CN107885926B - Spare part configuration optimization method for naval vessel equipment in maintenance-free state - Google Patents
Spare part configuration optimization method for naval vessel equipment in maintenance-free state Download PDFInfo
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Abstract
The invention discloses a spare part configuration optimization method of naval vessel equipment in a maintenance-free state, which comprises the steps of building a reliability calculation model during equipment storage and a reliability calculation model during equipment use; calculating a utilization reliability benefit value Δ p for equipmentxkObtaining a reliability benefit matrix of the equipment; and acquiring a group of reliability benefit values corresponding to the spare part configuration scheme in the reliability benefit matrix according to the initial spare part configuration scheme, selecting the maximum value in the reorganized reliability benefit values, replacing the maximum value with the corresponding reliability benefit value when the number of the spare parts is increased by one, simultaneously increasing the number of the corresponding spare parts by one, and updating the spare part configuration scheme so as to acquire the minimum use reliability of the equipment under the spare part scheme. The method of the technical scheme of the invention fully considers the spare part requirements of the equipment in the storage and use stages, obtains the corresponding reliability benefit value, and can further obtain the effective optimal spare part configuration scheme by solving and constraining the spare part configuration scheme.
Description
Technical Field
The invention belongs to the field of reliability and spare part evaluation of naval vessel equipment, and particularly relates to a spare part configuration optimization method of naval vessel equipment in a maintenance-free state.
Background
The naval vessel is a multifunctional independent combat unit integrating air, water surface and underwater, and comprises various equipment components. Besides the frequently used equipment, the equipment with extremely short use time and long non-operation time also exists, and the equipment can be called as the equipment with extremely low use duty ratio. For the equipment with the extremely low use duty ratio which is placed on the naval vessel after being arranged in a train, compared with the equipment with the packaged state, the environment of the equipment on the naval vessel during the non-working period can be regarded as a special storage environment, the state of the equipment on the naval vessel during the non-working period is called as the storage state, and the storage provided in the application document refers to the non-working state of the naval vessel equipment. For the equipment with extremely low use duty ratio, the proportion of the working time of the equipment in the whole task time is extremely small, and the non-working time of the equipment is extremely long. Due to the influence of factors such as high temperature, high humidity and high salt at sea, the equipment is easy to malfunction during storage.
Compared with the failure mechanism and maintenance of the equipment in the working state, the protection of the equipment in the storage period is different as follows: (1) component failures are independent of each other. In contrast to equipment failure during its use, equipment downtime will not generate spare part requirements after equipment failure during use, while other components in the equipment remain failed after component failure during equipment storage. (2) The failure manifests itself in a different form. When the equipment breaks down in the working period, the equipment can stop working immediately, so that the equipment can be replaced and maintained in time, and when the equipment breaks down in the storage period, the equipment can not know the failure time, can not be replaced and maintained in time, and can only be replaced and maintained when the equipment is used.
Generally, a virtual station is introduced during non-detection maintenance of equipment storage, when equipment fails in a storage state, the virtual station has no repair capability and spare part resources, so that replacement repair cannot be performed on the failed equipment. When the equipment fails in the use stage, the virtual station and the station j both implement (s-1, s) guarantee, and the spare part replenishment flow of different stages of the equipment is shown in fig. 1. At present, a method for formulating a scheme of queuing spare parts during a task is mainly determined according to the working time of equipment, and the consumption of the spare parts caused by the long-time storage failure of the equipment is less considered. Because equipment is used for a very short period of time, very low duty cycle equipment is more concerned about the integrity of the equipment before use, i.e., the reliability of the equipment during storage, than the time the equipment is in good condition during storage or use.
Disclosure of Invention
In view of the above drawbacks or needs for improvement in the prior art, the present invention provides a spare part configuration optimization method for vessel equipment in a maintenance-free state. The method of the technical scheme of the invention builds a reliability model of the equipment storage-use stage aiming at the condition that the requirement of the spare part during the equipment storage period is not considered in the spare part configuration scheme in the prior art, and can optimize the optimal spare part configuration scheme of the equipment storage-use stage.
To achieve the above object, according to one aspect of the present invention, there is provided a spare part configuration optimization method for vessel equipment in a maintenance-free state, comprising
S1, building a reliability calculation model during equipment storage and a reliability calculation model during equipment use, and acquiring the reliability calculation model of the equipment in a maintenance-free state according to the reliability model during equipment storage and the reliability model during equipment use;
s2, according to the reliability calculation model of the equipment in the non-maintenance state, obtaining the use reliability benefit value of the equipment when the configuration number of any part of the equipment at any site is increased by one at any moment; sequentially and transversely arranging the reliability benefit values of the same spare part project under different configuration numbers according to the configuration numbers, and longitudinally arranging the reliability benefit values of different spare part projects to obtain a reliability benefit matrix of the equipment;
s3, replacing the original benefit value in the matrix with the benefit value obtained by adding one to the configuration number of the spare part item with the maximum reliability benefit value in the first column of the reliability benefit matrix to update the reliability benefit matrix; according to a spare part configuration scheme corresponding to the reliability benefit value of the updated first column of the reliability benefit matrix, combining a reliability calculation model of the equipment in a non-maintenance state, and calculating the minimum use reliability of the equipment;
s4, judging whether the minimum use reliability of the equipment is smaller than a reliability target value, if so, entering the step S3; if not, taking the spare part configuration scheme corresponding to the reliability benefit value in the first column of the reliability benefit matrix updated in the step S3 as the optimal spare part configuration scheme;
wherein the device-during-storage reliability model building process in step S1 includes:
s11, calculating the demand rate of the component per unit time in the virtual site at any time during the storage period according to the storage failure rate of the component; the virtual station is a corresponding maintenance station during equipment storage;
s12, acquiring the number of unrepairable parts in the virtual station at any moment during storage according to the distribution function of part demand and the mean and variance distribution function of the spare part supply channel of the virtual station, and calculating the expected shortage number of the parts in the virtual station at any moment during storage;
s13, according to the probability that the component is intact at any time in the storage period, namely the probability that the shortage number of the component in the virtual site is 0, the reliability of the component at any time in the storage period can be calculated;
s14, according to the connection relation between different parts in the equipment, the reliability of the whole equipment at any time during the storage period is calculated.
As a preferable aspect of the present invention, the reliability model building process during use of the apparatus in step S1 includes,
s11' determining the service time of the equipment, and the equipment is preferably only detected and repaired before the equipment is used;
s12', calculating the spare part demand rate of the real station to the component after the equipment works according to the spare part demand of the component in the real station during the storage period and the spare part demand generated in unit time after the equipment starts to work; the real station is a corresponding maintenance station during the use period of the equipment;
s13', calculating and obtaining the expected shortage number of the spare parts in the real site at any moment according to the expected shortage number of the spare parts in the superior site at any moment and the mean value and the variance of the supply channel of the spare parts;
s14' calculates the reliability of the whole equipment at any time during use according to the connection relation between different parts in the equipment.
As a preferred embodiment of the present invention, the demand rate of the component l in the virtual station j' at time t in unit time is:
λj'l(t)＝γlAj'l(t-1)；
wherein A isj'l(t-1) is the reliability of component l at time t-1 in station j', and γ l is the failure rate of component l during storage of equipment e.
As a preferred aspect of the present invention, the demand of the component l during the storage period of the equipment e preferably follows a poisson distribution, and the spare parts of the component l in the virtual station j 'at time t preferably follow a poisson distribution with the same mean and variance of the supply channel, so that the number of the component l in the virtual station j' at time t is:
wherein λ isj'(l)And (t) is the demand rate of the components l in the virtual station j' per unit time at the moment t.
As a preferred embodiment of the present invention, the expected shortage number of the component l in the virtual station j' at the time t of the storage period t of the equipment e is:
the reliability at time t during storage of the component l is:
the different components of the equipment e are preferably in a serial relationship, the reliability of the equipment e during storage at time t is:
wherein NRPj'(l)(t) is the number of unrepairable components l in the virtual site j' at the moment t; BOj'(l)(0, t) is the probability that component l in virtual site j' is 0 short; EBOj'(l) (t) is the expected shortage of components l in virtual site j 'at time t during equipment e's storage period.
As a preferred embodiment of the present invention, the equipment e is arranged at T0When the time begins to work, T0The demand for part I at time j includes the spare part demand for part I at time j during storage, and part I is provided at time T0Spare part requirements generated in unit time after the work is started at any moment;
0-T in site j0The demand on part i during storage for the time period is:
demand rate lambda of station j to component l in unit time after equipment e worksj(l)(t) is:
wherein NRPj'(l)(t) is the number of unrepairable components l in the virtual site j' at the moment t; a. thee(t-1) availability of equipment e at time t-1, MelThe number of spare parts to be equipped with part i in e.
As a preferred preference of the technical scheme of the present invention, the requirements of the station j on the spare part l after the equipment works are as follows:
wherein, T0For the moment when equipment e starts to operate, NRPj(l)(T0) For 0-T in site j0The demand, lambda, for spare parts during storage of the time periodj(l)And (t) is the demand rate of the station j for the spare part l in unit time after the equipment e starts working.
As a preferred embodiment of the present invention, the reliability of the equipment e at time t is:
wherein, BOjl(x, t) is the probability that component l is missing x at time t in site j.
According to the technical scheme, a reliability calculation model during equipment storage and a reliability calculation model during equipment use are respectively established, and the reliability calculation model of the equipment in a maintenance-free state is obtained after the reliability calculation model during equipment storage is taken into consideration. By utilizing the model, the equipment reliability corresponding to the condition that the configuration number of spare parts of the parts in the equipment at any time and any station is different and the corresponding reliability benefit matrix can be calculated. That is, the equipment includes a plurality of components, and for any one component, the change of the number of the spare parts affects the reliability of the equipment, thereby affecting the benefit value of the reliability of the equipment.
Specifically, starting from 0, when the number of spare part configurations is increased by one, a corresponding reliability benefit value appears, and the reliability benefit values are sequentially and transversely arranged according to the size of the number of spare part configurations, namely, the first reliability benefit value is a reliability change index of the number of spare part configurations from 0 to 1, namely, the first reliability benefit value is a reliability benefit value when the number of spare part configurations is 1; the second reliability benefit value is a reliability change index of the spare part configuration number from 1 to 2, namely the reliability benefit value when the spare part configuration number is 2, and so on. The equipment comprises a plurality of components which have spare part requirements respectively, the reliability benefit values of each component under different spare part configuration numbers are arrayed according to the rule, and then the reliability benefit values of different components are arrayed longitudinally, so that the reliability benefit matrix is formed. That is, in one matrix, the reliability benefit matrixes of each row belong to the same component, and are arranged in an increasing manner from left to right according to the configuration number of spare parts; in this matrix, the reliability benefit values for each column belong to different components.
And after the reliability benefit value matrix is obtained, optimizing the reliability benefit value matrix to obtain an optimal spare part configuration scheme. Specifically, the original reliability benefit value is replaced by the reliability benefit value obtained by adding 1 to the spare part configuration number of the component corresponding to the maximum reliability benefit value in the first column, that is, the first reliability benefit value in the row of the maximum reliability benefit value in the first column is removed, the remaining benefit values are shifted to the left by one grid, that is, the current reliability benefit value is replaced by the reliability benefit value adjacent to the right of each reliability benefit value in sequence, and the updated reliability benefit value matrix is obtained. And determining the spare part configuration number corresponding to the reliability benefit value of the first column of the updated reliability benefit value matrix, and calculating the reliability of the equipment under the spare part configuration scheme. If the reliability of the equipment under the spare part configuration scheme is smaller than the target reliability, the reliability benefit matrix is continuously optimized by adopting the method, otherwise, the spare part configuration scheme is the optimal spare part configuration scheme. The target reliability can be set according to the requirement, and is preferably within the range of 0-1. Therefore, the optimal solution of spare part configuration may be different under different target reliability.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
1) the method of the technical scheme of the invention builds a reliability model of the equipment in the storage-use stage, calculates and obtains the reliability benefit value of each spare part in the equipment under different configuration schemes by using the model, obtains a corresponding reliability benefit value matrix, can identify the spare part with the maximum reliability benefit value under the current spare part configuration scheme by using the matrix, increases one spare part number as an optimized spare part scheme, and calculates and obtains the corresponding reliability value until reaching the target value of the reliability.
2) According to the method of the technical scheme, the reliability target value is decomposed to each spare part, so that each spare part has a certain reliability target value, and the reliability value under the spare part configuration scheme is finally calculated by optimally setting the spare part configuration scheme in the reliability benefit matrix.
3) The method of the technical scheme of the invention fully considers the spare part requirements of the equipment in the storage and use stages, obtains the corresponding reliability benefit value, and can further obtain the effective optimal spare part configuration scheme by solving and constraining the spare part configuration scheme.
Drawings
FIG. 1 is a flow of a repair and replacement part supply process introduced into a virtual site according to an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of a benefit matrix transformation according to an embodiment of the present invention;
FIG. 3(a) is a simulation flow of an embodiment of the present invention; fig. 3(b) is an initial failure time generation flow of the embodiment of the technical solution of the present invention;
FIG. 4 is a comparison graph of analysis and simulation results for an embodiment of the present invention;
FIG. 5(a) is a device e of an embodiment of the present invention1The equipment mission profile of (1); FIG. 5(b) is a device e of an embodiment of the present invention2The equipment mission profile of (1);
FIG. 6(a) is a device e of an embodiment of the present invention1The equipment reliability of the method changes along with the iteration times; FIG. 6(b) is a device e of an embodiment of the present invention2The equipment reliability of (2) is plotted as a function of the number of iterations.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. The present invention will be described in further detail with reference to specific embodiments.
According to the technical scheme, the reliability is selected as an evaluation index of the storage and use stage of the equipment with the extremely low use duty ratio, and the use and guarantee characteristics of the equipment with the extremely low use duty ratio are combined to carry out research on the spare part configuration optimization method of the equipment. Specifically, in the technical scheme of the invention, the configuration of the equipment spare parts is optimized preferably in a mathematical modeling mode. The optimization of the technical solution of the present invention is further described below with reference to specific examples.
In this embodiment, the LCU, the spare part l and the component l are different expressions of components having spare part requirements under different situations, and represent the same reference object, that is, any component having spare part requirements in the equipment. It should be noted that, for each component having spare part requirement in the equipment, the method of the present embodiment may be adopted to optimize the spare part requirement configuration.
According to the spare part maintenance replenishment process during equipment storage, in order to facilitate modeling, the following condition assumptions are made in the embodiment of the technical scheme of the invention:
the equipment uses all the same type equipment of site sites to detect at the same time.
And the failure rate of the part when the equipment part is in a storage state during the task is subject to exponential distribution.
And the influence of the non-replaceable part on the storage reliability of the equipment is not considered during the task.
The spare part storage environment is good, and the influence of the storage failure of the spare part on the requirement of the spare part is not considered;
under the above condition assumption, equipment storage-use phase reliability modeling is performed. In a preferred embodiment, reliability modeling under equipment storage conditions is first performed:
considering that the time is relatively short and the sea environment is approximately constant during the ship going out of the sea to perform a task, and the storage failure rate of the component I under the sea environment condition is set to be gamma for any component in the equipmentlThen, the demand rate of the LRU class in the virtual site j' at time t in unit time is:
λj'l(t)＝γlAj'l(t-1)(1)
wherein A isj'l(t-1) is the reliability of component l at time t-1 in station j'.
Because the spare number of the virtual station j ' is 0 and the repair probability of spare parts is 0, when the station j ' is not supplied from the outside, the supply channel of the spare parts of the part l in the virtual station j ' at the moment t is the accumulated quantity of the unrepairable parts, and because the demand of the part l obeys the poisson distribution, the spare parts l in the virtual station j ' at the moment t also obey the poisson distribution with the same mean value and variance of the supply channel, and the unrepairable quantity of the part l in the virtual station j ' at the moment t is:
the expected shortage of parts l in virtual site j' at time t, EBO, can be foundj'l(t) is
the probability that component l is sound at time t is the probability that there is a 0 shortage of components l in virtual site j', whereby the reliability at time t during the on-equipment component l storage is:
since the different components of the installation are in series, the reliability of installation e at time t is:
secondly, reliability modeling of the equipment use phase is performed: if the service time of the equipment is known, the equipment is only detected and repaired before being used, and if the equipment e is in T0When the time begins to work, T0The demand for spare part l in time station j consists of two parts: first, spare part demand occurs during storage of spare part l in site j; secondly, is equipped at T0When the work is started at any time, spare part requirements are generated in unit time.
Combination formula (2) can calculate 0-T in site j0Time periodThe demand for spare part l during storage is:
demand rate lambda of station j to spare part l in unit time after equipment worksjl(t) is:
in the formula: a. thee(t-1) availability of equipment e at time t-1, Ae(1)＝1，MelThe LRU (spare parts of components in the equipment) in equipment e is loaded.
The requirements of the station j after the equipment work on the spare part l are therefore:
as the battle ship j generally only has the capability of disassembling and replacing parts for equipment, the disassembled and replaced spare parts are sent to the guarantee ship H0And repairing and simultaneously applying the same number of spare parts to the safeguard ship. Warship H with safeguard0The repair probability for LRU is r, and the average time required to repair LRU is τlAnd the fault parts which cannot be repaired are sent to the base for repair after the task is finished. If the task time t is less than the LRU average repair time taulGuarantee ship H at time t0The repair quantity is: the sum of fault pieces generated by each warship within 0-t time and the guarantee warship H0Multiplying the LRU repair probabilities; if taulT is less than or equal to t, and t moment guarantees ship H0The repair quantity is: (t-T)l) Sum of fault pieces generated by each warship within t time and guarantee warship H0The product of the LRU repair probabilities. And at the time of t, the guarantee ship H0The medium LRU supply channel consists of a current repair quantity and a non-repair quantity, thereby ensuring the ship H0Has a mean value of
X0l(t) obeys Poisson distribution with the same mean and variance, so that the warship H is guaranteed at the moment t0The probability that the LRU supply channel number is x is:
guarantee warship H at time t0The expected shortage number and expected variance of the medium LRU are:
in the formula: s0lFor safeguard ship H0The number of inventories of the middle LRU.
Because the battle ship j only has the capacity of replacing and repairing, the replaced fault piece is sent to the guarantee ship H0Repairing and simultaneously applying the same number of spare parts to the safeguard ship. Due to the safeguard ship H0The inventory capacity is limited, the repair probability is less than 1, the inventory quantity of spare parts is reduced along with the advance of time, the requirement of the spare parts of the battleship j cannot be met, and the guarantee delay is generated. Guarantee ship H at time t0The proportion of the number of the delayed LRU to the total shortage number of the warships to the warships j is
Then
the supply channel of the battleship j at the moment t consists of two parts: first, guarantee warship H0The number of warship j guarantee delays caused by spare part shortage at the time of t-ost; second, guarantee warship H0And (4) supplying the part on the way to the warship j. Therefore, the LRU supply channel mean value in the battleship j at the moment t is
In the formula: ost is battle ship j to safeguard ship H0The transport time of (c).
Variance of
When the supply channel difference of the LRU in the battleship j is larger than 1 at the moment t, the supply channel of the LRU obeys the negative two-term distribution of gamma (a, b), and the distribution parameters (a, b) are
When the supply channel difference of the LRU in the battleship j is smaller than 1 at the moment t, the supply channel of the LRU obeys the binomial distribution of eta (p, n), and the distribution parameter (p, n) is
When the supply channel difference average ratio of the LRU in the battleship j is equal to 1 at the moment t, the supply channel obeying average value of the LRU is E [ X ]jl(t)]Poisson distribution of (a).
Selecting proper distribution according to the sizes of the formula (12), the formula (13) and the formula (1) to obtain the probability distribution P of the LRU supply channel in the station at the time t in the battleship jjl(x, t) the LRU expected value and the expected variance at time t can be obtained as
According to the LRU shortage number mean value and variance ratio obtained by the formula (16) and the value of 1, the corresponding distribution parameters can be obtained by combining the formula (14) and the formula (15), and the probability BO of LRU shortage x at the t moment in the battleship j is calculatedjl(x, t), and calculating the reliability of the equipment at the time t as follows:
and thirdly, optimizing a spare part scheme in a non-maintenance state on the basis of the reliability model. In the embodiment of the technical scheme, the minimum reliability of the extremely low use duty ratio equipment in the use stage is taken as a spare part optimization target, and if the minimum reliability of the extremely low use duty ratio equipment required by the upper level is R0Then, the objective function of the spare part configuration optimization model during the equipment task is as follows:
min(Re(t))≥R0(9)
further, the optimization algorithm for determining the model preferably comprises the following steps:
Step 2: and determining the optimal spare part scheme under the target reliability value. Different number of spare parts (m) in site j>0) The corresponding benefit value matrix is shown as matrix 1 in fig. 2. Setting the configuration quantity of the kth spare parts in the site j as x, the benefit value is delta pxk, and taking the 1 st benefit matrixColumn put matrix [ delta P ]1,ΔP2...ΔPj]Adding 1 to the number of station spare part items with the maximum benefit value, wherein the corresponding benefit value matrix is shown as a matrix 2 in fig. 2, and calculating the minimum use reliability R of the equipmente；
And step 3: if R ise＜R0And updating the benefit matrix. The spare part items with the largest benefit value are added by one, and the original benefit value in the matrix is replaced by the benefit value, for example, in the transformation process from the matrix 1 to the matrix 2 in fig. 2. Minimum reliability R of judging equipmenteAnd (4) whether the requirements are met, if so, finishing the operation, and otherwise, returning to the step 2.
And fourthly, analyzing and verifying the optimization algorithm model. According to the spare part guarantee flow when no maintenance detection is carried out during equipment storage, discrete event modeling and Monte Carlo simulation methods are preferably adopted to carry out modeling simulation verification on the optimization algorithm model of the technical scheme of the invention in the embodiment of the technical scheme of the invention. In the embodiment of the technical scheme, the reliability is adopted as an evaluation index, so that the equipment state at any moment needs to be counted, the equipment state without failure is recorded as 1, the component failure state is recorded as 0, the same task is simulated for N times, the equipment state at each time is recorded, and the equipment state mean value at each moment after N times of simulation is counted. The simulation process is shown in fig. 3(a) according to the spare part replenishment and maintenance process. The initial failure time generation method is shown in fig. 3 (b).
In a preferred embodiment, the component LRU reliability parameters are shown in table 2, and when the equipment storage duration is 1000h and the total number of simulations is 100, the LRU storage-use phase reliability resolution results and the simulation results are shown in fig. 3.
TABLE 2 spare parts guarantee information List
In particular, at a slave site j1Station j2Relay station H0In the embodiment of the ship formation composition, the time for going out to sea to execute the task is1000h, equipment site j1And j2All are provided with equipment e1And equipment e2Station j1And site j2The start and stop moments of the operation of the equipment of the same type and the same type are completely the same, and the equipment e is arranged during the task1And equipment e2As shown in FIGS. 5(a) and 5(b), equipment e1And e2The number of single ship installations is 2, and equipment e2And equipment e2The parts list and the safeguard information are shown in table 3.
TABLE 3 Equipment parts List and Provisioning information
Taking the minimum reliability of the equipment in the use stage as an optimization target, and adopting marginal algorithm to carry out equipment e in each station when the minimum reliability of the equipment in the use period is 0.65,0.75,0.85 and 0.95 respectively1And equipment e2The spare part solutions of (a) were optimized, and the spare part solutions obtained by optimization before and after the equipment storage were considered are shown in table 4.
TABLE 4 spare part scenarios for different target reliabilities when and when equipment storage failure is considered
As can be seen from a comparison of the recipes for spare parts before and after storage at the same target values in Table 3, the equipment e having a high duty ratio and a high frequency of use1Whether the target reliability is 0.95 or 0.65, equipment storage has no effect on the spare part solution. And for equipment e with long storage time and low use frequency2When the target reliability is 0.75,0.85,0.95, except that the case where the target reliability is 0.65, the case where the spare part recipe (0,0,0) before the stock is considered and the case where the spare part recipe (0,0,0) after the stock is considered are the sameThe total quantity of the spare parts of the spare part schemes after storage is more than that of the spare parts of the spare part schemes which are not considered for storage. Therefore, for equipment with high use frequency and high duty ratio, the influence of equipment storage failure on the spare part scheme can be basically ignored, and for equipment with low duty ratio, the spare part scheme cannot be determined according to the use time of the equipment.
When equipping with e1And equipment e2With a minimum reliability of 0.95, the minimum reliability of the equipment as a function of the number of iterations is shown in fig. 6.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A spare part configuration optimization method for naval vessel equipment in a maintenance-free state is characterized by comprising the following steps
S1, building a reliability calculation model during equipment storage and a reliability calculation model during equipment use, and acquiring the reliability calculation model of the equipment in a maintenance-free state according to the reliability model during equipment storage and the reliability model during equipment use;
s2, according to the reliability calculation model of the equipment in the non-maintenance state, obtaining the use reliability benefit value of the equipment when the configuration number of any part of the equipment at any site is increased by one at any moment; sequentially and transversely arranging the reliability benefit values of the same spare part project under different configuration numbers according to the configuration numbers, and longitudinally arranging the reliability benefit values of different spare part projects to obtain a reliability benefit matrix of the equipment;
s3, replacing the original benefit value in the matrix with the benefit value obtained by adding one to the configuration number of the spare part item with the maximum reliability benefit value in the first column of the reliability benefit matrix to update the reliability benefit matrix; according to a spare part configuration scheme corresponding to the reliability benefit value of the updated first column of the reliability benefit matrix, combining a reliability calculation model of the equipment in a non-maintenance state, and calculating the minimum use reliability of the equipment;
s4, judging whether the minimum use reliability of the equipment is smaller than a reliability target value, if so, entering the step S3; if not, taking the spare part configuration scheme corresponding to the reliability benefit value in the first column of the reliability benefit matrix updated in the step S3 as the optimal spare part configuration scheme;
wherein the device-during-storage reliability model building process in step S1 includes:
s11, calculating the demand rate of the component per unit time in the virtual site at any time during the storage period according to the storage failure rate of the component; the virtual station is a corresponding maintenance station during equipment storage;
s12, acquiring the number of unrepairable parts in the virtual station at any moment during storage according to the distribution function of part demand and the mean and variance distribution function of the spare part supply channel of the virtual station, and calculating the expected shortage number of the parts in the virtual station at any moment during storage;
s13, according to the probability that the component is intact at any time in the storage period, namely the probability that the shortage number of the component in the virtual site is 0, the reliability of the component at any time in the storage period can be calculated;
s14, according to the connection relation between different parts in the equipment, the reliability of the whole equipment at any time during the storage period is calculated.
2. The spare part configuration optimization method for vessel equipment in a non-maintenance state according to claim 1, wherein the reliability model building process in the step S1 during equipment use comprises,
s11' determining the service time of the equipment, and the equipment is preferably only detected and repaired before the equipment is used;
s12', calculating the spare part demand rate of the real station to the component after the equipment works according to the spare part demand of the component in the real station during the storage period and the spare part demand generated in unit time after the equipment starts to work; the real station is a corresponding maintenance station during the use period of the equipment;
s13', calculating and obtaining the expected shortage number of the spare parts in the real site at any moment according to the expected shortage number of the spare parts in the superior site at any moment and the mean value and the variance of the supply channel of the spare parts;
s14' calculates the reliability of the whole equipment at any time during use according to the connection relation between different parts in the equipment.
3. The spare part configuration optimization method for vessel equipment in the non-maintenance state according to claim 1 or 2, wherein a demand rate per unit time of a part l in a virtual station j' at the time t is as follows:
λj'l(t)＝γlAj'l(t-1)；
wherein A isj'l(t-1) is the reliability of the component l at the time t-1 in the station j', γlFailure rate of part i during storage of equipment e.
4. The method for optimizing the spare part configuration of the vessel equipment in the non-maintenance state according to claim 1, wherein the demand of the part l during the storage period of the equipment e preferably follows a poisson distribution, the spare part of the part l in the virtual station j 'at the time t preferably follows a poisson distribution with the same mean value and variance of a supply channel, and the number of the part l which can not be repaired in the virtual station j' at the time t is as follows:
wherein λ isj'(l)And (t) is the demand rate of the components l in the virtual station j' per unit time at the moment t.
5. The method as claimed in claim 1, wherein the expected shortage number of component/in virtual station j' at time t during storage of equipment e is:
the reliability at time t during storage of the component l is:
the different components of the equipment e are preferably in a serial relationship, the reliability of the equipment e during storage at time t is:
wherein NRPj'(l)(t) is the number of unrepairable components l in the virtual site j' at the moment t; BOj'(l)(0, t) is the probability that component l in virtual site j' is 0 short; EBOj'(l)(t) is the expected shortage of components l in virtual site j 'at time t during equipment e's storage period.
6. The method of claim 1, wherein the equipment e is at T0When the time begins to work, T0The demand for part I at time j includes the spare part demand for part I at time j during storage, and part I is provided at time T0Spare part requirements generated in unit time after the work is started at any moment;
0-T in site j0The demand on part i during storage for the time period is:
demand rate lambda of station j to component l in unit time after equipment e worksj(l)(t) is:
wherein NRPj'(l)(t) is the number of unrepairable components l in the virtual site j' at the moment t; a. thee(t-1) availability of equipment e at time t-1, MelThe number of spare parts to be equipped with part i in e.
7. The spare part configuration optimization method for vessel equipment in the non-maintenance state according to claim 1, wherein the requirement of a station j on a spare part l after the equipment works is as follows:
wherein, T0For the moment when equipment e starts to operate, NRPj(l)(T0) For 0-T in site j0The demand, lambda, for spare parts during storage of the time periodj(l)And (t) is the demand rate of the station j for the spare part l in unit time after the equipment e starts working.
8. The method of claim 1, wherein the reliability of equipment e at time t is as follows:
wherein, BOjl(x, t) is the probability that component l is missing x at time t in site j.
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| CN108564270B (en) * | 2018-04-09 | 2021-11-02 | 中国人民解放军海军工程大学 | Gamma type unit spare part demand calculation method under storage failure risk |
| CN108536960B (en) * | 2018-04-09 | 2022-04-05 | 中国人民解放军海军工程大学 | Method for calculating demand of exponential type unit spare parts under risk of storage failure |
| CN108733883B (en) * | 2018-04-16 | 2021-08-13 | 中国人民解放军海军工程大学 | Method for determining demand of subsequent spare parts of normal type unit |
| CN110288120B (en) * | 2019-05-16 | 2023-07-14 | 中国人民解放军海军工程大学 | Spare part scheme optimization method and device for multi-batch parts in integral storage mode |
| CN110287523B (en) * | 2019-05-16 | 2023-07-18 | 中国人民解放军海军工程大学 | Spare part scheme optimization method and device for multi-batch parts in modularized storage mode |
| CN110288119B (en) * | 2019-05-16 | 2023-01-06 | 中国人民解放军海军工程大学 | Optimization method and device for supplementary storage scheme in integral storage mode |
| CN110309950B (en) * | 2019-05-16 | 2022-12-30 | 中国人民解放军海军工程大学 | Method and device for optimizing initial storage scheme in modular storage mode |
| CN110298478B (en) * | 2019-05-16 | 2022-12-30 | 中国人民解放军海军工程大学 | Optimization method and device for supplementary storage scheme in modular storage mode |
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