CN105787245A - Repair rate and inventory based spare part optimization method - Google Patents

Abstract

The invention discloses a repair rate and inventory based spare part optimization method, particularly a repairable part inventory configuration optimization method used for considering the repair rate of spare parts in a certain expense restriction condition. According to the method, an average spare part shortage quantity is used as a target function and closely related to spare part supply, and can be reasonably controlled through the inventory and repair rate of the spare parts; the influence of the repair rate on the inventory is further considered, so that a constructed model is closer to an actual condition; and the method solves the problems that spare part supply performance parameters cannot truly reflect a spare part supply condition and are difficult to control, the influence of the repair rate of the spare parts on the inventory cannot be considered and the like in the prior art.

Description

A kind of spare parts optimization method based on repair rate Yu quantity in stock

Technical field

The present invention relates to repair rate and inventory technique field.More particularly, to a kind of spare parts optimization method based on repair rate Yu quantity in stock.

Background technology

Spare parts support and quantity in stock are the key factors of restriction Military Equipment Operational Readiness, and on the one hand quantity in stock is too big, spare part fund serious waste, the spare part storage of many enterprises of present China invest up to business equipment more than 10%；Quantity in stock is too low on the other hand, maintenance often occurs again without spare part and urgent procurement status.It is sufficiently expensive that some imports and exports the urgent buying expenses of spare part, and business burden is heavy.

Reasonably Parts Inventory is optimized the important means being to improve equipment life cycle management efficiency-cost ratio.Conventional Parts Inventory optimization method usually sets up the model being object function with parameters such as system availability, waiting time or spare parts support probability, utilizes the corresponding relation of quantity in stock and object function, it is considered under certain expense restriction, the optimal value of quantity in stock.These methods exist main deficiency be: the supply of spare part be influential system availability many factors one of them, it is difficult to directly set up the relation of spares provisioning and system availability；For Parts Inventory administration section, it is difficult in actual management the control waiting time；Spare parts support probability only considers the situation not having spare part to be fixed within a period of time, cannot consider the spare part reparation impact on spares provisioning；Conventional method does not account in multivariate situation, how to utilize marginal benefit method that average spare part short supply amount is optimized and solves.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of spare parts optimization method based on repair rate Yu quantity in stock, particularly a kind of under certain cost constraint, the salvageable component inventory rationing optimization method of spare part repair rate.The method solves spares provisioning effectiveness parameters of the prior art and cannot truly reflect spares provisioning situation, is difficult to control to, cannot consider that spare part repair rate is on problems such as stock's impacts.

For solving above-mentioned technical problem, the present invention adopts following technical proposals:

One, based on repair rate and quantity in stock spare parts optimization method, comprises the following steps:

(1) individual event average spare part short supply amount (EBO is set up_i) with quantity in stock s, repair rate μ relation；

Spare part short supply amount (BO) is within the time of regulation, the unsatisfied number of times of lasting spare parts demand.Individual event average spare part short supply amount (EBO_i)

${\mathrm{EBO}}_i=\underset{n=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)P\left(n\right)---\left(1\right)$

In formula: P (n) represents the probability distribution of spare part quantity Under Repair；S represents the stockpile number of spare part.

Wherein, described P (n) obeys Poisson distribution,

${\mathrm{EBO}}_i=\underset{n=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)P\left(n\right|\mathrm{\λt})=\underset{m=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)\frac{{\left(\mathrm{\λt}\right)}^n}{n!}{e}^{-\mathrm{\λt}}---\left(2\right)$

In formula: λ is Spare demand rate (being commonly referred to fault rate)；T is the spare part turnaround time.

Utilize the relation that spare part turnaround time and spare part repair rate are reciprocal each other, if μ is spare part repair rate, then μ=1/t, it is possible to obtain the relation of the average spare part short supply amount of individual event and spare part repair rate:

${\mathrm{EBO}}_i=\underset{m=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)\frac{{(\mathrm{\λ}/\mathrm{\μ})}^n}{n!}{e}^{-(\mathrm{\λ}/\mathrm{\μ})},(n\≥1)---\left(3\right)$

In formula (3), λ is Spare demand rate, and n represents part warehouse storage+1；

(2) constructing system Parts Inventory Optimized model

Average spare part short supply amount (EBO) of system is the average spare part short supply amount sum of composition system all LRUs LRU.Assume that the average spare part short supply amount being numbered the LRU of i is EBO_i；So the average spare part short supply amount of system is:

$\mathrm{EBO}=\underset{i=1}{\overset{N_L}{\mathrm{\Σ}}}{\mathrm{EBO}}_i---\left(4\right)$

In formula: N_LFor the number of LRU in system.

The condition of system Parts Inventory Optimized model is described as: under the premise ensureing the certain inventory cost of system, make the EBO of system minimum.The inventory cost of spare part unit price and turnaround time composition is only only considered if carried out Parts Inventory when optimizing.Now Optimized model can be written as:

$\min \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{EBO}}_i(s_i,{\mathrm{\μ}}_i)$

$s.t.\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[c_{1i}f\left(s_i\right)+c_{2i}f\left({\mathrm{\μ}}_i\right)]\≤C---\left(5\right)$

In formula: f (s_i) it is the function about s；M is the species number of LRU, C_1i(s μ) is for being numbered the unit price of the LRU of i, C_2iFor being numbered the unit price of the spare part repair rate of the LRU of i, C is for always retraining expense, if S_iAnd C_1i, μ_iAnd C_2iFor linear relationship, then constraints can be reduced to

$\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(c_{1i}{s}_i+c_{2i}{\mathrm{\μ}}_i)\≤C---\left(6\right)$

By object function is carried out specificity analysis, judge the concavo-convex characteristic of object function, obtain EBO (s, μ) it is the monotone decreasing convex function respectively about quantity in stock s and μ, because the linear combination of multiple convex functions remains convex function, so system average spare part short supply amount is interval in whole part warehouse storage and spare part repair rate interval is all monotone decreasing convex function, marginal analysis method is then used to find the optimal value of EBO.

3rd step: the quantity in stock s of control variable spare part, spare part repair rate μ, by iteration, analyzes the marginal benefit of the average spare part short supply amount EBO of individual event LRU LRU；

4th step, it is determined that in system, the initial EBO of m kind LRU is control variable, by iteration, analyzes the marginal benefit of the average spare part short supply amount EBO of system.

Preferably, described spare part refers to electronic product, complication system and through seasoned test the product carrying out periodic maintenance.

Preferably, described 3rd step is specifically:

The EBO of each LRU carries out marginal analysis respectively, by the trade-off analysis to the limit benefit of unit and expense, to reach the Appropriate application to the efficient resource resource of maintenance failure part (the part warehouse storage with).In each iteration taken turns, only increase by 1 part warehouse storage every time, or improve the maintenance rate of a unit value or increase a part warehouse storage simultaneously and reduce the maintenance rate of a unit value.Relatively under which kind of strategy, the minimizing amount of the EBO of brought LRU is maximum with spare part expense or repair rate expense ratio, namely the efficiency-cost ratio brought under this policy is, the control variable that the part warehouse storage that this strategy is corresponding adjusts as needs with repair rate, effectively to improve marginal benefit.Determine the N group part warehouse storage of each LRU and the value of the EBO corresponding to the combination of repair rate.

3.1 determine control variable, and give its initial value.Control variable is s, μ, it is determined that be numbered the initial spares amount s of the LRU of i₀With initial spares repair rate μ₀Value, it is determined that the value of N, make n=1, s=s₀, μ=μ₀。

In 3.2 each iterative process taken turns, adjust control variable, find maximum marginal benefit Δ EBO.Increase spare part quantity successively, or improve spare part repair rate, or increase spare part quantity simultaneously and reduce spare part repair rate, calculate and record the increase amount of the marginal benefit of corresponding every element number and the marginal cost increase amount of every unit.Namely the size of Δ EBO (s+1, μ), Δ EBO (s, μ+1) and Δ EBO (s+1, μ-1) three is compared.Wherein

Δ EBO (s+1, μ)=[EBO (s, μ)-EBO (s+1, μ)]/c₁Δ EBO (s, μ+1)=[EBO (s, μ)-EBO (s, μ+1)]/c₂, Δ EBO (s+1, μ-1)=[EBO (s, μ)-EBO (s+1, μ-1)]/| c₁-c₂| (if μ > μ₀)。

3.3 determine the control variable needing to adjust, and its value is changed.Finding out the variable that limit Efficiency is maximum or variable combination, its value is changed, remaining variables value remains unchanged.Namely find out the combination of maximum s' and μ ' corresponding for Δ EBO, as s and the μ of next round iteration, make s=s', μ=μ ', n=n+1, subsequently into step 4.

Step 4: as n=N, iteration completes；Otherwise, step 2, repeat the above steps are entered.

Preferably, described 4th step, the marginal benefit concrete analysis of system average spare part short supply amount (EBO) is as follows:

The EBO of every LRU in choosing comprehensively system, under certain cost constraint, solves the part warehouse storage of m LRU of optimum and the combination of repair rate by marginal analysis method.

4.1 determine that in system, the initial EBO of m kind LRU is control variable.If being numbered the value of the jth EBO of the LRU of i for (i=1,2,3......m), j=1.

4.2 in each iterative process taken turns, and makes the control variable of m kind LRU increase successively, calculates and record corresponding marginal benefit increase amount, it is determined that needs the control variable adjusted, namely finds maximum marginal benefit increase amount and marginal cost increase amount Δ EBO_i.For being numbered the Δ EBO of the LRU of i_iFormula be Δ EBO_i=[EBO_ij-EBO_i(j+1)]/Δ c, Δ c are the EBO that LRU is corresponding_i(j+1)Expense deduct EBO_ijExpense.

4.3 determine the limit maximum LRU of Efficiency, and think this take turns in the adjustment weight of this kind of LRU maximum, by the increase of its EBO value, by the EBO of this kind of LRU_i(j+1)As the EBO that it is initial, all the other EBO values corresponding for LRU remain unchanged.

4.4 repeat said process, until spare part total cost reaches constraints.The i.e. EBO according to m LRU, it is determined that the spare part total cost of system, if meeting target value, then iteration completes；Otherwise, enter step 2, repeat said process.

Beneficial effects of the present invention is as follows:

The present invention utilizes average spare part short supply amount as object function, because itself and spares provisioning are closely related, it is possible to by part warehouse storage and spare part repair rate conservative control；

Target component average spare part short supply amount selected by the present invention is associated with system-level maintenance support top layer parameter repair rate, is possible not only to weigh the quality of spares provisioning, it is also contemplated that the repair rate impact on stock, thus its model built is closer to practical situation；

The present invention considers quantity in stock and the impact on average spare part short supply amount of two variablees of repair rate simultaneously, improves original marginal benefit method and solves flow process in single argument optimizing situation.

Accompanying drawing explanation

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

Fig. 1 illustrates the analysis process figure of the embodiment of the present invention 1 step 3.

Fig. 2 illustrates the analysis process figure of the embodiment of the present invention 1 step 4.

Fig. 3 illustrates the average spare part short supply amount trendgram of the embodiment of the present invention 1.

Detailed description of the invention

In order to be illustrated more clearly that the present invention, below in conjunction with preferred embodiments and drawings, the present invention is described further.Parts similar in accompanying drawing are indicated with identical accompanying drawing labelling.It will be appreciated by those skilled in the art that following specifically described content is illustrative and be not restrictive, should not limit the scope of the invention with this.

Embodiment 1

Concretely comprising the following steps of a kind of spare parts optimization method based on repair rate and quantity in stock:

The first step: set up the relation of average spare part short supply amount and quantity in stock, repair rate

Spare part short supply amount (BO) is within the time of regulation, the unsatisfied number of times of lasting spare parts demand.The computing formula of average spare part short supply amount (EBO) is

$\mathrm{EBO}=\underset{n=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)P\left(n\right)---\left(1\right)$

In formula: P (n) represents the probability distribution of spare part quantity Under Repair；S represents the stockpile number of spare part.

In general, electronic product, complication system and through seasoned test the product carrying out periodic maintenance, exponential is obeyed in life-span distribution, and the model used when calculating spare parts demand amount is Poisson model.If P (n) obeys Poisson distribution, so

$\mathrm{EBO}=\underset{n=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)P\left(n\right|\mathrm{\λt})=\underset{m=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)\frac{{\left(\mathrm{\λt}\right)}^n}{n!}{e}^{-\mathrm{\λt}}---\left(2\right)$

In formula: λ is Spare demand rate (being commonly referred to fault rate)；T is the spare part turnaround time.

Utilize the relation that spare part turnaround time and spare part repair rate are reciprocal each other, if μ is spare part repair rate, then μ=1/t, it is possible to obtain the relation of average spare part short supply amount and spare part repair rate:

$\mathrm{EBO}=\underset{m=s+1}{\overset{\∞}{\mathrm{\Σ}}}(n-s)\frac{{(\mathrm{\λ}/\mathrm{\μ})}^n}{n!}{e}^{-(\mathrm{\λ}/\mathrm{\μ})},(n\≥1)---\left(3\right)$

Second step, Optimized model builds

Step 2.1: set up object function and constraints

The average spare part short supply amount of system is the average spare part short supply amount sum of all LRU of composition system.Assume that the average spare part short supply amount being numbered the LRU of i is EBO_i；So the average spare part short supply amount of system is:

$\mathrm{EBO}=\underset{i=1}{\overset{N_L}{\mathrm{\Σ}}}{\mathrm{EBO}}_i---\left(4\right)$

In formula: N_LFor the number of LRU in system.

The condition of system Parts Inventory Optimized model is described as: under the premise ensureing the certain inventory cost of system, make the EBO of system minimum.The inventory cost of spare part unit price and turnaround time composition is only only considered if carried out Parts Inventory when optimizing.Now Optimized model can be written as:

$\min \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{EBO}}_i(s_i,{\mathrm{\μ}}_i)$

$s.t.\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[c_{1i}f\left(s_i\right)+c_{2i}f\left({\mathrm{\μ}}_i\right)]\≤C---\left(5\right)$

In formula: m is the species number of LRU, c_1iS μ is the unit price of the LRU being numbered i, c_2iFor being numbered the unit price of the spare part repair rate of the LRU of i, C is for always retraining expense, if s_iAnd c_1i, μ_iAnd c_2iFor linear relationship, then constraints can be reduced to

$\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(c_{1i}{s}_i+c_{2i}{\mathrm{\μ}}_i)\≤C---\left(6\right)$

In present case, equipment is made up of LRU1 and LRU2, i.e. m=2, they are of equal importance.λ₁=λ₂The year repair rate μ of=0.0057/h, LRU1₁=12.5, the year repair rate μ of LRU2₂=10；The spare part unit price c of LRU1₁₁=3, the spare part unit price c of LRU2₁₂=5, unit is all ten thousand yuan；The repair rate unit price c of LRU1₂₁=1, the repair rate unit price c of LRU2₂₂=2, unit is all ten thousand yuan.Total constraint expense is 320,000 yuan i.e. C=32.Initial spares quantity in stock is 0, i.e. s₁=s₂=0.Now, the object function of Optimized model can be written as:

minEBO₁(s₁,μ₁)+EBO₂(s₂,μ₂)

s.t.[3s₁+(μ₁-12.5)+5s₂+2×(μ₂-10)]≤32

3rd step: the marginal analysis of individual event LRU average spare part short supply amount (EBO)

The EBO of each LRU is carried out marginal analysis respectively, by the trade-off analysis to the limit benefit of unit and expense, to reach the Appropriate application to the efficient resource resource of maintenance failure part (the part warehouse storage with).In each iteration taken turns, only increase by 1 part warehouse storage every time, or improve the maintenance rate of a unit value or increase a part warehouse storage simultaneously and reduce the maintenance rate of a unit value.Relatively under which kind of strategy, the minimizing amount of the EBO of brought LRU is maximum with spare part expense or repair rate expense ratio, namely the efficiency-cost ratio brought under this policy is, the control variable that the part warehouse storage that this strategy is corresponding adjusts as needs with repair rate, effectively to improve marginal benefit.Determine the N group part warehouse storage of each LRU and the value of the EBO corresponding to the combination of repair rate.

3.1 determine control variable, and give its initial value.Control variable is s, μ, it is determined that be numbered the initial spares amount s of the LRU of i₀With initial spares repair rate μ₀Value, it is determined that the value of N, make n=1, s=s₀, μ=μ₀。

In 3.2 each iterative process taken turns, adjust control variable, find maximum marginal benefit Δ EBO.Increase spare part quantity successively, or improve spare part repair rate, or increase spare part quantity simultaneously and reduce spare part repair rate, calculate and record the increase amount of the marginal benefit of corresponding every element number and the marginal cost increase amount of every unit.Namely the size of Δ EBO (s+1, μ), Δ EBO (s, μ+1) and Δ EBO (s+1, μ-1) three is compared.Wherein

Δ EBO (s+1, μ)=[EBO (s, μ)-EBO (s+1, μ)]/c₁Δ EBO (s, μ+1)=[EBO (s, μ)-EBO (s, μ+1)]/c₂, Δ EBO (s+1, μ-1)=[EBO (s, μ)-EBO (s+1, μ-1)]/| c₁-c₂| (if μ > μ₀)。

3.3 determine the control variable needing to adjust, and its value is changed.Finding out the variable that limit Efficiency is maximum or variable combination, its value is changed, remaining variables value remains unchanged.Namely find out the combination of maximum s' and μ ' corresponding for Δ EBO, as s and the μ of next round iteration, make s=s', μ=μ ', n=n+1, subsequently into step 4.

Step 4: as n=N, iteration completes；Otherwise, step 2, repeat the above steps are entered.

In present case, N=10.For LRU1, s₀=0, μ₀=12.5, in the iteration of the first round, Δ EBO (s+1, μ)=0.3272, Δ EBO (s, μ+1)=0.1956, Δ EBO (s+1, μ-1)=0.2137.Find out maximum Δ EBO, i.e. Δ EBO (s+1, μ), using s'=1 and the μ of its correspondence '=12.5 s and the μ as next round iteration, i.e. s=1, μ=12.5, n=n+1=2, now n < N, enter step 2, repeat the above steps.Until as n=N, iteration completes,.The iterative process of same LRU2 is similar with LRU1, shown in shown in the iterative data of LRU1, LRU2 such as table 1, table 2.

The iterative data of table 1LRU1

(s,μ)	EBO1	ΔEBO1
			(0,12.5)	4
(1,12.5)	3.0183	0.3272
			(2.12.5)	2.1099	0.3028
(2,13.5)	1.8442	0.2657
			(3,12.5)	1.3480	0.2481
(3,13.5)	1.1290	0.2190
			(3,14.5)	0.9521	0.1769
(4,13.5)	0.6224	0.1649
			(4,14.5)	0.4999	0.1225

(5,13.5)

0.3089

0.0955

The iterative data of table 2LRU2

(s,μ)	EBO2	ΔEBO2
			(0,10)	5
(0,11)	4.5455	0.2273
			(1,11)	3.5561	0.1979
(2,11)	2.6149	0.1882
			(2,12)	2.2623	0.1763
(3.11)	1.7835	0.1596
			(3,12)	1.4770	0.1533
(3,13)	1.2326	0.1222
			(4,12)	0.8786	0.1183
(4,13)	0,6966	0.0912

4th step: the marginal analysis of system average spare part short supply amount (EBO)

The EBO of every LRU in choosing comprehensively system, under certain cost constraint, solves the part warehouse storage of m LRU of optimum and the combination of repair rate by marginal analysis method.

4.1 determine that in system, the initial EBO of m kind LRU is control variable.If being numbered the value of the jth EBO of the LRU of i for (i=1,2,3......m), j=1.

4.2 in each iterative process taken turns, and makes the control variable of m kind LRU increase successively, calculates and record corresponding marginal benefit increase amount, it is determined that needs the control variable adjusted, namely finds maximum marginal benefit increase amount and marginal cost increase amount Δ EBO_i.For being numbered the Δ EBO of the LRU of i_iFormula be Δ EBO_i=[EBO_ij-EBO_i(j+1)]/Δ c, Δ c are the EBO that LRU is corresponding_i(j+1)Expense deduct EBO_ijExpense.

4.3 determine the limit maximum LRU of Efficiency, and think this take turns in the adjustment weight of this kind of LRU maximum, by the increase of its EBO value, by the EBO of this kind of LRU_i(j+1)As the EBO that it is initial, all the other EBO values corresponding for LRU remain unchanged.

4.4 repeat said process, until spare part total cost reaches constraints.The i.e. EBO according to m LRU, it is determined that the spare part total cost of system, if meeting target value, then iteration completes；Otherwise, enter step 2, repeat said process.

M=2 in present case.If LRU1 is initial EBO₁₁=4, the initial EBO of LRU2₂₁=5.The iteration of the first round compares Δ EBO₁With Δ EBO₂Size, due to Δ EBO₁=0.3272 more than Δ EBO₂=0.2273, so by the EBO of LRU1₁₂=3.0183 remain unchanged as the initial EBO of initial EBO, the LRU2 of LRU1, until expense exceedes constraints, equip average spare part short supply amount iterative process as shown in the figure.Analysis process experiences 13 altogether and takes turns iteration, and under the expense restriction of 320,000, the spare part back order amount of final system is 2.0994.

Average spare part short supply amount iterative process equipped by table 3

Sequence number	EBO1Combination	EBO2Combination	EBO sum	Expense
					1	(0,12.5)	(0,10)	9	0
2	(1,12.5)	(0,10)	8.0183	3
					3	(2,12.5)	(0,10)	7.1099	6
4	(2,13.5)	(0,10)	6.8442	7
					5	(3,12.5)	(0,10)	6.348	9
6	(3,12.5)	(0,11)	5.8935	11
					7	(3,13.5)	(0,11)	5.6745	14
8	(3,13.5)	(1,11)	4.6851	17
					9	(3,13.5)	(2,11)	3.7439	22
10	(3,14.5)	(2,11)	3.567	23
					11	(3,14.5)	(2,12)	3.2144	25
12	(3,14.5)	(3,11)	2.8847	28
					13	(4,13.5)	(3,11)	2.4059	30
14	(4,13.5)	(3,12)	2.0994	32

Obviously; the above embodiment of the present invention is only for clearly demonstrating example of the present invention; and be not the restriction to embodiments of the present invention; for those of ordinary skill in the field; can also make other changes in different forms on the basis of the above description; here cannot all of embodiment be given exhaustive, every belong to apparent change that technical scheme extended out or the variation row still in protection scope of the present invention.

Claims (5)

1. the spare parts optimization method based on repair rate Yu quantity in stock, it is characterised in that comprise the following steps:

The first step, sets up the average spare part short supply amount EBO of individual event_iRelation with the quantity in stock s of spare part, spare part repair rate μ:

${\mathrm{EBO}}_i=\underset{n=s+1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}(n-s)\frac{{(\mathrm{\&lambda;}/\mathrm{\&mu;})}^n}{n!}{e}^{-(\mathrm{\&lambda;}/\mathrm{\&mu;})},(n\&GreaterEqual;1)---\left(3\right)$

In formula (3), λ is Spare demand rate；

Second step, according to individual event average spare part short supply amount obtain the average spare part short supply amount of system, constructing system Parts Inventory Optimized model,

The average spare part short supply amount of system is:

$\mathrm{EBO}=\underset{i=1}{\overset{N_L}{\mathrm{\&Sigma;}}}{\mathrm{EBO}}_i---\left(4\right)$

EBO in formula (4)_iRepresent the average spare part short supply amount of the LRU being numbered i, N_LFor the number of LRU in system；

The condition of system Parts Inventory Optimized model is: under ensureing the premise of inventory cost of system, make the EBO of system minimum；And inventory cost is made up of spare part unit price and turnaround time, Optimized model is:

$\min \underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{EBO}}_i(s_i,{\mathrm{\&mu;}}_i)$

$s.t.\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}[c_{1i}f\left(s_i\right)+c_{2i}f\left({\mathrm{\&mu;}}_i\right)]\&le;C---\left(5\right)$

In formula: m is the species number of LRU, C_1i(s, μ) is for being numbered the unit price of the LRU of i, C_2iFor being numbered the unit price of the spare part repair rate of the LRU of i, C for always to retrain expense, S_iAnd C_1i, μ_iAnd C_2iFor linear relationship, constraints is reduced to:

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}(c_{1i}{s}_i+c_{2i}{\mathrm{\&mu;}}_i)\&le;C---\left(6\right)$

3rd step, using spare part quantity in stock s and spare part repair rate μ as control variable, by iteration, analyzes the average spare part short supply amount EBO of individual event LRU LRU_iMarginal benefit；

4th step, with the initial EBO of m kind LRU in system_iFor control variable, by iteration, analyze the marginal benefit of the average spare part short supply amount EBO of system；Under certain cost constraint, solve the part warehouse storage of m LRU of optimum and the combination of repair rate by marginal analysis method.

2. the spare parts optimization method based on repair rate Yu quantity in stock according to claim 1, it is characterized in that: described spare part refers to electronic product, complication system or through seasoned test the product carrying out periodic maintenance, exponential is obeyed in the life-span distribution of described spare part.

3. the spare parts optimization method based on repair rate Yu quantity in stock according to claim 2, it is characterised in that: Poisson distribution is obeyed in the life-span distribution of described spare part.

4. the spare parts optimization method based on repair rate Yu quantity in stock according to claim 1, it is characterised in that: described 3rd step farther includes:

Give initial value to the quantity in stock s and spare part repair rate μ of the LRU being numbered i respectively, make n=1, s=s₀, μ=μ₀,

In each iterative process taken turns, calculate and record the increase amount of the marginal benefit of corresponding every element number and the marginal cost increase amount of every unit, and compare Δ EBO_i(s+1,μ)、ΔEBO_i(s, μ+1) and Δ EBO_iThe size of (s+1, μ-1) three, to determine maximum marginal benefit △ EBO_i,

Wherein

ΔEBO_i(s+1, μ)=[EBO (s, μ)-EBO (s+1, μ)]/c₁

ΔEBO_i(s, μ+1)=[EBO (s, μ)-EBO (s, μ+1)]/c₂

ΔEBO_i(s+1, μ-1)=[EBO (s, μ)-EBO (s+1, μ-1)]/| c₁-c₂| (if μ > μ₀),

Determine maximum marginal benefit △ EBO_iCorresponding variable or variable combination, as n=N, iteration completes；Otherwise, the value increasing 1 that corresponding variable or variable are combined is as s and the μ of next round iteration, and n=n+1, repeat the above steps.

5. the spare parts optimization method based on repair rate Yu quantity in stock according to claim 1, it is characterised in that: described 4th step specifically:

With the initial EBO of m kind LRU in system_iFor control variable, if being numbered the jth EBO of the LRU of i_ijValue be (i=1,2,3......m), j=1,

In each iterative process taken turns, make the control variable EBO of m kind LRU successively_iIncrease, calculate and record corresponding marginal benefit increase amount, it is determined that maximum marginal benefit increase amount and marginal cost increase amount Δ EBO_i, for being numbered the Δ EBO of the LRU of i_iFormula be Δ EBO_i=[EBO_ij-EBO_i(j+1)]/Δ c, Δ c are the EBO that LRU is corresponding_i(j+1)Expense deduct EBO_ijExpense,

Determine the LRU that limit Efficiency is maximum, its EBO value is increased to EBO_i(j+1)As the initial EBO of next round, EBO value corresponding for all the other LRU remains unchanged, and repeats said process, until spare part total cost reaches constraints iteration and completes.