CN104657785A - Method for determining and optimizing system maintenance rate - Google Patents
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Abstract
The invention discloses a method for determining and optimizing a system maintenance rate. The method is characterized in that the maintenance rate is adopted to ensure the system availability when a storage element and the element failure rate are affected by the working environment, the system is shown by using a dynamic fault tree, and the distribution of the element failure rate is determined by using the space fault tree theory to further determine the distribution of the element maintenance rate. The method comprises the following steps: solving a subtree and the system, determining the distribution of the element maintenance rate after giving the system availability, and determining the maintenance rate under different optimization objectives. The method can be used for determining and optimizing the system maintenance rate.
Description
Technical field
The present invention relates to safety system engineering, particularly relate to system maintenance rate and determine and optimize.
Background technology
In reality, generally wish that system is macroscopically reaching certain target, as the reliability, availability, failure rate, total maintenance cost etc. of system.The realization of system macro-goal, is difficult to ensure from the general level of system, should by controlling to the primary element parameter of composition system the target ensureing system, and these parameters comprise: the crash rate, maintenance rate, maintenance cost etc. of element.Parameter as part failure rate is that element nature determines, user cannot change; And maintenance rate can adjust at work, namely reach some macro-goal of system by the adjustment of maintenance rate.Be generally a definite value for part failure rate, but in fact a lot of part failure rate is subject to the impact of working environment, is namely become crash rate, as temperature, working time, air pressure etc.Another problem is modern system is ensure that reliability all can take spare part strategy.So how component maintenance rate in certainty annuity after consideration the problems referred to above, thus the realization of the system of guarantee macro-goal just becomes problem.
According to the research to system reliability, the change crash rate that usage space fault tree theory represents element is proposed, use dynamic fault tree theory to represent contacting containing spare part system architecture and system macro-goal and component parameters, thus the component maintenance rate being met requirement distribute.And expect to obtain corresponding component maintenance rate distribution for system performance in three kinds of situations in reality.
Summary of the invention
1 space fault tree
Space fault tree (Space Fault Tree, SFT) proposed in 2012, had achieved some achievements in research up to now.The basic theories of space fault tree thinks that system works is among environment, because the composition elementary event of system or the character of physical component determine its fault rate difference worked at different conditions.Such as, as the diode in electrical system, its probability of malfunction is just with working time, working temperature, have direct relation by electric current and voltage etc.If analyzed this system, the working time of each element and the temperature of work accommodation etc. may be all different, and along with the working time of entire system and the change of environment temperature, the probability of malfunction of system is also different.This phenomenon is in esse, but unheeded often, and thinks that probability of malfunction is invariable.
The author attempts the change crash rate using element in SFT expression system.In order to describe SFT theory and analytic process below clearly, list the example of necessary SFT related content and analyzed system.Discuss with regard to simple electrical system, this system is constituted by a diode, and the rated operation of diode affects by several factors, wherein importantly working time
tand working temperature
c.For the electrical system affected by these two factors as research object.Related definition is as follows:
1) space fault tree (or hyperspace event tree): the probability of happening of elementary event is not fixing, be by
nindividual factor determines, such event tree is called multidimensional event tree, represents with T.
2) influence factor of elementary event: make the factor that elementary event probability of happening changes.In this example,
trepresent time factor,
crepresent temperature factor.
3) fundamental function (fundamental function) of the probability of happening of elementary event: elementary event under the impact of single influence factor, the probability of happening variation characteristic that the change with influence factor shows.It can elementary function, and piecewise function etc., use P
x ix () represents,
irepresent the
iindividual element,
xreplace influence factor.As this example
ithe temporal characteristics function P of individual original paper
t i(t)=1-e
-λ t, and temperature profile function P
c i(c)=0.5 (cos (2 π c/A)+1), wherein,
tfor element service time, λ is cell failure rate,
afor temperature variation is divided into.
4) the probability of happening space distribution of elementary event: elementary event exists
nunder individual influence factor impact, the probability of happening change that the change with them shows in hyperspace.
nindividual influence factor is as separate independent variable, and elementary event probability of happening is as functional value.Use P
i(x
1, x
2..., x
n) represent, i.e. P
i(x
1, x
2..., x
n)=1-П (1-P
xi i(xi)), wherein i=1,2 ..., n,
nfor influence factor number, be P in this example
i(t, c)=1-(1-P
t i(t)) (1-P
c i(c)).
2 Dynamic fault trees
A kind of analysis that the reliability that Dynamic fault tree method is the nineties in 20th century is analysis space station and air-traffic control system by professor J.B.Dugan proposes has the method for the system reliability of dynamic random fault characteristic.Dynamic fault tree method introduces dynamic logic gate on the basis of fault tree, as cold reserve door, hot reserve door, order associated gate, preferential and door etc., for characterization system cold reserve, hot reserve, can repair, the dynamic perfromance such as resource sharing.
Here adopt Markov state transition matrix to process problem, comprise analytical method and matrix iteration.When calculating the repaiied reliability index of single system, adopt analytical method; Calculate comparatively complication system time, especially application matrix process of iteration when the fiduciary level of solving system and failure frequency.Analytical method is the feature according to logic gate, sets up the system of equations based on Markov state transition diagram, in conjunction with the feature of logic gate, derives and can obtain the expression formula of reliability index, directly apply mechanically the method calculating reliability index.Matrix iteration is probability matrix and the systematic state transfer matrix multiple iteration of foundation system, solves the probability of different conditions residing for given time system, in conjunction with normal working probability, the malfunction probability of the feature compartment system of Different Logic door.Whole dynamic fault tree model is finally utilized to carry out each reliability index of evaluating system.
λcrash rate,
μit is maintenance rate.The function of each logic gate is respectively: with door: the incoming event of and if only if door
x,
ywhen all occurring, the outgoing event of door
zoccur; Or door: when the incoming event of door
x 1,
x 2,
x 3has 1 generation at least, the outgoing event of door
zoccur; Cold reserve door: primary input event
xin running order, stand-by equipment
ybe in cold standby state, only when master/slave device all fault time, the outgoing event of door
zoccur; Hot reserve door: primary input event
xin running order, stand-by equipment
ybe in hot stand-by duty, only when master/slave device all fault time, the outgoing event of door
zoccur.
In 3 systems, the maintenance rate of element is determined
First studied Dynamic fault tree is provided, as shown in Figure 1.
3.1
x 1with
x 2subnumber solves
x 1subtree module is the hot standby combination of element, and the crash rate of element is
λ, maintenance rate is
μ. define its shape space: state 0 represents that 2 modules all normally work, system worked well; Shape 1 represents in 2 modules, and one lost efficacy in maintenance, and another module normally works, system worked well; State 2 represents that 2 modules all lost efficacy, and a module is in repairing, and another module is to be repaired, thrashing.
According to the feature of probability in conjunction with hot reserve door, the expression formula formula (1) as shown in Figure 2 of each reliability index of deriving to obtain
In formula (1), availability
awhen expression system reaches steady operational status can probability.Failure frequency is
m(
t) refer to [0,
t] the mean failure rate number of times of system in the time, be the failure-frequency of system in the unit interval.
3.2
tsolve
System
tby or door connect lower floor event.Definition status space is: state 0 is that 2 modules are all normal, system worked well; State 1 is
x 1subtree module failure is being repaired,
x 2subtree module is normal,
tlost efficacy; State 2 is
x 2subtree module failure is being repaired,
x 1subtree module is normal,
tlost efficacy.
Combine or the feature of door according to probability, the expression formula of each reliability index as shown in Figure 3 shown in formula (2) of deriving to obtain, in formula,
Λ=
λ 1+
λ 2.
After 3.3 given system availabilities, the distribution of component maintenance rate is determined
If system availability
t a=0.8, ask μ
e1E2and μ
e3E4, due to
e 1with
e 2be
x 1hot reserve event, use μ
e1E2represent
e 1with
e 2maintenance rate (element
x 1maintenance rate), μ
e3E4in like manner define.By in formula (2)
a=
t aavailability known, 1/TA=1+ λ
x1/ μ
x1+ λ
x2/ μ
x2, wherein λ
x1represent
x 1having in hot reserve situation (
e 1→
e 2) crash rate, λ
x2in like manner define; μ
x1represent
x 1having in hot reserve situation (
e 1→
e 2) maintenance rate, μ
x2in like manner define.Know λ again
x1/ μ
x1=(1/MUT
e1E2)/(1/MDT
e1E2), wherein MUT
e1E2represent E
1and E
2average operation time, MDT
e1E2represent E
1and E
2average shut down time, according to formula (1), obtain λ
x1/ μ
x1=1/ (μ
e1E2/ λ
e1E2+ 0.5 (μ
e1E2/ λ
e1E2)
2), λ in formula
e1E2represent
e 1with
e 2maintenance rate (element
x 1maintenance rate), λ
e3E4in like manner define.For separating the problems referred to above, introduce variable
k, k=(λ
x1/ μ
x1): (λ
x2/ μ
x2), consider than symmetry to facilitate research, if
k∈{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1/0.9,1/0.8,1/0.7,1/0.6,1/0.5,1/0.4,1/0.3,1/0.2,1/0.1}。Arrange said process and obtain formula (3) as shown in Figure 4.
If the working field of element, namely the variation range of condition of work be A total={ t ∈ [0,100] sky ∩ c ∈ [0,50] DEG C }, namely the time of system works is 100 days, and operating temperature range is 0 to 50 DEG C.Discuss according to first segment, the failure probability distributions λ under the fault tree state of space
e1E2and λ
e3E4(namely
x 1,
x 2)
.so can according to λ
e1E2and λ
e3E4with formula (3), draw this Dynamic fault tree and exist
k=1,
t aμ when=0.8
e1E2and μ
e3E4distribution plan.
Meet system availability as seen
t a=0.8,
kunder=1 condition, for system element
x 1hot reserve event
e 1,
e 2maintenance rate to meet in working field maintenance rate distribution; And
x 2meet maintenance rate distribution, such system can reach
t athe macro-goal of=0.8.
The determination of maintenance rate under 4 Different Optimization targets
First three kinds of in esse system optimization problems are proposed, 1) when research range (working field) is determined, whole system maintenance rate summation is minimum.The meaning of this actual demand wishes that maintenance frequency is minimum in whole working field, and maintenance frequency minimum like this can reduce shut down time, can reduce maintenance cost simultaneously.2) in Practical Project, generally all can a given acceptable minimal maintenance rate, just implement maintenance when the maintenance rate of element exceedes minimal maintenance rate, or standby preparations of maintenance personal is keeped in repair.Generally wish that system is in whole working field, the region being greater than minimal maintenance rate is the smaller the better, and then minimizing maintenance personal's waiting time improves maintenance efficiency.3) when the expense of element dissimilar in maintenance system is different, maintenance rates different between element can cause system maintenance total expensess different in working field, certainly more low better.Certainly above-mentioned 3 all will ensure that system held is on certain availability basis, otherwise nonsensical.
For Section of three system mentioned, due to
t a=0.8, and λ
e1E2and λ
e3E4to know, so determine that the key of maintenance rate depends on variable
k.Due to 1/TA=1+ λ
x1/ μ
x1+ λ
x2/ μ
x2with k=(λ
x1/ μ
x1): (λ
x2/ μ
x2), namely exist
t awhen fixing,
krepresent a kind of distributional effects, so different distribution (
kdifferent) different μ can be brought
e1E2/ λ
e1E2and μ
e3E4/ λ
e3E4, so by regulating
kunder can meeting the condition of above-mentioned three problems, determine the μ in working field
e1E2and μ
e3E4.
4.1 maintenance rate distributions when asking maintenance rate summation minimum
For first problem, make A maintenance rate minimum μm of in always={ t ∈ [0,100] sky ∩ c ∈ [0,50] DEG C } in working field, it defines formula (4) as shown in Figure 5.
4.2 ask the minimum zone of specifying maintenance rate
If the tolerable maintenance rate of system, so will determine μ in working field
e1E2and μ
e3E4be greater than respectively 2 scope minimum time
kvalue.Method is the whole working field of traversal,
kto μ time different
e1E2and μ
e3E4the region being greater than 2 counts, and count results reckling is corresponding
krequired by value is.
4.3 maintenance rate distributions when asking total upkeep cost minimum
In order to be described element expense difference, definition C
x1and C
x2be respectively element
x 1with
x 2upkeep cost, total maintenance cost defines as shown in Figure 6 shown in formula (5).
Can according to the C of element
x1: C
x2value finds corresponding
kvalue is to determine μ
e1E2and μ
e3E4distribution in working field.Such as, if element
x 1with
x 2upkeep cost be 20 yuan and 100 yuan, i.e. C
x1: C
x2=2:10, so
kwhen=0.3, the maintenance cost of entire system is minimum, the availability of certain system
t a=0.8.
Accompanying drawing explanation
The Dynamic fault tree of Fig. 1 system.
Fig. 2 formula (1).
Fig. 3 formula (2).
Fig. 4 formula (3).
Fig. 5 formula (4).
Fig. 6 formula (5).
Embodiment
1 space fault tree
Space fault tree (Space Fault Tree, SFT) proposed in 2012, had achieved some achievements in research up to now.The basic theories of space fault tree thinks that system works is among environment, because the composition elementary event of system or the character of physical component determine its fault rate difference worked at different conditions.Such as, as the diode in electrical system, its probability of malfunction is just with working time, working temperature, have direct relation by electric current and voltage etc.If analyzed this system, the working time of each element and the temperature of work accommodation etc. may be all different, and along with the working time of entire system and the change of environment temperature, the probability of malfunction of system is also different.This phenomenon is in esse, but unheeded often, and thinks that probability of malfunction is invariable.
The author attempts the change crash rate using element in SFT expression system.In order to describe SFT theory and analytic process below clearly, list the example of necessary SFT related content and analyzed system.Discuss with regard to simple electrical system, this system is constituted by a diode, and the rated operation of diode affects by several factors, wherein importantly working time
tand working temperature
c.For the electrical system affected by these two factors as research object.Related definition is as follows:
1) space fault tree (or hyperspace event tree): the probability of happening of elementary event is not fixing, be by
nindividual factor determines, such event tree is called multidimensional event tree, represents with T.
2) influence factor of elementary event: make the factor that elementary event probability of happening changes.In this example,
trepresent time factor,
crepresent temperature factor.
3) fundamental function (fundamental function) of the probability of happening of elementary event: elementary event under the impact of single influence factor, the probability of happening variation characteristic that the change with influence factor shows.It can elementary function, and piecewise function etc., use P
x ix () represents,
irepresent the
iindividual element,
xreplace influence factor.As this example
ithe temporal characteristics function P of individual original paper
t i(t)=1-e
-λ t, and temperature profile function P
c i(c)=0.5 (cos (2 π c/A)+1), wherein,
tfor element service time, λ is cell failure rate,
afor temperature variation is divided into.
4) the probability of happening space distribution of elementary event: elementary event exists
nunder individual influence factor impact, the probability of happening change that the change with them shows in hyperspace.
nindividual influence factor is as separate independent variable, and elementary event probability of happening is as functional value.Use P
i(x
1, x
2..., x
n) represent, i.e. P
i(x
1, x
2..., x
n)=1-П (1-P
xi i(xi)), wherein i=1,2 ..., n,
nfor influence factor number, be P in this example
i(t, c)=1-(1-P
t i(t)) (1-P
c i(c)).
2 Dynamic fault trees
A kind of analysis that the reliability that Dynamic fault tree method is the nineties in 20th century is analysis space station and air-traffic control system by professor J.B.Dugan proposes has the method for the system reliability of dynamic random fault characteristic.Dynamic fault tree method introduces dynamic logic gate on the basis of fault tree, as cold reserve door, hot reserve door, order associated gate, preferential and door etc., for characterization system cold reserve, hot reserve, can repair, the dynamic perfromance such as resource sharing.
Here adopt Markov state transition matrix to process problem, comprise analytical method and matrix iteration.When calculating the repaiied reliability index of single system, adopt analytical method; Calculate comparatively complication system time, especially application matrix process of iteration when the fiduciary level of solving system and failure frequency.Analytical method is the feature according to logic gate, sets up the system of equations based on Markov state transition diagram, in conjunction with the feature of logic gate, derives and can obtain the expression formula of reliability index, directly apply mechanically the method calculating reliability index.Matrix iteration is probability matrix and the systematic state transfer matrix multiple iteration of foundation system, solves the probability of different conditions residing for given time system, in conjunction with normal working probability, the malfunction probability of the feature compartment system of Different Logic door.Whole dynamic fault tree model is finally utilized to carry out each reliability index of evaluating system.
λcrash rate,
μit is maintenance rate.The function of each logic gate is respectively: with door: the incoming event of and if only if door
x,
ywhen all occurring, the outgoing event of door
zoccur; Or door: when the incoming event of door
x 1,
x 2,
x 3has 1 generation at least, the outgoing event of door
zoccur; Cold reserve door: primary input event
xin running order, stand-by equipment
ybe in cold standby state, only when master/slave device all fault time, the outgoing event of door
zoccur; Hot reserve door: primary input event
xin running order, stand-by equipment
ybe in hot stand-by duty, only when master/slave device all fault time, the outgoing event of door
zoccur.
In 3 systems, the maintenance rate of element is determined
First studied Dynamic fault tree is provided, as shown in Figure 1.
3.1
x 1with
x 2subnumber solves
x 1subtree module is the hot standby combination of element, and the crash rate of element is
λ, maintenance rate is
μ. define its shape space: state 0 represents that 2 modules all normally work, system worked well; Shape 1 represents in 2 modules, and one lost efficacy in maintenance, and another module normally works, system worked well; State 2 represents that 2 modules all lost efficacy, and a module is in repairing, and another module is to be repaired, thrashing.State transition diagram as shown in Figure 1.
According to the feature of probability in conjunction with hot reserve door, the expression formula formula (1) as shown in Figure 2 of each reliability index of deriving to obtain
In formula (1), availability
awhen expression system reaches steady operational status can probability.Failure frequency is
m(
t) refer to [0,
t] the mean failure rate number of times of system in the time, be the failure-frequency of system in the unit interval.
3.2
tsolve
System
tby or door connect lower floor event.Definition status space is: state 0 is that 2 modules are all normal, system worked well; State 1 is
x 1subtree module failure is being repaired,
x 2subtree module is normal,
tlost efficacy; State 2 is
x 2subtree module failure is being repaired,
x 1subtree module is normal,
tlost efficacy.
Combine or the feature of door according to probability, the expression formula of each reliability index as shown in Figure 3 shown in formula (2) of deriving to obtain, in formula,
Λ=
λ 1+
λ 2.
After 3.3 given system availabilities, the distribution of component maintenance rate is determined
If system availability
t a=0.8, ask μ
e1E2and μ
e3E4, due to
e 1with
e 2be
x 1hot reserve event, use μ
e1E2represent
e 1with
e 2maintenance rate (element
x 1maintenance rate), μ
e3E4in like manner define.By in formula (2)
a=
t aavailability known, 1/TA=1+ λ
x1/ μ
x1+ λ
x2/ μ
x2, wherein λ
x1represent
x 1having in hot reserve situation (
e 1→
e 2) crash rate, λ
x2in like manner define; μ
x1represent
x 1having in hot reserve situation (
e 1→
e 2) maintenance rate, μ
x2in like manner define.Know λ again
x1/ μ
x1=(1/MUT
e1E2)/(1/MDT
e1E2), wherein MUT
e1E2represent E
1and E
2average operation time, MDT
e1E2represent E
1and E
2average shut down time, according to formula (1), obtain λ
x1/ μ
x1=1/ (μ
e1E2/ λ
e1E2+ 0.5 (μ
e1E2/ λ
e1E2)
2), λ in formula
e1E2represent
e 1with
e 2maintenance rate (element
x 1maintenance rate), λ
e3E4in like manner define.For separating the problems referred to above, introduce variable
k, k=(λ
x1/ μ
x1): (λ
x2/ μ
x2), consider than symmetry to facilitate research, if
k∈{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1/0.9,1/0.8,1/0.7,1/0.6,1/0.5,1/0.4,1/0.3,1/0.2,1/0.1}。Arrange said process and obtain formula (3) as shown in Figure 4.
If the working field of element, namely the variation range of condition of work be A total={ t ∈ [0,100] sky ∩ c ∈ [0,50] DEG C }, namely the time of system works is 100 days, and operating temperature range is 0 to 50 DEG C.Discuss according to first segment, the failure probability distributions λ under the fault tree state of space
e1E2and λ
e3E4(namely
x 1,
x 2)
.so can according to λ
e1E2and λ
e3E4with formula (3), draw this Dynamic fault tree and exist
k=1,
t aμ when=0.8
e1E2and μ
e3E4distribution plan.
Meet system availability as seen
t a=0.8,
kunder=1 condition, for system element
x 1hot reserve event
e 1,
e 2maintenance rate to meet in working field maintenance rate distribution; And
x 2meet maintenance rate distribution, such system can reach
t athe macro-goal of=0.8.
The determination of maintenance rate under 4 Different Optimization targets
First three kinds of in esse system optimization problems are proposed, 1) when research range (working field) is determined, whole system maintenance rate summation is minimum.The meaning of this actual demand wishes that maintenance frequency is minimum in whole working field, and maintenance frequency minimum like this can reduce shut down time, can reduce maintenance cost simultaneously.2) in Practical Project, generally all can a given acceptable minimal maintenance rate, just implement maintenance when the maintenance rate of element exceedes minimal maintenance rate, or standby preparations of maintenance personal is keeped in repair.Generally wish that system is in whole working field, the region being greater than minimal maintenance rate is the smaller the better, and then minimizing maintenance personal's waiting time improves maintenance efficiency.3) when the expense of element dissimilar in maintenance system is different, maintenance rates different between element can cause system maintenance total expensess different in working field, certainly more low better.Certainly above-mentioned 3 all will ensure that system held is on certain availability basis, otherwise nonsensical.
For Section of three system mentioned, due to
t a=0.8, and λ
e1E2and λ
e3E4to know, so determine that the key of maintenance rate depends on variable
k.Due to 1/TA=1+ λ
x1/ μ
x1+ λ
x2/ μ
x2with k=(λ
x1/ μ
x1): (λ
x2/ μ
x2), namely exist
t awhen fixing,
krepresent a kind of distributional effects, so different distribution (
kdifferent) different μ can be brought
e1E2/ λ
e1E2and μ
e3E4/ λ
e3E4, so by regulating
kunder can meeting the condition of above-mentioned three problems, determine the μ in working field
e1E2and μ
e3E4.
4.1 maintenance rate distributions when asking maintenance rate summation minimum
For first problem, make A maintenance rate minimum μm of in always={ t ∈ [0,100] sky ∩ c ∈ [0,50] DEG C } in working field, it defines formula (4) as shown in Figure 5.
4.2 ask the minimum zone of specifying maintenance rate
If the tolerable maintenance rate of system, so will determine μ in working field
e1E2and μ
e3E4be greater than respectively 2 scope minimum time
kvalue.Method is the whole working field of traversal,
kto μ time different
e1E2and μ
e3E4the region being greater than 2 counts, and count results reckling is corresponding
krequired by value is.
4.3 maintenance rate distributions when asking total upkeep cost minimum
In order to be described element expense difference, definition C
x1and C
x2be respectively element
x 1with
x 2upkeep cost, total maintenance cost defines as shown in Figure 6 shown in formula (5).
Can according to the C of element
x1: C
x2value finds corresponding
kvalue is to determine μ
e1E2and μ
e3E4distribution in working field.Such as, if element
x 1with
x 2upkeep cost be 20 yuan and 100 yuan, i.e. C
x1: C
x2=2:10, so
kwhen=0.3, the maintenance cost of entire system is minimum, the availability of certain system
t a=0.8.
Claims (3)
1. the system maintenance rate method determining and optimize, it is characterized in that, when affecting by working environment containing storage element and part failure rate for understanding, for ensureing the maintenance rate that system availability is taked, this system is used dynamic fault tree representation, usage space fault tree theory determines that its part failure rate distributes, and then determines the distribution of component maintenance rate; It comprises the steps: that subtree solves, solving of system, and after given system availability, the distribution of component maintenance rate is determined, the determination of maintenance rate under Different Optimization target; The present invention can be used for system maintenance rate and determines and optimize.
2. the determination of maintenance rate under Different Optimization target according to claim 1, it is characterized in that, 1) when research range (working field) is determined, whole system maintenance rate summation is minimum, the meaning of this actual demand wishes that maintenance frequency is minimum in whole working field, maintenance frequency minimum like this can reduce shut down time, can reduce maintenance cost simultaneously; 2) in Practical Project, general all can a given acceptable minimal maintenance rate, maintenance is just implemented when the maintenance rate of element exceedes minimal maintenance rate, or the standby preparation maintenance of maintenance personal, generally wish that system is in whole working field, the region being greater than minimal maintenance rate is the smaller the better, and then minimizing maintenance personal's waiting time improves maintenance efficiency; 3) when the expense of element dissimilar in maintenance system is different, maintenance rates different between element can cause system maintenance total expensess different in working field, certainly more low better.
3. the determination of maintenance rate under Different Optimization target according to claim 1, it is characterized in that, if tolerable maintenance rate=2 of system, so will determine in working field μ E1E2 and μ E3E4 be greater than respectively 2 scope minimum time k value, method is the whole working field of traversal, when k is different, the region that μ E1E2 and μ E3E4 is greater than 2 is counted, required by the k value that count results reckling is corresponding is.
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