Ship spare part reliability evaluation method based on fault-free interval time failure data

Abstract

The invention relates to a ship spare part reliability evaluation method based on failure-free interval time failure data, which comprises the following steps: determining ship spare part field use data D at a failure-free interval time as (Ti, si, ri), Ti being the working time of equipment in an ith task, si being the number of parts installed by the equipment, ri being the total failure frequency of the equipment in the ith task, i being equal to 1, 2,..., n; obtaining a likelihood function Lp (lambda) of the failure rate lambda based on the ship spare part field use data D and the Poisson distribution principle; determining prior distribution of the failure rate lambda; the priori distribution is weighted to obtain a weighted comprehensive priori distribution type pi < s > (lambda), the weighted comprehensive priori distribution type pi < s > (lambda) is combined with a likelihood function Lp (lambda), a Bayesian formula is utilized to obtain posterior distribution of the failure rate lambda, and ship spare part reliability evaluation is carried out based on the posterior distribution of the failure rate lambda; fault-free interval time failure data in field use information is effectively utilized, and a proper likelihood function is constructed according to the characteristics of the fault-free interval time failure data to carry out Bayesian reliability evaluation on the 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 failure-free interval time 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, details of repair and replacement, etc. Non-failure data refers to the detailed information recorded during a specific period of time that spare parts have not failed or been 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. This type of data includes the use time, operating environment, performance indicators, etc. of spare parts. How to effectively use field usage information and construct a suitable likelihood function based on its characteristics is the key to the Bayesian reliability evaluation method. 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 the failure interval time data of the failure-free interval, which effectively utilizes the failure interval time failure data in the field use information and constructs a suitable likelihood function according to its characteristics to perform Bayesian reliability assessment of ship spare parts.

[0005] According to a first aspect of the present invention, a method for evaluating the reliability of ship spare parts based on failure interval time failure data is provided, comprising:

[0006] Step 1: Determine the on-site usage data D of ship spare parts during the trouble-free interval (T i ,s i ,r i ), where T i is the working time of the equipment in the i-th task, s i is the number of components installed on the equipment, r iis the total number of failures of the equipment in the i-th mission, i=1,2,...,n;

[0007] Step 2: Based on the on-site usage data D of the ship spare parts and the Poisson distribution principle, the likelihood function L of the failure rate λ is obtained. p (λ);

[0008] Step 3, determine the prior distribution of failure rate λ;

[0009] Step 4: weight the prior distribution to obtain a weighted comprehensive prior distribution π s (λ), the weighted integrated prior distribution π s (λ) and the likelihood function L p (λ), the posterior distribution of the failure rate λ is obtained by using the Bayesian formula, and the reliability of ship spare parts is evaluated based on the posterior distribution of the failure rate λ.

[0010] Based on the above technical solution, the present invention can also make the following improvements.

[0011] Optionally, the likelihood function L of the failure rate λ in step 2 is p The calculation formula of (λ) is:

[0012]

[0013] Optionally, weighting the prior distribution includes: linear weighting;

[0014] After linear weighting, the weighted comprehensive prior distribution is obtained as follows:

[0015] Where m is the number of prior distributions, w j represents the weight of the jth prior distribution, π j (λ) represents the j-th prior distribution.

[0016] Optionally, weighting the prior distribution includes: geometric weighting;

[0017] After geometric weighting, the weighted comprehensive prior distribution is obtained as follows:

[0018] Where m is the number of prior distributions, w j represents the weight of the jth prior distribution, π j (λ) represents the j-th prior distribution.

[0019] Optionally, the j-th prior distribution

[0020] Among them, a jrepresents the shape parameter of the j-th prior distribution, b j represents the scale parameter of the j-th prior distribution and Γ(·) represents the gamma function.

[0021] Optionally, the posterior distribution of the failure rate λ obtained in step 4 is:

[0022]

[0023] Optionally, when the prior distribution is linearly weighted, the posterior distribution of the failure rate λ is:

[0024]

[0025] Optionally, when the prior distribution is geometrically weighted, the posterior distribution of the failure rate λ is:

[0026]

[0027] The present invention provides a method for evaluating the reliability of ship spare parts based on failure data of trouble-free interval time. The method analyzes the characteristics of on-site usage information, establishes a likelihood function model of the trouble-free interval time in the presence of failures, and then constructs a fused prior distribution based on linear weighting or geometric weighting. The posterior distribution of the failure rate is obtained based on the prior distribution and the likelihood function model. The effectiveness of the constructed model and method is illustrated by examples, thereby realizing the reliability evaluation of ship spare parts. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 A flow chart of a method for evaluating the reliability of ship spare parts based on failure interval time failure data provided by the present invention. DETAILED DESCRIPTION

[0029] 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.

[0030] Figure 1 The present invention provides a flow chart of a method for evaluating the reliability of ship spare parts based on failure interval time failure data, such as Figure 1 As shown, the reliability assessment method includes:

[0031] Step 1: Determine the on-site usage data D of ship spare parts during the trouble-free interval (T i ,s i ,r i ), where T i is the working time of the equipment in the i-th task, s i is the number of components installed on the equipment, r iis the total number of failures of the equipment in the i-th mission, i=1,2,...,n.

[0032] When a 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 equipment working time is approximately equal to the spare part working time, 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 set redundantly, and the number of components installed on a type of equipment is usually s≥2.

[0033] When there is no fault interval, the ship spare parts on-site usage data structure is mainly composed of equipment working time, number of installed parts, number of carried spare parts, and spare parts fault interval, and its form is: (T i ,s i ,N i ,τ ij ).

[0034] 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 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, is the total number of failures in the ith task. The specific data collection form is shown in Table 1.

[0035] Table 1 Spare parts field use data

[0036]

[0037] Step 2: Based on the on-site usage data D of ship spare parts and the Poisson distribution principle, the likelihood function L of the failure rate λ is obtained: p (λ).

[0038] Step 3: Determine the prior distribution of the failure rate λ.

[0039] Step 4: Weight the prior distribution to obtain the weighted comprehensive prior distribution π s (λ), the weighted integrated prior distribution π s(λ) and the likelihood function L p The posterior distribution of failure rate λ is obtained by using the Bayesian formula, and the reliability of ship spare parts is evaluated based on the posterior distribution of failure rate λ.

[0040] The present invention provides a ship spare parts reliability assessment method based on the failure interval time failure data, which effectively utilizes the failure interval time failure data in the field use information and constructs a suitable likelihood function according to its characteristics to perform Bayesian reliability assessment of ship spare parts.

[0041] Example 1

[0042] Embodiment 1 of the present invention is an embodiment of a method for evaluating the reliability of ship spare parts based on failure interval time failure data provided by the present invention, combined with Figure 1 It can be seen that the embodiment of the reliability evaluation method includes:

[0043] Step 1: Determine the on-site usage data D of ship spare parts during the trouble-free interval (T i ,s i ,r i ), where T i is the working time of the equipment in the i-th task, s i is the number of components installed on the equipment, r i is the total number of failures of the equipment in the i-th mission, i=1,2,...,n.

[0044] Step 2: Based on the on-site usage data D of ship spare parts and the Poisson distribution principle, the likelihood function L of the failure rate λ is obtained: p (λ).

[0045] In a possible implementation manner, it is assumed that the life of the equipment component follows an exponential distribution. Obviously, the number of failures r is a random variable and follows a Poisson distribution:

[0046]

[0047] So the likelihood function L of the failure rate λ is p The calculation formula of (λ) is:

[0048]

[0049] Step 3: Determine the prior distribution of the failure rate λ.

[0050] In one possible implementation manner, the jth prior distribution

[0051] Among them, a j represents the shape parameter of the j-th prior distribution, b jrepresents the scale parameter of the j-th prior distribution and Γ(·) represents the gamma function.

[0052] Step 4: Weight the prior distribution to obtain the weighted comprehensive prior distribution π s (λ), the weighted integrated prior distribution π s (λ) and the likelihood function L p The posterior distribution of failure rate λ is obtained by using the Bayesian formula, and the reliability of ship spare parts is evaluated based on the posterior distribution of failure rate λ.

[0053] In a possible implementation manner, weighting the prior distribution includes: linear weighting.

[0054] After linear weighting, the weighted comprehensive prior distribution is:

[0055] Where m is the number of prior distributions, w j represents the weight of the jth prior distribution, π j (λ) represents the j-th prior distribution.

[0056] In a possible implementation manner, weighting the prior distribution includes: geometric weighting.

[0057] After geometric weighting, the weighted comprehensive prior distribution is:

[0058] Where m is the number of prior distributions, w j represents the weight of the jth prior distribution, π j (λ) represents the j-th prior distribution.

[0059] In a possible implementation manner, the posterior distribution of the failure rate λ obtained in step 4 is:

[0060]

[0061] In a possible implementation manner, when the prior distribution is linearly weighted, the numerator of the posterior distribution formula is:

[0062]

[0063] in, Substituting into formula (2) we get

[0064]

[0065] For the denominator part of the posterior distribution formula:

[0066]

[0067] in Substituting into formula (4) we get

[0068]

[0069] Substituting equations (3) and (5) into (1), the posterior distribution of the gain / loss efficiency λ is:

[0070]

[0071] The posterior distribution in the above formula is the weighted sum of multiple gamma distributions.

[0072] In a possible implementation manner, when the prior distribution is geometrically weighted, the numerator of the posterior distribution formula is:

[0073]

[0074] For the denominator part of the posterior distribution formula:

[0075]

[0076] Substituting equations (6) and (7) into (1), the posterior distribution of the gain / loss efficiency λ is:

[0077]

[0078] The posterior distribution of the above formula is in the form of a gamma distribution, and the shape parameter is The scale parameter is

[0079] An embodiment of the present invention provides a method for evaluating the reliability of ship spare parts based on failure data of trouble-free interval time. The method analyzes the characteristics of on-site usage information, establishes a likelihood function model of the trouble-free interval time in the presence of failures, and then constructs a fused prior distribution based on linear weighting or geometric weighting. The posterior distribution of the failure rate is obtained based on the prior distribution and the likelihood function model. The effectiveness of the constructed model and method is illustrated by examples, thereby realizing the reliability evaluation of ship spare parts.

[0080] 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.

[0081] Those skilled in the art will appreciate 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. Moreover, 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.

[0082] 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 generate 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.

[0083] 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 including 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.

[0084] 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.

[0085] 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.

[0086] 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 method for evaluating the reliability of ship spare parts based on failure interval time failure data, characterized in that: The reliability evaluation method comprises: Step 1: Determine the on-site usage data D of ship spare parts during the trouble-free interval (T i ,s i ,r i ), where T i is the working time of the equipment in the i-th task, s i is the number of components installed on the equipment, r i is the total number of failures of the equipment in the i-th mission, i=1,2,...,n; Step 2: Based on the on-site usage data D of the ship spare parts and the Poisson distribution principle, the likelihood function L of the failure rate λ is obtained. p (λ); Step 3, determine the prior distribution of failure rate λ; Step 4: weight the prior distribution to obtain a weighted comprehensive prior distribution π s (λ), the weighted integrated prior distribution π s (λ) and the likelihood function L p (λ), the posterior distribution of the failure rate λ is obtained by using the Bayesian formula, and the reliability of ship spare parts is evaluated based on the posterior distribution of the failure rate λ.

2. The reliability evaluation method according to claim 1, characterized in that: The likelihood function L of the failure rate λ in step 2 p The calculation formula of (λ) is:

3. The reliability evaluation method according to claim 1, characterized in that: The weighting of the prior distribution includes: linear weighting; After linear weighting, the weighted comprehensive prior distribution is obtained as follows: Where m is the number of prior distributions, w j represents the weight of the jth prior distribution, π j (λ) represents the j-th prior distribution.

4. The reliability evaluation method according to claim 1, characterized in that: The weighting of the prior distribution includes: geometric weighting; After geometric weighting, the weighted comprehensive prior distribution is obtained as follows: Where m is the number of prior distributions, w j represents the weight of the jth prior distribution, π j (λ) represents the j-th prior distribution.

5. The reliability evaluation method according to claim 3 or 4, characterized in that: The j-th prior distribution Among them, a j represents the shape parameter of the j-th prior distribution, b j represents the scale parameter of the j-th prior distribution and Γ(·) represents the gamma function.

6. The reliability evaluation method according to claim 1, characterized in that: The posterior distribution of the failure rate λ obtained in step 4 is:

7. The reliability evaluation method according to claim 5, characterized in that: When the prior distribution is linearly weighted, the posterior distribution of the failure rate λ is:

8. The reliability evaluation method according to claim 5, characterized in that: The posterior distribution of the failure rate λ when the prior distribution is geometrically weighted is:

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