CN106777819A - A kind of Normal Type has the computational methods of part replacement cycle in longevity - Google Patents

Abstract

The invention discloses the computational methods that a kind of Normal Type has the part replacement cycle in longevity, this computational methods mainly comprises the following steps：Calculate to longevity replacement probability, calculating uses availability, and utilizes using Calculation of Availability spare parts demand amount, wherein calculate use in availability, including following two important core procedures：Step 1)：Having the working life of longevity part to the Normal Type, to carry out normal state equivalent；Step 2)：According to the step 1) the normal state equivalent parameters obtained calculates and uses availability, by the use Calculation of Availability spare parts demand amount.According to the computational methods that the present invention is realized, the computational methods not made a distinction to the life-span for having longevity part and working life in the prior art are different from, the accuracy of result of calculation can be significantly increased.

Description

A kind of Normal Type has the computational methods of part replacement cycle in longevity

Technical field

The invention belongs to there is longevity part to change evaluation areas, it is related to a kind of Normal Type there are the computational methods of part replacement cycle in longevity.

Background technology

It is to define preventative maintenance to change or scrap the part in time limit and it is anticipated that the part of service life to have longevity part, also known as Limit longevity part.In aviation field, aircraft spare parts are generally divided into initial spares, replenished spares and have longevity spare part.Can be had using there is longevity part Effect ground trouble saving occurs, therefore the use problem for especially having longevity part in aviation field has great practice significance.Change week Phase is an important parameter for having longevity part, takes which kind of method to obtain the scientific and rational replacement cycle, at present domestic correlation Research is few.

The life-span and working life for having longevity part are two different concepts, and the life-span is not consider the replacement cycle, the unit from Start working until what is hindered for some reason and scrap dies naturally.Working life considers the influence of replacement cycle, it be In replacement cycle, unit from start working until hinder for some reason and scrap or because reach the time limit change this for a period of time, work Make the no more than replacement cycle in life-span.

The characteristics of having longevity part maximum is to try hard to trouble saving, is tieed up after before failure occurs rather than failure Repair, this equipment very serious to consequence after the generation of some failures is especially meaningful, such as the key components and parts on aircraft.

When it is determined that there is the replacement cycle of longevity part, two problems can be considered：

1) longevity part works the probability normally changed to the prescribed time-limit (i.e. replacement cycle) (hereinafter referred to as to longevity replacing generally Rate) index request can be met

2) in the case where Combat readiness index request is met, spare part can as few as possible be configured

For problem 1), having longevity part to work, to be changed to the time limit be its optimal working condition, is hindered for some reason and replacing is then Undesirable, consequence may be very serious.Obviously, shorter when the replacement cycle, the possibility broken down in the time limit is lower, arrives Longevity replacement probability is higher.

For problem 2), when the replacement cycle more in short-term, it is possible to need more spare parts.Problem 2) from spare parts purchasing expense Angle describe select certain replacement cycle financial cost.Using availability be the accumulated operating time with the support mission time it Between ratio, be a kind of common index for reflecting Military Equipment Operational Readiness, be also that the top layer of the leading spare parts support work of the military refers to One of mark.

Thus, it is existing at present under the background more than, it is especially desirable to propose a kind of method calculated the replacement cycle Solution in the middle of technology is exactly come to problem 1 using empirical value) and problem 2) parameter calculate, in such case Under, (reasonability is primarily referred to as the balance of cost absorbing and benefit, and wherein cost is embodied in spare part to cause the reasonability of replacement cycle Buying expenses, income is embodied in longevity replacement probability) be difficult to ensure that, it is quantitative to calculate substantially impossible.

The content of the invention

For the disadvantages described above or Improvement requirement of prior art, there is the part replacement cycle in longevity the invention provides a kind of Normal Type Computational methods, it is characterised in that the method comprises the following steps

Step one：Calculate to longevity replacement probability R (T_rep)：

Wherein, T_repTo treat the selected replacement cycle, μ, σ have part longevity, Parameters of Normal Distribution life-span for described；π is pi Constant；

Step 2：Calculating uses availability, and using using Calculation of Availability spare parts demand amount, the wherein step includes Following sub-step：

Step 1)：Having the working life of longevity part to the Normal Type, to carry out normal state equivalent, including following sub-step：

Step 1.1)：Equal difference array [x of the selection comprising m numbers in the range of (0, μ+4 σ)₁,…,x_m], 1≤i≤m；

Step 1.2)：Traversal calculates f₁(x_i),

Step 1.3)：Traversal is calculatedTo 100 × f₂(x_i) carry out round after obtain N₂(x_i)；

Step 1.4)：In the equal difference array [x₁,…,x_m] in find closest to T_repSeveral x_r, i.e. x_r≤T_repAnd x_r+1 ＞ T_rep；

Step 1.5)：By N₂(x_i) obtain array [N₃(x₁),…N₃(x_r)],

Step 1.6)：The generation equal difference array [μ in scope (0, μ)₁,…,μ_n], in scope (0,0.4 μ)

Generation equal difference array [σ₁,…,σ_q]；

Step 1.7)：In the way of following traversal, matrix of the generation comprising n × q rows

Wherein

Step 1.8)：To the weight coefficient group [P1 of the matrix₁,…,P1_n·_q] initialized, make

Step 1.9)：To the weight coefficient group [P1₁,…,P1_n·_q] it is circulated renewal, sub-step specific as follows：

Step 1.9.1)：Make i₁=1, wherein 1≤i₁≤r；

Step 1.9.2)：Make x₂=x_i1, i₂=1, wherein 1≤i₂≤n·q；

Step 1.9.3)：To g_i2Traversal calculating is carried out, is obtained

Step 1.9.4)：Update i₂, make i₂=i₂+ 1, if i₂≤ nq, then perform 1.9.3), otherwise perform 1.9.5)；

Step 1.9.5)：Update weight coefficient group [P1₁,…,P1_n·_q], order

Step 1.9.6)：Update i₁, make i₁=i₁+1；If i₁≤ r, then perform 1.9.2), otherwise perform 1.10)；

Step 1.10) according to the weight coefficient group [P1 after the renewal₁,…,P1_n·_q], calculate it is equivalent go out normal state ginseng Number μ ', σ '：

Step 2)：According to the step 1) the normal state equivalent parameters obtained calculates and uses availability, by institute

State using Calculation of Availability spare parts demand amount：

It is calculated as follows and uses availability P_a, set the threshold value of the use availability so that P_aMore than or equal to the threshold The Z values of value are the spare parts demand amount for calculating；

Wherein, b is the spare parts demand quantitative change amount, T_wIt it is the support mission time, the support mission time refers to described standby Expected accumulated operating time of the part when a certain task is completed；

Step 3：The selection replacement cycle

Index request is not less than to longevity replacement probability using what the step one was obtained, according to the step 2) obtain most Few spare parts demand amount, treats to determine the replacement cycle in the selected replacement cycle described.

In general, by the contemplated above technical scheme of the present invention compared with prior art, algorithm for design is quantified Calculate to longevity replacement probability and spare part and use availability two indices, the two indices more than select the replacement cycle；

Wherein to the application reliability degree calculation method for relating generally to of longevity replacement probability, because to the mathematics of longevity replacement probability Essence is exactly reliability, and this method application is come actually also to have reached accurate calculating effect；

Wherein spare part mainly employs that to carry out normal state to the working life of spare part equivalent using the computational methods of availability, The life-span and working life that have longevity part are not made a distinction in the prior art, more be may not realize that life-span distribution and worked Life-span distribution can be what is differed, also just not allow to be readily conceivable that that normal state is carried out to working life is equivalent, and the present invention is contemplated and adopted Calculated with the equivalent method of normal state and use availability, see that result of calculation accuracy is improved in implementation.

Brief description of the drawings

Fig. 1 is the schematic flow sheet of the computational methods that the Normal Type realized according to the present invention has the part replacement cycle in longevity.

Specific embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples The present invention is further elaborated.It should be appreciated that instantiation described herein is only used to explain the present invention, not For limiting the present invention.As long as additionally, technical characteristic involved in invention described below each implementation method that Conflict is not constituted between this can be just mutually combined.

Specifically, there are the computational methods of the replacement cycle of longevity part the invention provides a kind of Normal Type, normally use Mechanical parts life-span general Normal Distribution, such as collector ring, gear-box, decelerator.The analysis pair that emphasis is directed to likes the life-span Normal Distribution has longevity part, is designated as N (μ, σ²), the replacement cycle is designated as T_rep, the support mission time is designated as T_w, the replacement cycle is Refer to time of the spare part from starting working to being replaced for the replacement cycle, the replacing reaches one not because failure because of it The working time of individual regulation；The support mission time refers to just expected accumulated operating time of the spare part when a certain task is completed.

Reliability is a conventional spare part reliability index, and it is defined as：Spare part under conditions of regulation and regulation In time t, the probability of predetermined function is completed, represented with R (t).From definition：R (t)=P (T>T), wherein T refers to the spare part longevity Life.For life-span T Normal Distribution N (μ, σ²) spare part for, to longevity replacement probability be equal in replacement cycle T_repInterior reliability Work, trouble-proof probability R (T_rep), such as formula (1)：

The use of the essence of Calculation of Availability is a guarantee recruitment evaluation problem, i.e.,：Rule are distributed when the life-span of known units When rule, replacement cycle, spare part quantity and support mission cycle, calculating can be quantified and use availability, once can quantify exactly Calculating uses availability, it is possible to calculate the spare parts demand amount for meeting spare parts support index request.

The alternate maintenance for having longevity part has two kinds：Changed to the longevity and failure replacement, the former refers to have longevity part in work to its rule Periodically limit has not occurred the replacing that failure needs to carry out preventative maintenance and carries out, and the latter refers to have longevity part not work to the regulation phase The replacing that limit is carried out with regard to having broken down.If only being changed to the longevity, as long as preparingPart spare part just expire by energy 100% Sufficient spare parts demand.But there is longevity part to be likely to occur failure in the specified period, therefore only preparePart can not reliably expire Sufficient spare parts demand.This has caused that longevity part spare parts support recruitment evaluation works becomes complexity.

Having being changed to the longevity for longevity part means its working life this moment stops abruptly in the replacement cycle.This and normal state are divided " concentration " failure (99.73% normal variate falls in the range of (μ -3 σ, μ+3 σ)) of cloth has similarity in phenomenon, can be with Trial carrys out approximate description with normal distribution the distribution of longevity part working life, recycles Normal Type spare parts support computational methods to count Calculation uses availability.

As shown in figure 1, the computational methods of the replacement cycle realized according to the present invention, mainly comprise the following steps：

First, calculate to longevity replacement probability：

2nd, calculate and be made up of following two parts using the method for availability：

1) to carry out normal state to the working life for having longevity part equivalent

Comprise the following steps that：

1.1) equal difference array [x of the selection comprising m numbers in the range of (0, μ+4 σ)₁,…,x_m], it is proposed thatx_mThe σ of≤μ+4 and1≤i≤m；I.e. more than above-mentioned 99.73% Selected within the scope of security probability, certainly, the selection of equal difference not considered critical as above, equal difference spacing m suggestions are not small In 20；

1.2) traversal calculates f₁(x_i),Obtain x_iThe frequency of appearance；

1.3) traversal is calculatedTo 100 × f₂(x_i) carry out round after obtain N₂ (x_i), as x_iThe number of times of appearance；

1.4) in array [x₁,…,x_m] in find closest to T_repSeveral x_r, i.e. x_r≤T_repAnd x_r+1＞ T_rep；

1.5) by N₂(x_i) obtain array [N₃(x₁),…N₃(x_r)],The parameter is anti- Reflect x_jThe number of times of appearance；I.e. equivalent to working life x_jThe number of times of appearance is life-span x_iThe a subset of the number of times of appearance；

1.6) the generation equal difference array [μ in scope (0, μ)₁,…,μ_n], it is proposed that

μ_n≤ μ and μ_n+ d μ ＞ μ；The selection of equal difference not considered critical as above, Equal difference spacing n suggestions are not less than 10；

The generation equal difference array [σ in scope (0,0.4 μ)₁,…,σ_q], it is proposed that σ_q≤ 0.4 μ and σ_qThe μ of+d σ ＞ 0.4；The selection of equal difference not considered critical as above, equal difference spacing q suggestion be not less than 50；

1.7) in the way of following traversal, matrix of the generation comprising n × q rows

Above-mentioned matrix is wherein obtained using following program

Make k=1

1.8) to weight coefficient group [P1₁,…,P1_n·_q] initialized, make

1.9) to weight coefficient group [P1₁,…,P1_n·_q] renewal is circulated, it is specific as follows：

1.9.1 i) is made₁=1, wherein 1≤i₁≤r；

1.9.2) makei₂=1, wherein 1≤i₂≤n·q；

1.9.3) to i₂Traversal calculating is carried out, is obtained

1.9.4 i) is updated₂, make i₂=i₂+ 1, if i₂≤ nq, then perform 1.9.3), otherwise perform 1.9.5)；

1.9.5 weight coefficient group [P1) is updated₁,…,P1_n·_q], order

1.9.6 i) is updated₁, make i₁=i₁+1；If i₁≤ r, then perform 1.9.2), otherwise perform 1.10).

1.10) according to weight coefficient group [P1₁,…,P1_n·_q], calculate it is equivalent go out normal state parameter μ₁、σ₁：

2) according to use Calculation of Availability spare parts demand amount

When b spare part is configured, can be calculated with formula (2) and use availability P_a.Spare part is calculated to can be used to calculate spare parts demand Amount：Make s increases one by one since 0, until certain Z value so that P_aThe use availability index of >=regulation, the Z values are and are asked for perfection Part demand.

It is assumed that：Life-span T Normal Distribution N (μ, the σ of certain unit²), it is stipulated that its replacement cycle is T_rep, during support mission Between be T_w, it is desirable to index request must not be less than using availability, spare parts demand amount is designated as Z.

3rd, the replacement cycle is selected

Index request is not less than to longevity replacement probability using what step one was obtained, under the conditions of this is met, according to step 2) the minimum spare parts demand amount for obtaining then can determine that the replacement cycle.

It is assumed that the replacement cycle of candidate is 100,200,300,400,500, it is desirable to must not be less than 0.8 to longevity replacement probability, According to step one obtain it is corresponding be respectively 0.95,0.9,0.86,0.78,0.65 to longevity replacement probability, find to reduce and change week Phase scope is 100,200,300, and according to step 2) to obtain corresponding spare parts demand amount be 5,4,3, this when of selection 300 is made It is the replacement cycle for determining.

In order to verify the validity of the above method, the spare parts support simulation model for having longevity part as follows is set up, carry out emulation and test Card.The simulation model simulates a support mission process.The idiographic flow of simulation model is as follows：

1) life-span is simulated

Produce 1+Z random number t_i, t_iNormal Distribution N (μ, σ²)；

2) working life is simulated

To this 1+Z random number t_iTraversal amendment is carried out, is obtainedModification method such as following formula：

3) analog result is exported

Analog result has 2：Use availability simP_aWith the normal ratio simR changed to the longevity in the guarantee phase；SimR determines Justice is：Within the support mission phase, the ratio between the number of times and total replacing number of times of simulation of simulation to longevity replacing.

CalculateThe use availability degree simP for then simulating_aSuch as following formula:

After the simulation model is run multiple times, to simP_aCounted, its averageAs use the mould of availability Intend result, simR is counted, its averageAs to longevity replacement probability.

The parameter of example 1：Certain spare part life-span Normal Distribution N (μ, σ²), μ=600, σ=130, support mission time It is T_w=2000h, it is desirable to be not less than 0.95, replacement cycle T using availability_repSpan be 200~500h.Emulation knot Fruit and the result such as table 1 of context of methods.

The simulation result of the example 1 of table 1 and the result of context of methods

If it is required that be not less than 0.85 to longevity replacement probability, as known from Table 1：Selected 450h is above-mentioned time as the replacement cycle Preferable selection in option, spare parts demand amount now is 4.

The parameter of example 2：Certain cell life Normal Distribution N (μ, σ²), μ=600, σ=230, remaining parameter is with calculation Example 1.The result of simulation result and context of methods such as table 2.The cell life root variances sigma of example 2 is larger with respect to for its mean μ.

The simulation result of the example 2 of table 2 and the result of context of methods

If it is required that be not less than 0.85 to longevity replacement probability, as known from Table 2：Selected 350h is above-mentioned time as the replacement cycle Preferable selection in option, spare parts demand amount now is 5.

Tables 1 and 2 represents the smaller and larger both of these case of root variance of cell life respectively.A large amount of simulating, verifying knots Fruit shows：Result (spare parts demand amount, using availability and to longevity replacement probability) and the emulation being calculated using context of methods Result is all very close to.Context of methods can make related personnel accurately understand the spare parts purchasing cost and safety of various replacement cycles In the case of income, auxiliary determines the replacement cycle for having longevity part.

Herein by life-span Normal Distribution have longevity part as a example by, " concentration " failure and convolution using normal distribution can add Characteristic, the working life that carrying out approximate expression with normal distribution has longevity part is distributed, by quantum chemical method each replacement cycle corresponding peace Full income and spare parts cost, give a kind of method for aiding in and determining to have the part replacement cycle in longevity.Simulation results show：The party Method result can accurately reflect the assessment for having the part replacement cycle in longevity to Normal Type.

As it will be easily appreciated by one skilled in the art that the foregoing is only presently preferred embodiments of the present invention, it is not used to The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles in the present invention etc., all should include Within protection scope of the present invention.

Claims (1)

1. a kind of Normal Type has the computational methods of part replacement cycle in longevity, it is characterised in that the method comprises the following steps

Step one：Calculate to longevity replacement probability R (T_rep)：

$R\left(T_{rep}\right)=1-\frac{1}{\mathrm{\σ}\sqrt{2\mathrm{\π}}}{\∫}_{-\mathrm{\∞}}^{T_{rep}}{e}^{\frac{-{(x-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}dx;$

Wherein, T_repTo treat the selected replacement cycle, μ, σ have part longevity, Parameters of Normal Distribution life-span for described；π is pi constant；

Step 2：Calculating uses availability, and using Calculation of Availability spare parts demand amount is used, the wherein step includes as follows Sub-step：

Step 1)：Having the working life of longevity part to the Normal Type, to carry out normal state equivalent, including following sub-step：

Step 1.1)：Equal difference array [x of the selection comprising m numbers in the range of (0, μ+4 σ)₁,…,x_m], 1≤i≤m；

Step 1.2)：Traversal calculates f₁(x_i),

Step 1.3)：Traversal is calculatedTo 100 × f₂(x_i) carry out round after obtain N₂ (x_i)；

Step 1.4)：In the equal difference array [x₁,…,x_m] in find closest to T_repSeveral x_r, i.e. x_r≤T_repAnd x_r+1＞ T_rep；

Step 1.5)：By N₂(x_i) obtain array [N₃(x₁),…N₃(x_r)],Step 1.6)：The generation equal difference array [μ in scope (0, μ)₁,…,μ_n], the generation equal difference array [σ in scope (0,0.4 μ)₁,…, σ_q]；

Step 1.7)：In the way of following traversal, matrix of the generation comprising n × q rows

Wherein

Step 1.8)：To the weight coefficient group [P1 of the matrix₁,…,P1_n·q] initialized, make

$P{1}_s=\frac{1}{n\·q},1\≤s\≤n\·q;$

Step 1.9)：To the weight coefficient group [P1₁,…,P1_n·q] it is circulated renewal, sub-step specific as follows：

Step 1.9.1)：Make i₁=1, wherein 1≤i₁≤r；

Step 1.9.2)：Orderi₂=1, wherein 1≤i₂≤n·q；

Step 1.9.3)：It is rightTraversal calculating is carried out, is obtained

Step 1.9.4)：Update i₂, make i₂=i₂+ 1, if i₂≤ nq, then perform 1.9.3), otherwise perform 1.9.5)；

Step 1.9.5)：Update weight coefficient group [P1₁,…,P1_n·q], orderStep 1.9.6)：Update i₁, make i₁=i₁+1；If i₁≤ r, then perform 1.9.2), otherwise perform 1.10)；

Step 1.10) according to the weight coefficient group [P1 after the renewal₁,…,P1_n·q], calculate it is equivalent go out normal state parameter μ ', σ′：

Step 2)：According to the step 1) the normal state equivalent parameters obtained calculates and uses availability, by the use availability meter Calculate spare parts demand amount：

It is calculated as follows and uses availability P_a, set the threshold value of the use availability so that P_aMore than or equal to the threshold value Z values are the spare parts demand amount for calculating；

$R\left(x\right)=1-\frac{1}{{\mathrm{\σ}}^{\′}\sqrt{2\mathrm{\π}(1+b)}}{\∫}_{-\mathrm{\∞}}^x{e}^{\frac{-{(y-(1+b\left){\mathrm{\μ}}^{\′}\right)}^2}{2(1+b){\mathrm{\σ}}^{\′2}}}dy$

$P_a=\frac{{\∫}_0^{T_w}R\left(x\right)dx}{T_w}$

Wherein, b is the spare parts demand quantitative change amount, T_wIt it is the support mission time, the support mission time refers to the spare part complete Into expected accumulated operating time during a certain task；

Step 3：The selection replacement cycle

Using the step one obtain be not less than index request to longevity replacement probability, according to the step 2) obtain it is minimum standby Part demand, treats to determine the replacement cycle in the selected replacement cycle described.