CN110321239A - System reliability estimation method based on system survival feature - Google Patents
System reliability estimation method based on system survival feature Download PDFInfo
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- CN110321239A CN110321239A CN201910558008.2A CN201910558008A CN110321239A CN 110321239 A CN110321239 A CN 110321239A CN 201910558008 A CN201910558008 A CN 201910558008A CN 110321239 A CN110321239 A CN 110321239A
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Abstract
The invention discloses a kind of system reliability estimation methods based on system survival feature.This method can accurately and efficiently assess the reliability of the complication system with multiple types component.Steps are as follows: 1 utilizes general generating function computing system survival properties.2 are based on system survival feature calculation system dependability.
Description
Technical field
The present invention provides one kind to be based on general generating function computing system survival properties, and is commented using system survival feature
Estimate the method for system reliability.It is suitable for the reliability assessment of the complication system with multiple types component.Utilize general life
It on this basis can be with estimating system using system survival feature at the survival properties that function easy can calculate system
The parameters such as reliability complete the assessment to system reliability.The invention belongs to reliabilities and system engineering field.
Background technique
Modern project system structure becomes increasingly complex, and the type of included unit or assembly is also more and more, conventional reliable
Property appraisal procedure be unable to satisfy Complex System Reliability assessment require.Therefore, it is necessary to find new measure or index
The reliability of such complication system is modeled and analyzed.System survival feature (survivalsignature) is used as one
New degree of reiability concept, by since formally proposing, constantly had scholar to carry out research and development to it, gradually from 2012
As quantization complication system or a powerful of Network System Reliability.It is by the reliability of the reliability of system and component
It separates, provides more generally method for evaluating reliability for the complication system with multiple types component.However, current
It is less to the research of the calculating of system survival feature, how correctly and efficiently the survival properties of computing system there has been no it is relatively clear,
Ideal method.
The invention proposes a kind of novel system survival feature calculation method based on general generating function and it is based on this
The system reliability estimation method of calculation method.This method utilizes general generating function, can effectively calculate the life of system
Feature is deposited, and is based on this, estimates the reliability indexs such as the reliability of system, realizes the reliability assessment to complication system.
Summary of the invention
General generating function computing system survival properties are utilized the present invention provides a kind of, and are based on system survival feature,
The method that reliability assessment is carried out to system.Purpose and solves the problems, such as be: by expanding universal generating function, establish system and give birth to
It is regular at feature calculation, and calculated system features, assessment system reliability.
The present invention is a kind of system reliability estimation method based on system survival feature, mainly includes following two part:
First part: general generating function computing system survival properties are based on.
Computing system survival properties are the bases of subsequent reliability assessment, and computing system survival properties include following four step
It is rapid:
Step 1: according to failure rate or other reliability indexs of correlation, classify to all component units in system,
Determine the unit total quantity m for belonging to kth class in classification k, system belonging to all unitskWith total classification number K of unit in system.
Step 2: initial table being carried out to all component units of system using UGF and is reached, the UGF expression formula of all units is obtained
It is as follows:
Wherein, gksIt is the state vector of kth class unit, includes altogether K element, in gk0Middle K element is all 0, in gk1In
K-th of element value is 1, and other elements are all 0；pksIt is and gksCorresponding system function impact factor, pk0Value be that (φ is φ
Symbolic constant), pk1Value be 1, it is specific as follows:
Step 3: according in system reliability block diagram, the difference connection type such as series, parallel between unit is to unit
UGF expression formula is calculated, and the UGF expression formula of system is obtained.
If the connection type between n unit is parallel connection, by the UGF expression formula u for the system that these units compose in parallels
(z) calculation formula are as follows:
Wherein, operatorOperation rule it is as follows:
By taking the system composed in parallel by Unit two as an example, the UGF expression formula u of the systems(z) calculating process is as follows:
If the connection type between n unit is series connection, by the UGF expression formula u for the system that these units are composed in seriess
(z) calculation formula are as follows:
Wherein, operatorOperation rule it is as follows:
By taking the system being composed in series by Unit two as an example, the UGF expression formula u of the systems(z) calculating process is as follows:
If in reliability block diagram, connection type is nested multi-level series-parallel between n component units of system, then first count
The UGF expression formula for the lowest level submodule being simply connected in series or in parallel in calculation system by unit, further according to lowermost layer second son
The UGF expression formula of module calculates the UGF expression formula of a layer module thereon, repeats this step, the UGF table until calculating system
Up to formula.
Step 4: according to the UGF expression formula u of systems(z) survival properties of computing systemCalculation method is as follows:
It enables
Wherein, gs=(l1, l2..., lK), then
Second part: using the calculated result of system survival feature, it is reliable to complete system for the indexs such as estimating system reliability
Property assessment.
Estimating system reliability index mainly includes with next step:
Step 1: survival properties are based on, derive that system dependability calculation formula is as follows:
Assuming that the out-of-service time of different component types is mutually indepedent, then in above formula
Therefore, system dependability can be calculated by the fault probability function of system survival feature and different component types
It arrives:
Detailed description of the invention
Fig. 1 is method flow diagram
Fig. 2 is the structural schematic diagram of system
Fig. 3 is that the cell type of system divides and layer of structure division schematic diagram
Specific embodiment
Below in conjunction with attached drawing, specific embodiments of the present invention will be described in detail, these embodiments are shown if it exists
The content of example property, should not be construed to limitation of the present invention.
According to specific calculation process shown in FIG. 1, with shown in Fig. 2 by A, B, C, D, E mixing that totally five units form
Series-parallel system is object, calculates the survival properties of the system.Wherein the random failure time of each unit obeys exponential distribution,
Specific crash rate is such as
Shown in table 1.
1 example system each unit crash rate of table
First part: system survival feature is calculated based on general generating function.
Computing system survival properties are the bases of subsequent reliability assessment, and computing system survival properties include following four step
It is rapid:
Step 1: according to the reliabilities index of correlation such as crash rate of system unit, system unit being divided into 2 classes, first kind list
Member includes A, B, and the second class unit includes C, D, E, as shown in Figure 3.
Step 2: according to the classification of step 1, the UGF expression formula for initializing all units of system is as follows:
uA(z)=uB(z)=φ z(0,0)+1z(1,0)
uC(z)=uD(z)=uE(z)=φ z(0,0)+1z(0,1)
Step 3: the UGF expression formula u of computing subsystem 1., 2. first①(z)、u②(z) as follows:
The UGF expression formula u of last computing systems(z) as follows:
Step 4: according to the UGF expression formula u of systems(z) survival properties (survival of system is calculated
signature)It is as follows:
The survival properties of 2 example system of table
Second part: utilizing system survival feature calculation as a result, the indexs such as estimating system reliability, complete system reliability
Assessment.
Estimating system reliability index mainly includes with next step:
Step 1: according to formula
System dependability is calculated are as follows:
λ1=5 × 10-6h-1
λ2=2 × 10-7h-1
Claims (1)
1. a kind of system reliability estimation method based on system survival feature, it is characterised in that: this method mainly includes following
Two parts:
First part: general generating function computing system survival properties are based on.
Computing system survival properties are the bases of subsequent reliability assessment, and computing system survival properties include following four step:
Step 1: according to failure rate or other reliability indexs of correlation, classifying to all component units in system, determine
Belong to the unit total quantity m of kth class in classification k, system belonging to all unitskWith total classification number K of unit in system.
Step 2: initial table being carried out to all component units of system using UGF and is reached, obtains the UGF expression formula of all units such as
Under:
Wherein, gksIt is the state vector of kth class unit, includes altogether K element, in gk0Middle K element is all 0, in gk1Middle kth
A element value is 1, and other elements are all 0；pksIt is and gksCorresponding system function impact factor, pk0Value be that (φ is symbol to φ
Constant), pk1Value be 1, it is specific as follows:
Step 3: according in system reliability block diagram, UGF table of the difference connection type such as series, parallel between unit to unit
It is calculated up to formula, obtains the UGF expression formula of system.
If the connection type between n unit is parallel connection, by the UGF expression formula u for the system that these units compose in parallels(z) meter
Calculate formula are as follows:
Wherein, operatorOperation rule it is as follows:
By taking the system composed in parallel by Unit two as an example, the UGF expression formula u of the systems(z) calculating process is as follows:
If the connection type between n unit is series connection, by the UGF expression formula u for the system that these units are composed in seriess(z) meter
Calculate formula are as follows:
Wherein, operatorOperation rule it is as follows:
By taking the system being composed in series by Unit two as an example, the UGF expression formula u of the systems(z) calculating process is as follows:
If in reliability block diagram, connection type is nested multi-level series-parallel between n component units of system, then system is first calculated
The UGF expression formula for the lowest level submodule being simply connected in series or in parallel in system by unit, further according to lowest level submodule
UGF expression formula calculate the UGF expression formula of a layer module thereon, repeat this step, the UGF until calculating system is expressed
Formula.
Step 4: according to the UGF expression formula u of systems(z) survival properties of computing systemCalculation method is as follows:
It enables
Wherein, gs=(l1, l2..., lK), then
Second part: using the calculated result of system survival feature, the indexs such as estimating system reliability are completed system reliability and are commented
Estimate.
Estimating system reliability index mainly includes with next step:
Step 1: survival properties are based on, derive that system dependability calculation formula is as follows:
Assuming that the out-of-service time of different component types is mutually indepedent, then in above formula
Therefore, system dependability can be calculated by the fault probability function of system survival feature and different component types:
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