CN110414552B - A Bayesian Evaluation Method and System for Spare Parts Reliability Based on Multi-source Fusion - Google Patents

Abstract

The invention relates to a Bayesian evaluation method and system of spare parts reliability based on multi-source fusion. The likelihood weight coefficient is the ratio of the likelihood functions of the prior distributions of the two information sources; the prior distribution of the failure rate of spare parts is obtained by fusing each information source according to the likelihood weight coefficients; the likelihood function corresponding to the guarantee task result is determined, According to the likelihood function corresponding to the guarantee task results and the prior distribution of the spare part failure rate, the posterior distribution of the spare part failure rate is determined, and the Bayesian evaluation result of the spare part reliability is obtained. In view of the characteristics of less data on the field use of the spare parts, the likelihood weight is adopted. The coefficient quantifies the reliability of reliability information from different sources, which can reduce the influence of human factors, and can effectively and reasonably integrate each spare parts reliability information source for reliability evaluation, which has better estimation accuracy.

Description

A Bayesian Evaluation Method and System for Spare Parts Reliability Based on Multi-source Fusion

technical field

The invention relates to the field of spare parts reliability prediction, in particular to a Bayesian evaluation method and system of spare parts reliability based on multi-source fusion.

Background technique

When the actual reliability law of spare parts is inconsistent with the design parameters, it will lead to an increase in the number of guarantee failures or a backlog of spare parts. Under special working environments, such as marine working environments such as ships, the actual reliability laws and design parameters will be more different.

There are many sources of information in the spare parts reliability assessment method. Different information sources have different effectiveness in the assessment of spare parts reliability under different circumstances. Reasonable fusion of various information sources can improve the accuracy of spare parts reliability assessment results.

SUMMARY OF THE INVENTION

Aiming at the technical problems existing in the prior art, the present invention provides a Bayesian evaluation method and system for the reliability of spare parts based on multi-source fusion.

The technical solution of the present invention to solve the above technical problems is as follows: a Bayesian evaluation method for the reliability of spare parts based on multi-source fusion, the method includes:

Step 1: Determine the likelihood weight coefficient of the prior distribution of one information source of spare parts reliability and the prior distribution of each other information source, where the likelihood weight coefficient is the likelihood of the prior distribution of the two information sources ratio of functions;

Step 2: Integrate each information source according to each likelihood weight coefficient to obtain a priori distribution of the failure rate of spare parts;

Step 3: Determine the likelihood function corresponding to the support task result, determine the posterior distribution of the spare part failure rate according to the likelihood function corresponding to the support task result and the prior distribution of the spare part failure rate, and obtain the spare part reliability Bayesian evaluation result.

A Bayesian evaluation system for spare parts reliability based on multi-source fusion, the system includes: a likelihood weight coefficient determination module, a prior distribution determination module for spare parts failure rates, and a spare parts reliability Bayesian evaluation module;

Likelihood weight coefficient determination module, used to determine the likelihood weight coefficient of the prior distribution of one information source of spare parts reliability and the prior distribution of each other information source, and the likelihood weight coefficient is the difference between the two information sources. The ratio of the likelihood functions of the prior distribution;

A priori distribution determination module of spare parts failure rate, which is used to obtain the prior distribution of spare parts failure rate by fusing each information source according to each likelihood weight coefficient;

The spare parts reliability Bayesian evaluation module is used to determine the likelihood function corresponding to the results of the support task. According to the likelihood function corresponding to the support task results and the prior distribution of the spare part failure rate, the posterior distribution of the spare part failure rate is determined, and the reliability of the spare parts is obtained. Sexual Bayesian evaluation results.

The beneficial effects of the present invention are: in view of the characteristics of less data used in the field of spare parts, the likelihood weight coefficient is used to quantify the reliability of reliability information from different sources, which can reduce the influence of human factors and effectively and reasonably integrate the reliability of each spare part Reliability evaluation is carried out after the information source, which has better estimation accuracy, and with the increase of the number of guarantee tasks, the estimation accuracy gradually improves.

On the basis of the above technical solutions, the present invention can also be improved as follows.

Further, the information sources in the multi-source fusion include: engineering experience information, equipment development and production test information, and on-site consumption information of maintenance support.

In the step 1, the likelihood function of the prior distribution π(λ) of the information source is the marginal distribution m(Data丨π(λ)) of the field test data Data:

λ is an unknown parameter representing the failure rate of spare parts, L(Data|λ) is the likelihood function corresponding to the field test data Data, and π(λ) is the prior distribution of the information source with respect to the parameter λ;

The formula of the likelihood weight coefficient C is expressed as:

π ₁ (λ) is the prior distribution of the first information source with respect to the parameter λ, and π ₂ (λ) is the prior distribution of the second information source with respect to the parameter λ.

In the step 2, the prior distribution of the spare parts failure rate is the product of the prior distribution of the one information source and the adjustment value of the prior distribution of the other information sources. The adjustment value of the distribution is determined according to its corresponding likelihood weight coefficient.

When the information sources are engineering experience information and equipment development and production test information, the step 2 includes:

Step 201, the prior distributions π ₁ (λ) and π ₂ (λ) when the information sources are respectively the engineering experience information and the equipment development and production test information are determined:

π ₁ (λ)=μ ₀ exp(-λμ ₀ ), λ>0;

Tw₀为任务时间，

是χ²分布的上分位数，S₀为建议备件的配置数，T₀为备件在研制生产试验期间所累积的试验时间，r₀为备件在研制生产试验期间对应的故障次数，K为装备研制生产试验信息环境与实际运行之间的环境因子；

Tw ₀ is the task time,

is the upper quantile of the χ2 distribution, S ⁰ is the _number of recommended spare parts configuration, T ₀ is the test time accumulated during the development and production test of the spare part, r ₀ is the number of failures corresponding to the spare part during the development and production test, K is the Environmental factors between equipment development and production test information environment and actual operation;

Step 202, calculate the likelihood weight coefficient:

D is the on-site consumption data of spare parts for equipment maintenance support;

In step 203, the prior distribution of the spare parts failure rate is determined as:

Wherein, when the likelihood weight coefficient C is greater than 1, the value of the likelihood weight coefficient C is modified to 1.

In the step 3, the likelihood function corresponding to the guarantee task result is determined to include:

Step 301, determine the guarantee task result:

[Tw _i , F _i , N _i ], i=1,2,...,n.;

i represents the serial number of the number of times of the guarantee task, n represents the number of times of the guarantee task, Twi represents the time of the ith guarantee task, F _i is the symbol of the success of the ith mission guarantee, and when the guarantee task is successful, F _i is equal to 1, F _i is equal to 0 when the support task fails, and N _i represents the number of spare parts consumed by the i-th support task;

Step 302, determining the probability of the success of the guarantee task and the failure of the guarantee task in the guarantee task:

The probability of the success of the assurance mission is:

The probability of failure of the assurance mission is:

S _i is the amount of spare parts carried, and k is the serial number of the spare parts;

Step 303, determine that the likelihood function corresponding to the guarantee task is:

D为装备维修保障的备件现场消耗数据，λ为表示备件故障率的未知参数。

D is the on-site consumption data of spare parts for equipment maintenance support, and λ is an unknown parameter representing the failure rate of spare parts.

The posterior distribution of the spare part failure rate determined in step 3 is:

π(λ) is the prior distribution of the information source.

The Bayesian evaluation result of the spare parts reliability obtained in the step 3 includes:

The Bayesian estimate of the spare part failure rate is:

The Bayesian estimate of the average life of the spare part is:

The beneficial effect of adopting the above-mentioned further scheme is: the reliability evaluation is carried out after effectively and reasonably integrating the two information sources of engineering experience information and equipment development and production test information.

Description of drawings

FIG. 1 is a flowchart of a Bayesian evaluation method for spare parts reliability based on multi-source fusion provided by an embodiment of the present invention;

FIG. 2 is a structural block diagram of an embodiment of a Bayesian evaluation system for spare parts reliability based on multi-source fusion provided by the present invention.

In the accompanying drawings, the list of components represented by each number is as follows:

1. Likelihood weight coefficient determination module, 2. A priori distribution determination module of spare parts failure rate, 3. Spare parts reliability Bayesian evaluation module.

Detailed ways

The principles and features of the present invention will be described below with reference to the accompanying drawings. The examples are only used to explain the present invention, but not to limit the scope of the present invention.

As shown in FIG. 1 , a flowchart of a Bayesian evaluation method for spare parts reliability based on multi-source fusion provided by an embodiment of the present invention includes:

Step 1: Determine the likelihood weight coefficient of the prior distribution of one information source of spare parts reliability and the prior distribution of each other information source, and the likelihood weight coefficient is the ratio of the likelihood functions of the prior distributions of the two information sources. .

Step 2: Integrate each information source according to each likelihood weight coefficient to obtain a priori distribution of the spare parts failure rate.

Step 3: Determine the likelihood function corresponding to the support task result, determine the posterior distribution of the spare part failure rate according to the likelihood function corresponding to the support task result and the prior distribution of the spare part failure rate, and obtain the spare part reliability Bayesian evaluation result.

The invention provides a Bayesian evaluation method for the reliability of spare parts in multi-source fusion. According to the characteristics of less data used in the field of spare parts, the likelihood weight coefficient is used to quantify the reliability of reliability information from different sources, which can reduce the need for artificial Influenced by factors, the reliability evaluation is carried out after effectively and reasonably fusing each spare part reliability information source, which has a good estimation accuracy, and with the increase of the number of guarantee tasks, the estimation accuracy gradually improves.

Example 1

Embodiment 1 provided by the present invention is an embodiment of a Bayesian evaluation method for spare parts reliability based on multi-source fusion provided by the present invention. As shown in FIG. 1, an embodiment of the present invention provides a multi-source fusion-based Spare parts reliability Bayesian assessment methods, including:

Step 1: Determine the likelihood weight coefficient of the prior distribution of one information source of the spare part and the prior distribution of each other information source, where the likelihood weight coefficient is the ratio of the likelihood functions of the prior distributions of the two information sources.

Spare parts are non-repairable parts during the execution of the task, and their lifespan obeys exponential distribution. The probability density function is:

f(t)=λexp(-λt)

where t is time, λ is an unknown parameter representing the failure rate of spare parts, and μ=1/λ is the average life of spare parts.

From the perspective of the whole life cycle process of equipment, the information sources of spare parts mainly include engineering experience information, equipment development and production test information, and on-site consumption of maintenance support.

Engineering experience information is mainly the experience and knowledge accumulated in the process of equipment development and design, production management and use guarantee, and is an important basis for carrying out equipment reliability design. There are many sources and various forms of engineering experience information. Some engineering experience information is reflected in equipment design specifications or design manuals, such as the MTBF (Mean Time Between Failure) design value of components or spare parts, which is convenient for designers to use when designing equipment; Subjective judgment or estimation. For example, when formulating the initial spare parts configuration plan, a large number of initial configuration suggestions for spare parts are put forward based on engineering experience information. For example, under the specified mission profile (the mission time is Tw ₀ ), it is recommended that the configuration number of spare parts be S ₀ , the number of spare parts to be carried is N, and the corresponding spare part guarantee probability is P, that is, the inequality is satisfied

Obviously, the above prior information can be rewritten as:

是χ²分布的上分位数，k为备件的序号数。in,

is the upper quantile of the χ2 distribution, and ^k is the serial number of spare parts.

In the early stage of equipment development, the spare parts reliability information that people can use mainly comes from engineering experience information.

The equipment development and production test information is mainly the spare parts reliability information accumulated through various performance tests of equipment development and production, and component environmental stress screening tests. Especially for spare parts that are equipped with important functional units, more reliability information can be accumulated through various tests of functional units. For a certain spare part, the reliability information of the spare part obtained through the development and production test can generally be expressed as

(T ₀ ,r ₀ )

Among them, T ₀ is the test time accumulated during the development and production test of the spare part, and r ₀ is the corresponding number of failures. Considering that the various tests in the equipment development or production stage are often different from the actual operating environment of the equipment, the environmental factor method is used for conversion in the actual information processing. The environmental factor between the equipment development and production test information environment and the actual operation is K (0<K<1), then the equivalent data after conversion is (KT ₀ , r ₀ ). Obviously, the equipment development test information is the true reflection of the reliability of this type of spare parts actually installed on the equipment, and it is the important information on which the reliability assessment of the spare parts is carried out.

During the combat readiness mission of a ship at sea, its equipment is generally in a state of operation, standby, fault maintenance or waiting for maintenance. For example, in the running state of the equipment, it is necessary to record the information such as the running time of the equipment or the time when the fault occurs. In the state of equipment failure maintenance, it is necessary to record the types and quantities of spare parts replaced by the repair activities. It can be seen that the reliability information of spare parts recorded by the ship during the combat readiness mission at sea can be expressed as:

[Tw _i , F _i , S _i ], i=1,2,...,n.

Among them, i represents the serial number of the number of support tasks, n represents the number of support tasks, Tw _i represents the time of the i-th support task; F _i is the symbol of the success of the task support, when all the spare parts requirements during the task period are When satisfied, F _i is equal to 1, otherwise F _i is equal to 0; S _i ={N _1i ,N _2i ,...,N _Mi } indicates the number of spare parts actually consumed by this task, such as N _1i indicates that the first type of spare parts is in this The actual consumption in the secondary task, N _1i ≥ 0. Taking a spare part as an example, if a guarantee task time is 1000h, and 3 faults occur during the period and all of them are satisfied, the guarantee task is successful, and it is recorded as [1000, 1, 3]; if 3 faults occur If only 2 times are satisfied, the guarantee mission fails, and it is recorded as [1000,0,2].

Further, the likelihood function of the prior distribution π(λ) of the information source is the marginal distribution m(Data丨π(λ)) of the field test data Data:

L(Data|λ) is the likelihood function corresponding to the field test data Data, π(λ) is the prior distribution of the information source about the parameter λ, L(Data|λ)π(λ) is the parameter λ and the field test data Joint distribution of Data.

The magnitude of the likelihood function of the prior distribution π(λ) reflects a reasonable measure of choosing π(λ) as an information source. If m(D丨π(λ)) is larger, it indicates that the prior distribution π(λ) supports the field test data Data higher, and the selection of π(λ) as the prior distribution is more reasonable. Therefore, the ratio of the likelihood functions of the prior distributions of the two information sources represents a comparison of the confidence levels of the two information sources.

The likelihood weight coefficient C is expressed as

Wherein, π ₁ (λ) is the prior distribution of the first information source with respect to the parameter λ, and π ₂ (λ) is the prior distribution of the second information source with respect to the parameter λ.

The likelihood weight coefficient C reflects the degree of support for the field test data Data from the two information sources. When C<1, it means that the first information source supports the field test data Data is lower than the second information source; when C>1, it means that the first information source supports the field test data Data is higher than the second information source. source. In this sense, the likelihood weight coefficient C can be used to convert the credibility of two information sources with different degrees of credibility. Therefore, C is called a likelihood weight coefficient.

Step 2: Integrate each information source according to each likelihood weight coefficient to obtain a priori distribution of the spare parts failure rate.

In step 1, after determining the likelihood weight coefficient of the prior distribution of one information source of spare parts reliability and the prior distribution of other information sources, each likelihood weight coefficient is obtained, and each information source is fused according to each likelihood weight coefficient to obtain spare parts. The prior distribution of the failure rate, the prior distribution of the spare part failure rate is the product of the prior distribution of the one information source and the adjustment value of the prior distribution of each other information source, and the adjustment value of the prior distribution of each other information source Determined according to its corresponding likelihood weight coefficient.

Specifically, the one information source can be selected according to actual experience with high reliability, such as equipment development and production test information. Taking the two information sources of engineering experience information and equipment development and production test information as examples, the spare parts failure rate is obtained in step 2. The prior distribution process includes:

Step 201, the prior distributions π ₁ (λ) and π ₂ (λ) when the information sources are respectively the engineering experience information and the equipment development and production test information are determined:

π ₁ (λ)=μ ₀ exp(-λμ ₀ ), λ＞0

Specifically, the gamma distribution is selected as the prior distribution of the spare parts failure rate:

Among them, a and b are hyperparameters.

When the information source is engineering experience information, the maximum entropy method is used to determine the hyperparameters as a ₁ =1, b ₁ =μ ₀ ; when the information source is the equipment development and production test information, the a priori moment method is used to determine the hyperparameters respectively as a ₂ =r ₀ +1, b ₂ =KT ₀ .

Step 202, calculate the likelihood weight coefficient:

D is the on-site consumption data of spare parts for equipment maintenance support.

Step 203, determine the prior distribution of the spare parts failure rate as

Wherein, when the likelihood weight coefficient C is greater than 1, the value of the likelihood weight coefficient C is modified to 1.

Specifically, when C < 1, it indicates that there is a large gap between the engineering experience information and the on-site consumption data of spare parts, and the prior distribution π ₁ (λ) needs to be properly compressed during prior information fusion; when C > 1, It shows that compared with the equipment development and production test information, the engineering experience information is in better agreement with the on-site consumption data of spare parts. This phenomenon is generally caused by the lack of equipment development and production test information. Therefore, when the actual a priori information is fused, The method of not compressing the engineering experience information can be used for processing. To sum up, when the prior information of spare parts is fused, the likelihood weight coefficient C is taken as:

实际上是logπ(λ)的数学期望，因此，认为函数logπ(λ)是先验分布π(λ)的信息量的近似。因此，融合后的先验信量为When two information sources are independent of each other, the fusion of information sources is actually the superposition of the information of the two information sources. Taking into account the entropy of the prior distribution π(λ)

It is actually the mathematical expectation of logπ(λ), therefore, the function logπ(λ) is considered to be an approximation of the information content of the prior distribution π(λ). Therefore, the priori after fusion is

logπ(λ)=logπ ₁ (λ)+logπ ₂ (λ)

That is, the prior distribution of the spare parts failure rate obtained by fusion is:

π(λ)=π ₁ (λ)π ₂ (λ)

Independent fusion of two sources of information with different levels of confidence. When the credibility of the two information sources is different, the prior distribution π ₁ (λ) is compressed by the likelihood weight coefficient, that is, the amount of engineering experience information is reduced to Clogπ ₁ (λ). The amount of prior information can be expressed as

logπ(λ)=Clogπ ₁ (λ)+logπ ₂ (λ)

That is, the prior distribution of the spare parts failure rate obtained by fusion is:

π(λ)=(π ₁ (λ)) ^C π ₂ (λ).

Step 3: Determine the likelihood function corresponding to the support task result, determine the posterior distribution of the spare part failure rate according to the likelihood function corresponding to the support task result and the prior distribution of the spare part failure rate, and obtain the spare part reliability Bayesian evaluation result.

In order to establish a statistical model for evaluating the life characteristics of spare parts, the field consumption information of the maintenance support of the spare parts is firstly analyzed.

In this step 3, the likelihood function corresponding to the guarantee task result is determined to include:

Step 301, determine the guarantee task result:

[Tw _i , F _i , N _i ], i=1, 2, . . . , n.

Step 302: Determine the probability of mission success and mission failure in the assurance mission.

For the ith (1≤i≤n) guarantee mission, record the amount of spare parts carried for a certain spare part as S _i . If F _i =1, it indicates that the support mission is successful, that is, the spare parts required due to equipment failure in this support mission are all guaranteed, so _{Ni ≤S i .} At this point, the probability of the event occurring is

When F _i =0, it indicates that the support mission has failed, that is, the spare parts required due to equipment failure in this support mission exceed the number of spare parts carried, then _{Ni >S i .} From this, the probability of spare parts guarantee failure is:

Step 303: Determine the likelihood function corresponding to the guarantee task.

The on-site consumption information for the maintenance support of spare parts, that is, the likelihood function corresponding to the support task is:

in

Further, using the prior distribution, the posterior distribution of the spare parts failure rate can be determined as:

Further, the obtained Bayesian evaluation results of spare parts reliability include:

When taking the squared damage function, the Bayesian estimate of the spare part failure rate is

Correspondingly, the Bayesian estimate of the average life of spare parts is:

Example 2

Embodiment 2 provided by the present invention is an embodiment of a Bayesian evaluation system for spare parts reliability based on multi-source fusion provided by the present invention. As shown in FIG. 2 , in this embodiment, the system includes: a likelihood weight coefficient Determination module 1, prior distribution determination module 2 of spare parts failure rate, and spare part reliability Bayesian evaluation module 3;

Likelihood weight coefficient determination module 1, used to determine the likelihood weight coefficient of a priori distribution of spare parts reliability and the prior distribution of each other information source, the likelihood weight coefficient is the prior distribution of the two information sources The ratio of the likelihood function of ;

A priori distribution determination module 2 of the spare parts failure rate, which is used to obtain the prior distribution of the spare parts failure rate by fusing each information source according to each likelihood weight coefficient;

The spare parts reliability Bayesian evaluation module 3 is used to determine the likelihood function corresponding to the results of the support task, and determine the posterior distribution of the failure rate of the spare parts according to the likelihood function corresponding to the results of the support task and the prior distribution of the failure rate of the spare parts, and obtain the spare parts Reliability Bayesian Assessment Results.

The Bayesian evaluation method and system for the reliability of spare parts based on multi-source fusion provided by the embodiments of the present invention can prove its effectiveness through actual simulation and calculation example analysis.

In the simulation process, the true value of the life distribution parameter of exponential spare parts is μ, and the parameter reference value given by the manufacturer is μ ₀ , and n groups of assurance information are generated by simulating n times of assurance process. The simulation steps of a guarantee process are as follows:

1) Set the guarantee task time _Tw ;

2) According to the parameter reference value μ ₀ given by the manufacturer, under the condition that the guarantee probability reaches 0.8, calculate the number n of spare parts to be equipped;

3) Generate an exponential distribution according to the true value of the parameter μ, and generate 1+n random numbers t _j , which are used to simulate the life values of one component and n spare parts;

1≤i≤n+1，simT表示配备i-1个备件的最大工作时间；4) Order

1≤i≤n+1, simT represents the maximum working time with i-1 spare parts;

5) Starting from i=1, find the number simT _k that is greater than Tw first in all simTs, that is, satisfy simT _k-1 <T _w and _{simT k} > _Tw , if it exists, then the guarantee task is successful, record The guarantee result is [T _w ,1,k-1], otherwise, the guarantee task fails this time, and the guarantee result is recorded as [T _w ,0,n].

In the process of example analysis, let the true value of the life distribution parameter of an exponential spare part be μ = 350, and the reference value given by the manufacturer is μ ₀ =500. The accumulated test time of this kind of spare parts during equipment development and production is T ₀ =1500, and the number of failures is r ₀ =3. The environmental factor takes K=0.9.

Taking 10 support missions as an example, according to the reference value given by the contractor, the 10 missions are equipped with corresponding quantities of spare parts. Through the above simulation process, the execution of the 10 missions is simulated. The results are shown in Table 1.

Table 1 Guarantee task implementation

可见在承制方所给参考值偏离参数真值的情况下，本文方法仍能得到的较为准确的参数估计值。Using the Bayesian estimation formula of the average life of spare parts, it is obtained by numerical integration

It can be seen that when the reference value given by the manufacturer deviates from the true value of the parameter, the method in this paper can still obtain a relatively accurate parameter estimation value.

In order to verify the stability of the method, the above estimation process is repeated many times under different task times, and the mean and mean square error of the parameter estimates are calculated respectively. The results are shown in Table 2.

Table 2 Estimation results under different number of tasks

It can be seen from Table 2 that with the increase of the number of guarantee tasks, the accuracy of the parameter estimation value gradually increases, and at the same time the mean square error gradually decreases, which shows that with the increase of field consumption data, the method in this paper can estimate more accurately The true value of the parameter; however, the number of guarantee tasks in practice is often small, and it is difficult to accumulate a large amount of field data in a short period of time. It can be seen from Table 2 that when the number of guarantee tasks reaches 8, the estimated value of the parameters is relatively accurate, and both The variance is small, which shows that the method in this paper can achieve high estimation accuracy when the number of tasks is small, and has good practical value.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

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；

Tw₀In order to be the time of the task,

is x²Upper quantile of distribution, S₀To suggest the number of spare parts, T₀For the accumulated test time, r, of spare parts during the development and production test₀The corresponding failure times of the spare parts during the development and production test are provided, and K is an environmental factor between the information environment and the actual operation of the equipment development and production test;

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:

[Tw_i,F_i,N_i]，i＝1,2,…,n.；

i denotes a serial number of the number of secured tasks, n denotes the number of secured tasks, Tw_iIndicating the ith guaranteed task time, F_iA mark for guaranteeing whether the ith task is successful or not, wherein F is the successful guarantee of the task_iEqual to 1, when said assurance task fails F_iIs equal to 0, N_iRepresenting 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, S_iThe 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:

d is spare part field consumption data of equipment maintenance support.

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；

Tw₀In order to be the time of the task,

is x²Upper quantile of distribution, S₀To suggest the number of spare parts, T₀For the accumulated test time, r, of spare parts during the development and production test₀The corresponding failure times of the spare parts during the development and production test are provided, and K is an environmental factor between the information environment and the actual operation of the equipment development and production test;

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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