CN110414552B - Bayesian evaluation method and system for spare part reliability based on multi-source fusion - Google Patents
Bayesian evaluation method and system for spare part reliability based on multi-source fusion Download PDFInfo
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Abstract
The invention relates to a Bayesian evaluation method and a Bayesian evaluation system for spare part reliability based on multi-source fusion, wherein the Bayesian evaluation method comprises the following steps: determining a likelihood weight coefficient of prior distribution of one information source of the reliability of the spare part and prior distribution of other information sources, wherein the likelihood weight coefficient is the ratio of likelihood functions of the prior distribution of the two information sources; fusing each information source according to each likelihood weight coefficient to obtain prior distribution of the spare part failure rate; the method comprises the steps of determining a likelihood function corresponding to a guarantee task result, determining posterior distribution of spare part failure rates according to the likelihood function corresponding to the guarantee task result and prior distribution of the spare part failure rates to obtain a Bayesian evaluation result of spare part reliability, and quantifying credibility of reliability information of different sources by adopting likelihood weight coefficients aiming at the characteristic that the spare part has less data used in the field, so that the influence of human factors can be reduced, reliability evaluation is carried out after each spare part reliability information source is effectively and reasonably fused, and the method has better estimation precision.
Description
Technical Field
The invention relates to the field of spare part reliability estimation, in particular to a Bayesian spare part reliability assessment method and system based on multi-source fusion.
Background
When the actual reliability rule of the spare part is inconsistent with the design parameter, the number of guarantee failures is increased or the spare part is overstocked. Under special working environments, such as marine working environments like ships, the difference between the actual reliability rule and the design parameter is larger.
The spare part reliability evaluation method has the advantages that the number of information sources is large, the effectiveness of different information sources in different conditions and environments for spare part reliability evaluation is different, and the accuracy of a spare part reliability evaluation result can be improved by reasonably fusing all the information sources.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a Bayesian assessment method and a Bayesian assessment system for spare part reliability based on multi-source fusion.
The technical scheme for solving the technical problems is as follows: a Bayesian assessment method for reliability of spare parts based on multi-source fusion, the method comprises the following steps:
and 3, determining a likelihood function corresponding to the guarantee task result, determining posterior distribution of the spare part fault rate according to the likelihood function corresponding to the guarantee task result and the prior distribution of the spare part fault rate, and obtaining a Bayesian evaluation result of the spare part reliability.
A Bayesian evaluation system for spare part reliability based on multi-source fusion, the system comprising: the system comprises a likelihood weight coefficient determining module, a spare part failure rate prior distribution determining module and a spare part reliability Bayesian evaluating module;
the likelihood weight coefficient determining module is used for determining the likelihood weight coefficient of the prior distribution of one information source of the reliability of the spare part and the prior distribution of other information sources, and the likelihood weight coefficient is the ratio of likelihood functions of the prior distributions of the two information sources;
the prior distribution determining module of the spare part failure rate is used for fusing each information source according to each likelihood weight coefficient to obtain the prior distribution of the spare part failure rate;
and the spare part reliability Bayesian evaluation module is used for determining a likelihood function corresponding to the guarantee task result, determining posterior distribution of the spare part fault rate according to the likelihood function corresponding to the guarantee task result and the prior distribution of the spare part fault rate, and obtaining a spare part reliability Bayesian evaluation result.
The invention has the beneficial effects that: according to the characteristic that field use data of spare parts is few, the likelihood weight coefficients are adopted to quantify credibility of reliability information of different sources, influence of human factors can be reduced, reliability evaluation is carried out after reliability information sources of the spare parts are effectively and reasonably fused, estimation accuracy is better, and the estimation accuracy is gradually improved along with increase of guaranteed task times.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, the information sources in the multi-source fusion include: engineering experience information, equipment development and production test information and field consumption information of maintenance support.
In the step 1, the likelihood function of the prior distribution pi (λ) of the information source is the marginal distribution m (Data pi (λ)) of the field test Data:
λ is an unknown parameter representing the failure rate of the spare part, L (Data | λ) is a likelihood function corresponding to the field test Data, and π (λ) is the prior distribution of the information source with respect to the parameter λ;
the likelihood weight coefficient C is formulated as:
π1(λ) is the prior distribution of the first information source with respect to the parameter λ, π2(λ) is an a priori distribution of the second information source with respect to the parameter λ.
The prior distribution of the spare part failure rate in the step 2 is a product of the prior distribution of the information source and adjustment values of the prior distributions of the other information sources, and the adjustment values of the prior distributions of the other information sources are determined according to the likelihood weight coefficients corresponding to the adjustment values.
When the information source is two information of engineering experience information and equipment development and production test information, the step 2 comprises the following steps:
step 201, respectively determining prior distribution pi when information sources are engineering experience information and equipment development and production test information1(lambda) and pi2(λ)：
π1(λ)＝μ0exp(-λμ0),λ＞0；
step 202, calculating likelihood weight coefficients:
d is spare part field consumption data of equipment maintenance support;
step 203, determining the prior distribution of the spare part failure rate as:
and when the likelihood weight coefficient C is larger than 1, modifying the value of the likelihood weight coefficient C to 1.
The determining the likelihood function corresponding to the guarantee task result in the step 3 includes:
step 301, determining the guarantee task result:
[Twi,Fi,Ni]，i＝1,2,…,n.；
i represents the serial number of the guarantee task times, n represents the guarantee task times, Twi represents the ith guarantee task time, FiA mark for guaranteeing whether the ith task is successful or not, wherein F is the successful guarantee of the taskiEqual to 1, when said assurance task fails FiIs equal to 0, NiRepresenting the number of spare parts consumed by the ith guarantee task;
step 302, determining the probability of guarantee task success and guarantee task failure in the guarantee tasks:
the probability of guaranteeing the success of the task is as follows:
the probability of the guarantee task failure is as follows:
Sithe number of the carried spare parts is k, and the number of the carried spare parts is k;
step 303, determining that the likelihood function corresponding to the safeguard task is:
And 3, determining the posterior distribution of the spare part fault rate as follows:
pi (λ) is the prior distribution of the information sources.
The step 3 of obtaining the Bayesian evaluation result of the spare part reliability comprises the following steps:
the Bayesian estimation of the spare part failure rate is as follows:
the Bayesian estimation of the average life of the spare parts is as follows:
the beneficial effect of adopting the further scheme is that: and the reliability evaluation is carried out after two information sources of engineering experience information and equipment development and production test information are effectively and reasonably fused.
Drawings
Fig. 1 is a flowchart of a bayesian evaluation method for reliability of a spare part based on multi-source fusion according to an embodiment of the present invention;
fig. 2 is a structural block diagram of an embodiment of a bayesian evaluation system for reliability of a spare part based on multi-source fusion provided by the present invention.
In the drawings, the components represented by the respective reference numerals are listed below:
1. the system comprises a likelihood weight coefficient determining module, a spare part failure rate prior distribution determining module and a spare part reliability Bayesian evaluating module.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, a flowchart of a bayesian method for evaluating reliability of a spare part based on multi-source fusion provided by the embodiment of the present invention includes:
And 2, fusing each information source according to each likelihood weight coefficient to obtain prior distribution of the spare part failure rate.
And 3, determining a likelihood function corresponding to the guarantee task result, determining posterior distribution of the spare part fault rate according to the likelihood function corresponding to the guarantee task result and the prior distribution of the spare part fault rate, and obtaining a Bayesian evaluation result of the spare part reliability.
The invention provides a Bayesian evaluation method for reliability of spare parts in multi-source fusion, which is characterized in that likelihood weight coefficients are adopted to quantify credibility of reliability information of different sources aiming at the characteristic that field use data of the spare parts are few, so that the influence of human factors can be reduced, reliability evaluation is carried out after each spare part reliability information source is effectively and reasonably fused, better estimation precision is achieved, and the estimation precision is gradually improved along with the increase of guaranteed task times.
Example 1
The spare part is an unthinkable part during the execution of the task, the life of the spare part follows an exponential distribution, and the probability density function is:
f(t)＝λexp(-λt)
where t is time, λ is an unknown parameter indicating the failure rate of the spare part, and μ ═ 1/λ is the average life of the spare part.
From the whole life cycle process of the equipment, the information sources of the spare parts mainly comprise engineering experience information, equipment development and production test information, field consumption of maintenance guarantee and the like.
The engineering experience information is mainly the experience knowledge accumulated in the process of equipment development and design, production management and use guarantee, and is an important basis for developing equipment reliability design. The engineering experience information has multiple sources and various expression forms. Some engineering experience information is reflected in equipment design specifications or design manuals, such as MTBF (mean time between failure) design values of parts or spare parts and the like are specified, and the design method is convenient for designers to use when developing equipment design; some of the proposals are subjective judgments or estimations of spare parts, for example, when an initial spare part configuration scheme is prepared, a great number of initial configuration suggestions of the spare parts are provided according to engineering experience information. For example, in a predetermined mission profile (mission time Tw)0) The configuration number of the spare parts is S0The number of the carried spare parts is N, the corresponding spare part guarantee probability is P, namely, the inequality is satisfied
Obviously, the above prior information can be rewritten as:
wherein,
is x2The upper quantile of distribution, k is the number of the spare parts.
In the early stage of equipment development, the reliability information of the spare parts which can be used by people mainly comes from engineering experience information, which is a main information source for people to make a spare part configuration scheme and is also important prior information used when carrying out the reliability evaluation of the spare parts.
The equipment development and production test information is mainly spare part reliability information obtained by accumulating various performance tests, element and component environmental stress screening tests and the like in equipment development and production. Especially for spare parts which are equipped with important functional units, more reliability information can be accumulated through various tests of the functional units. For a certain spare part, the reliability information of the spare part obtained by development and production tests can be generally expressed as
(T0,r0)
Wherein T is0For the accumulated test time, r, of spare parts during the development and production test0Is the corresponding failure number. Considering that various tests at the equipment development or production stage are often different from the actual operation environment of the equipment, the environmental factor mode is used for conversion during actual information processing. If the environmental factor between the information environment of equipment development and production test and the actual operation is K (K is more than 0 and less than 1), the equivalent data after conversion is (KT)0,r0). Obviously, the equipment development test information is a real reflection that the reliability of the spare parts is actually installed on the equipment and is important information for developing the reliability evaluation of the spare parts.
During the combat readiness mission of a ship at sea, the equipment is generally in the states of operation, standby, trouble shooting, or waiting for repair. For example, in the equipment operating state, information such as the equipment operating time or the time when a failure occurs needs to be recorded, and in the equipment failure maintenance state, the variety and the number of the spare parts to be replaced by the repair activity need to be recorded. It can be seen that the spare part reliability information recorded by the ship during the execution of the combat readiness mission on the sea can be expressed as:
[Twi,Fi,Si]，i＝1,2,…,n.
wherein i represents the number of guaranteed tasks' number of times, n represents the number of guaranteed tasks, TwiRepresenting the ith guarantee task time; fiIs the mark of the success of the task guarantee, when all the spare part requirements in the task period are satisfied, FiEqual to 1, otherwise FiEqual to 0; si＝{N1i,N2i,…,NMiIndicates the number of spare parts actually consumed by the task, e.g. N1iRepresents the actual consumption quantity, N, of the 1 st spare part in the task1iIs more than or equal to 0. Taking a spare part as an example, if the time of a certain guarantee task is 1000h, and 3 faults occur in the period and are all satisfied, the guarantee task is successful and is marked as [1000,1,3 ]](ii) a If the 3 faults are met for only 2 times, the guarantee task fails, and the result is recorded as [1000,0,2]。
Further, the likelihood function of the prior distribution pi (λ) of the information source is the marginal distribution m (Data i pi (λ)) of the field test Data:
l (Data | lambda) is a likelihood function corresponding to the field test Data, pi (lambda) is prior distribution of the information source about the parameter lambda, and L (Data | lambda) pi (lambda) is joint distribution of the parameter lambda and the field test Data.
The magnitude of the likelihood function of the prior distribution pi (λ) reflects a reasonable measure of the choice of pi (λ) as the information source. If m (D | π (λ)) is larger, it means that the prior distribution π (λ) supports the field test Data to a higher degree, and it is more reasonable to select π (λ) as the prior distribution. The ratio of the likelihood functions of the prior distributions of the two information sources thus represents a comparison of the degree of trustworthiness of the two information sources.
Likelihood weight coefficient C is formulated as
Wherein, pi1(λ) is the prior distribution of the first information source with respect to the parameter λ, π2(λ) is an a priori distribution of the second information source with respect to the parameter λ.
The likelihood weight coefficient C reflects the support degree of two information sources to the field test Data. When C is less than 1, the support degree of the first information source to the field test Data is lower than that of the second information source; when C is more than 1, the support degree of the first information source to the field test Data is higher than that of the second information source. In this sense, the likelihood weight coefficient C can be used to convert the credibility of two information sources with different credibility, and the two information sources have the same credibility through the conversion, which is convenient for the fusion of the prior information, so that C is called as the likelihood weight coefficient.
And 2, fusing each information source according to each likelihood weight coefficient to obtain prior distribution of the spare part failure rate.
After likelihood weight coefficients of prior distribution of one information source of the reliability of the spare part and prior distribution of other information sources are determined in the step 1, obtaining each likelihood weight coefficient, fusing each information source according to each likelihood weight coefficient to obtain prior distribution of the fault rate of the spare part, wherein the prior distribution of the fault rate of the spare part is the product of the prior distribution of the information source and adjustment values of the prior distribution of other information sources, and the adjustment values of the prior distribution of other information sources are determined according to the corresponding likelihood weight coefficients.
Specifically, the information source may select information with high reliability according to actual experience, for example, information of equipment development and production test, and taking two information sources of engineering experience information and information of equipment development and production test as an example, the prior distribution process of obtaining the failure rate of the spare part in step 2 includes:
step 201, respectively determining prior distribution pi when information sources are engineering experience information and equipment development and production test information1(lambda) and pi2(λ)：
π1(λ)＝μ0exp(-λμ0),λ＞0
Specifically, the gamma distribution is selected as the prior distribution of the spare part failure rate:
wherein a and b are hyper-parameters.
When the information source is engineering experience information, determining that the hyper-parameters are a respectively by adopting a maximum entropy method1＝1,b1＝μ0(ii) a When the information source is equipment development and production test information, a priori moment method and the like are adopted to determine that the hyper-parameters are respectively a2＝r0+1,b2＝KT0。
Step 202, calculating likelihood weight coefficients:
d is spare part field consumption data of equipment maintenance support.
Step 203, determining the prior distribution of the failure rate of the spare parts as
And when the likelihood weight coefficient C is larger than 1, modifying the value of the likelihood weight coefficient C to 1.
Specifically, when C is less than 1, the engineering experience information and the field consumption data of the spare parts have a large difference, and the prior distribution pi is required to be subjected to prior distribution during the fusion of the prior information1(λ) performing appropriate compression; when C is larger than 1, the engineering experience information is better matched with the field consumption data of the spare parts compared with the equipment development and production test information, and the phenomenon is generally caused by less equipment development and production test information, so that a method of temporarily not compressing the engineering experience information can be adopted for processing when actual prior information is fused. In summary, when merging the prior information of the spare parts, the likelihood weight coefficient C is taken as:
when two information sources are independent from each other, the fusion of the information sources actually superimposes the information quantities of the two information sources. Entropy taking into account a prior distribution pi (lambda)
In fact is a mathematical expectation of log pi (λ), and therefore the function log pi (λ) is considered to be an approximation of the information content of the prior distribution pi (λ). Thus, the a priori confidence after fusion is
logπ(λ)＝logπ1(λ)+logπ2(λ)
Namely, the prior distribution of the spare part failure rate obtained by fusion is as follows:
π(λ)＝π1(λ)π2(λ)
independent fusion of two information sources with different credibility degrees. When the credibility of the two information sources is different, the likelihood weight coefficient is utilized to carry out prior distribution pi1(lambda) compressing, i.e. reducing the information content of the engineering experience information to Clog pi1(λ), in this case, the amount of a priori information after fusion can be expressed as
logπ(λ)＝Clogπ1(λ)+logπ2(λ)
Namely, the prior distribution of the spare part failure rate obtained by fusion is as follows:
π(λ)＝(π1(λ))Cπ2(λ)。
and 3, determining a likelihood function corresponding to the guarantee task result, determining posterior distribution of the spare part fault rate according to the likelihood function corresponding to the guarantee task result and the prior distribution of the spare part fault rate, and obtaining a Bayesian evaluation result of the spare part reliability.
In order to create a statistical model for evaluating the life characteristics of a spare part, the field consumption information of the repair and maintenance of the spare part is first analyzed.
The determining the likelihood function corresponding to the guarantee task result in the step 3 includes:
step 301, determining a guarantee task result:
[Twi,Fi,Ni]，i＝1,2,…,n.。
step 302, determining probabilities of task success and task failure in the assurance task.
For the ith (i is more than or equal to 1 and less than or equal to n) guarantee task, the quantity of the carried spare parts of a certain spare part is recorded as Si. If FiIf 1, this guarantee task is successful, i.e. the spare parts required for the equipment failure are guaranteed in this guarantee task, N is therefore the casei≤Si. At this time, the event occurrence probability is
When F is presentiIf 0, this safeguard task fails, i.e. the number of spare parts required for the equipment failure exceeds the number of spare parts to be carried in this safeguard task, N is presenti＞Si. Therefore, the probability of failure of spare part guarantee is as follows:
step 303, determining a likelihood function corresponding to the safeguard task.
The on-site consumption information of the maintenance support of the spare parts, namely the likelihood function corresponding to the support task, is as follows:
wherein
Further, the posterior distribution that can determine the failure rate of the spare part by using the prior distribution is as follows:
further, obtaining a bayesian evaluation result of the reliability of the spare part comprises:
when the square damage function is taken, the Bayesian estimation of the failure rate of the spare part is
Accordingly, the bayesian estimate of the average life of the spare part is:
example 2
the likelihood weight coefficient determining module 1 is used for determining the likelihood weight coefficient of the prior distribution of one information source of the reliability of the spare part and the prior distribution of other information sources, wherein the likelihood weight coefficient is the ratio of likelihood functions of the prior distributions of the two information sources;
the prior distribution determining module 2 of the spare part failure rate is used for fusing each information source according to each likelihood weight coefficient to obtain the prior distribution of the spare part failure rate;
and the spare part reliability Bayesian evaluation module 3 is used for determining a likelihood function corresponding to the guarantee task result, determining posterior distribution of the spare part fault rate according to the likelihood function corresponding to the guarantee task result and the prior distribution of the spare part fault rate, and obtaining a spare part reliability Bayesian evaluation result.
The Bayesian evaluation method and the Bayesian evaluation system for the reliability of the spare parts based on the multi-source fusion can prove the effectiveness of the spare parts through actual simulation and example analysis.
In the simulation process, the real value of the life distribution parameter of the index type spare part is recorded as mu, and the reference value of the parameter given by the undertaking party is recorded as mu0And generating n groups of guarantee information by simulating n guarantee processes. The simulation steps of the primary guarantee process are as follows:
1) setting guarantee task time Tw；
2) Reference value mu of the parameter given by the receiver0Under the condition that the guarantee probability reaches 0.8, the number n of spare parts to be equipped is calculated;
3) generating an exponential distribution according to the parameter truth value mu and generating 1+ n random numbers tjSimulating life values for 1 part and n spare parts;
4) order to
I is more than or equal to 1 and less than or equal to n +1, and simT represents the maximum working time for preparing i-1 spare parts;
5) starting from i ═ 1, search for the first larger than T among all simTswNumber simT ofkI.e. satisfy simTk-1＜TwAnd simTk＞TwIf yes, the guarantee task is successful, and the guarantee result is recorded as [ T ]w,1,k-1]Otherwise, the guarantee task fails, and the guarantee result is recorded as [ T ]w,0,n]。
In the course of example analysis, the real value of life distribution parameter of some exponential type spare parts is defined as mu-350, and the reference value given by manufacturer is mu0500. The accumulated test time of the spare part during the equipment development and production is T01500, the number of failures is r 03. The environmental factor K is 0.9.
Taking 10 guarantee tasks as an example, respectively allocating a corresponding number of spare parts for the 10 tasks according to the reference values given by the bearing party, and simulating the execution condition of the 10 tasks through the simulation process, wherein the result is shown in table 1.
TABLE 1 guarantee task execution
The average service life of the spare parts is obtained by numerical integration by using a Bayesian estimation formula
It can be seen that the method can still obtain a more accurate parameter estimation value under the condition that the reference value given by the receiving party deviates from the true parameter value.
In order to verify the stability of the method, the above estimation process was repeated several times at different task times, and the mean and mean square error of the parameter estimation values were calculated, respectively, and the results are shown in table 2.
TABLE 2 estimation results for different task times
As can be seen from table 2, as the number of guaranteed tasks increases, the accuracy of the parameter estimation value gradually increases, and at the same time, the mean square error gradually decreases, which indicates that the method can more accurately estimate the true value of the parameter as the consumption data used on site increases; however, in practice, the number of guaranteed tasks is often small, it is difficult to accumulate a large amount of field data in a short time, as can be seen from table 2, when the number of guaranteed tasks reaches 8, the parameter estimation value is accurate, and the mean square error is small, which indicates that the method can reach higher estimation accuracy when the number of tasks is small, and has better practical value.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (6)
1. A Bayesian assessment method for reliability of spare parts based on multi-source fusion is characterized by comprising the following steps:
step 1, determining a likelihood weight coefficient of prior distribution of one information source of reliability of a spare part and prior distribution of other information sources, wherein the likelihood weight coefficient is a ratio of likelihood functions of the prior distribution of the two information sources;
step 2, fusing each information source according to each likelihood weight coefficient to obtain prior distribution of the spare part failure rate;
step 3, determining a likelihood function corresponding to the guarantee task result, determining posterior distribution of the spare part fault rate according to the likelihood function corresponding to the guarantee task result and the prior distribution of the spare part fault rate, and obtaining a Bayesian evaluation result of the spare part reliability;
in the step 1, the likelihood function of the prior distribution pi (λ) of the information source is the marginal distribution m (Data pi (λ)) of the field test Data:
λ is an unknown parameter representing the failure rate of the spare part, L (Data | λ) is a likelihood function corresponding to the field test Data, and π (λ) is the prior distribution of the information source with respect to the parameter λ;
the likelihood weight coefficient C is formulated as:
π1(λ) is the prior distribution of the first information source with respect to the parameter λ, π2(λ) is an a priori distribution of the second information source with respect to the parameter λ;
the prior distribution of the spare part failure rate in the step 2 is the product of the prior distribution of the information source and the adjustment values of the prior distributions of the other information sources, and the adjustment values of the prior distributions of the other information sources are determined according to the likelihood weight coefficients corresponding to the adjustment values;
when the information source is two information of engineering experience information and equipment development and production test information, the step 2 comprises the following steps:
step 201, respectively determining prior distribution pi when information sources are engineering experience information and equipment development and production test information1(lambda) and pi2(λ)：
π1(λ)＝μ0exp(-λμ0),λ＞0；
step 202, calculating likelihood weight coefficients:
d is spare part field consumption data of equipment maintenance support;
step 203, determining the prior distribution of the spare part failure rate as:
and when the likelihood weight coefficient C is larger than 1, modifying the value of the likelihood weight coefficient C to 1.
2. The method of claim 1, wherein the information sources in the multi-source fusion comprise: engineering experience information, equipment development and production test information and field consumption information of maintenance support.
3. The method of claim 1, wherein the determining the likelihood function corresponding to the guarantee task result in step 3 comprises:
step 301, determining the guarantee task result:
[Twi,Fi,Ni]，i＝1,2,…,n.；
i denotes a serial number of the number of secured tasks, n denotes the number of secured tasks, TwiIndicating the ith guaranteed task time, FiA mark for guaranteeing whether the ith task is successful or not, wherein F is the successful guarantee of the taskiEqual to 1, when said assurance task fails FiIs equal to 0, NiRepresenting the number of spare parts consumed by the ith guarantee task;
step 302, determining the probability of guarantee task success and guarantee task failure in the guarantee tasks:
the probability of guaranteeing the success of the task is as follows:
the probability of the guarantee task failure is as follows:
λ is an unknown parameter representing the failure rate of the spare part, SiThe number of the carried spare parts is k, and the number of the carried spare parts is k;
step 303, determining that the likelihood function corresponding to the safeguard task is:
4. The method of claim 3, wherein the posterior distribution of the spare part failure rates determined in step 3 is:
pi (λ) is the prior distribution of the information source, T0For the accumulated test time, r, of spare parts during the development and production test0The failure times of the spare parts during the development and production test are determined, and K is an environmental factor between the information environment and the actual operation of the equipment development and production test.
5. The method of claim 3, wherein the obtaining the Bayesian evaluation of spare part reliability result in the step 3 comprises:
the Bayesian estimation of the spare part failure rate is as follows:
the Bayesian estimation of the average life of the spare parts is as follows:
6. a Bayesian evaluation system for reliability of spare parts based on multi-source fusion is characterized in that the system comprises: the system comprises a likelihood weight coefficient determining module, a spare part failure rate prior distribution determining module and a spare part reliability Bayesian evaluating module;
the likelihood weight coefficient determining module is used for determining the likelihood weight coefficient of the prior distribution of one information source of the reliability of the spare part and the prior distribution of other information sources, and the likelihood weight coefficient is the ratio of likelihood functions of the prior distributions of the two information sources;
the likelihood function of the prior distribution pi (lambda) of the information source is the marginal distribution m (Data pi (lambda)) of the field test Data:
λ is an unknown parameter representing the failure rate of the spare part, L (Data | λ) is a likelihood function corresponding to the field test Data, and π (λ) is the prior distribution of the information source with respect to the parameter λ;
the likelihood weight coefficient C is formulated as:
π1(λ) is the prior distribution of the first information source with respect to the parameter λ, π2(λ) is an a priori distribution of the second information source with respect to the parameter λ;
the prior distribution determining module of the spare part failure rate is used for fusing each information source according to each likelihood weight coefficient to obtain the prior distribution of the spare part failure rate;
the prior distribution of the spare part failure rate is the product of the prior distribution of the information source and the adjustment values of the prior distributions of the other information sources, and the adjustment values of the prior distributions of the other information sources are determined according to the likelihood weight coefficients corresponding to the adjustment values;
when the information sources are engineering experience information and equipment development and production test information, the process of determining the likelihood weight coefficient of the prior distribution of one information source and the prior distribution of other information sources for the reliability of the spare parts comprises the following steps:
step 201, respectively determining prior distribution pi when information sources are engineering experience information and equipment development and production test information1(lambda) and pi2(λ)：
π1(λ)＝μ0exp(-λμ0),λ＞0；
step 202, calculating likelihood weight coefficients:
d is spare part field consumption data of equipment maintenance support;
step 203, determining the prior distribution of the spare part failure rate as:
when the likelihood weight coefficient C is larger than 1, modifying the value of the likelihood weight coefficient C to 1;
and the spare part reliability Bayesian evaluation module is used for determining a likelihood function corresponding to the guarantee task result, determining posterior distribution of the spare part fault rate according to the likelihood function corresponding to the guarantee task result and the prior distribution of the spare part fault rate, and obtaining a spare part reliability Bayesian evaluation result.
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