y ₆|Y ₃，Y ₄，Y ₅)

×P(Y ₃|X ₂，Y ₁)×P(X ₂|X _i＝0)×P(Y ₁|X _i＝0)

×P(Y ₄|X ₅，X ₆)×P(X ₅|X _i＝0)×P(X ₆|X _i＝0)

×P(Y ₅|X ₇，X ₈)×P(X ₇|X _i＝0)×P(X ₈|X _i＝0)

×P(Y ₂|X ₉，X ₁₀)×P(X ₉|X _i＝0)×P(X ₀|X _i＝0)

To imply variable conditional probability distribution set CP again and bring formula (22) into, can calculate equipment posterior probability based on different parts

As shown in table 2.

Table 2

Step 6 is carried out reasoning according to Bayesian formula and conditional probability distribution set CP, calculates basic variable X respectively _i=1, (i=1 ..., in the time of n), the posteriority distributions P (Y of equipment variables _m=0|X _i=1), (i=1 ..., n), its concrete mode is as follows:

According to formula (8), P (Y ₇=0|X _i=1) can write following form, as the formula (25).

P(Y ₇＝0|X _i＝1)＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁，Y ₆，Y ₂|X _i＝1)

＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁|X _i＝1)×P(Y ₆|X _i＝1)×P(Y ₂|X _i＝1)

＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁|X _i＝1)

×P(Y ₆|Y ₃，Y ₄，Y ₅)×P(Y ₃|X _i＝1)×P(Y ₄|X _i＝1)×P(Y ₅|X _i＝1)

×P(Y ₂|X ₉，X ₁₀)×P(X ₉|X _i＝1)×P(X ₁₀|X _i＝1)

(25)

＝P(Y ₇＝0|X ₁，Y ₆，Y ₂)×P(X ₁|X _i＝1)×P(Y ₆|Y ₃，Y ₄，Y ₅)

×P(Y ₃|X ₂，Y ₁)×P(X ₂|X _i＝1)×P(Y ₁|X _i＝1)

×P(Y ₄|X ₅，X ₆)×P(X ₅|X _i＝1)×P(X ₆|X _i＝1)

×P(Y ₅|X ₇，X ₈)×P(X ₇|X _i＝1)×P(X ₈|X _i＝1)

×P(Y ₂|X ₉，X ₁₀)×P(X ₉|X _i＝1)×P(X ₁₀|X _i＝1)

To imply variable conditional probability distribution set CP again and bring formula (25) into, can calculate equipment posterior probability based on different parts

As shown in table 2.

Step 7 is calculated the maintenance importance degree of each variable in the basic variable set respectively

Its concrete mode is as follows:

Respectively with basic variable X _iP (X _i=0), P (Y ₇=0|X _i=0), P (Y ₇=0|X _i=1) etc. information is brought formula (9) into, can calculate the maintenance importance degree set of basic variable in the basic variable set

As shown in table 2.

Step 8 sorts from high to low to the maintenance importance degree of all basic variables, determines most important Awaiting Parts in the equipment, and its concrete mode is as follows:

Will

In the ordering from big to small of each value, as shown in table 2, finally determine parts C ₉For needing most the parts of maintenance in the current device.

In addition,,, calculated the reliability importance and the structure importance of each parts respectively according to formula (1) and formula (2) for same embodiment 2 shown in Figure 4 for the physical significance of further Verify Repair importance degree, as shown in table 2.According to the comparing result of table 2 as seen, though parts C ₁Still be the configuration aspects analysis no matter, all be in most important status from reliability.But, because its reliability is high, generally can not break down, it is carried out excessive concern only can waste great amount of manpower and material resources, ignored inspection on the contrary to the high parts of other failure rate.

Claims (1)

1. a method for computing importance in maintaining components of equipment is characterized in that comprising the steps:

1) according to the component set C={C that comprises among the device systems S ₁, C ₂..., C _i..., C _n, C wherein _iRepresent i parts, n represents all number of components in the system, with each parts C _iUse variable X _iExpression,

I=1 wherein ..., n, and called after basic variable set X={X ₁, X ₂..., X _i..., X _n, X wherein _iI variable in the set of expression basic variable, the basic variable sum also is n;

2) each part reliability function set R={R (C that provides according to the device design document ₁), R (C ₂) ..., R (C _i) ..., R (C _n), set up the probability distribution over states of the basic variable of each parts correspondence and gather P={P (X ₁=0), P (X ₂=0) ..., P (X _i=0) ..., P (X _n=0) }, P (X wherein _i=0) probability distribution over states of i basic variable of expression, P (X _i=0)=R (C _i), i=1 wherein ..., n;

3) the modular construction relational matrix E=[E that provides according to the device design document _Ij], 1≤i.j≤n presses the series parallel structure relation with a plurality of parts in the equipment and forms an assembly, uses variable Y _kExpression when the assembly operate as normal, is 0 to the value of dependent variable, when component faults, is 1 to the value of dependent variable, and the implicit variable of called after, with π (Y _k) the implicit variable Y of expression _kThe variable that is comprised, by constantly parts and assembly being made up by the connection in series-parallel relation, final formation implied variable set Y={Y ₁, Y ₂..., Y _k..., Y _m, Y wherein _kThe implicit variable of representing k assembly correspondence, Y _mThe implicit variable of expression entire equipment system component correspondence, m represents the sum of all implicit variablees in the system;

4) the modular construction relational matrix E that provides according to the device design document determines { π (Y ₁), π (Y ₂) ..., π (Y _k) ..., π (Y _m) in institute comprised actual connection in series-parallel relation between variable, and the conditional probability distribution of calculating all implicit variablees is based on this gathered CP={P (Y ₁| π (Y ₁)), P (Y ₂| π (Y ₂)) ..., P (Y _k| π (Y _k)) ..., P (Y _m| π (Y _m)), P (Y wherein _k| π (Y _k)) conditional probability distribution of expression k implicit variable; As π (Y _k) when middle variable is cascaded structure,

As π (Y _k) when middle variable is parallel-connection structure,

5) carry out reasoning according to Bayesian formula and conditional probability distribution set CP, calculate basic variable X respectively _i=0, (i=1 ..., in the time of n), the posteriority distributions of device systems variable set { P (Y _m=0|X ₁=0) ..., P (Y _m=0|X _i=0) ..., P (Y _m=0|X _n=0) }, P (Y wherein _m=0|X _iWhen=0) i parts of expression normally move, the probability of the normal operation of device systems;

P (Y _m=0|X _i=0)=P (Y _m=0| π (X _i)) * P (π (X _i) | X _i=0), and wherein (i=1 ..., n);

6) carry out reasoning according to Bayesian formula and conditional probability distribution set CP, calculate basic variable X respectively _i=1, (i=1 ..., in the time of n), the posteriority distributions of equipment variables set { P (Y _m=0|X ₁=1) ..., P (Y _m=0|X _i=1) ..., P (Y _m=0|X _n=1) }, P (Y wherein _m=0|X _iWhen=1) representing i unit failure, the probability of the normal operation of device systems;

P (Y _m=0|X _i=1)=P (Y _m=0| π (X _i)) * P (π (X _i) | X _i=1), and wherein (i=1 ..., n);

7) calculate each variable X in the basic variable set respectively _i, (i=1 ..., maintenance importance degree n)

(i=1 ..., n);

8) the maintenance importance degree to all basic variables sorts from high to low, determines most important Awaiting Parts in the equipment.

Images