CN1858753A - Simulation technology based on after repair and repair time product effectiveness - Google Patents

Abstract

This invention discloses an emulation technology based on post maintenance and the validity of products in maintenance including: a, structuring a maintenance vector or a sequence, b, structuring a fault frequency sequence, c, structuring a repairing sequence, d, computing the elements of the fault frequency sequence and reparing sequence, e, computing the validity of products and total fault frequency, which makes up some shortcomings of the Markov and Monte-Carlo method and is used in researching the influence of maintenance mode and time to product reliabilities.

Description

Based on correction maintenance and servicing time validity of products emulation technology

Technical field

The present invention relates to a kind of Reliablility simulation technology, particularly a kind of based on correction maintenance and servicing time validity of products emulation technology.

Technical background

Here product refers to mechanical component, parts, mechanical subsystem or mechanical system, as parts in production equipment, weaponry, aerospace appts, the nuclear power generating equipment or equipment itself.

Product in use all will break down usually, and the user takes various maintenance modes according to factors such as the importance of system, its usage economy, securities of system, waits the validity of the system of assurance as correction maintenance, preventive maintenance, state monitor maintenance.

Validity is meant under the prerequisite that certain external resource guarantees, product is under defined terms and be in the ability of the functional status that can put rules into practice in the moment of regulation or the time interval.It is the concentrated expression of product reliability, maintainability and maintenance support.Validity also is called serviceability.

Maintenance plays crucial effects to the reliability of production equipment, weaponry system etc., shortens servicing time, improves repair quality and just means the reliability that improves production equipment, weaponry system

Correction maintenance is meant after product breaks down and just it is repaired, and recovers a kind of maintenance mode of its function.Break down the back by maintenance can restore funcitons product be called as repairable item in the reliability engineering field, most products all belong to repairable item in production practices.

The Markov method is adopted in the analysis of repairable item reliability theory usually, and the Monte-Carlo method is more widely used because of it is practical in engineering practice.See document: " Monte Carlo method in the systems reliability analysis " that Xiao Gang, Li Tian girder write, Beijing: Science Press, 2003; JoseE.Ramirez-Marquez, " the A Monte-Carlo simulation approach forapproximating multi-state two-terminal reliability " of David W.Coit, Reliability Engineering andSystem Safety 87 (2005) 253-264; " the reliability engineering principle " that Guo Yongji writes, publishing house of Tsing-Hua University, Springer Verlag publishing house, 2002 and Bertsche, B.; Lechner, " the Zuverl  ssigkeitim Maschinenbau " of G., Springer-Verlag 1990.

When life-span of product and servicing time obeys index distribution, reliability of products can adopt the Markov method to describe, and can resolve or numerical solution.The limitation of this method is: 1) be subjected to the life of product distribution pattern and servicing time distribution pattern limit, life-span of engineering goods distributes disobeys exponential distribution usually, and mostly be to obey Weibull distribution.When 2) analyzing the system reliability of being made up of product on the basis of product, if only consider the product two states, Markov state transition equation number is counted n with the composition system product and is become 2 ⁿRelation, " blast " takes place with the increase of product number in calculated amount, can't accept to such an extent as to calculated amount is big.Even static system, system's bottom event has only two states, adopts inclusion-exclusion principle, and system availability calculates need carry out 2 ⁵⁰Inferior summation; Move computing machine more than 1,000,000,000 times with per second, the time of cost was also taken more than 13 days.3) the Markov method needs the transition probability between each state of known product, and this almost is impossible in practice.

The Monte-Carlo method is to propose in the nuclear physics research field in 20th century, has stronger practicality, also obtains using more widely in the Reliablility simulation field.The great advantage of this method is that adaptability is strong, not limited by assumed condition, deficiency is: 1) though the simulation calculation amount is littler than Markov method, raising that requires along with computational accuracy and the increase of forming the increase calculated amount of system product number also are very important.Along with the increase of calculated amount, the necessary pseudo random number of Monte-Carlo method shows periodic problem simultaneously.2) result with the emulation of Monte-Carlo method has randomness.In fact the reliability index of Monte-Carlo method emulation is the reliability index of some samples of parent, be of the deduction of the reliability index of sample to parent, simulation result is unrepeatable under identical simulated environment, and simulation result has randomness.

Foundation based on correction maintenance and servicing time the validity of products mathematical model be the key that the repairable item Quantitative Reliability is analyzed, for improving the repairable item design, rationally using product and maintenance and renewal decision-making that theoretical foundation is provided.The present invention will propose a kind of simple, effective, the emulation mode that between the description correction maintenance that can apply in the engineering practice and servicing time and validity of products, concerns, and this method will remedy some deficiency of above-mentioned two kinds of methods to a certain extent.

Summary of the invention

When product bug interval time and servicing time smaller (＜60), can not ignore the influence of validity of products servicing time, describes servicing time the influence of validity of products to be used guide product and keeped in repair just to demonstrate necessity.The purpose of this invention is to provide a kind of based on correction maintenance and servicing time repairable item validity model and emulation mode, be described under the correction maintenance mode with different servicing time distribution situation under the validity of product with the Changing Pattern of service time, for product reliability designs and product uses maintenance schedule and ensures that decision-making provides theoretical foundation.

For realizing this purpose the technical solution used in the present invention, comprise the following step of carrying out by computer system:

1, step a

1) makes up maintenance vector

The product that breaks down will be keeped in repair, and the function by maintenance product will at a time be restored with certain probability.Product is called servicing time from entering maintenance up to function used time that is restored.Be subjected to the influence of multiple uncertain factor the servicing time of product, so it is a stochastic variable, obeys certain distribution, can describe with the stochastic variable distribution function servicing time of product in other words, this function also is called the maintainability function, is designated as M (t).The maintainability function is the maintainability density function to the derived function of time, is designated as m (t).The maintenance vector of product makes up as follows:

W＝(w ₁，w ₂，…w _i，…w _m)

$w_i={\∫}_{(i-1)\mathrm{\Δt}}^{\mathrm{i\Δt}}m\left(t\right)\mathrm{dt}+\frac{{\∫}_{-\∞}^{0}m\left(t\right)\mathrm{dt}+{\∫}_{\mathrm{m\Δt}}^{\∞}m\left(t\right)\mathrm{dt}}{m}$

In the formula:

The W-maintenance vector;

w _iI element of-maintenance vector;

M (t)-servicing time distribution probability density function;

The number of elements that the m-maintenance vector is comprised;

Between Δ t-time microcell;

M determines that should satisfy following formula requires:

${\∫}_{m\×\mathrm{\Δt}}^{\∞}m\left(t\right)\mathrm{dt}=P(t>{\mathrm{\τ}}_{\max })\≤\mathrm{\ϵ}$

In the formula:

ε-given decimal is usually less than 0.00001;

τ _Max-maximum servicing time;

τ _max＝m×Δt；

Definite principle of Δ t is that Δ t is the smaller the better as far as possible between microcell, can artificially determine by principle, also can be calculated as follows:

$\mathrm{\Δt}=\frac{t_{\max }}{n}$

In the formula: the n-interval number, n gets positive integer, usually n＞60; t _MaxThe product maximum life;

The maintenance vector that makes up by following formula has been avoided the density function independent variable to get negative value and has been got infinitely-great problem.After maintenance vector has been described product failure, with the probability that certain probability obtains repairing, the product maintenance process has been described between a certain microcell through maintenance.

2) make up the maintenance sequence

In emulation, also available maintenance sequence replaces maintenance vector, and the method that makes up maintenance sequence and structure maintenance vector has difference slightly, and the maintenance sequence is more accurate than maintenance vector in emulation, but calculated amount wants big, and its construction method is as follows:

V＝v ₁，v ₂，…v _i，…＝{v _i}

$v_i={\∫}_{(i-1)\mathrm{\Δt}}^{\mathrm{i\Δt}}m\left(t\right)\mathrm{dt}+\frac{{\∫}_{-\∞}^{0}m\left(t\right)\mathrm{dt}}{m}$

In the formula:

V-keeps in repair sequence;

v _iI element of-maintenance sequence;

After the maintenance sequence has equally been described product failure with maintenance vector, with the probability that certain probability obtains repairing, the product maintenance process has been described between a certain microcell through maintenance.

2, the failure-frequency sequence among the step b makes up as follows

The product that at a time comes into operation will break down in the probabilistic law of fault vectors defined is between some microcells, the product that breaks down will be keeped in repair, again come into operation after the reparation, the probability of malfunction of product in use between each microcell constituted the failure-frequency sequence, the failure-frequency sequence description course of work, probability of malfunction and the fault moment of product under repair.

$g^w=g_1^w,g_2^w,\·\·\·,g_i^w,\·\·\·=\left\{g_i^w\right\}$

Wherein:

g ^w-be illustrated in the failure-frequency sequence of product under the repair;

g _i ^w-be illustrated in the probability that product breaks down under the repair between i microcell, in order to distinguish the failure-frequency of also being called product mutually with the probability of malfunction of non-repairable item, the computing method of its value are seen steps d;

3, the repairing sequence among the step c makes up as follows

The product that at a time breaks down will be keeped in repair, and obtains repairing in the probabilistic law of maintenance vector regulation is between a certain microcell, and comes into operation.The product in use repairability probability between each microcell has constituted repairing sequence, and maintenance process, repairability probability and reparation that repairing sequence has been described product are constantly

q＝q ₀，q ₁，q ₂，…，q _i，…＝{q _i}

Wherein:

Q-represents repairing sequence

q _iI element of-repairing sequence, the computing method of its value are seen steps d.

When product t=0 service time, q ₀=1, represent the overall of the product that comes into operation, there are not the product of reparation, q this moment ₁, q ₂..., q _i=0.

4, steps d

1) element of failure-frequency sequence calculates as follows:

A) when emulation interval number i≤n

$g_i^w=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{q}_{i-j}{g}_j$

B) when emulation interval number i＞n

$g_i^w=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{q}_{i-j}{g}_j$

In the formula:

g _j-be j element of product bug vector;

N-is a product bug element vector prime number;

The element of probability of malfunction vector G is calculated as follows:

$g_j=F(\mathrm{\Δt}\·i)-F\left[\mathrm{\Δt}(i-1)\right]+\frac{\mathrm{\δ}+F\left(0\right)}{n}$

In the formula:

J-represents between j microcell, 1≤j≤n;

g _i-be illustrated in the probability that breaks down between j microcell, also be j element of fault vector simultaneously;

G＝(g ₁，g ₂，g ₃，……g _j，……g _n)

2) element of repairing sequence calculates as follows:

A) when emulation interval number i≤m;

$q_i=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_j$

B) when emulation interval number i＞m;

$q_i=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_j$

Perhaps utilize the maintenance sequence to calculate:

$q_i=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_{i-j+1}{v}_j$

5, step e

1) calculating of the availability of product

Because the effect of servicing time, product not necessarily obtain repairing between this microcell after losing efficacy between a certain microcell, thus product in this is interval except the product of new inefficacy is arranged, repairing product in addition.Therefore, the validity of product should be calculated as follows:

$A_i=1-\underset{j=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{k=j+1}{\overset{m}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_k$

A _iThe availability of-product between i microcell;

Perhaps with distribution function calculating servicing time:

$A_i=1-\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_j[1-M\{(i-j)\mathrm{\Δt}\left\}\right]$

Wherein:

M (t)-element distribution probability servicing time function;

Following formula has been described the availability of product between i microcell, and it depends on the distribution situation of inherent reliability, maintenance mode and the servicing time of product.

2) the total failare frequency of product is calculated as follows:

$z_i=\underset{j=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{k=j+1}{\overset{m}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_k$

In the formula:

z _i-product is in the i * Δ t moment failure probability summation;

Perhaps with distribution function calculating servicing time:

$z_i=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_j[1-M\{(i-j)\mathrm{\Δt}\left\}\right]$

Following formula has been described the products that all lost efficacy before between i microcell, the probability that also is not repaired heretofore, the probability sum that should be understood to be in t=i * Δ t whole before constantly products that the lost efficacy probability that is repaired and the products that just lost efficacy in this interval after the i interval deducts the probability that all over products is repaired in this interval again.

Utilize total failure frequency expression formula of product and availability expression formula can describe the Changing Pattern of product that different life-spans distribute product availability and failure-frequency under different servicing time distribution situation, provide effective analytical approach and instrument to the influence of product (product) reliability for analyzing correction maintenance mode and different servicing times of distributions.

The invention has the beneficial effects as follows: this emulation mode not distributed by life of product and servicing time distributed model limit.No matter the reliability index that is all available this method artificial product of index distribution, normal distribution, lognormal distribution or Weibull distribution under correction maintenance and different maintenance time conditions that the life-span of product distributes is rule over time.This emulation mode may be used on system reliability emulation equally.The simulation result of this emulation mode has uniqueness.Simulation result can repetition under identical simulated conditions, and simulation result is the reliability index approximate value of product parent, is different from the Mote-Carlo method, does not need sampling, and precision and simulation times have nothing to do.The simulation accuracy of this emulation mode is controlled.By the division of time interval, primary fault at most only takes place between microcell in product, and the probability that fault takes place repeatedly is minimum, and this can handle product by non-repairable item in an interval.It is abstract approximate that but this process is to the repairable item use, so simulation result has certain error, and size presents sexual intercourse between error size and microcell.More little simulation result is accurate more between microcell.The calculated amount of this emulation mode is little, the simulation velocity height.The correction maintenance mechanical system simulation time of being made up of 50 products is no more than 1 minute, far below using Monte-Carlo and needed time of Markov method emulation.Confirm that by the Drenick law emulation is correct.This method can be applicable to the maintenance schedule and the logistics support decision-making of weaponry system, in the fail-safe analysis of engineering goods, nuclear power device, various production equipments and use in the maintenance decision and also there is significant application value in the after services of product field.

Description of drawings

Fig. 1 is a computer programme flow diagram;

Fig. 2 is the total failure frequency between the tractor chassis unit's microcell that distributes different servicing times;

Fig. 3 is the availability between the tractor chassis unit's microcell that distributes different servicing times;

Fig. 4 is the total failure frequency between the automotive ignition system unit's microcell that distributes different servicing times;

Fig. 5 is the availability between the automotive ignition system unit's microcell that distributes different servicing times.

Embodiment

Embodiment 1

With the tractor chassis is that example is simulated under difference distribution situation servicing time the validity of this tractor chassis.Reliability index according to known this tractor chassis of data: the mean time between failures milimeter number is MTBF 〉=450km.This tractor chassis adopts correction maintenance, and the availability to tractor chassis of distributing different servicing time influences situation and can adopt emulation mode of the present invention to simulate.Analog result can instruct the operation maintenance of tractor chassis and for guarantee plan decision-making provides theoretical foundation, and is significant to the availability or the attendance rate that guarantee tractor.

The life-span of this tractor chassis can be used the Weibull Function match, the availability under the emulation tractor chassis reliability worst condition, i.e. MTBF=450km.The life-span distribution parameter of tractor chassis sees Table 1.Adopt to distribute 6 kinds of different servicing times (maintenance 0 to 5), so that observe the influence situation of servicing time to the tractor chassis availability.Tractor chassis 6 kinds servicing time distribution parameter see Table 2.Be divided into 5km between microcell.

Table 3 and table 4 have provided unit interval total failare frequency and the availability partial simulation result data of tractor chassis under correction maintenance and different servicing time distribution situation respectively, and Fig. 2 and Fig. 3 are corresponding simulation result curves.

The mean time to repair of maintenance 0 is the shortest, less than the equivalent servicing time of 5km, the chassis of breaking down obtains repairing in can be between a microcell, reach maximal value in total crash rate of tractor chassis under this repair during 485 kilometers of tractor operations: 1.298%, promptly per 100 tractors move to 485 kilometers meetings from 480 kilometers and have 1.298 and be in malfunction.With the increase of servicing time, the total failare frequency on chassis also constantly increases, and the maximum failure frequency on corresponding maintenance 5 chassis reaches 2.984%.This shows influences highly significant to the availability of product servicing time, and the quality assurance and the level that improve product just mean the availability that improves product.

Embodiment 2

With certain automotive ignition system is that example is simulated under difference distribution situation servicing time the validity of this automotive ignition system.Reliability index according to known this automotive ignition system of data: the mean time between failures is MTBF 〉=200h ^[1]This automotive ignition system adopts correction maintenance, and different distributions servicing time influences situation to the automotive ignition system availability and can adopt emulation mode of the present invention to simulate.

The life-span of this automotive ignition system can be used the Weibull Function match, the availability under the emulation automotive ignition system reliability worst condition, i.e. MTBF=200h.Automotive ignition system life-span distribution parameter sees Table 5.Adopt distribute different servicing time, so that observe the influence situation of servicing time to the automotive ignition system availability.Distribution parameter servicing time of automotive ignition system sees Table 6.Be divided into 3h between microcell.

Table 7 and table 8 have provided unit interval total failare frequency and the availability partial simulation result data of automotive ignition system under correction maintenance and different servicing time distribution situation respectively, and Fig. 4 and Fig. 5 are corresponding simulation result curves.

The mean time to repair of maintenance 0 is the shortest, less than 3h, the automotive ignition system that breaks down obtains repairing in can be between a microcell, reach maximal value in automotive ignition system under this repair in total crash rate of work in the time of 231 hours: 1.58%, promptly per 100 automotive ignition systems can have 1.58 automotive ignition systems from work in 231 hours to 234 hours and be in malfunction.With the increase of servicing time, the total failare frequency of automobile also constantly increases, and the maximum failure frequency of corresponding maintenance 5 automotive ignition systems reaches 4.284%.This shows influences highly significant to the availability of automotive ignition system servicing time, and the quality assurance of raising product and level are just boiled distinguishing the flavor of and improved the availability of product.

Table 1 tractor chassis life-span Weibull distribution parameter

Form parameter δ	Scale parameter η (km)	Location parameter t 0(km)
			2.9	500	0

The different Weibull distribution servicing time parameters of table 2 tractor chassis

Maintenance	Form parameter δ scale parameter η (km) location parameter t 0(km)
		Maintenance 0 maintenance 1 maintenance 2 maintenances 3 maintenances 4 maintenances 5	Maintenance time, Zu was enough fast, but repaired 1.5 61 1.5 71 1.5 81 1.5 91 1.5 10 1 between microcell of the chassis Zai that breaks down

Total failure frequency between table 3 different servicing time of tractor chassis unit's microcell

Between microcell	Maintenance	0	Maintenance 1	Maintenance 2	Maintenance 3	Maintenance 4	Maintenance 5
								1 30 60 90 120 150 180	0.00000162 0.00277865 0.00890346 0.01283984 0.01193205 0.01051214 0.010976	0.00000162 0.00475266 0.01554668 0.02261073 0.02103552 0.01843215 0.0192449	0.00000162 0.00520178 0.01709423 0.02490782 0.02317765 0.02028362 0.02117786	0.00000162 0.00564171 0.01862598 0.02719094 0.02530828 0.02212022 0.0230949	0.00000162 0.00607299 0.02014357 0.02946249 0.02742979 0.02394402 0.02499809	0.00000162 0.00649602 0.02164805 0.03172406 0.02954374 0.02575638 0.02688876

Availability between table 4 different servicing time of tractor chassis unit's microcell

Between microcell	Maintenance	0	Maintenance 1	Maintenance 2	Maintenance 3	Maintenance 4	Maintenance 5
								1 30 60 90 120 150 180	0.999998 0.997221 0.991097 0.98716 0.988068 0.989488 0.989024	0.999998 0.995247 0.984453 0.977389 0.978964 0.981568 0.980755	0.999998 0.994798 0.982906 0.975092 0.976822 0.979716 0.978822	0.999998 0.994358 0.981374 0.972809 0.974692 0.97788 0.976905	0.999998 0.993927 0.979856 0.970538 0.97257 0.976056 0.975002	0.999998 0.993504 0.978352 0.968276 0.970456 0.974244 0.973111

Table 5 automotive ignition system life-span Weibull distribution parameter

Form parameter δ	Scale parameter η (h)	Location parameter t 0(h)
			2.3	225	0

The different Weibull distribution servicing time parameters of table 6 automotive ignition system

Maintenance	Form parameter δ scale parameter η (km) location parameter t 0(km)
		Maintenance 0 maintenance 1 maintenance 2 maintenances 3 maintenances 4 maintenances 5	Maintenance time, Zu was enough fast, but (3h) repairs 3.5 3 0.5 3.5 4 0.5 3.5 5 0.5 3.5 6 0.5 3.5 7 0.5 between microcell of the automotive ignition system Zai that breaks down

Total failure frequency between table 7 different servicing time of automotive ignition system unit's microcell

Between microcell	Maintenance	0	Maintenance 1	Maintenance 2	Maintenance 3	Maintenance 4	Maintenance 5
								1 30 60 90 120 150 180	0.00004873 0.00833374 0.01495607 0.01562869 0.01481901 0.01486333 0.0149724	0.00004873 0.01751211 0.03185804 0.03328066 0.03145775 0.0315633 0.03181691	0.00004873 0.0147214 0.02666319 0.02785495 0.02635549 0.02644111 0.02664758	0.00004873 0.01984176 0.03622144 0.03783391 0.03573141 0.03585508 0.03615003	0.00004873 0.02203272 0.0403541 0.04214486 0.03977036 0.03991212 0.04024789	0.00004873 0.01303914 0.02358964 0.02465588 0.02334062 0.0234135 0.02359388

Availability between table 8 different servicing time of automotive ignition system unit's microcell

Between microcell	Maintenance	0	Maintenance 1	Maintenance 2	Maintenance 3	Maintenance 4	Maintenance 5
								1 30 60 90 120 150 180	0.999951 0.991666 0.985044 0.984371 0.985181 0.985137 0.985028	0.999951 0.986961 0.97641 0.975344 0.976659 0.976587 0.976406	0.999951 0.985279 0.973337 0.972145 0.973645 0.973559 0.973352	0.999951 0.982488 0.968142 0.966719 0.968542 0.968437 0.968183	0.999951 0.980158 0.963779 0.962166 0.964269 0.964145 0.96385	0.999951 0.977967 0.959646 0.957855 0.96023 0.960088 0.959752

Claims (6)

1, a kind of based on correction maintenance and servicing time validity of products emulation technology, it is characterized in that: comprise the following step of carrying out by computer system:

A, structure maintenance vector or maintenance sequence;

B, structure failure-frequency sequence;

C, structure repairing sequence;

The element of d, failure-frequency sequence and repairing sequence calculates;

E, product availability and total failare frequency computation part.

2, according to claim 1 based on correction maintenance and servicing time validity of products emulation technology, it is characterized in that:

1) maintenance vector makes up as follows among the step a:

W＝(w ₁，w ₂，Λw _i，Λw _m)

$w_i={\∫}_{(i-1)\mathrm{\Δt}}^{\mathrm{i\Δt}}m\left(t\right)\mathrm{dt}+\frac{{\∫}_{-\∞}^{0}m\left(t\right)\mathrm{dt}+{\∫}_{\mathrm{m\Δt}}^{\∞}m\left(t\right)\mathrm{dt}}{m}$

In the formula:

The W-maintenance vector;

w _iI element of-maintenance vector;

M (t)-servicing time distribution probability density function;

The number of elements that the m-maintenance vector is comprised;

Between Δ t-time microcell

The requirement of determining to satisfy following formula of m:

${\∫}_{m\×\mathrm{\Δt}}^{\∞}m\left(t\right)\mathrm{dt}=P(t>{\mathrm{\τ}}_{\max })\≤\mathrm{\ϵ}$

In the formula:

ε-given decimal is usually less than 0.00001;

τ _Max-maximum servicing time;

τ _max＝m×Δt

Definite principle of Δ t is that Δ t is the smaller the better as far as possible between microcell, can artificially determine by principle, also can be calculated as follows:

$\mathrm{\Δt}=\frac{t_{\max }}{n}$

In the formula: the n-interval number, n gets positive integer, usually n＞60; t _MaxThe product maximum life;

2) maintenance vector makes up as follows among the step a:

V＝v ₁，v ₂，Λv _i，Λ＝{v _i}

$v_i={\∫}_{(i-1)\mathrm{\Δt}}^{\mathrm{i\Δt}}m\left(t\right)\mathrm{dt}+\frac{{\∫}_{-\∞}^{0}m\left(t\right)\mathrm{dt}}{m}$

In the formula:

V-keeps in repair sequence;

v _iI element of-maintenance sequence;

Maintenance vector and maintenance sequence have identical functions, utilize maintenance vector simulation calculation amount less, but not as accurate with the maintenance sequence, utilize maintenance sequence simulation calculation amount big slightly with maintenance vector, but accuracy are higher.

3, according to claim 1 based on correction maintenance and servicing time validity of products emulation technology, it is characterized in that: the failure-frequency sequence among the step b makes up as follows:

$g^w=g_1^w,g_2^w,\mathrm{\Λ},g_i^w,\mathrm{\Λ}=\left\{g_i^w\right\}$

Wherein:

g ^w-be illustrated in the failure-frequency sequence of product under the correction maintenance situation;

g _i ^w-be illustrated in the probability that product breaks down under the correction maintenance situation between i microcell;

4, according to claim 1 based on correction maintenance and servicing time validity of products emulation technology, it is characterized in that: the repairing sequence among the step c makes up as follows:

q＝q ₀，q ₁，q ₂，Λ，q _i，Λ＝{q _i}

Wherein:

Q-represents repairing sequence;

q _iI element of-repairing sequence is illustrated in the faulty item that is repaired between i microcell;

5, according to claim 1 based on correction maintenance and servicing time validity of products emulation technology, it is characterized in that:

1) element of failure-frequency sequence calculates as follows in the steps d:

A) when emulation interval number i≤n

$g_i^w=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{q}_{i-j}{g}_j$

B) when emulation interval number i＞n

$g_i^w=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{q}_{i-j}{g}_j$

In the formula:

g _i-be j element of product bug vector;

N-is a product bug element vector prime number;

The element of probability of malfunction vector G is calculated as follows:

$g_j=F(\mathrm{\Δt}\·i)-F\left[\mathrm{\Δt}(i-1)\right]+\frac{\mathrm{\δ}+F\left(0\right)}{n}$

In the formula:

J-represents between j microcell, 1≤j≤n;

g _i-be illustrated in the probability that breaks down between j microcell, also be j element of fault vector simultaneously;

G＝(g ₁，g ₂，g ₃，ΛΛg _j，ΛΛg _n)；

2) element of repairing sequence calculates as follows in the steps d:

A) when emulation interval number i≤m;

$q_i=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_j$

B) when emulation interval number i＞m;

$q_i=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_j$

Perhaps utilize the maintenance sequence to calculate:

$q_i=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_{i-j+1}{v}_j$

6, according to claim 1 based on correction maintenance and servicing time validity of products emulation technology, it is characterized in that:

1) availability of product is calculated as follows among the step e:

$A_i=1-\underset{j=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{k=j+1}{\overset{m}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_k$

Perhaps with distribution function calculating servicing time:

$A_i=1-\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_j[1-M\{(i-j)\mathrm{\Δt}\left\}\right]$

Wherein:

M (t)-element distribution probability servicing time function;

2) the total failare frequency of product is calculated as follows among the step e:

$z_i=\underset{j=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{k=j+1}{\overset{m}{\mathrm{\Σ}}}{g}_{i-j+1}{w}_k$

Perhaps with distribution function calculating servicing time:

$z_i=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}{g}_j[1-M\{(i-j)\mathrm{\Δt}\left\}\right]$

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