CN107066817A - A kind of competitive risk fail-safe analysis and preventive maintenance method - Google Patents
A kind of competitive risk fail-safe analysis and preventive maintenance method Download PDFInfo
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Abstract
The present invention relates to a kind of competitive risk fail-safe analysis and preventive maintenance method, including step：Set up competitive risk reliability model；Emulated using the step S1 reliability models set up, obtain product failure accumulated time distribution function；The product failure accumulated time distribution function that is obtained using step S2 is set up preventive maintenance method model and optimized while consider operating conditions.Unlike the prior art, this application provides a kind of comprehensive competitive risk reliability analysis model for considering three kinds of impacts to product degenerative process impact effect；Simultaneously when formulating the preventive maintenance strategy for the product being in competitive risk, the optimization of preventive maintenance time is not only allowed for, it is also considered that the control and optimization of product operating mode.
Description
Technical field
The present invention relates to product reliability field of engineering technology, more particularly to a kind of competitive risk fail-safe analysis and prevention
Method for maintaining.
Background technology
In the prior art, various product may undergo a variety of failure procedures vied each other during operation or use,
Any failure procedure may cause product failure when meeting certain condition.The main product failure process of two classes is decline
Process and random shock.Various product is often because the factor such as abrasion, fatigue, burn into aging gradually fails or loses set
Function.On the other hand, impact, overload or other external stresses may also cause product to be stopped.
These failure procedures are probably independent, it is also possible to related.The current achievement in research on many failure procedures
Assume mostly each failure procedure be it is independent, but above-mentioned hypothesis be sometimes be not inconsistent it is actual, for example：Outside impact may
Decay rates are influenceed, or even change decline failure threshold etc..For the degenerative process of product, the influence of impact may have three kinds：
1) decline amount is increased；2) degenerative process is accelerated；3) reduction (deterioration) decline failure threshold.
Research on decline impact relevant failure process at present considers one in first two in above-mentioned three kinds of influences mostly
Plant or two kinds, have no the competitive risk reliability analysis models for considering all impact influence factors.On the other hand, on competition
The product of risk failure procedure, is not only considered as the optimization of preventive maintenance time during its preventive maintenance strategy is formulated,
Also contemplate for product operating mode (such as：Impact occurrence frequency) control and optimization, and correlative study is not reported yet.
The content of the invention
In view of above-mentioned analysis, the present invention is intended to provide a kind of competitive risk fail-safe analysis and preventive maintenance method, are used
To solve above-mentioned technical problem.
The purpose of the present invention is mainly achieved through the following technical solutions：
There is provided a kind of competitive risk fail-safe analysis and preventive maintenance in one embodiment based on the inventive method
Method, including step：
S1, set up competitive risk reliability model；
S2, using step S1 set up reliability model emulated, obtain product failure accumulated time distribution function；
S3, the product failure accumulated time distribution function obtained using step S2 are while consider operating conditions, and foundation prevents
Method for maintaining model simultaneously optimizes.
In based on another of the inventive method embodiment, step S1 is specifically included：
It is fatal impact when impulsive force size is more than product failure threshold value, product fails immediately；
It is non-lethal impact, product decline value X when impulsive force size is less than product failure threshold values(t) with non-lethal punching
Hit number of times increase and increase, when decline value is more than decline failure threshold, product failure.
In based on another of the inventive method embodiment, when impulsive force size is less than product failure threshold value, judge
Whether impulsive force size, which is more than state, is shifted threshold value：
No, then impact causes recession level to increase；
It is then to cause recession level and decay rates to increase and decline failure threshold reduction；
Wherein recession level and decay rates increase cause the increase of decline value.
In based on another of the inventive method embodiment,
Wherein,It is μ for average0, variance beNormal distribution intercept parameter；βkBefore the transfer of kth next state
Average is μ1, variance beNormal distribution decay rates parameter, β1Decay rates before being shifted for the first next state；tckFor
The time of kth next state transfer occurs for product；YiDecline increase degree caused by correspondence ith impact；ε (t) be average be zero,
Variance is σ2Normal distribution process noise；N (t) is to shift number to the moment t states occurred, and N (t) is to occur to moment t
Number of strokes；
When the transfer of kth next state occurs for product, product decay rates are by βkIt is changed into βk+1, definition：
βk+1=βk+ηk (2)
Wherein ηkIt is μ for averageη, variance beNormal distribution positive stochastic variable；
Meanwhile, product fails failure threshold by DsfkIt is changed into Dsf(k+1), definition：
Dsf(k+1)=Dsfk-θk (3)
Wherein θkIt is μ for averageθ, variance beNormal distribution positive stochastic variable；
The arrival time respectively impacted meets the homogeneous distribution that arrival rate is λ, and unrelated with impact size with degenerative process, then
The number of shocks N (t) being subject to moment t product meets Poisson distributions, i.e.,：
J is the integer (4) more than or equal to 0
WiFor a series of independent identically distributed non-negative stochastic variables, and there are identical cumulative distribution function G (w)=P (Wi＜
W), wherein G (w) and De、DhfUnrelated, w is a stochastic variable for representing impact size；
According to the cumulative distribution function of impact size, it is for the probability that hard failure does not occur for ith impact product then：
P(Wi＜ Dhf) (5)
On the other hand, YiWith WiCorrelation, is designated as：
Yi=Q (Wi) (6)
Wherein, Q (Wi) it is an incremental mapping function.
In based on another of the inventive method embodiment, step S2 is specifically included：
S21, determine simulation sample quantity N, time shaft length Ts, simulation step length Δ t；
S22, selection sample n, initial value n=1；
S23, the Poisson processes generation sample n defined based on formula (4) sequence of impacts, the correspondence time is t1、t2、…
tN, size is W1、W2、…WN, wherein tN≤Ts, number of shocks mark i, initial value i=1；State transfer mark k, initial value k=
1；
S24, into emulation, emulation produces ε (t), Wi、βk、
S25, judge t whether be more than or equal to ti, no, Xs(t)=Xs(t-Δt)+βkΔ t+ ε (t), and perform S26；It is to sentence
Disconnected WiWhether D is more than or equal tohf；It is then to perform step S28, no, execution S27；
S26, judge Xs(t) whether it is more than or equal to Dsfk；It is no, t=t+ Δ t, and step S24 is performed, it is then to perform S28；
S27, judge WiWhether D is more than or equal toe；
It is that then emulation produces θk、ηk, i=i+1, k=k+1, Dsfk=Dsf(k-1)-θ(k-1)、βk=β(k-1)+η(k-1)；Xs(t)
=Xs(t-Δt)+βk(t-tk)Δt+β(k-1)(tk-t+Δt)+Yi+ ε (t) simultaneously performs step S26；
It is no, then i=i+1, Xs (t)=Xs (t- Δ t)+βkΔt+Yi+ ε (t) simultaneously performs step S26；
S28, record sample n out-of-service time t, sample sequence number n=n+1；And judge whether n is more than N；It is no, then perform step
Rapid S22, is that then emulation terminates, and obtains product failure accumulated time distribution function F (t).
In based on another of the inventive method embodiment, time shaft length TsSo that whole samples are in TsWithin fail；
Simulation step length △ t are met will not occur two Secondary Shocks in △ t.
In based on another of the inventive method embodiment, step S3 is specifically included：
S31, set up preventive maintenance model；
S32, the combination for considering different preventive maintenance time and operating modes, and select to cause product preventive maintenance scale of charges most
Low combination.
In based on another of the inventive method embodiment, step S31 is specifically included：Product is in a maintenance cycle
Expected cost of maintenance rate be：
Wherein, tpmFor planning preventive maintenance time, oc is product operating mode, Foc(t) be operating mode oc in the case of product failure when
Between cumulative distribution function, Cpm、CcmRespectively carry out the expense of a preventive maintenance and correction maintenance, CocFor product operating mode control
The expense of system, E [to] it is expected the working time for product in a maintenance cycle.
In based on another of the inventive method embodiment, step S32 is specifically included：
According to formula (7) so that the minimum preventive maintenance time of product repairing scale of charges is with load cases combination：
(tpm, oc) and=argmin [r (tpm,oc)] (8)。
The present invention has the beneficial effect that：Unlike the prior art, three kinds of impacts pair are considered comprehensively this application provides a kind of
The competitive risk reliability analysis model of product degenerative process impact effect；Formulating the product in competitive risk simultaneously
During preventive maintenance strategy, the optimization of preventive maintenance time is not only allowed for, it is also considered that the control and optimization of product operating mode.
Other features and advantages of the present invention will be illustrated in the following description, also, the partial change from specification
Obtain it is clear that or being understood by implementing the present invention.The purpose of the present invention and other advantages can be by the explanations write
Specifically noted structure is realized and obtained in book, claims and accompanying drawing.
Brief description of the drawings
Accompanying drawing is only used for showing the purpose of specific embodiment, and is not considered as limitation of the present invention, in whole accompanying drawing
In, identical reference symbol represents identical part.
Fig. 1 is a kind of competitive risk fail-safe analysis and preventive maintenance method；
Fig. 2 is two class affiliated competitive failure procedures (upper figure is soft failure, and figure below is hard failure)；
Fig. 3 is the simulation sample out-of-service time to obtain flow；
Fig. 4 is product failure accumulated time distribution function；
Fig. 5 is product expected cost of maintenance rate.
Embodiment
The preferred embodiments of the present invention are specifically described below in conjunction with the accompanying drawings, wherein, accompanying drawing constitutes the application part, and
It is used for the principle for explaining the present invention together with embodiments of the present invention.
This application provides a kind of competitive risk fail-safe analysis and preventive maintenance method, as shown in figure 1, specifically including：
S1, set up competitive risk reliability model；
Competitive risk reliability model is set up, that is, sets up and considers decline, two kinds of Failure Factors of impact, while considering impact pair
The reliability model of the possibility influence of degenerative process.As shown in Fig. 2 demonstrating two class relevant failure processes：Led by constantly decline
The soft failure of cause and the hard failure caused by random shock.
As shown in Fig. 2 when product is impacted by ith, working as WiMore than DhfThen product fails immediately, that is, there occurs hard mistake
Effect, wherein, tiThe time for beginning to be impacted by ith from coming into operation for product, WiFor impulsive force size, DhfFor impact failure threshold
Value.
And non-lethal impact then influences the decline value X of products(t), the present embodiment portrays X using stochastic linear degenerated modes
(t), i.e.,：
Wherein,It is μ for average0, variance beNormal distribution intercept parameter；βkBefore the transfer of kth next state
Average is μ1, variance beNormal distribution decay rates parameter, β1Decay rates before being shifted for the first next state；tckFor
The time of kth next state transfer occurs for product；YiDecline increase degree caused by correspondence ith impact；ε (t) is that average is zero,
Variance is σ2Normal distribution process noise；N (t) is to shift number to the moment t states occurred, and N (t) is to occur to moment t
Number of strokes；
Work as WiLess than state transfer threshold value DeWhen, causing the recession level of product degenerative process increases Yi；Work as WiMore than DeWhen,
Next state transfer is designated as, Y is not only resulted ini、βkIncrease, and cause DsfkReduction.Until working as Xs(t) it is more than DsfkRepresent product
Failure.
Wherein, Dsf1Decline failure threshold before being shifted for the 1st next state；DsfkCorrespond respectively to kth (k >=2) secondary shape
Before state transfer, the decline failure threshold after the transfer of (k-1) next state；
When the transfer of kth next state occurs for product, product decay rates are by βkIt is changed into βk+1, definition：
βk+1=βk+ηk (2)
Wherein ηkIt is μ for averageη, variance beThe positive stochastic variable of normal distribution；
Meanwhile, product fails failure threshold by DsfkIt is changed into Dsf(k+1), definition：
Dsf(k+1)=Dsfk-θk (3)
Wherein θkIt is μ for averageθ, variance isNormal distribution positive stochastic variable；
The arrival time respectively impacted meets the homogeneous distribution that arrival rate is λ, and unrelated with impact size with degenerative process, then
The number of shocks N (t) being subject to moment t product meets Poisson distributions, i.e.,：
J is the integer (4) more than or equal to 0
WiFor a series of independent identically distributed non-negative stochastic variables, and there are identical cumulative distribution function, G (w)=P (Wi＜
W), wherein G (w) and De、DhfUnrelated, w is a stochastic variable for representing impact size.
According to the cumulative distribution function of impact size, it is for the probability that hard failure does not occur for ith impact product then：
P(Wi＜ Dhf) (5)
On the other hand, YiWith WiCorrelation, is designated as：
Yi=Q (Wi) (6)
In formula (6), Q (Wi) it is an incremental mapping function.
So, G (w), Q (W are giveni) concrete form, and in formula (1)~(6) each parameter specific value, you can carry out
Fail-safe analysis of the product in decline impact competition degenerative process.
S2, using step S1 set up reliability model emulated, obtain product failure accumulated time distribution function；
The present embodiment uses the reliability of great amount of samples sampling method analysis and evaluation product, the i.e. reality based on great amount of samples
The reliability of failure procedure data analysis product, each of which sample standard deviation experience from bring into operation until failure process.
S21, determine simulation sample quantity N, time shaft length Ts, simulation step length Δ t；
Simulation sample quantity N typically answer it is larger with cause whole simulation result have higher accuracy, time shaft length
TsTypically should be longer to cause whole samples in TsWithin fail；Simulation step length △ t should typically be much smaller than TsMeet simultaneously in △ t
Interior will not occur two Secondary Shocks and be advisable.
S22, selection sample n, initial value n=1；
S23, the Poisson processes generation sample n defined based on formula (4) sequence of impacts, the correspondence time is t1、t2、…
tN, size is W1、W2、…WN, wherein tN≤Ts, number of shocks mark i, initial value i=1；State transfer mark k, initial value k=
1；
S24, into emulation, emulation produces ε (t), Wi、βk、
S25, judge t whether be more than or equal to ti, no, Xs(t)=Xs(t-Δt)+βkΔ t+ ε (t), and perform S26；It is to sentence
Disconnected WiWhether D is more than or equal tohf；It is then to perform step S28, no, execution S27；
tiThe time of ith impact is represented, judges whether the current emulation moment reaches the generation ith impact moment.
S26, judge Xs(t) whether it is more than or equal to Dsfk；No, t=t+ Δ t, return to step S24, are then to perform S28；
S27, judge WiWhether D is more than or equal toe；
It is that then emulation produces θk, η k, i=i+1, k=k+1, Dsfk=Dsf(k-1)-θ(k-1)、βk=β(k-1)+η(k-1)；Xs(t)
=Xs(t-Δt)+βk(t-tk)Δt+β(k-1)(tk-t+Δt)+Yi+ ε (t) simultaneously performs step S26；
It is no, then i=i+1, Xs (t)=Xs (t- Δ t)+βkΔt+Yi+ ε (t) simultaneously performs step S26；
Judge whether impact is more than DeSerious impact, and by being with not being that the situation of serious impact considers product respectively
The development of decline.
S28, record sample n out-of-service time t, sample sequence number n=n+1；And judge whether n is more than N；It is no, then perform step
Rapid S22, is that then emulation terminates, and obtains product failure accumulated time distribution function F (t).
Generally, should choose simulation step length Δ t allows the probability that two Secondary Shocks occur in Δ t to ignore.Obtaining
After the out-of-service time data of these samples, you can according to conventional empirical cumulative distribution function method of estimation (i.e. Kaplan-
Meier methods of estimation) estimation product failure accumulated time distribution function F (t), then the reliability function of product is 1-F (t).
More preferably, the application is that the fail-safe analysis emulated based on Monte Carlo is assessed, as shown in figure 3, giving base
Flow is obtained in the Monte Carlo sample out-of-service times emulated.Typically, larger sample size need to be chosen (for example：N=
1000), simulation time shaft length T in additionsAlso long enough is answered to also ensure that all simulation samples fail before emulation terminates.
S3, the product failure accumulated time distribution function obtained using step S2 consider that operating conditions set up prevention dimension simultaneously
Repair method model and optimize；
In the present embodiment, preventive maintenance key element includes four altogether：
Repair target：Minimize the maintenance cost rate of product；
Maintenance effect：Preventive maintenance " is repaired as new " with correction maintenance；
Maintenance policy：Sequence type is repaired, i.e. the adjacent maintenance time twice of product does not limit, completely according to optimum results
It is determined that；
Maintenance limitation：Nothing, i.e., wait in the absence of spare part, the constraint such as product availability index.
Only consider that preventive maintenance time has different, the application of corresponding influence on maintenance policy from conventional preventive maintenance strategy
Also contemplate influence and its expense of the operating conditions (intervene impact and produce frequency, size etc.) to product reliability.
Based on above-mentioned it is assumed that expected cost of maintenance rate of the product in a maintenance cycle is：
Wherein, tpmFor planning preventive maintenance time, oc is product operating mode, Foc(t) be operating mode oc in the case of product failure when
Between cumulative distribution function, Cpm、CcmRespectively carry out the expense of a preventive maintenance and correction maintenance, CocFor product operating mode control
The expense of system, E [to] it is expected the working time for product in a maintenance cycle.
In formula (7), product operating conditions expense CocF can typically be influenceedoc(t), such influence is needed using other
Ripe statistical method, such as：Histogram method etc..Influence of the operating mode to product reliability is investigated in the case of different operating modes.So,
According to formula (7) so that the minimum preventive maintenance time of product repairing scale of charges is with load cases combination：
(tpm, oc) and=arg min [r (tpm,oc)] (8)
In a specific embodiment, μ is defined0=4, σ0=1, μ1=4, σ1=1, σ=1, μη=0, ση=1, μθ=
0, σθ=1, λ=5,10,15, De=0.7, Dhf=0.95, Dsf1=200, XiIt is 0 for average, variance is 1 non-negative normal distribution
Variable, Yi=Xi。
Based on step S1, S2, Fig. 4 gives the product failure accumulated time distribution function under different λ levels.To formulate production
Product preventive maintenance strategy, defined parameters Cpm=1000, Ccm=4000, at the same consider for operating mode control (such as：Distinct device
Lubrication level) the frequency parameter λ (lamda i.e. in figure) of product impact generation can be influenceed, and have：Coc=3 λ.According to formula
(7), Fig. 5 gives the product expected cost of maintenance rate in the case of different operating modes and preventive maintenance time, the result in figure,
Combine (tpm=23, λ=and minimum maintenance cost rate 15) is given, select this group of parameter to formulate product preventive maintenance plan for this
Slightly.
The present invention has the beneficial effect that：
This application provides a kind of comprehensive three kinds of impacts of consideration are reliable to the competitive risk of product degenerative process impact effect
Property analysis model；Simultaneously when formulating the preventive maintenance strategy for the product being in competitive risk, preventive maintenance is not only allowed for
The optimization of time, it is also considered that the control and optimization of product operating mode.
It will be understood by those skilled in the art that realizing all or part of flow of above-described embodiment method, meter can be passed through
Calculation machine program instructs the hardware of correlation to complete, and described program can be stored in computer-readable recording medium.Wherein, institute
It is disk, CD, read-only memory or random access memory etc. to state computer-readable recording medium.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art the invention discloses technical scope in, the change or replacement that can be readily occurred in,
It should all be included within the scope of the present invention.
Claims (9)
1. a kind of competitive risk fail-safe analysis and preventive maintenance method, it is characterised in that including step：
S1, set up competitive risk reliability model；
S2, using step S1 set up reliability model emulated, obtain product failure accumulated time distribution function；
S3, the product failure accumulated time distribution function obtained using step S2 set up preventive maintenance while consider operating conditions
Method model simultaneously optimizes.
2. the method as described in claim 1, it is characterised in that the step S1 is specifically included：
It is fatal impact when impulsive force size is more than product failure threshold value, product fails immediately；
It is non-lethal impact, product decline value X when impulsive force size is less than product failure threshold values(t) with non-lethal number of shocks
Increase and increase, when decline value is more than decline failure threshold, product failure.
3. method as claimed in claim 2, it is characterised in that when impulsive force size is less than product failure threshold value, judge punching
Hit whether power size is more than state transfer threshold value：
No, then impact causes recession level to increase；
It is then to cause recession level and decay rates to increase and decline failure threshold reduction；
Wherein recession level and decay rates increase cause the increase of decline value.
4. method as claimed in claim 2 or claim 3, it is characterised in that
Wherein,It is μ for average0, variance beNormal distribution intercept parameter；βkAverage before being shifted for kth next state
For μ1, variance beNormal distribution decay rates parameter, β1Decay rates before being shifted for the first next state；tckFor product
Occurs the time of kth next state transfer；YiDecline increase degree caused by correspondence ith impact；ε (t) is that average is zero, variance
For σ2Normal distribution process noise；N (t) is to shift number to the moment t states occurred, and N (t) is to rushing that moment t occurs
Hit number；
When the transfer of kth next state occurs for product, product decay rates are by βkIt is changed into βk+1, definition：
βk+1=βk+ηk (2)
Wherein ηkIt is μ for averageη, variance beNormal distribution positive stochastic variable；
Meanwhile, product fails failure threshold by DsfkIt is changed into Dsf(k+1), definition：
Dsf(k+1)=Dsfk-θk (3)
Wherein θkIt is μ for averageθ, variance beNormal distribution positive stochastic variable；
The arrival time respectively impacted meet arrival rate be λ homogeneous distribution, and with degenerative process with impact size it is unrelated, then to when
Carve the number of shocks N (t) that is subject to of t products and meet Poisson distributions, i.e.,：
J is the integer (4) more than or equal to 0
WiFor a series of independent identically distributed non-negative stochastic variables, and there are identical cumulative distribution function G (w)=P (Wi＜ w), its
Middle G (w) and De、DhfUnrelated, w is a stochastic variable for representing impact size；
According to the cumulative distribution function of impact size, it is for the probability that hard failure does not occur for ith impact product then：
P(Wi＜ Dhf) (5)
On the other hand, YiWith WiCorrelation, is designated as：
Yi=Q (Wi) (6)
Wherein, Q (Wi) it is an incremental mapping function.
5. method as claimed in claim 4, it is characterised in that the step S2 is specifically included：
S21, determine simulation sample quantity N, time shaft length Ts, simulation step length Δ t；
S22, selection sample n, initial value n=1；
S23, the Poisson processes generation sample n defined based on formula (4) sequence of impacts, the correspondence time is t1、t2、…tN, greatly
Small is W1、W2、…WN, wherein tN≤Ts, number of shocks mark i, initial value i=1；State transfer mark k, initial value k=1；
S24, into emulation, emulation produces ε (t), Wi、βk、
S25, judge t whether be more than or equal to ti, no, Xs(t)=Xs(t-Δt)+βkΔ t+ ε (t), and perform S26；It is to judge Wi
Whether D is more than or equal tohf；It is then to perform step S28, no, execution S27；
S26, judge Xs(t) whether it is more than or equal to Dsfk；It is no, t=t+ Δ t, and step S24 is performed, it is then to perform S28；
S27, judge WiWhether D is more than or equal toe；
It is that then emulation produces θk、ηk, i=i+1, k=k+1, Dsfk=Dsf(k-1)-θ(k-1)、βk=β(k-1)+η(k-1)；Xs(t)=Xs
(t-Δt)+βk(t-tk)Δt+β(k-1)(tk-t+Δt)+Yi+ ε (t) simultaneously performs step S26；
It is no, then i=i+1, Xs (t)=Xs (t- Δ t)+βkΔt+Yi+ ε (t) simultaneously performs step S26；
S28, record sample n out-of-service time t, sample sequence number n=n+1；And judge whether n is more than N；It is no, then perform step
S22, is that then emulation terminates, and obtains product failure accumulated time distribution function F (t).
6. method as claimed in claim 5, it is characterised in that time shaft length TsSo that whole samples are in TsWithin fail；It is imitative
True step-length △ t are met will not occur two Secondary Shocks in △ t.
7. the method as described in claim 1, it is characterised in that the step S3 is specifically included：
S31, set up preventive maintenance model；
S32, the combination for considering different preventive maintenance time and operating modes, and select make it that product preventive maintenance scale of charges is minimum
Combination.
8. method as claimed in claim 7, it is characterised in that the step S31 is specifically included：Product is in a maintenance cycle
Interior expected cost of maintenance rate is：
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Wherein, tpmFor planning preventive maintenance time, oc is product operating mode, Foc(t) it is in the case of operating mode oc the product failure time
Cumulative distribution function, Cpm、CcmRespectively carry out the expense of a preventive maintenance and correction maintenance, CocFor product operating conditions
Expense, E [to] it is expected the working time for product in a maintenance cycle.
9. method as claimed in claim 7, it is characterised in that the step S32 is specifically included：
According to formula (7) so that the minimum preventive maintenance time of product repairing scale of charges is with load cases combination：
(tpm, oc) and=argmin [r (tpm,oc)] (8)。
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