Ship spare part reliability evaluation method based on field failure data
By obtaining the on-site failure interval time data of ship spare parts, constructing a likelihood function and deriving a posterior distribution using Bayesian theory, the problem of reliability evaluation of ship spare parts is solved, and the accurate evaluation of ship spare parts failure interval time is achieved. and reliability assessment.
Patent Information
- Application Number
- CN202411258782.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-09
- Publication Date
- 2024-12-31
AI Technical Summary
It is difficult to effectively evaluate the reliability of ship spare parts, especially in the differences in on-site data formats caused by ships' different tasks and equipment complexity, making it difficult to accurately analyze the failure interval time and performance stability of spare parts.
By obtaining the on-site failure interval time data of ship spare parts, a failure interval time likelihood function of single and multiple components is constructed, and a posterior distribution is derived using Bayesian theory to achieve the evaluation of the reliability of ship spare parts.
A method based on field failure data is provided, which can accurately estimate the failure interval time between single and multiple components and derive the posterior distribution, thereby effectively evaluating the reliability of ship spare parts and improving the accuracy and reliability of evaluation.
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Figure CN119228356A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of ship equipment, and more specifically, to a ship spare parts reliability assessment method based on field failure data. Background Art
[0002] The field 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. Due to the different types of missions performed by ships, and the large number of equipment on board and the complex functions, the collected field data may vary greatly. After analysis, the field data of ship spare parts consumption is 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, and details of repair and replacement. Failure data plays an important role in evaluating the reliability, lifespan and performance stability of spare parts. Summary of the invention
[0004] In view of the technical problems existing in the prior art, the present invention provides a ship spare parts reliability assessment method based on field failure data, comprising:
[0005] Obtaining the on-site failure interval time failure data of ship spare parts, wherein the on-site failure interval time failure data of ship spare parts includes the working time of ship equipment, the number of installed parts, the number of carried spare parts and the spare parts failure interval time;
[0006] According to the on-site failure interval time failure data of the ship spare parts, a likelihood function of the failure interval time of a single component and a likelihood function of the failure interval time of multiple components are respectively constructed;
[0007] Based on Bayesian theory, a first posterior distribution of the failure interval time of a single component and a second posterior distribution of the failure interval time of multiple components are derived respectively;
[0008] Based on the first posterior distribution and the second posterior distribution, the reliability of ship spare parts is evaluated.
[0009] The present invention provides a ship spare parts reliability assessment method based on field failure data. The method collects the failure data of the failure interval time of the ship spare parts on site, and uses the likelihood estimation method to respectively estimate the failure interval time of a single component and the failure interval time of multiple components, and derives the posterior distribution, so as to realize the reliability assessment of the ship spare parts based on the posterior distribution. BRIEF DESCRIPTION OF THE DRAWINGS
[0010] Figure 1 A flow chart of a method for evaluating the reliability of ship spare parts based on field failure data provided by the present invention. DETAILED DESCRIPTION
[0011] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention can be arbitrarily combined with each other to form a feasible technical solution. This combination is not subject to the constraints of the sequence of steps and / or the structural composition mode, but must be based on the ability of ordinary technicians in this field to achieve. When the combination of technical solutions is contradictory or cannot be achieved, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.
[0012] Figure 1 A flow chart of a method for evaluating the reliability of ship spare parts based on field failure data provided by the present invention is as follows: Figure 1 As shown, the method includes:
[0013] Step S1, obtaining the on-site failure interval time failure data of ship spare parts, wherein the on-site failure interval time failure data of ship spare parts includes the working time of ship equipment, the number of installed parts, the number of carried spare parts and the spare parts failure interval time.
[0014] Among them, when the ship is performing a mission, the crew can only record the working time of the equipment when recording the operating data of the equipment, but cannot record the working time of each component. When the equipment fails, the fault location is located through fault detection and the fault time is recorded, so as to determine the faulty component and replace the spare part. Therefore, it is assumed that all components of the equipment are working normally during operation, the working time of the equipment is approximately equal to the working time of the spare parts, and the number of spare parts carried for each mission is N. In order to ensure that the equipment can work normally when a certain component fails, the equipment spare parts are generally redundantly set, and usually the number of components installed on a type of equipment is s≥2. After sorting, the data structure of ship spare parts on-site use is mainly composed of equipment working time, number of installed parts, number of spare parts carried, and spare parts failure interval time, and its form is:
[0015] (T i ,s i ,N i ,τ ij )(1);
[0016] Among them, Ti ,i=1,2,...,n is the working time of the equipment in the i-th mission, s i is the number of components installed on the equipment, N i is the number of spare parts carried for the i-th mission, τ ijk ,j=1,2,...,s i , is the kth failure interval of the jth component in the i-th task, r ij ,j=1,2,...,s i is the number of failures of the jth component in the i-th task. The specific data collection format is shown in Table 1.
[0017] Table 1 Spare parts field use data
[0018]
[0019]
[0020] make is the total number of failures in the i-th task.
[0021] Failure data with fault interval time, for important and high-value components, usually accurately records the time when the fault occurs or the time when the spare part is replaced. Assuming that the time for replacing the faulty part is not counted, the spare part failure interval time can be obtained by subtracting adjacent times. The data format is as shown in the above formula (1).
[0022] Step S2, constructing a likelihood function of the failure interval time of a single component and a likelihood function of the failure interval time of multiple components respectively according to the on-site failure interval time failure data of the ship spare parts.
[0023] Step S3, deriving a first posterior distribution of the failure interval time of a single component and a second posterior distribution of the failure interval time of multiple components based on the Bayesian theory.
[0024] It can be understood that according to the failure interval failure data of the ship spare parts on site, the failure interval of a single component and the failure interval of multiple components are analyzed respectively.
[0025] For a single component, when there is a failure interval, the data format is as shown in formula (1), τ ij is the failure interval of a component. At this time, the field data contains two parts of information. One part is the spare parts life information, and its life obeys exponential distribution. Obviously, the failure interval τ is a random variable and obeys exponential distribution, so its likelihood function is:
[0026]
[0027] Where n represents the number of tasks, ri represents the number of component failures in the i-th task, λ represents the component failure rate, Indicates that the component in the i-th task has r i The time interval between failures.
[0028] The other part is the right end data information, that is, the spare parts have not failed at the end of the task. i is the indicator function, when r i ≤N i Time I i =1; otherwise I i =0. Its meaning is:
[0029] (1) If r i -1=N i , that is, all spare parts have been replaced during the mission period and the last spare part fails, then I i =0, there is no right end data.
[0030] (2) If r i ≤N i , that is, there is a spare part that has not failed at the end of the task, then I i =1, there is a final term.
[0031] Therefore, the likelihood function of the right-end data information can be expressed as:
[0032]
[0033] Where F(t) is the exponential life distribution function, represents the survival probability after the last failure in the i-th mission.
[0034] In order to make the likelihood function contain the above two parts of information, the likelihood functions of the two parts of information are combined to obtain the comprehensive likelihood function:
[0035]
[0036] In order to explore whether the construction of the comprehensive likelihood function is reasonable and its practical significance, the maximum likelihood estimate (MLE) of equation (4) is derived. Taking the log-likelihood function and setting it equal to zero, we get
[0037]
[0038] in, The expression of the maximum likelihood estimate λ is solved as
[0039]
[0040] From the result of formula (6), we can see that the form of the estimated value is consistent with statistical expectations, and it can be considered that the construction of the comprehensive likelihood function is reasonable.
[0041] After constructing the likelihood function of the fault interval time of a single component, the posterior analysis of the fault interval time of a single component is analyzed using Bayesian theory. Among them, the present invention mainly derives the linear weighted posterior distribution and geometric weighted posterior distribution of the fault interval time of a single component.
[0042] For the linearly weighted posterior distribution, its expression is:
[0043]
[0044] For the molecule part:
[0045]
[0046] For the denominator:
[0047]
[0048] The linear weighted posterior distribution of the failure interval time of a single component is expressed as:
[0049] but
[0050]
[0051] Among them, w k represents the weight of the kth prior distribution, m is the number of prior distributions, b k represents the scale parameter of the kth prior distribution, a k denotes the shape parameter of the kth prior distribution and Γ(·) denotes the gamma function.
[0052] For the geometrically weighted posterior distribution, the expression of the posterior distribution is as shown in formula (7), where for the numerator:
[0053]
[0054] For the denominator:
[0055]
[0056] The geometrically weighted posterior distribution of the failure interval time of a single component is expressed as:
[0057]
[0058] Among them, a k represents the shape parameter of the kth prior distribution, b k represents the scale parameter of the kth prior distribution, w i ′ represents the weight of the kth prior distribution, and Γ(·) represents the gamma function.
[0059] Among them, the geometric weighted posterior distribution of the failure interval time of a single component is a gamma distribution, and its shape parameter is The scale parameter is
[0060] For multiple tasks and multiple components, when multiple components are installed for each task, that is, s i >1,τ ijk is the kth failure interval of the jth component in the i-th task. The failure interval τ, which represents the spare part life information, is a random variable that obeys an exponential distribution, and its likelihood function is:
[0061]
[0062] in is the total number of failures in the i-th task, let represents the sum of the failure intervals of the jth component during the i-th mission, then:
[0063]
[0064] End data information, that is, the spare parts have not failed at the end of the task, considering the i-th task j=1,2,...,s i The last faulty spare part of a component, whether the right-truncation data of the jth component is generated depends on whether its last faulty spare part is replaced; assuming that the replacement time of the equipment component is not counted, the last spare part failure time should be t ij Sort from smallest to largest to generate order statistics x=1,2,...,s i ,in
[0065] Assume the number of spare parts carried during the mission is N i , whether the last faulty spare part is replaced is determined by the following formula:
[0066]
[0067] Among them, when N i ≥r i When the number of spare parts carried is greater than the total number of failures, s i The last faulty spare parts of all components have been replaced, and all faults have occurred by the end of the task. This task has s i Right-censored data;
[0068] When N i =r i -s i When iThe last faulty spare parts of the components were not replaced at all, and there were 0 right-truncated data in this task;
[0069] When i -s i <N i <r i When i The last faulty spare part of a component is replaced, let x = N i -(r i -s i ), then there are x right-truncated data in this task;
[0070] According to the principle of immediate replacement of faults, the parts with the smallest faults at the time of failure are replaced first. x=1,2,...,X The corresponding component has right-end data, and the variable x can be expressed as:
[0071]
[0072] The likelihood function of the right end data information of a task is expressed as:
[0073]
[0074] The likelihood function of the right end data information of n tasks can be expressed as:
[0075]
[0076] The likelihood function of spare parts life information and the likelihood function of right tail data information are combined to obtain the comprehensive likelihood function of the failure interval time of multiple components:
[0077]
[0078] In order to explore whether the construction of the comprehensive likelihood function is reasonable and its practical significance, the maximum likelihood estimate (MLE) of equation (21) is derived. Taking the log-likelihood function and setting it equal to zero, we get
[0079]
[0080] in, The expression of the maximum likelihood estimate λ is solved as
[0081]
[0082] Judging from the MLE results, the form of the estimated value is consistent with statistical expectations, and it can be considered that the construction of the comprehensive likelihood function is reasonable.
[0083] After constructing the comprehensive likelihood function of the multi-component fault interval time, its posterior distribution is derived. The present invention mainly derives the linear weighted posterior distribution and the geometric weighted posterior distribution of the multi-component fault interval time.
[0084] For the linearly weighted posterior distribution, its expression is:
[0085]
[0086] For the molecule part:
[0087]
[0088] For the denominator:
[0089]
[0090] Linearly weighted posterior distribution of the time between failures for multiple components:
[0091]
[0092] The geometrically weighted posterior distribution of the failure interval time of multiple components is expressed as formula (24).
[0093] For the molecular part:
[0094]
[0095] For the denominator:
[0096]
[0097] The geometrically weighted posterior distribution of the time between failures of multiple components is:
[0098]
[0099] The geometrically weighted posterior distribution of the failure intervals of multiple components is a gamma distribution with a shape parameter of The scale parameter is
[0100] Step S4: evaluating the reliability of ship spare parts based on the first posterior distribution and the second posterior distribution.
[0101] It is understandable that the above step S3 respectively constructs the likelihood function of the single-component failure interval time and derives its posterior distribution, and constructs the likelihood function of the multi-component failure interval time and derives its posterior distribution.
[0102] According to the posterior distribution of the single-component failure interval time and the posterior distribution of the multi-component failure interval time, the distribution expectation value of the ship's reliability parameters is calculated, and the reliability of the ship's spare parts can be evaluated.
[0103] It should be noted that the focus of the present invention is on the expression of the failure data of the fault interval time of ship spare parts, and the failure data of the fault interval time of ship spare parts, respectively constructing the likelihood function of the failure interval time of a single component and deriving its posterior distribution, as well as constructing the likelihood function of the failure interval time of multiple components and deriving its posterior distribution, for the subsequent reliability evaluation of ship spare parts.
[0104] The embodiment of the present invention provides a ship spare parts reliability assessment method based on field failure data. According to the acquired field failure interval time failure data of ship spare parts, the likelihood function of the failure interval time of a single component and the likelihood function of the failure interval time of multiple components are respectively constructed; based on the Bayesian theory, the first posterior distribution of the failure interval time of a single component and the second posterior distribution of the failure interval time of multiple components are respectively derived; based on the first posterior distribution and the second posterior distribution, the reliability of the ship spare parts is assessed. The present invention collects the field failure interval time failure data of ship spare parts, estimates the failure interval time of a single component and the failure interval time of multiple components respectively by using the likelihood estimation method, and derives the posterior distribution, so as to provide a data basis for the subsequent evaluation of the reliability of ship spare parts.
[0105] 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.
[0106] 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.
[0107] 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 field failure data, characterized in that: include: Obtaining the on-site failure interval time failure data of ship spare parts, wherein the on-site failure interval time failure data of ship spare parts includes the working time of ship equipment, the number of installed parts, the number of carried spare parts and the spare parts failure interval time; According to the on-site failure interval time failure data of the ship spare parts, a likelihood function of the failure interval time of a single component and a likelihood function of the failure interval time of multiple components are respectively constructed; Based on Bayesian theory, a first posterior distribution of the failure interval time of a single component and a second posterior distribution of the failure interval time of multiple components are derived respectively; Based on the first posterior distribution and the second posterior distribution, the reliability of ship spare parts is evaluated.
2. The ship spare parts reliability assessment method based on field failure data according to claim 1 is characterized in that: The structure of the on-site fault interval failure data of the ship spare parts is expressed as (T i ,s i ,N i ,τ ij ); Among them, T i ,i=1,2,...,n is the working time of the equipment in the i-th mission, s i is the number of components installed on the equipment, N i is the number of spare parts carried by the i-th mission equipment, τ ijk ,j=1,2,...,s i ,k=1,2,...,r isi is the kth failure interval of the jth component in the i-th task, r ij ,j=1,2,...,s i is the number of failures of the jth component in the i-th task.
3. The ship spare parts reliability assessment method based on field failure data according to claim 2 is characterized in that: The on-site failure interval time failure data of ship spare parts includes spare parts life information and right end data information. According to the on-site failure interval time failure data of ship spare parts, a likelihood function of the failure interval time of a single component is constructed, including: The failure interval time τ that represents the spare parts life information is a random variable that obeys an exponential distribution. The likelihood function of the failure interval time τ is: Where n represents the number of tasks, r i represents the number of component failures in the i-th task, λ represents the component failure rate, Indicates that the component in the i-th task has r i The time interval between failures; The right end data information is that the spare part has not failed at the end of the task, assuming that i is the indicator function, when r i ≤N i Time I i =1; otherwise I i =0; its meaning is: If r i -1=N i , that is, all spare parts have been replaced during the mission period and the last spare part fails, then I i =0, there is no right end data; If r i ≤N i , that is, there is a spare part that has not failed at the end of the task, then I i =1, there is a terminal item; The likelihood function of the right-end data information is expressed as: Where F(t) is the exponential life distribution function, represents the survival probability after the last failure in the i-th task; The comprehensive likelihood function of the failure interval time of a single component is:
4. The ship spare parts reliability assessment method based on field failure data according to claim 3 is characterized in that: The first posterior distribution is a linear weighted posterior distribution or a geometric weighted posterior distribution, and the linear weighted posterior distribution of the failure interval time of a single component is derived based on the Bayesian theory, including: According to the comprehensive likelihood function of the failure interval time of a single component, the linear weighted posterior distribution of the failure interval time of a single component is derived based on the Bayesian theory: For the molecule part: For the denominator: The linear weighted posterior distribution of the failure interval time of a single component is expressed as: Among them, w k represents the weight of the kth prior distribution, m is the number of prior distributions, b k represents the scale parameter of the kth prior distribution, a k denotes the shape parameter of the kth prior distribution and Γ(·) denotes the gamma function.
5. The ship spare parts reliability assessment method based on field failure data according to claim 4 is characterized in that: The geometric weighted posterior distribution of the failure interval time of a single component is derived based on Bayesian theory, including: According to the comprehensive likelihood function of the failure interval time of a single component, the geometric weighted posterior distribution of the failure interval time of a single component is derived based on the Bayesian theory: For the molecule part: For the denominator: The geometrically weighted posterior distribution of the failure interval time of a single component is expressed as: Among them, the geometric weighted posterior distribution of the failure interval time of a single component is a gamma distribution, and its shape parameter is The scale parameter is Among them, a k represents the shape parameter of the kth prior distribution, b k represents the scale parameter of the kth prior distribution, w′ i represents the weight of the kth prior distribution and Γ(·) represents the gamma function.
6. The ship spare parts reliability assessment method based on field failure data according to claim 2 is characterized in that: The on-site failure interval time failure data of ship spare parts includes spare parts life information and right end data information. According to the on-site failure interval time failure data of ship spare parts, a likelihood function of the failure interval time of multiple components is constructed, including: When multiple components are installed per task, s i >1,τ ijk is the kth failure interval of the jth component in the i-th task. The failure interval τ, which represents the spare part life information, is a random variable that obeys an exponential distribution, and its likelihood function is: in is the total number of failures in the i-th task, let represents the sum of the failure intervals of the jth component during the i-th mission, then: The end data information, i.e., the spare parts are not invalid at the end of the task, consider the i-th task j=1, 2, ..., s i The last faulty spare part of a component, whether the right-truncation data of the jth component is generated depends on whether its last faulty spare part is replaced; assuming that the replacement time of the equipment component is not counted, the last spare part failure time should be t ij Sort from smallest to largest to generate order statistics in Assume the number of spare parts carried during the mission is N i , whether the last faulty spare part is replaced is determined by the following formula: Among them, when N i ≥r i When the number of spare parts carried is greater than the total number of failures, s i The last faulty spare parts of all components have been replaced, and all faults have occurred by the end of the task. This task has s i Right-censored data; When N i =r i -s i When i The last faulty spare parts of the components were not replaced at all, and there were 0 right-truncated data in this task; When i -s i <N i <r i When i The last faulty spare part of a component is replaced, let x = N i -(r i -s i ), then there are x right-truncated data in this task; According to the principle of immediate replacement of faults, the parts with the smallest faults at the time of failure are replaced first. The corresponding component has right-end data, and the variable X can be expressed as: The likelihood function of the right end data information of a task is expressed as: The likelihood function of the right end data information of n tasks can be expressed as: The likelihood function of spare parts life information and the likelihood function of right tail data information are combined to obtain the comprehensive likelihood function of the failure interval time of multiple components:
7. The ship spare parts reliability assessment method based on field failure data according to claim 6 is characterized in that: The second posterior distribution is a linear weighted posterior distribution or a geometric weighted posterior distribution, and the linear weighted posterior distribution of the failure interval time of multiple components is derived based on the Bayesian theory, including: For the molecule part: For the denominator: Linearly weighted posterior distribution of the time between failures for multiple components: Among them, w k represents the weight of the kth prior distribution, b k represents the scale parameter of the kth prior distribution, a k denotes the shape parameter of the kth prior distribution and Γ(·) denotes the gamma function.
8. The ship spare parts reliability assessment method based on field failure data according to claim 7 is characterized in that: Based on Bayesian theory, the geometrically weighted posterior distribution of the failure interval time of multiple components is derived, including: For the molecule part: For the denominator: The geometrically weighted posterior distribution of the time between failures of multiple components is: The geometrically weighted posterior distribution of the failure intervals of multiple components is a gamma distribution with a shape parameter of The scale parameter is Among them, w k represents the weight of the kth prior distribution, b k represents the scale parameter of the kth prior distribution, a k denotes the shape parameter of the kth prior distribution and Γ(·) denotes the gamma function.