CN112528510A - Method for predicting repairable aviation material spare parts based on life-extinction process model - Google Patents
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Abstract
The invention belongs to the technical field of aviation material guarantee, and particularly relates to a repairable aviation material spare part prediction method based on a life-extinction process model. According to the method, a life-going process mathematical model with limited capacity is established according to the reliability data and the historical fault data of the repairable aviation materials, and aviation material spare part prediction based on the requirement of the armies on the completion rate is realized.
Description
Technical Field
The invention belongs to the technical field of aviation material guarantee, and particularly relates to a repairable aviation material spare part prediction method based on a life-extinction process model.
Background
The aeronautical materials can be repaired, and the aeronautical materials are defined as aeronautical materials which can be renovated and repaired after a fault occurs. The completeness rate, which reflects the rate of the mission-capable aircrafts of the air force army, is an important factor influencing the fighting capacity of the air force army. The decision problem of the stock of spare parts of the aviation materials directly influences the completeness rate of the airplane.
The expense of the spare parts of the aviation materials accounts for a large proportion of the total life cycle expense of the airplane, and the problem of inventory decision-making is solved in order to avoid the capital waste as much as possible while meeting the flight task.
The operation process of the repairable aeronautical material comprises the following steps: and (4) randomly generating faults, calling stock spare parts after the faults occur, returning the fault parts to a finished product factory for repair, and returning the repaired aviation materials to the army to enter the stock. If the failed aviation material is not replaced by spare parts, the airplane is not intact due to the lack of spare parts. The process is very well in line with the birth and death process model in the queuing theory.
At present, in the prior art, when a marine material spare part is predicted, a used birth and death process model is based on a poisson distribution model, and a simpler approximate estimation method is adopted when a system fault rate lambda is estimated, or a military manual is inquired to obtain the general fault rate of the marine material. The method uses the most approximate likelihood estimation method, usually only according to the reliability data obtained by the aviation material test, neglects the failure rate of the aviation material in actual use, and does not fit a failure probability curve and test after fitting; the method has the advantages that the military manual is used for inquiring the failure rate of the aviation materials, the aviation materials of the airplane are complex, the manual cannot record the reliability data of all the aviation materials, in addition, the aviation material technology is continuously updated and iterated, and the reliability of the same aviation materials produced at different time is probably inconsistent. The above two points may result in the failure to accurately predict the requirements of spare parts of the marine materials.
In addition, in the prior art, when a mathematical model of a life-extinction process is established, the default whole system capacity is infinite, or when the default system is limited, the condition that the rebuilt sailing material returns to the system is not considered, which is different from the actual application condition of the repairable sailing material.
Disclosure of Invention
The purpose of the invention is as follows: the method for predicting the repairable aviation material spare parts based on the life-extinction process model is characterized in that a life-extinction process mathematical model with limited capacity is established according to reliability data and historical fault data of the repairable aviation materials, and aviation material spare part prediction based on the requirement of the completion rate of an army is achieved.
The technical scheme of the invention is to provide a method for predicting repairable aviation material spare parts based on a life-extinction process model, which comprises the following steps:
step 1: screening out reliability data or historical fault data and maintenance data of any repairable materials needing spare part prediction, drawing out a fault-free time interval frequency histogram corresponding to the repairable materials according to the screened reliability data or historical fault data, and drawing out a fault repair time interval frequency histogram according to the maintenance data;
step 2: drawing a corresponding failure-free time interval probability distribution curve according to the failure-free time interval frequency histogram, and fitting the failure-free time interval probability distribution curve to obtain a first average failure rate lambda; drawing a repair time interval probability distribution curve according to the fault repair time interval frequency histogram, and then fitting or directly calculating the average repair time repair rate mu;
and step 3: carrying out Pearson inspection on the first average failure rate lambda, and obtaining a second average failure rate lambda by checking a reliability standard manual if the first average failure rate lambda does not meet the Pearson inspection;
and 4, step 4: drawing a life and death process stable state chain with limited capacity and the repaired sailing materials can return to a spare part library; establishing a closed equation set according to the stable state chain in the life-extinction process;
and 5: if the first average fault rate lambda meets the Pearson test, substituting the first average fault rate lambda, the maintenance rate mu, the number of airplanes and the requirement of the completeness rate into a closed equation set, and calculating to obtain an initial probability value P0, wherein P0 represents the probability that all the screened repairable aviation materials of a certain type have no fault; calculating the number of the repairable spare parts according to the P0 value;
if the first average fault rate lambda does not meet the Pearson test, substituting the second average fault rate lambda, the maintenance rate mu, the number of airplanes and the requirement of the perfectness rate into a closed equation set, and calculating to obtain an initial probability value P0; and calculating the number of the repairable spare parts according to the P0 value.
Optionally, the prediction method further includes cleaning the screened reliability data or historical fault data and maintenance data, and deleting redundant invalid data.
Optionally, according to the screened reliability data, fitting the probability distribution curve of the fault-free time interval by using a constant number truncation service life test method to obtain a first average fault rate lambda.
Optionally, the fixed number tailgating life test method comprises:
performing reliability test on n repairable navigation materials in any screened repairable navigation materials, and ending the test at the time t 0; if r sailing materials have faults in the test, recording the failure time of each faulted sailing material as t1, t2, … and tr in sequence; the first average failure rate λ is then estimated as:
alternatively, if the first average failure rate λ satisfies the pearson test, the probability distribution of the no-failure time interval is a negative exponential distribution.
Optionally, according to the screened historical fault data, fitting a fault-free time interval probability distribution curve by using a fault frequency histogram method to obtain a first average fault rate λ.
Optionally, the failure frequency histogram method includes:
dividing a statistical failure time range of the repairable aviation material sample into k intervals at a group interval of time delta t, and then drawing a histogram according to frequency numbers falling in each interval; then, taking the accumulated frequency as a vertical coordinate and the time as a horizontal coordinate to make an accumulated frequency distribution graph; finally, fitting the cumulative frequency distribution curve to obtain a first average failure rate lambda; the cumulative frequency represents the sum of the probabilities of the reworkable materials failing over time in the system.
Alternatively, if the first average failure rate λ satisfies the pearson test, the probability distribution of the no-failure time interval is a negative exponential distribution.
Optionally, for a certain type of aircraft material, the maintenance rate μ remains stable, and the calculation formula of the average repair time maintenance rate μ is:
wherein r is the number of repaired sailing materials in the time interval Delta T, K is the total number of fault sailing materials in the time interval,
optionally, the formula of the closed system of equations is:
wherein m: the number of airplanes owned by the army is in units of frames;
n: the number of repair shops;
n: the number of the repairable spare parts of the aviation material is in units of parts;
l: the total number of the aircraft materials in the whole system, i.e., L is m + N (if each aircraft has 3 aircraft materials, L is 3m + N), and the unit is one;
ρ: service strength, which is the ratio of lambda to mu;
q: the number of failed pieces in the system;
θ: airplane readiness of the fleet.
The invention has the technical effects that:
(1) the reliability receipt library, the historical fault database and the reliability manual of the repairable aviation material are comprehensively used, and the reliability of the original data is higher;
(2) when the mean failure rate lambda value is calculated by fitting a curve, if estimation is carried out according to reliability data, a fixed number truncation service life test method and a failure frequency histogram method are used. In addition, the Pearson test is carried out on the lambda obtained by curve fitting, so that the average failure rate obtained by estimation is closer to the real failure rate of the aviation material;
(3) the invention improves the life-time process state model, changes the system with infinite capacity into the system with finite capacity, allows the repaired sailing timber to return to the stock to be spare parts, and the model is more consistent with the actual running process of the sailing timber repairable by the army.
Description of the drawings:
FIG. 1 is a flow chart of a prediction method of the present invention;
FIG. 2 is a schematic diagram of the Pearson assay;
FIG. 3 is a finite capacity stateful process model;
FIG. 4 is a histogram of frequency intervals of faults;
FIG. 5 is a schematic of curve fitting.
Detailed Description
The main parameter meanings of the mathematical model in the embodiment are as follows:
λ: average failure rate of the aviation materials and expected value of failure occurrence are in units of pieces/day;
μ: the average repair rate of the aeronautical materials and the expected value of the repair speed are in units of pieces/day;
m: the number of airplanes owned by the army is in units of frames;
n: the number of repair shops;
n: the number of the repairable spare parts of the aviation material is in units of parts;
l: the total number of the aircraft materials in the whole system, i.e., L is m + N (if each aircraft has 3 aircraft materials, L is 3m + N), and the unit is one;
P0: the repair line idle probability is the theoretical probability that a certain type of repairable aviation material in the whole system has no fault when the life and death process tends to be stable;
Pk: after the birth and death process tends to be stable, the theoretical probability of k fault parts exists in the whole system;
ρ: service strength, which is the ratio of lambda to mu;
q: the number of fault parts in the system is in parts;
w: the average time interval between the occurrence of the fault and the completion of the repair of each faulty aviation material is expected, and the unit is day;
theta; the airplane integrity of the airplane team refers to the ratio of the number of intact airplanes (airplanes without parts) in the system to the total number of airplanes in the airplane team.
As shown in fig. 1, in the present embodiment, a method for predicting a repairable marine material spare part based on a life-time process model is provided, where the method includes:
step 1: screening out reliability data or historical fault data and maintenance data of any type of repairable materials needing spare part prediction, drawing out a fault-free time interval histogram corresponding to the repairable materials according to the screened reliability data or historical fault data, and drawing out a fault repair time interval histogram according to the maintenance data.
Step 2: drawing a corresponding failure-free time interval probability distribution curve according to the failure-free time interval frequency histogram, and fitting the failure-free time interval probability distribution curve to obtain a first average failure rate lambda; and drawing a repair time interval probability distribution curve according to the fault repair time interval frequency histogram, and then fitting or directly calculating the average repair time repair rate mu.
In the embodiment, an algorithm for calculating the lambda value is determined according to the data type (reliability data or historical fault data),
(1) obtaining a first average fault rate lambda according to the screened reliability data
In this embodiment, a fixed number truncation life test method is adopted to fit a probability distribution curve of a time interval without a fault, so as to obtain a first average fault rate λ.
The fixed number truncated life test method comprises the following steps: performing reliability test on n repairable navigation materials in any screened repairable navigation materials, and ending the test at the time t 0; if r sailing materials have faults in the test, recording the failure time of each faulted sailing material as t1, t2, … and tr in sequence; the first average failure rate λ is then estimated as:
(2) and obtaining a first average fault rate lambda according to the screened historical fault data.
In this embodiment, a failure frequency histogram method is adopted to fit a failure-free time interval probability distribution curve to obtain a first average failure rate λ.
The failure frequency histogram method comprises the following steps: the method comprises the steps of dividing a statistical failure time range of a repairable material sample into k intervals (a0, a 1), (a1, a 2), … and (ak-1, ak) according to a group pitch of time delta t, drawing a histogram according to frequency numbers falling in each interval, drawing a cumulative frequency distribution graph by taking cumulative frequency as a vertical coordinate and time as a horizontal coordinate, fitting the cumulative frequency distribution graph to obtain a first average failure rate lambda, wherein the cumulative frequency represents the sum of probabilities of increasing the repairable material failure in the system along with the time.
In this embodiment, according to the maintenance data, in the case that the maintenance line or the maintenance technology of the finished product factory does not change greatly, the maintenance rate μ of a certain aviation material remains stable, and the calculation method is as follows:
in the formula, r is the number of repaired sailing materials in a time interval delta T, and K is the total number of fault sailing materials in the time interval.
And step 3: as shown in fig. 2, performing pearson inspection on the first average failure rate λ, and if the first average failure rate λ does not satisfy the pearson inspection, obtaining a second average failure rate λ by checking a reliability standard manual; if the first average failure rate λ satisfies the pearson test, the probability distribution of the no-failure time interval is a negative exponential distribution.
And 4, step 4: as shown in fig. 3, a chain of steady state life-out processes is depicted where the flight materials are of limited capacity and repaired and can be returned to the spare parts library; and establishing a closed equation set according to the stable state chain of the birth and death process.
(1) Chain of stable states for life-extinguishing process
If there are L pieces of flight materials in the whole system, the probability that the queuing system has k faulty flight materials at the time t is PkAnd then:
as time t approaches ∞ the queuing system will become stable and the "in" from each state equals the "out" at which point the probability P for each state iskWill not change over time. The state diagram of the birth and death process is shown in figure 3.
(2) Establishment of closed system of equations
Establishing a mathematical formula according to three conditions of an actual problem;
when k is more than or equal to 0 and less than or equal to n, the fault plane material in the system is less than the repair shop, namely all fault parts are repaired in the repair shop, and the fault plane material waiting to be repaired is not in the team, then Pk：
When n is<k is less than or equal to N, at the moment, the number of the failed aviation materials in the system is more than that of repair plants, the queuing phenomenon occurs, however, the spare parts can sufficiently replace the failed parts on the airplane, the airplane integrity of the fleet is 100 percent, and then P isk：
When N is present<k is less than or equal to L, the number of the failed aircraft materials in the system is greater than the number of spare parts, the aircraft availability of the fleet is lower than 100 percent, and P isk：
Combining the mathematical formulas of the three cases to obtain P0：
Number of failed parts in system Q:
airplane readiness rate of the fleet θ:
and 5: if the first average fault rate lambda meets the Pearson test, substituting the first average fault rate lambda, the maintenance rate mu, the number of airplanes and the requirement of the completeness rate into a closed equation set, and calculating to obtain an initial probability value P0, wherein P0 represents the probability that all the screened repairable aviation materials of a certain type have no fault; calculating the number of the repairable spare parts of the navigation material according to the P0 value
If the first average fault rate lambda does not meet the Pearson test, substituting the second average fault rate lambda, the maintenance rate mu, the number of airplanes and the requirement of the perfectness rate into a closed equation set, and calculating to obtain an initial probability value P0; and calculating the number of the repairable spare parts according to the P0 value.
Example 2
Specifically, the spare part prediction is carried out on the hydraulic pump aircraft material of a certain type of airplane, assuming that 31 airplanes are provided, the hydraulic pump repair shop has two units, the average repair rate mu is known and is 0.39 pieces/day, and if the completeness requirement value of the airplane in the fleet is 80%, the specific method comprises the following steps:
(1) counting a hydraulic historical fault database, and drawing a frequency histogram as shown in FIG. 4;
(2) the frequency histogram is converted into a frequency cumulative distribution graph, and curve fitting is performed, as shown in fig. 5, to obtain a cumulative distribution function f (t):
F(t)＝1-e-0.03t
(3) obtained by pearson test:
χ2＝17.452<χ0.99 2 (8)
the historical fault data of the hydraulic pump sailing timber is proved to accord with the exponential distribution, and the historical fault data can be substituted into a closed equation set formula for calculation to obtain:
p0＝0.0095,N＝2
q is 7.92 pieces, W is 10.56 days
The results show that at least 2 hydraulic pump flights are required as spare parts if the fleet aircraft health requirement is 80%. Further analysis can yield:
(a) when the fleet has no spare parts, the aircraft availability of the fleet is 76%;
(b) when a repair shop closes a repair line, the fleet aircraft availability will drop to 43%;
(c) when a repair line is added in a repair factory, the aircraft availability of the fleet can reach 89% under the condition that no spare parts exist, and the aircraft availability of the fleet can reach 100% under the condition that the fleet has 4 spare parts;
(d) if the maintenance efficiency of a repair shop is improved by 1 time, the crew availability can reach 95.1% under the condition of no spare parts, and the availability can reach 100% when two spare parts are provided.
The basic principle and the main features of the invention are explained above, and the expected value of the aircraft serviceability rate of a certain airplane team caused by the missing piece of the hydraulic pump is estimated through the examples.
Claims (10)
1. A method for predicting repairable aviation material spare parts based on a life-extinction process model is characterized by comprising the following steps:
step 1: screening out reliability data or historical fault data and maintenance data of any repairable materials needing spare part prediction, drawing out a fault-free time interval frequency histogram corresponding to the repairable materials according to the screened reliability data or historical fault data, and drawing out a fault repair time interval frequency histogram according to the maintenance data;
step 2: drawing a corresponding failure-free time interval probability distribution curve according to the failure-free time interval frequency histogram, and fitting the failure-free time interval probability distribution curve to obtain a first average failure rate lambda; drawing a repair time interval probability distribution curve according to the fault repair time interval frequency histogram, and then fitting or directly calculating the average repair time repair rate mu;
and step 3: carrying out Pearson inspection on the first average failure rate lambda, and obtaining a second average failure rate lambda by checking a reliability standard manual if the first average failure rate lambda does not meet the Pearson inspection;
and 4, step 4: drawing a life and death process stable state chain with limited capacity and the repaired sailing materials can return to a spare part library; establishing a closed equation set according to the stable state chain in the life-extinction process;
and 5: if the first average fault rate lambda meets the Pearson test, substituting the first average fault rate lambda, the maintenance rate mu, the number of airplanes and the requirement of the completeness rate into a closed equation set, and calculating to obtain an initial probability value P0, wherein P0 represents the probability that all the screened repairable aviation materials of a certain type have no fault; calculating the number of the repairable spare parts according to the P0 value;
if the first average fault rate lambda does not meet the Pearson test, substituting the second average fault rate lambda, the maintenance rate mu, the number of airplanes and the requirement of the perfectness rate into a closed equation set, and calculating to obtain an initial probability value P0; and calculating the number of the repairable spare parts according to the P0 value.
2. The repairable marine spare part predicting method according to claim 1, further comprising cleaning the screened reliability data or historical failure data, and the service data to remove redundant invalid data.
3. The method for predicting a repairable marine material spare part according to claim 1, wherein the first average failure rate λ is obtained by fitting a failure-free time interval probability distribution curve by a constant number truncation life test method according to the screened reliability data.
4. The repairable marine material spare part predicting method according to claim 3, wherein the constant number tailgating life test method includes:
performing reliability test on n repairable navigation materials in any screened repairable navigation materials, and ending the test at the time t 0; if r sailing materials have faults in the test, recording the failure time of each faulted sailing material as t1, t2, … and tr in sequence; the first average failure rate λ is then estimated as:
5. the method of predicting a repairable marine material spare part according to claim 4, wherein the probability distribution of the non-failure time interval is a negative exponential distribution if the first average failure rate λ satisfies the pearson test.
6. The method for predicting the repairable marine craft spare part according to claim 1, wherein the first average failure rate λ is obtained by fitting a failure-free time interval probability distribution curve by using a failure frequency histogram method according to the screened historical failure data.
7. The repairable marine material spare part prediction method of claim 6, wherein the failure frequency histogram method comprises:
dividing a statistical failure time range of the repairable aviation material sample into k intervals at a group interval of time delta t, and then drawing a histogram according to frequency numbers falling in each interval; then, taking the accumulated frequency as a vertical coordinate and the time as a horizontal coordinate to make an accumulated frequency distribution graph; finally, fitting the cumulative frequency distribution curve to obtain a first average failure rate lambda; the cumulative frequency represents the sum of the probabilities of the reworkable materials failing over time in the system.
8. The method of predicting a repairable marine material spare part of claim 6, wherein the probability distribution of the non-failure time interval is a negative exponential distribution if the first average failure rate λ satisfies the pearson test.
9. The method of claim 1, wherein the repair rate μ for a particular type of aircraft is stable, and the average repair time repair rate μ is calculated by the formula:
in the formula, r is the number of repaired sailing materials in a time interval delta T, and K is the total number of fault sailing materials in the time interval.
10. The method of predicting a repairable marine material spare part according to claim 1, wherein the formula of the closed system of equations is:
wherein m: the number of airplanes owned by the army is in units of frames; n: the number of repair shops; n: the number of the repairable spare parts of the aviation material is in units of parts;
l: the total number of the aircraft materials in the whole system, i.e., L is m + N (if each aircraft has 3 aircraft materials, L is 3m + N), and the unit is one;
ρ: service strength, which is the ratio of lambda to mu; q: the number of failed pieces in the system; θ: airplane readiness of the fleet.
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| 刘任洋等: "多级可修备件库存的生灭过程建模与优化", 《国防科技大学学报》 * |
| 柴志君等: "舰载机着舰引导装备体系系统级备件保障", 《兵工自动化》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113705886A (en) * | 2021-08-26 | 2021-11-26 | 成都飞机工业（集团）有限责任公司 | Dynamic MTBF (mean time between failures) based aviation material spare part demand analysis and prediction method |
| CN113705886B (en) * | 2021-08-26 | 2023-10-10 | 成都飞机工业（集团）有限责任公司 | Method for analyzing and predicting demands of aviation material spare parts based on dynamic MTBF |
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|---|---|
| CN112528510B (en) | 2022-05-27 |
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