A Reliability Assessment Method for Ship Spare Parts Based on Quasi-Cumulative Failure Data

Abstract

The present invention relates to a reliability assessment method for ship spare parts based on quasi-cumulative failure data, comprising: using a multi-layer Bayesian method to estimate the failure probability, and obtaining the quasi-cumulative failure number of components based on the failure probability; calculating the modified likelihood function of the failure rate based on the cumulative failure number; determining the prior distribution of the failure rate; weighting the prior distribution to obtain a weighted comprehensive prior distribution, combining the weighted comprehensive prior distribution with the modified likelihood function, using the Bayesian formula to obtain the posterior distribution of the failure rate, and performing reliability assessment on ship spare parts based on the posterior distribution of the failure rate; in the absence of failure data, introducing the parameter of the quasi-cumulative failure number to construct the modified likelihood function, establishing and improving the quasi-cumulative failure number model, and obtaining its estimated value using the multi-layer Bayesian method, so as to realize the reliability assessment of ship spare parts.

Description

Technical Field

[0001] The invention relates to the field of spare parts reliability assessment, and in particular to a ship spare parts reliability assessment method based on quasi-cumulative failure data. Background Art

[0002] The on-site usage data of ship spare parts refers to the detailed information about the use, consumption, replacement and inventory of spare parts recorded and collected during the actual operation and maintenance of the ship. It is the most reliable source of information in the reliability assessment of ship spare parts. Due to the different types of missions performed by ships, and the large number and complex functions of the equipment on board, the forms of the collected on-site data may vary greatly. After analysis, the on-site data of ship spare parts consumption are mainly divided into two categories: failure data and non-failure data.

[0003] Failure Data refers to the detailed information recorded during a specific period of time that spare parts need to be replaced or repaired due to failure, damage or performance degradation. Failure data includes the time of failure, failure type, failure cause, repair and replacement details, etc. Non-Failure Data refers to the detailed information recorded during a specific period of time that spare parts have not failed or damaged during use. Due to the high reliability of ship equipment and the high level of daily maintenance of ships, most of the field data obtained by ships during missions are non-failure data, which includes the use time, operating environment, performance indicators, etc. of spare parts.

[0004] Due to the continuous improvement of equipment reliability and maintenance strategies, it is difficult for equipment to fail during the mission of a ship, resulting in the fact that the field use data of spare parts is mostly zero-failure data, which is particularly evident in long-life components. How to evaluate the reliability of ship spare parts without failure data is currently a problem to be solved. Summary of the invention

[0005] In view of the technical problems existing in the prior art, the present invention provides a ship spare parts reliability assessment method based on quasi-accumulated failure data, so as to realize ship spare parts reliability assessment without failure data.

[0006] According to a first aspect of the present invention, a method for evaluating the reliability of ship spare parts based on quasi-accumulative failure data is provided, comprising:

[0007] Step 1: Use the multi-layer Bayesian method to estimate the failure probability , based on the failure probability Get the quasi-cumulative failure number , the proposed cumulative failure number 0 to The quasi-accumulative failure number of components within the time range of time, i represents the i-th task;

[0008] Step 2: Based on the proposed cumulative failure number Calculate the failure rate The modified likelihood function ;

[0009] Step 3: Determine the failure rate The prior distribution of

[0010] Step 4: weight the prior distribution to obtain a weighted comprehensive prior distribution , the weighted integrated prior distribution With the modified likelihood function Combined with the Bayesian formula, the failure rate is obtained The posterior distribution of The reliability of ship spare parts is evaluated based on the posterior distribution of

[0011] Optionally, the failure probability estimated in step 1 is The process includes:

[0012] Step 101, select the Beta distribution in the range of (0, 1) as Prior distribution of :

[0013] ;

[0014] in, is a hyperparameter, for function;

[0015] Step 102, calculate failure probability The marginal distribution of is:

[0016] ;

[0017] in, , Indicated in The uniform distribution on The hyperprior distribution within its value range is uniform distribution, and c is a constant within the range of 2 to 5;

[0018] Step 103, calculating the failure probability based on steps 101 and 102 The expectation of the posterior distribution of is the failure probability under squared loss Bayesian estimation of :

[0019] ;

[0020] in, is the normalization constant, is the working time of the equipment in the i-th task, The number of components installed for the equipment, is the total number of equipment failures in the i-th mission.

[0021] Optionally, the failure probability estimated in step 1 is The process includes:

[0022] Step 111, calculate failure probability The prior distribution of is:

[0023] ;

[0024] in, is a hyperparameter;

[0025] , , Indicated in The uniform distribution on , , is the working time of the equipment in the i-th task;

[0026] Step 112, calculate failure probability The posterior distribution of is:

[0027] ; is the beta function; The number of components installed for the equipment;

[0028] Step 113, calculating the failure probability based on steps 101 and 102 The expectation of the posterior distribution of is the failure probability under squared loss Bayesian estimation of :

[0029] .

[0030] Optionally, in step 1, based on the failure probability Get the quasi-cumulative failure number ; Where s represents the number of components.

[0031] In step 2, based on the proposed cumulative failure number Calculate the failure rate The modified likelihood function is:

[0032] ;in, is the life distribution of spare parts, is the probability density function, The number of components installed for the equipment.

[0033] Optionally, the prior distribution is weighted as linear weighting or geometric weighting.

[0034] Optionally, the failure rate is obtained after linear weighting The posterior distribution of is:

[0035] ;

[0036] in, is the working time of the equipment in the i-th task, The number of components installed for the equipment, represents the shape parameter of the j-th prior distribution, represents the scale parameter of the j-th prior distribution, represents the gamma function, m is the number of prior distributions, represents the weight of the j-th prior distribution.

[0037] Optionally, the failure rate is obtained after geometric weighting The posterior distribution of is:

[0038] ;

[0039] in, , is the working time of the equipment in the i-th task, The number of components installed for the equipment, represents the shape parameter of the j-th prior distribution, represents the scale parameter of the j-th prior distribution, represents the gamma function, m is the number of prior distributions, represents the weight of the j-th prior distribution.

[0040] The present invention provides a ship spare parts reliability assessment method based on quasi-cumulative failure data. In order to make full use of the on-site usage information data of ship spare parts, the data structure of the on-site usage information is analyzed. In the case of no failure, the parameter of the quasi-cumulative failure number is introduced to construct a modified likelihood function, and the quasi-cumulative failure number model is established and improved. The multi-layer Bayesian method is used to obtain its estimated value, thereby deducing the posterior distribution of the no-failure field data, and the effectiveness of the constructed model and method is illustrated by a numerical example, thereby realizing the reliability assessment of ship spare parts. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1A flow chart of a method for evaluating the reliability of ship spare parts based on quasi-accumulative failure data provided by the present invention;

[0042] FIG. 2 (a) is a Beta distribution curve diagram under different hyperparameters provided by an embodiment of the present invention;

[0043] FIG2( b ) is a diagram of hyperparameters provided in an embodiment of the present invention. The Beta distribution curve below;

[0044] Figure 3 Conventional method provided by the embodiment of the present invention and Relationship diagram;

[0045] Figure 4 The failure probability provided by the embodiment of the present invention is Graph with different parameters. DETAILED DESCRIPTION

[0046] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0047] Figure 1 A flow chart of a ship spare parts reliability assessment method based on quasi-cumulative failure data provided by the present invention is as follows: Figure 1 As shown, the reliability assessment method includes:

[0048] Step 1: Use the multi-layer Bayesian method to estimate the failure probability , based on the failure probability Get the quasi-cumulative failure number , the proposed cumulative failure number 0 to The quasi-cumulative failure number of components within the time range of time, i represents the i-th task.

[0049] Step 2: Based on the proposed cumulative failure number Calculate the failure rate The modified likelihood function .

[0050] Step 3: Determine the failure rate The prior distribution of .

[0051] Step 4: weight the prior distribution to obtain a weighted comprehensive prior distribution , the weighted integrated prior distribution With the modified likelihood function Combined with the Bayesian formula, the failure rate is obtained The posterior distribution of The reliability of ship spare parts is evaluated based on the posterior distribution of

[0052] Due to the continuous improvement of equipment reliability and the continuous improvement of maintenance strategies, it is difficult for equipment to fail during the execution of a ship's mission, resulting in the fact that the on-site usage data of spare parts are mostly failure-free data. The present invention provides a ship spare parts reliability assessment method based on quasi-accumulated failure data, which realizes ship spare parts reliability assessment without failure data.

[0053] Example 1

[0054] Embodiment 1 of the present invention is an embodiment of a ship spare parts reliability assessment method based on quasi-accumulative failure data provided by the present invention, combined with Figure 1 It can be seen that the embodiment of the reliability evaluation method includes:

[0055] Step 1: Use the multi-layer Bayesian method to estimate the failure probability , based on the failure probability Get the quasi-cumulative failure number , the proposed cumulative failure number 0 to The quasi-cumulative failure number of components within the time range of time, i represents the i-th task.

[0056] For The failure probability within, for exponential distribution, So make sure The key is to determine the probability of failure .

[0057] In a possible embodiment, a multi-layer Bayesian method is used to calculate the failure probability Make an estimate.

[0058] Specifically, the failure probability estimated in step 1 is The process includes:

[0059] Since each mission None of the components fail, so the likelihood function is:

[0060] (1)

[0061] Because the components are There is no failure in the In the range (0, 1), smaller values ​​are more likely and larger values ​​are less likely.

[0062] In step 101, researchers usually choose a Beta distribution in the range of (0, 1) as The prior distribution of , the probability density function of the Beta distribution is:

[0063] .

[0064] in, is a hyperparameter, for function.

[0065] As shown in FIG. 2( a ) and FIG. 2( b ), different hyperparameters and hyperparameters provided in the embodiments of the present invention are shown in FIG. The beta distribution curve below.

[0066] because The characteristic of is that it is more likely to be close to 0 and less likely to be close to 1. As shown in Figure 2 (a) and Figure 2 (b), when When the Beta distribution curve is monotonically decreasing, it is consistent with the failure probability Features on [0, 1). Let the hyperparameter , The hyperprior distribution within its value range is uniform.

[0067] .

[0068] in Indicated in Uniform distribution on, c is a constant, and the value of c in the calculation is between 2 and 5.

[0069] As shown in Figure 2(b), when <1 o'clock, The larger the value, the thinner the tail of the Beta distribution density function. In this case, even a small change in the data may significantly affect the result of the Bayesian estimation, making the estimation unstable. If the value is too large, the probability mass of the prior distribution in the right tail is almost zero, which will cause the prior information to have too much influence on the posterior distribution and cause the "prior dominance" problem. A smaller value should be taken, usually the value of c is 2-5.

[0070] Step 102, assuming hyperparameters , Independent of each other, calculate the probability of failure The marginal distribution of is:

[0071] (2)

[0072] Formula (2) is the failure probability Since the parameters of the prior distribution also obey a distribution, the above method for determining the prior distribution is called the multi-level Bayesian method.

[0073] Step 103, in order to make full use of the data , first calculate the failure rate The posterior distribution of and The relationship between The posterior distribution of Bayesian estimation of .

[0074] Combining equation (1) and equation (2), we can deduce The posterior distribution of is:

[0075] (3)

[0076] in, is the normalization constant.

[0077] Known , using the Jacobi determinant to transform the distribution from Transfer to The Jacobi determinant is right The absolute value of the derivative is Substituting into formula (3), we get:

[0078] .

[0079] in, is the working time of the equipment in the i-th task, The number of components installed for the equipment, is the total number of equipment failures in the i-th mission.

[0080] Probability of failure under squared loss The Bayesian estimate of is equal to the expectation of the posterior distribution, that is:

[0081] (4)

[0082] In one possible embodiment, the failure probability estimated in step 1 is The process includes:

[0083] Analyzing formula (4), we can see that the estimated failure probability is Derived results and task time according to the above method No. However, for spare parts with exponential life distribution, the failure probability and Positively correlated, for The task with the larger value is It should also be larger. In the distribution of As shown in Figure 2(b), when the hyperparameter Under certain conditions, The smaller it is, the wider the tail of the beta distribution density function is. The larger the value, the greater the possibility of taking it, so the hyperparameter is derived Task time To correct the hyperparameters Make The prior distribution model is more accurate.

[0084] The expected value of the Beta distribution is:

[0085] (5)

[0086] Combine formula (5) with Combining the definitions of

[0087] .

[0088] The solution is:

[0089] (6)

[0090] From formula (6), we can see that the hyperparameter and The relationship is an exponential decay relationship.

[0091] set up is an exponential decay function of the form:

[0092] (7)

[0093] As mentioned above The value of cannot be too large, and its value range is , using boundary conditions to limit the values ​​of the parameters in equation (7), when hour =5, when hour =2, for the convenience of calculation =1 Substituting into formula (7) we get:

[0094] .

[0095] In summary, hyperparameters and The relationship is:

[0096] (8)

[0097] Step 111, the parameters shown in formula (2) The prior distribution of changes to:

[0098] (9)

[0099] in, It is shown in formula (8).

[0100] Step 112, combine equation (9) and equation (1) to derive the failure probability The posterior distribution of is:

[0101] ; is the beta function; The number of components installed for the equipment.

[0102] Step 113, calculating the failure probability based on steps 101 and 102 The expectation of the posterior distribution of is the failure probability under squared loss Bayesian estimation of :

[0103] (10)

[0104] Using the recurrence relation of the beta function Simplifying formula (10) we get:

[0105] .

[0106] in , , , .

[0107] In a possible embodiment, the actual meaning of the simulated cumulative failure number L is the sum of the possible failure times of s components within each task end time T. The failure events of all components are independent and, by definition, the failure probability Get the quasi-cumulative failure number .

[0108] Step 2: Based on the proposed cumulative failure number Calculate the failure rate The modified likelihood function .

[0109] In a possible embodiment, in step 2, based on the quasi-cumulative failure number Calculate the failure rate The process of modifying the likelihood function includes:

[0110] Assume that the life distribution of equipment components is , the probability density function is , the working time of the equipment during the ship's nth mission is now observed , the number of spare parts installed for each task is , the observed failure interval is . For the i-th task, the likelihood function is:

[0111] (11)

[0112] For n tasks, the likelihood function is:

[0113] .

[0114] The average life span is obtained by performing maximum likelihood estimation on equation (11): The estimated value is:

[0115] (12)

[0116] When the observation time is over, there are Failure data, then the time Should be located at , +1 failure. Assuming that the +1 failure time is , then we can get the average life span The estimate is:

[0117] (13)

[0118] Obviously, is an unbiased estimate of the average lifespan. Comparing equation (12) with equation (13), we can see that the total working time is not much different, but the number of failures differs by 1, which makes the estimated value biased when r is small. So Make the following corrections:

[0119] .

[0120] Its essence is to modify formula (11) to:

[0121] (14)

[0122] Where L is the Failure time to In the absence of failure data =0, equation (14) becomes:

[0123] .

[0124] For n tasks, the modified likelihood function is:

[0125] (15)

[0126] in, is the life distribution of spare parts, is the probability density function, The number of components installed for the equipment.

[0127] From the above derivation, we can see that the key to constructing the modified likelihood function is to determine the quasi-cumulative failure number L. For the exponential distribution, we use a confidence coefficient of 1- The lower confidence limit of the mean lifespan A suitable estimate of the average lifespan under the exponential distribution assumption is The confidence coefficient is 1- The lower confidence limit is:

[0128] .

[0129] Where T is the total working time, for The upper quantile of the distribution, while the average life expectancy The maximum likelihood estimate of is:

[0130] .

[0131] Because the function is continuous, so choose the appropriate So that:

[0132] ;at this time .

[0133] For different parameters and r, The values ​​are shown in Table 1.

[0134] Table 1 Value

[0135]

[0136] From Table 1, we can see that when r=1, we get =0.7; when r=2, we get =0.67. For data without failure, the reference failure scenario is generally taken as , The value of is generally 0.7, etc., and the specific value needs to be determined in combination with the actual problem. Although the above calculation method is simple and convenient, the determination of the quasi-cumulative failure number L is artificial. Based on this, it is proposed to use multi-layer Bayesian to estimate the quasi-cumulative failure number L.

[0137] Step 3: Determine the failure rate The prior distribution of .

[0138] Step 4: weight the prior distribution to obtain a weighted comprehensive prior distribution , the weighted integrated prior distribution With the modified likelihood function Combined with the Bayesian formula, the failure rate is obtained The posterior distribution of The reliability of ship spare parts is evaluated based on the posterior distribution of

[0139] Get an estimate of the probability of failure Then calculate the quasi-cumulative failure number , substituting into formula (15) to obtain the modified likelihood function, for spare parts whose life obeys exponential distribution, the modified likelihood function is:

[0140] .

[0141] in, .

[0142] The posterior distribution of the field zero-failure data is derived by combining the comprehensive prior distribution with the modified likelihood function.

[0143] In a possible embodiment, the prior distribution is weighted as linear weighting or geometric weighting.

[0144] In a possible embodiment, the failure rate is obtained by linear weighting: The posterior distribution of is:

[0145] .

[0146] in, is the working time of the equipment in the i-th task, The number of components installed for the equipment, represents the shape parameter of the j-th prior distribution, represents the scale parameter of the j-th prior distribution, represents the gamma function, m is the number of prior distributions, represents the weight of the j-th prior distribution.

[0147] In a possible embodiment, the failure rate is obtained after geometric weighting. The posterior distribution of is:

[0148] .

[0149] in, , is the working time of the equipment in the i-th task, The number of components installed for the equipment, represents the shape parameter of the j-th prior distribution, represents the scale parameter of the j-th prior distribution, represents the gamma function, m is the number of prior distributions, represents the weight of the j-th prior distribution.

[0150] Example 2

[0151] Example 2 provided by the present invention is a specific application example of a ship spare parts reliability evaluation method based on quasi-accumulated failure data provided by the present invention, in order to illustrate the failure probability and the cumulative failure number The feasibility of the improved multi-layer Bayesian estimation method is shown in Table 2. Assume that the field zero-failure data of a component of a ship with a lifespan that obeys an exponential distribution is as follows:

[0152] Table 2 No failure data of ship components

[0153]

[0154] The data in Table 2 are respectively estimated using the traditional multi-level Bayesian method and the improved multi-level Bayesian method. The failure probability at time is estimated based on the proposed cumulative number of failures.

[0155] (1) Traditional multi-layer Bayesian estimation method. Using formula (4), we can calculate the failure probability when c takes different values: The expectation of the posterior distribution, the specific calculation results are shown in Table 3, and the visualization is as follows Figure 3 The conventional method provided by the embodiment of the present invention is shown and relationship diagram.

[0156] Table 3 Traditional methods Estimated value of

[0157] Depend on Figure 3 It can be seen that the failure probability The estimated value of The range of >2 is basically as decreases with the increase of =2, and when the equation (4) is analyzed, =2, the parameter of the beta function in the numerator is ; The parameter in the denominator is ( , ), at this time, the parameters in the numerator and denominator just make the integral value reach the local minimum, resulting in the appearance of extreme values.

[0158] From the data of Task 5 and Task 6 in Table 2, we can see that when Same, even if the task working time is different, The estimated value of is also the same, which is different from the actual situation. In addition, it can be clearly seen that The estimated value of increases as the parameter c increases. How to determine the value of parameter c to make it more accurate? This is also an issue that needs to be considered.

[0159] (2) Improved multi-layer Bayesian estimation method. Use formula (10) to calculate the failure probability in , , the specific calculation results are shown in Table 4.

[0160] Table 4 Estimated values ​​of parameters of the improved method

[0161]

[0162] like Figure 4 The failure probability provided by the embodiment of the present invention is shown as follows Graph with different parameters.

[0163] It can be seen from Table 4 that the failure probability estimated by the improved method is Affected by the task time and the number of parts to be installed, It increases with the increase of task time and decreases with the increase of installation quantity, which is in line with the actual situation.

[0164] After obtaining the quasi-cumulative failure number L, it can be determined that L is equal to the failure number r, formula Indicates that if , then the confidence lower limit estimate of the parameter is equal to the maximum likelihood estimate, and the confidence level is 1- , 1- The higher the confidence level is, the more confidence in the estimated reliability index is, and the more appropriate the value of L is. The calculation results are shown in Table 5.

[0165] Table 5 Confidence Level 1- Calculation results

[0166]

[0167] It can be seen from Table 5 that the confidence levels calculated from the quasi-cumulative failure number L of the six tasks in the example are all greater than 80%. Compared with the results in Table 1, the quasi-cumulative failure number L estimation method proposed in this paper is more appropriate.

[0168] An embodiment of the present invention provides a ship spare parts reliability assessment method based on quasi-cumulative failure data. In order to make full use of the on-site usage information data of ship spare parts, the data structure of the on-site usage information is analyzed. In the case of no failure, the parameter of the quasi-cumulative failure number is introduced to construct a modified likelihood function, and the quasi-cumulative failure number model is established and improved. The multi-layer Bayesian method is used to obtain its estimated value, thereby deducing the posterior distribution of the no-failure field data. The effectiveness of the constructed model and method is illustrated by a numerical example, thereby realizing the reliability assessment of ship spare parts.

[0169] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and for parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0170] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0171] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0172] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0173] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0174] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0175] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A ship spare parts reliability assessment method based on quasi-cumulative failure data, characterized in that: The reliability evaluation method comprises: Step 1: Use the multi-layer Bayesian method to estimate the failure probability , based on the failure probability Get the quasi-cumulative failure number , the proposed cumulative failure number 0 to The quasi-accumulative failure number of components within the time range of time, i represents the i-th task; Step 2: Based on the proposed cumulative failure number Calculate the failure rate The modified likelihood function ; Step 3: Determine the failure rate The prior distribution of Step 4: weight the prior distribution to obtain a weighted comprehensive prior distribution , the weighted integrated prior distribution With the modified likelihood function Combined with the Bayesian formula, the failure rate is obtained The posterior distribution of The reliability of ship spare parts is evaluated based on the posterior distribution of In step 1, based on the failure probability Get the quasi-cumulative failure number ; Where s represents the number of components; In step 2, based on the proposed cumulative failure number Calculate the failure rate The modified likelihood function is: ;in, is the life distribution of spare parts, is the probability density function, The number of components installed for the equipment.

2. The reliability evaluation method according to claim 1, characterized in that: The failure probability is estimated in step 1 The process includes: Step 101, select the Beta distribution in the range of (0, 1) as Prior distribution of : ； in, is a hyperparameter, for function; Step 102, calculate failure probability The marginal distribution of is: ； in, , Indicated in The uniform distribution on The hyperprior distribution within its value range is uniform distribution, and c is a constant within the range of 2 to 5; Step 103, calculating the failure probability based on steps 101 and 102 The expectation of the posterior distribution of is the failure probability under squared loss Bayesian estimation of : ； in, is the normalization constant, is the working time of the equipment in the i-th task, The number of components installed for the equipment, is the total number of equipment failures in the i-th mission.

3. The reliability evaluation method according to claim 1, characterized in that: The failure probability is estimated in step 1 The process includes: Step 111, calculate failure probability The prior distribution of is: ； in, is a hyperparameter; , , Indicated in The uniform distribution on , , is the working time of the equipment in the i-th task; Step 112, calculate failure probability The posterior distribution of is: ; is the beta function; The number of components installed for the equipment; Step 113, calculating the failure probability based on steps 101 and 102 The expectation of the posterior distribution of is the failure probability under squared loss Bayesian estimation of : 。 4. The reliability evaluation method according to claim 1, characterized in that: The prior distribution is weighted as linear weighting or geometric weighting.

5. The reliability evaluation method according to claim 4, characterized in that: The failure rate is obtained after linear weighting The posterior distribution of is: ； in, is the working time of the equipment in the i-th task, The number of components installed for the equipment, represents the shape parameter of the j-th prior distribution, represents the scale parameter of the j-th prior distribution, represents the gamma function, m is the number of prior distributions, represents the weight of the j-th prior distribution.

6. The reliability evaluation method according to claim 4, characterized in that: After geometric weighting, the failure rate is obtained The posterior distribution of is: ； in, , is the working time of the equipment in the i-th task, The number of components installed for the equipment, represents the shape parameter of the j-th prior distribution, represents the scale parameter of the j-th prior distribution, represents the gamma function, m is the number of prior distributions, represents the weight of the j-th prior distribution.

Images