CN108595847A - A kind of appraisal procedure for gas extinguishing system reliability - Google Patents
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Abstract
The invention discloses a kind of appraisal procedures for gas extinguishing system reliability.This method establishes gas extinguishing system reliability failure tree elementary event first by realizing the assessment of gas extinguishing system reliability with Fault Tree Analysis Bayes computational methods FMEA analytic approach；Secondly, according to fault tree, the reliability of each bottom trouble unit in fault tree is calculated with Bayes methods；Again, according to the reliability of each bottom trouble unit successively computing system reliability；Finally, in conjunction with the result of calculation of reliability, gas extinguishing system is assessed with FMEA analytic approach.It using this method, solves the problems, such as to be difficult to assessment reliability since gas extinguishing system sample is few, helps to improve gas extinguishing system reliability according to assessment result, reduce failure and causality loss to the maximum extent.
Description
Technical field
The present invention relates to fire engineering fields, more particularly, to a kind of assessment side for gas extinguishing system reliability
Method.
Background technology
Gas extinguishing system, which is generally used in, needs the place laid special stress on protecting, such as communication base station, computer room, library and rich
Object shop etc. plays an important role in terms of the person and property safety protection.In order to reach the purpose, gas extinguishing system is necessary
It is in standby at any time, ensures that once fire behavior occur can start in time.And only system time keeps high reliability, ability
Guarantee successfully starts up in time.
Currently, gas extinguishing system reliability has the characteristics that：(1) Finite Samples, quantity are few；(2) sample is from each
The data that a enterprise provides, i.e., the information that different information sources provides；(3) underlying reli-ability shortage of data.Due to classical statistics
Method etc. needs big-sample data to support, therefore for gas extinguishing system and is not suitable for.
Therefore, there is an urgent need for a kind of reliability estimation methods for gas extinguishing system, can utilize the information and data of multi-source, in time
It was found that the weak link of gas extinguishing system, finds out certain fault observer, to instruct gas extinguishing system design, life
Production, construction, maintenance and maintenance work, improve its reliability, reduce failure and causality loss to the maximum extent.
Invention content
It is an object of the invention to expand fire-fighting reliability estimation method, provide a kind of reliable for gas extinguishing system
The appraisal procedure of property.
The technical solution adopted by the present invention is that：A kind of appraisal procedure for gas extinguishing system reliability, feature exist
In：The assessment of gas extinguishing system reliability is realized with Fault Tree Analysis-Bayes computational methods-FMEA analytic approach, it is first
First, gas extinguishing system reliability failure tree elementary event as shown in Table 1 is established；Secondly, according to fault tree, with Bayes
Method calculates the reliability of each bottom trouble unit in fault tree；Again, according to the reliability of each bottom trouble unit by
Layer computing system reliability；Finally, in conjunction with the result of calculation of reliability, gas extinguishing system is commented with FMEA analytic approach
Estimate；
1 gas extinguishing system reliability failure tree elementary event of table
In the calculating fault tree of the present invention with Bayes methods when the reliability of each bottom trouble unit, first
The screening of multi-source prior information and conversion are carried out, the empirical prior information after conversion is merged；Secondly by the empirical prior information after fusion into
Row distribution inspection judges its distribution pattern；It is computed the weight of determining empirical prior information again；Finally according to empirical prior information and scene
Sample information, carry out consistency check after, be calculated by formula the reliability mean value of each trouble unit point estimation and
Its confidence lower limit.
Bottom trouble unit of the present invention includes exponential type Life Type unit and Weibull type Life Type units：
(1) exponential type Life Type unit
It is calculated through following formula, the point estimation μ of its reliability mean value can be obtainedkeAnd confidence lower limit RLe, the point of reliability mean value is taken to estimate
It is calculated as the point estimation μ of its reliability mean valueke, the results are shown in Table 7.
In formula
μke--- the point estimation of reliability mean value, ke=1；
Γ () --- gamma is distributed；
M --- when field test, stop Failure count when experiment；
η --- Equivalent task number when field testTotal testing time is τ, task time t, field test sample
Number is n；
A --- in empirical prior information, stop equivalent Failure count when experiment；
ν --- the Equivalent task number in empirical prior informationTotal testing time is τ0, task time t, empirical prior information
Equivalent sample number is b；
γ --- confidence level；
R --- reliability.
(2) Weibull types Life Type unit
If
The then point estimation μ of its reliability mean valuekWAnd its confidence lower limit RLWCalculation formula it is as follows：
In formula：μkW--- the point estimation of Weibull type Life Type unit reliability mean values, kW=1；
τ0--- the deadline of empirical prior information fixed time test；
M --- live fixed time test stops Failure count when experiment；
ti--- live fixed time test, the out-of-service time or deadline of a certain sample；
T --- the task time of field test sample；
β --- the form parameter of Weibull distributions；
δ --- 1 is taken when no prior distribation, and 0 is taken when being uniformly distributed；
A --- the equivalent Failure count in empirical prior information；
B --- the equivalent sample number in empirical prior information；
γ --- confidence level；
R --- reliability；
The domain of B --- β；B(β1, β2) be calculated by following formula：
In formula：α --- confidence level；
M --- live fixed time test stops Failure count when experiment；
N --- field test sample number；
ti--- live fixed time test, the out-of-service time or deadline of a certain sample.
It is of the present invention when carrying out the conversion of multi-source prior information, will be before the testing of multi-source according to field samples information
Information is converted to the data under identical conditions, or set of metadata of similar data is converted to equivalent data.
When empirical prior information of the present invention after fusion carries out distribution inspection, take confidence lower limit is higher to be distributed as it
Distribution pattern.
When the weight of the present invention for calculating determining empirical prior information, field samples information is weight constant, passes through calculating
Compare the distribution matching degree of empirical prior information and field samples information to determine the weight of empirical prior information.
It is of the present invention when carrying out consistency check according to empirical prior information and field samples information, using Parametric test
Test, if it is determined that compatible, then carry out subsequent bottom trouble unit Calculation of Reliability, you can by spend mean value point estimation and
The calculating of its confidence lower limit；If it is determined that it is incompatible, then empirical prior information is screened again.
When computing system reliability of the present invention, the distribution of bottom trouble unit reliability is all converted into binomial point
Cloth, the reliability distribution of comprehensive each bottom trouble unit and the sample size and the frequency of failure of system itself, you can pass through binomial
The reliability mean value and its confidence lower limit of system is calculated in distribution.
The invention has the advantages that：The present invention provides a kind of based on fault tree-Bayes methods-FMEA's
For the appraisal procedure of gas extinguishing system reliability, solves and be difficult to assessment reliability since gas extinguishing system sample is few
The problem of, help to improve gas extinguishing system reliability according to assessment result, reduces failure and causality loss to the maximum extent.
Description of the drawings
Fig. 1 gas extinguishing system failure of removal trees
Specific implementation mode
Below in conjunction with drawings and examples, the invention will be further described：
Referring to Fig.1, according to following table 1, Fig. 1 gives the Case Number and title of gas extinguishing system failure of removal figure.
1 gas extinguishing system fault tree elementary event of table
Embodiment 1 --- calculating the reliability of each bottom trouble unit in fault tree with Bayes methods is, first into
The screening and conversion of row multi-source prior information.
The conversion of empirical prior information with merge：Multi-source prior information after screening is as shown in the following Table 2, field samples information
As shown in the following Table 3：
2 extinguishing chemical bottle group container value seal failure historical data of table
3 extinguishing chemical bottle group container value field samples data of table
Since the sample size of gas extinguishing system is few, therefore in the case where empirical prior information sample size is inadequate, can incite somebody to action
The reliability of like product is converted, and reliability conversion factor is calculated, and to obtain equivalent reliability data, reaches expansion
The purpose of big empirical prior information sample size.Assuming that A, B are the similar product of structure, the conversion factor ω n's of empirical prior information source n
Shown in the following formula of computational methods：
In formula：λAB--- A, B share the sum of the failure probability of unit；
λA--- the sum of the element failure probability for having in A, not having in B；
λB--- the sum of the element failure probability for not having in A, having in B.
The wherein conversion factor ω in the consistent empirical prior information source of product structuren=1, in the folding for obtaining each empirical prior information source
After calculating coefficient, you can carry out the fusion of multi-source prior information, it is assumed that there is the N number of information source, the number of success of wherein information source n to be
sn, frequency of failure an, then the equivalent number of success s and frequency of failure a after conversion is merged, can calculate according to following formula
It obtains：
If information source n has hnBatch tests preceding Test Information, then according to Bayes methods, can be calculated by following formula：
Wherein
For the point estimate of each batch product reliability；
lij、sij, it is the test number (TN) and the frequency of failure of each batch；
For the average value of the Reliability point estimation of information source i.
Data after conversion is merged are as shown in the following Table 4：
4 multi-source prior information fused data table of table
When calculating the weight for determining empirical prior information, field samples information is weight constant, compares empirical prior information by calculating
With the distribution matching degree of field samples information, so that it is determined that the weight of empirical prior information, effectively prevents due to empirical prior information number
According to measure larger and field samples information data amount it is smaller when, " flooding " effect of appearance, i.e. empirical prior information are by field samples information
Flood, field samples information caused to lose meaning, the calculating of final reliability can no specific aim, i.e., all system reliabilities are equal
It is not much different.
When computing system reliability, the reliability that the distribution of unit reliability is all converted to Success-failure Type is distributed, comprehensive each list
The reliability distribution of member and the sample size and the frequency of failure of system itself, you can by Beta distributions be calculated system can
By property mean value and its confidence lower limit.
The inspection of embodiment 2 --- empirical prior information determines that empirical prior information belongs to which type of distribution.
The inspection of exponential distribution：
In formula：T* --- total testing time；
Tk--- there is total testing time when kth time failure.
In formula：
t0--- the deadline of fixed time test；
tr--- in fixed failure number test, the time of r-th of faulty item failure；
N --- life test sample size；
R --- the number of faults at the end of life test；
ti--- the fault time of i-th of faulty item.
Separately have
Inspection rule is, ifThen the distribution belongs to exponential distribution, otherwise refuses.Specific meter
It calculates as a result, as shown in the following Table 5：
5 index prior distribation of table is examined
The inspection of Weibull distributions：
Life test is carried out to n product, in time t0Locate cutoff test, fault time is arranged from small to large, obtains r
A fault time is
0 ＜ t1≤t2≤t3≤Λ≤tr≤t0
If xi=lnti
If test statistics
In above formula,[] is rounding symbol herein, and the integer taken is less than or equal to numerical value in bracket
Maximum value separately has
Inspection rule is, if W ＜ Fα(2(r-r1-1),2r1), then the distribution meets Weibull distributions, otherwise refuses.Tool
Body result of calculation, as shown in the following Table 6：
6 Weibull prior distribations of table are examined
Embodiment 3 --- empirical prior information and field samples information consistency check.
It determines that the prior distribation of reliability θ is π (θ) in conjunction with empirical prior information, can be obtained by significance test in this way
Confidence interval is (θ before Bayes is tested1,θ2), wherein θ1、θ2It is determined by following formula：
Noninformative priors are taken to be distributed at this time, you can the Bayes estimated values for obtaining unknown parameter θ by field data areIfIt falls in (θ1,θ2) in, then it is assumed that two it is overall there was no significant difference, that is, before testing, to test rear data be compatible for reliability θ.It is no
Then, which cannot use, some is calculated may not meet actual conditions in link.
Through examining, empirical prior information is compatible with field samples information, can carry out follow-up calculating.
Embodiment 4 --- the calculating of empirical prior information weight
The calculating of empirical prior information weight T can be carried out by following formula：
T=P (χ2＞ K)
In formula：The successful number of s --- field test information；
The failure number of m --- field test information；
The successful number of c --- empirical prior information；
The failure number of a --- empirical prior information；
It is computed, the weight T=0.77 of empirical prior information, therefore in subsequent calculating, the successful number of all empirical prior informations, mistake
It loses number and total sample number is both needed to reuse after being multiplied by 0.77.
The reliability assessment of embodiment 5 --- unit
Basic principle：If reliability R meets a certain distribution, distribution function is π (R | D), and D indicates field test information,
Distribution first moment μ1For the point estimation of its reliability R mean values, it is confidence level to take γ, and γ=1- α can acquire it according to the following formula
Confidence lower limit RL and μ1。
(1) exponential type is distributed
Exponential type Life Type unit is calculated through following formula, can obtain the point estimation μ of its reliability mean valuekeAnd confidence lower limit RLe, knot
Fruit is shown in Table 7.
In formula
μke--- the point estimation of reliability mean value, ke=1；
Γ () --- gamma is distributed；
M --- when field test, stop Failure count when experiment；
η --- Equivalent task number when field testTotal testing time is τ, task time t, field test sample
Number is n；
A --- in empirical prior information, stop equivalent Failure count when experiment；
ν --- the Equivalent task number in empirical prior informationTotal testing time is τ0, task time t, empirical prior information
Equivalent sample number is b.
7 exponential distribution reliability of table
(2) Weibull types are distributed
If
The then point estimation μ of its reliability mean valuekWAnd its confidence lower limit RLWIt can be calculated through following formula, the results are shown in Table 8.
In formula：μkW--- the point estimation of Weibull type Life Type unit reliability mean values, kW=1；
τ0--- the deadline of empirical prior information fixed time test；
M --- live fixed time test stops Failure count when experiment；
ti--- live fixed time test, the out-of-service time or deadline of a certain sample；
T --- the task time of field test sample；
β --- the form parameter of Weibull distributions；
δ --- 1 is taken when no prior distribation, and 0 is taken when being uniformly distributed；
A --- the equivalent Failure count in empirical prior information；
B --- the equivalent sample number in empirical prior information；
γ --- confidence level；
R --- reliability；
The domain of B --- β；B(β1, β2) be calculated by following formula：
In formula：α --- confidence level；
M --- live fixed time test stops Failure count when experiment；
N --- field test sample number；
ti--- live fixed time test, the out-of-service time or deadline of a certain sample.
Parameter is prior distribation in the formula, in formulaWithFor the expectation of empirical prior information and the point estimation of variance.
8 Weibull of table is distributed reliability
The Reliability confidence lower limit that Weibull distributions are found out is higher than exponential distribution, i.e. confidence interval is narrower, finds out
Reliability is more accurate, therefore uses the reliability data of Weibull distributions.
The reliability assessment of embodiment 6 --- system
The reliability distribution that the distribution of unit reliability is all converted to Success-failure Type, obtains the equivalent sample number of event elements i
niAnd equivalent frequency of failure mi, calculation formula is as follows：
The reliability distribution of comprehensive each unit and the sample size N ' and frequency of failure M ' of system itself, you can pass through Beta
The reliability mean value of system is calculated in distributionAnd its confidence lower limit RL, calculation formula are as follows：
It is computed, extinguishing chemical bottle group container value reliability data.See following table 9：
9 extinguishing chemical bottle group container value reliability of table
Each bottom event and each failure mode, the reliability of inoperative component and gas fire-extinguishing facility ginseng can similarly be calculated
Number, as shown in the following Table 10：
The failure dependability parameter of table 10
Embodiment 7 --- FMEA is analyzed
Since the minimal cut set of the fault tree is each bottom event, therefore as can be seen from Table 10, event X110,
X101, X200 and X510 influence maximum for the failure probability of heptafluoro-propane fire-extinguishing apparatus, and failure mode is carried out on it to be influenced to divide
Analysis, as shown in the following Table 11：
11 FEMA analytical tables of table
Claims (8)
1. a kind of appraisal procedure for gas extinguishing system reliability, it is characterised in that：With Fault Tree Analysis-Bayes
Computational methods-FMEA analytic approach realizes that the assessment of gas extinguishing system reliability establishes extinction using gas as shown in Table 1 first
System reliability fault tree elementary event；Secondly, according to fault tree, each bottom event in fault tree is calculated with Bayes methods
Hinder the reliability of unit；Again, according to the reliability of each bottom trouble unit successively computing system reliability；Finally, in conjunction with
The result of calculation of reliability assesses gas extinguishing system with FMEA analytic approach；
1 gas extinguishing system reliability failure tree elementary event of table
2. a kind of appraisal procedure for gas extinguishing system reliability as described in claim 1, it is characterised in that：With
When Bayes methods calculate the reliability of each bottom trouble unit in fault tree, the screening of multi-source prior information is carried out simultaneously first
The empirical prior information after conversion is merged in conversion；Secondly the empirical prior information after fusion is subjected to distribution inspection, judges its distributional class
Type；It is computed the weight of determining empirical prior information again；Finally according to empirical prior information and field samples information, consistency check is carried out
Afterwards, point estimation and its confidence lower limit of the reliability mean value of each trouble unit are calculated by formula.
3. a kind of appraisal procedure for gas extinguishing system reliability as claimed in claim 2, it is characterised in that：Described
Bottom trouble unit includes exponential type Life Type unit and Weibull type Life Type units：
(1) exponential type Life Type unit
The point estimation μ of its reliability mean valuekeAnd its confidence lower limit RLeCalculation formula it is as follows：
In formula：μke--- the point estimation of reliability mean value, ke=1；
Γ () --- gamma is distributed；
M --- when field test, stop Failure count when experiment；
η --- Equivalent task number when field testTotal testing time is τ, task time t, and field test sample number is
n；
A --- in empirical prior information, stop equivalent Failure count when experiment；
ν --- the Equivalent task number in empirical prior informationTotal testing time is τ0, task time t, empirical prior information it is equivalent
Sample number is b；
γ --- confidence level；
R --- reliability；
(2) Weibull types Life Type unit
If
The then point estimation μ of its reliability mean valuekWAnd its confidence lower limit RLWCalculation formula it is as follows：
In formula：μkW--- the point estimation of Weibull type Life Type unit reliability mean values, kW=1；
τ0--- the deadline of empirical prior information fixed time test；
M --- live fixed time test stops Failure count when experiment；
ti--- live fixed time test, the out-of-service time or deadline of a certain sample；
T --- the task time of field test sample；
β --- the form parameter of Weibull distributions；
δ --- 1 is taken when no prior distribation, and 0 is taken when being uniformly distributed；
A --- the equivalent Failure count in empirical prior information；
B --- the equivalent sample number in empirical prior information；
γ --- confidence level；
R --- reliability；
The domain of B --- β；B(β1, β2) be calculated by following formula：
In formula：α --- confidence level；
M --- live fixed time test stops Failure count when experiment；
N --- field test sample number；
ti--- live fixed time test, the out-of-service time or deadline of a certain sample.
4. a kind of appraisal procedure for gas extinguishing system reliability as claimed in claim 2, it is characterised in that：Carry out
When the conversion of multi-source prior information, according to field samples information, the empirical prior information of multi-source is converted into the data under identical conditions,
Or set of metadata of similar data is converted into equivalent data.
5. a kind of appraisal procedure for gas extinguishing system reliability as claimed in claim 2, it is characterised in that：It is merging
When empirical prior information afterwards carries out distribution inspection, take confidence lower limit is higher to be distributed as its distribution pattern.
6. a kind of appraisal procedure for gas extinguishing system reliability as claimed in claim 2, it is characterised in that：It calculates true
When determining the weight of empirical prior information, field samples information is weight constant, compares empirical prior information and field samples information by calculating
Distribution matching degree determine the weight of empirical prior information.
7. a kind of appraisal procedure for gas extinguishing system reliability as claimed in claim 2, it is characterised in that：According to testing
When preceding information and field samples information carry out consistency check, tested using Parametric test, if it is determined that it is compatible, then it carries out
Subsequent bottom trouble unit Calculation of Reliability, you can by spending the point estimation of mean value and its calculating of confidence lower limit；If it is determined that not
It is compatible, then empirical prior information is screened again.
8. a kind of appraisal procedure for gas extinguishing system reliability as claimed in claim 2, it is characterised in that：Calculate system
When reliability of uniting, the distribution of bottom trouble unit reliability is all converted into bi-distribution, integrates the reliable of each bottom trouble unit
Property distribution and system itself sample size and the frequency of failure, you can the reliability mean value of system is calculated by bi-distribution
And its confidence lower limit.
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