CN108108542A - The life-span prediction method of low-voltage complete switch equipment - Google Patents
The life-span prediction method of low-voltage complete switch equipment Download PDFInfo
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Abstract
The invention discloses a kind of life-span prediction methods of low-voltage complete switch equipment, method assumes that the service life of low-voltage complete switch equipment obeys three-parameter Weibull distribution, grey estimation method is proposed, distributed constant is estimated, finally the reliable remaining life of equipment is predicted.The invention has the advantages that according to life prediction as a result, formulating perfect plant maintenance, maintenance project, it is ensured that the promptness of maintenance of equipment, and the unnecessary interruption maintenance of equipment is avoided, it can be achieved that the minimal maintenance cost of equipment.
Description
Technical field
The present invention relates to fields, particularly a kind of life-span prediction method of low-voltage complete switch equipment.
Background technology
Low-voltage complete switch equipment is the important power equipment of low-voltage power supply system, is responsible for electric energy in low-voltage power supply system
Control, protection, conversion and distribution, securely and reliably whether directly influence the normal operation of low-voltage power system.It is current low
Switchgear assembly is pressed using preventative planned maintenance pattern, as long as equipment reaches the predetermined cycle of operation, no matter its failure with
It is no, it will maintenance down.Since this maintenance mode does not account for the specific operation conditions of equipment, it is lack of pertinence, not only
There are many unnecessary maintenance downs；And unreasonable maintenance time is easy to cause maintenance of equipment not in time, causes system
The accidents such as power failure.In order to ensure that low-voltage power supply system is safely and steadily run, the economy of maintenance of equipment is improved, realizes equipment dimension
The minimum of cost is protected, Weibull distribution model is introduced herein, the reliability index of equipment life is assessed, with equipment
Assessment result is foundation, formulates perfect maintenance of equipment scheme.
Weibull distribution is one of mostly important Lifetime Distribution Model in Reliability Engineering field.Weibull distribution proposes certainly
Since, it has been widely used among the various fields such as statistics, economics, medicine and biology, achieves numerous achievements.Practice
It proves, the Weibull Distributed Units of most equipment.Zhong Qianghui etc. describes laser using three-parameter Weibull distribution model
The service life of device, by analyzing its deterioration law come assessment reliability；Liu Gang etc. assumes that the service life of weaponry obeys two parameter prestige
Boolean is distributed, and the remaining life of weaponry is predicted；Yang Xian etc. according to Weibull distribution be randomly assigned casing it is each absolutely
The edge layer service life is calculated the service life distribution of oilpaper set interior insulation system and the remaining life point of rear sleeve occurs for interlayer breakdown
Cloth；Du Xiong etc. describes the wind speed distribution characteristics of wind power plant using the probability density function of Weibull distribution, establishes power device
The probability assessment model in service life.
The content of the invention
The purpose of the present invention is to solve the above problems, devise a kind of life prediction side of low-voltage complete switch equipment
Method.
Realize above-mentioned purpose the technical scheme is that, 1, a kind of life-span prediction method of low-voltage complete switch equipment,
It is characterized in that, this method includes：
If the service life T of low-voltage complete switch equipment obeys three-parameter Weibull distribution, and probability density function f (t)
For[12]：
Wherein t0For minimum life parameter, taLife parameter is characterized, b is form parameter；Formula (1) is known with formula (37) comparison：
t0For location parameter γ, b is form parameter β, ta-t0For scale parameter η；
Cumulative failure probability function F (t) is：
Reliability Function R (t) is：
Work as t=t0When, R (t0)=1, that is minimum life is the safe life that reliability is 100%；Work as t=ta
When, R (ta)=0.368, i.e. ta=t0.368, the service life is characterized, this is also taThe referred to as cause of characteristics life parameter；
At this point, the mathematic expectaion and variance of stochastic variable T are respectively：
It is defined by median life：
Simultaneous formula (40), formula (41) and formula (42) establish Nonlinear System of Equations, by solving equation group, obtain Weibull
It is distributed the estimate of three parametersThe method for parameter estimation is known as analytic method；
If equipment at work between t moment remain to normal use, equipment is continued to come into operation to be passed through until scrapping
The time gone through is known as the remaining life of equipment；Remaining life is also stochastic variable, represented with Tt as the service life of equipment, if
Its distribution function is Ft (x), then has：
Ft(x)=P (Tt≤x) (43)
Formula (43) is made with reference to the conditional probability theory in statistics further to calculate[13]：
It considers：
F (t)=1-R (t) (45)
F (x+t)=1-R (x+t) (46)
Formula (45) and formula (46) are substituted into formula (44) to obtain：
Formula (39) is substituted into formula (47) and obtains the distribution function F of equipment remaining lifet(x) it is：
Usage time be t equipment, remaining life TtThe probability that x can be reached is known as the reliability R of equipment remaining lifet
(x), expression formula is as follows：
The probability density function f of equipment remaining lifet(x) it is：
2nd, the life-span prediction method of low-voltage complete switch equipment according to claim 1, which is characterized in that described three
Parameters of Weibull be with the naming of Sweden scientist Waloddi Weibull, Waloddi Weibull in
Nineteen fifty-one proposes the three-parameter Weibull distribution model comprising location parameter γ, scale parameter η and form parameter β；
If stochastic variable T obeys the Weibull distribution of three parameters, probability density function f (t) is[6]：
Cumulative failure probability function F (t) is：
Wherein, β>0 is form parameter, η>0 is scale parameter, and γ >=0 is location parameter；
The mathematic expectaion E (T) and variance Var (T) of stochastic variable T for obeying Weibull distribution be：
Wherein Γ () is Gamma functions；
As location parameter γ=0, three-parameter Weibull distribution translates into two parameters of Weibull, probability at this time
Density function f (t) and cumulative failure probability function F (t) is respectively：
3rd, the life-span prediction method of low-voltage complete switch equipment according to claim 2, which is characterized in that the prestige
The method for parameter estimation of boolean's distribution includes：
Moments estimation method
If T is random variable of continuous type, probability density function is：
f(t；θ1,θ2,…,θk), wherein θ1,θ2,…,θkFor k parameters to be estimated, if (T1,T2,…,Tk) it is from totality
A sample of T, it is assumed that the preceding k ranks square of overall T
In the presence of, and be θ1,θ2,…,θkFunction, wherein l=1,2 ..., k；
The preceding k ranks square A of samplelFor：
Sample moment A is understood by knowledge of statisticslConvergence in (with)probability is in corresponding population moment μl；
Order：
μl=Al (9)
It can obtain containing k unknown parameter θ1,θ2,…,θkK equation, Simultaneous Equations solve：
WithAs θiThe estimate of (i=1,2 ..., k), here it is moments estimation methods；The essence of moments estimation method is exactly to use sample
This each rank square removes the overall each rank square of estimation；
The square of Weibull distribution is defined in document [8], overall k rank squares μkFor：
The k rank squares A of sample momentkFor：
Wherein, ti(i=1,2 ..., n) is sampled data values, and t0=0；
Make μk=Ak, k=1,2,4, it solves：
Above-mentioned form parameter β, scale parameter η, the estimate of location parameter γ of having obtained be respectively
The related coefficient estimation technique
Formula (2) transposition is deformed：
Natural logrithm is taken to obtain formula (16):
OrderX=ln (t- γ), b=- β ln η, a=β, obtain：
Y=aX+b (18)
The linearization process to Weibull model is completed above, and theoretically, Y and X is stringent linear relationship；Phase relation
Number ρ is the statistic for weighing linearly related degree between variable X and Y, and -1≤ρ≤1, ρ are closer to 1, then linear
Degree of correlation is higher；
If one group of lifetime data of low-voltage complete switch equipment is t1,t2,…,tn, experience distribution is calculated by Median rank formula
Function, Median rank formula are as follows[9]：
n>When 20：
During n≤20：
Then there is Xi=ln (ti- γ),
So, the correlation coefficient ρ of X and Y is[10]：
Observation type (21) is it is not difficult to find that correlation coefficient ρ is the function of γ, then selects suitable γ, makes | ρ | it obtains maximum
Value, at this timeThe as estimate of location parameter γ；
Since location parameter γ has been acquired, three-parameter Weibull distribution originally deteriorates to two parameters of Weibull, should
The estimate of form parameter β and scale parameter η are solved with least square method；
Grey estimation method
It is deformed by formula (16)：
Above formula is further arranged：
C=η are made,B=γ, then have：
T=ce-ax+b (24)
The albefaction equation of Grey Differential Equation in gray system theory is：
The time response function of albefaction solution of equation is：
It is not difficult to find that formula (24) has identical form with formula (26), therefore, grey GM (1,1) model pair can be passed through
The parameter of Weibull distribution is estimated that specific method is as follows：
Firstth, by the lifetime data t of equipment1,t2,…,tnTemporally front and rear order is ranked up；
Secondth, suitable Median rank formula is selected according to the number n of lifetime data, experience is calculated by formula (19) or formula (20)
Distribution function
3rd, willSubstitute into formulaIn, obtain xi(i=1,2 ..., n)；
4th, by (ti,xi) sequence establishes Grey Differential EquationAnd unknown parameter a is solved by formula (27)
And u；
[a,u]T=(BTB)-1BTY (27)
Wherein：
After solving a and u, then the relevant parameter of Weibull distribution can be obtained Scale parameter
It can be calculated by the initial value of model.
4th, the life-span prediction method of low-voltage complete switch equipment according to claim 1, which is characterized in that it is described can
It is to obey three-parameter Weibull distribution in the service life of equipment by degree function R (t), the fault time of equipment is represented by stochastic variable T,
The Reliability Function R (t) of so equipment is：
As γ=0, the Reliability Function R (t) that can obtain two parameters of Weibull is：
It is easy to get by formula (2) and formula (30)：R (t)=1-F (t)；
It was found from the expression formula of Reliability Function R (t), the reliability R of equipment is reduced with the increase of usage time；This
It is because of the increase with usage time, wear and aging phenomenon occurs in equipment, and the failure rate of equipment increases, and reliability is caused to drop
It is low；
Failure rate estimation
The crash rate of equipment t in a flash in office refers to that equipment work is general to failing in the unit interval after t moment
Rate；Obviously, crash rate is the function of time t, is thus generically referred to as failure rate estimation, is denoted as：λ(t)；
By formula (32) both sides simultaneously divided by Δ t, limit when and taking Δ t → 0, obtains：
If equipment life obeys three-parameter Weibull distribution, failure rate estimation λ (t) is：
As γ=0, the failure rate estimation λ (t) that can obtain two parameters of Weibull is：
Work as β it can be seen from the expression formula of the failure rate estimation of Weibull distribution<When 1, the crash rate of equipment is at any time
Successively decrease, suitable for the early application stage of equipment, corresponding to the earlier failure period of tub curve；As β=1, the failure of equipment
Rate is constant, suitable for equipment serviceability limit stage, corresponding to the random failure period of tub curve；Work as β>When 1, the failure of equipment
Rate is incremented by any time, suitable for the service stage in later stage of equipment, corresponding to the wear-out failure period of tub curve；Therefore, Weibull
Distribution is more vivid compared with other distribution patterns, flexible, can describe situation of change of the equipment life in entire life cycle；Bath
Pelvic curvature line is equipment typical failure rate curve, as shown in Figure 1；
Q-percentile life
Reliability Function R (t) is the function of working time t, is reduced with the increase of t, when Reliability Function is with work
Between there are one-to-one relationships；The working time when reliability of equipment being made to be reduced to set-point R (0≤R≤1) is known as reliability
For the Q-percentile life of R, t is denoted asR, relationship is：
R(tR)=R (36)
Q-percentile life during equipment reliability R=0.5 is known as median life, with t0.5
It represents；Q-percentile life during reliability R=exp (- 1)=0.368 is known as characteristics life, with t0.368It represents；Reliably
Spend R and Q-percentile life tRBetween relation can be represented with Fig. 2.
Using the life-span prediction method for the low-voltage complete switch equipment that technical scheme makes, according to life prediction
As a result, formulate perfect plant maintenance, maintenance project, it is ensured that the promptness of maintenance of equipment, and avoid equipment is unnecessary from stopping
The minimal maintenance cost, it can be achieved that equipment is repaiied in electric-examination.
Description of the drawings
Fig. 1 is the tub curve figure of the life-span prediction method of low-voltage complete switch equipment of the present invention；
Fig. 2 is Q-percentile life graph of the present invention；
Fig. 3 is reliability curves figure of the present invention；
Fig. 4 is the Life Table of low-voltage complete switch equipment of the present invention；
Fig. 5 is parameter Estimation table of the present invention；
Fig. 6 is service life reliability calculating numerical tabular of the present invention；
Fig. 7 is reliability data table of the present invention.
Specific embodiment
The present invention is specifically described below in conjunction with the accompanying drawings, as shown in Fig. 1-3 and table 1-4,
Embodiment 1
It is collated to have obtained 20 low-voltage complete switch and set according to the data after sale of certain low-voltage complete switch equipment producer
It is arranged sequentially according to descending in table 1, life unit 10 by standby lifetime data5h。
The distribution of three-parameter Weibull distribution is joined using the above-mentioned analytic method introduced, moments estimation method and grey estimation method
Number is estimated that estimated result is as shown in table 2.
In order to weigh the quality of above-mentioned three kinds of method for parameter estimation, opposite root-mean-square error (RRMSE), which will be incorporated herein, to join
The result of number estimation method quantifies[14].It is as follows with respect to the calculating formula of root-mean-square error：
In above formula,For the reliability being calculated by Median rank formula,(j=1,2,3) it is by jth kind in table 2
The estimates of parameters that method acquires substitutes into formula (39) counted reliability.Represent analytic method during wherein j=1, when j=2 represents square
The estimation technique, when j=3, represent grey estimation method.Specific result of calculation is as shown in table 3.
Reliability numerical value substitution formula (51) is calculated to the reliability under analytic method, moments estimation method and grey estimation method respectively
With respect to root-mean-square error, result of calculation is：
RRMSE1=0.0910
RRMSE2=0.0958
RRMSE3=0.0890
Therefore, it is more accurate the parameter of three-parameter Weibull distribution to be estimated using grey estimation method.
The estimated result of grey estimation method is substituted into formula (48) respectively and formula (49) obtains the surplus of low-voltage complete switch equipment
The distribution function and Reliability Function in remaining service life：
Assuming that the working time of certain low-voltage complete switch equipment for 0.438 × 105h (5 years), it is necessary to solve the low-voltage complete
Remaining life of the switchgear in the case of reliability R=0.7 is how many.
It is now predicted using the predicting residual useful life model shown in formula (53), it is known that condition：Equipment task time t=
0.4380 × 105h, reliability Rt (x)=0.7.Known conditions is substituted into formula (53), remaining life x is solved, solves knot
Fruit is x=0.6007 × 105h (6.86).
In order to deepen the understanding to the prediction model, designated firing duration is 0.4380 × 10 respectively5h、0.5256×
105h、0.6132×105h、0.7008×105h、 0.7884×105H and 0.8760 × 105H (i.e. 5,6,7,8,9,10 years) feelings
Under condition, remaining life is 0.4380 × 105h、0.5256×105h、0.6132×105h、 0.7008×105h、0.7884×
105H and 0.8760 × 105The reliability of h.Result of calculation is as shown in table 4.
From data in table 4：Working time is 0.5256 × 105The equipment of h, remaining life reach 0.4380 × 105h
Reliability R=0.7646；The working time is 0.5256 × 10 in other words5The equipment of h, in reliability R=0.7646
The remaining life that can reach is 0.4380 × 105H, and so on.
It can be drawn a conclusion by data in table 4：With the increase of equipment usage time, reach same remaining life can
It is decreased by degree, this is identical with equipment actual conditions.The usage time of low-voltage complete switch equipment is longer, internal each
The wear and agings such as class low tension switch device, busbar are more serious, then equipment is completed to advise under the defined conditions, in the defined time
Determine that the probability of function is smaller, this also demonstrates the validity of the predicting residual useful life model.
Reliability curves are drawn by data in table 4, as shown in Figure 3：
From reliability curves：With the increase of equipment usage time, the equipment remaining lifetime value under same reliability
It is less and less；With the increase of equipment usage time, equipment reliability, which reduces, to be getting faster, and reliability curves are more and more steeper
It is high and steep.
Assuming that the service life of low-voltage complete switch equipment obeys three-parameter Weibull distribution, proposed with reference to gray system theory
The grey parameter estimation technique, while application moments estimation method and analytic method estimate Weibull distribution parameters, introduce reliability
Opposite root-mean-square error, the accuracy of the estimates of parameters obtained to the different estimations technique compares, and finally chooses grey
The estimates of parameters of the estimation technique thereby establishes the predicting residual useful life model of low-voltage complete switch equipment, passes through specific example
Demonstrate the reasonability and validity of the model.
It can be using designated firing duration as the low-voltage complete switch equipment of t, in reliability R according to the predicting residual useful life model
Under the conditions of remaining lifetime value；The low-voltage complete switch equipment that the working time is t can also be obtained, when reaching remaining life x
Reliability value.It in practical applications can be according to prediction remaining lifetime value or reliability value, in combination with low-voltage complete switch
The operating condition of equipment formulates corresponding maintenance standard, then implements to the standard among the repair schedule for formulating equipment.This
A kind of maintenance project using reliability assessment result as foundation of sample has very strong specific aim, can reduce the repair of equipment into
This, ensures the economy of maintenance of equipment.
Above-mentioned technical proposal only embodies the optimal technical scheme of technical solution of the present invention, those skilled in the art
The principle of the present invention is embodied to some variations that some of which part may be made, belongs to the scope of protection of the present invention it
It is interior.
Claims (4)
1. a kind of life-span prediction method of low-voltage complete switch equipment, which is characterized in that this method includes：
If the service life T of low-voltage complete switch equipment obeys three-parameter Weibull distribution, and probability density function f (t) is[12]：
Wherein t0For minimum life parameter, taLife parameter is characterized, b is form parameter；Formula (1) is known with formula (37) comparison：t0For
Location parameter γ, b are form parameter β, ta-t0For scale parameter η；
Cumulative failure probability function F (t) is：
Reliability Function R (t) is：
Work as t=t0When, R (t0)=1, that is minimum life is the safe life that reliability is 100%；Work as t=taWhen, R
(ta)=0.368, i.e. ta=t0.368, the service life is characterized, this is also taThe referred to as cause of characteristics life parameter；
At this point, the mathematic expectaion and variance of stochastic variable T are respectively：
It is defined by median life：
Simultaneous formula (40), formula (41) and formula (42) establish Nonlinear System of Equations, by solving equation group, obtain Weibull distribution
The estimate of three parametersThe method for parameter estimation is known as analytic method；
If equipment at work between t moment remain to normal use, equipment is continued to come into operation what is undergone until scrapping
Time is known as the remaining life of equipment；Remaining life is also stochastic variable, is represented with Tt, if its point as the service life of equipment
Cloth function is Ft (x), then has：
Ft(x)=P (Tt≤x) (43)
Formula (43) is made with reference to the conditional probability theory in statistics further to calculate[13]：
It considers：
F (t)=1-R (t) (45)
F (x+t)=1-R (x+t) (46)
Formula (45) and formula (46) are substituted into formula (44) to obtain：
Formula (39) is substituted into formula (47) and obtains the distribution function F of equipment remaining lifet(x) it is：
Usage time be t equipment, remaining life TtThe probability that x can be reached is known as the reliability R of equipment remaining lifet(x),
Expression formula is as follows：
The probability density function f of equipment remaining lifet(x) it is：
2. the life-span prediction method of low-voltage complete switch equipment according to claim 1, which is characterized in that three parameter
Weibull distribution is with the naming of Sweden scientist Waloddi Weibull, and Waloddi Weibull are carried in nineteen fifty-one
The three-parameter Weibull distribution model for including location parameter γ, scale parameter η and form parameter β is gone out；
If stochastic variable T obeys the Weibull distribution of three parameters, probability density function f (t) is[6]：
Cumulative failure probability function F (t) is：
Wherein, β>0 is form parameter, η>0 is scale parameter, and γ >=0 is location parameter；
The mathematic expectaion E (T) and variance Var (T) of stochastic variable T for obeying Weibull distribution be：
Wherein Γ () is Gamma functions；
As location parameter γ=0, three-parameter Weibull distribution translates into two parameters of Weibull, probability density at this time
Function f (t) and cumulative failure probability function F (t) is respectively：
3. the life-span prediction method of low-voltage complete switch equipment according to claim 2, which is characterized in that the Weibull
The method for parameter estimation of distribution includes：
Moments estimation method
If T is random variable of continuous type, probability density function is：
f(t；θ1,θ2,…,θk), wherein θ1,θ2,…,θkFor k parameters to be estimated, if (T1,T2,…,Tk) for from overall T one
A sample, it is assumed that the preceding k ranks square of overall T
In the presence of, and be θ1,θ2,…,θkFunction, wherein l=1,2 ..., k；
The preceding k ranks square A of samplelFor：
Sample moment A is understood by knowledge of statisticslConvergence in (with)probability is in corresponding population moment μl；
Order：
μl=Al (9)
It can obtain containing k unknown parameter θ1,θ2,…,θkK equation, Simultaneous Equations solve：
WithAs θiThe estimate of (i=1,2 ..., k), here it is moments estimation methods；The essence of moments estimation method is exactly with sample
Each rank square removes the overall each rank square of estimation；
The square of Weibull distribution is defined in document [8], overall k rank squares μkFor：
The k rank squares A of sample momentkFor：
Wherein, ti(i=1,2 ..., n) is sampled data values, and t0=0；
Make μk=Ak, k=1,2,4, it solves：
Above-mentioned form parameter β, scale parameter η, the estimate of location parameter γ of having obtained be respectively
The related coefficient estimation technique
Formula (2) transposition is deformed：
Natural logrithm is taken to obtain formula (16):
OrderX=ln (t- γ), b=- β ln η, a=β, obtain：
Y=aX+b (18)
The linearization process to Weibull model is completed above, and theoretically, Y and X is stringent linear relationship；Correlation coefficient ρ
It is the statistic for weighing linearly related degree between variable X and Y, and -1≤ρ≤1, ρ are closer to 1, then linearly related
Degree is higher；
If one group of lifetime data of low-voltage complete switch equipment is t1,t2,…,tn, experience distribution letter is calculated by Median rank formula
Number, Median rank formula are as follows[9]：
n>When 20：
During n≤20：
Then there is Xi=ln (ti- γ),
So, the correlation coefficient ρ of X and Y is[10]：
Observation type (21) is it is not difficult to find that correlation coefficient ρ is the function of γ, then selects suitable γ, makes | ρ | maximum is obtained,
At this timeThe as estimate of location parameter γ；
Since location parameter γ has been acquired, three-parameter Weibull distribution originally deteriorates to two parameters of Weibull, using most
Small square law solves the estimate of form parameter β and scale parameter η；
Grey estimation method
It is deformed by formula (16)：
Above formula is further arranged：
C=η are made,B=γ, then have：
T=ce-ax+b (24)
The albefaction equation of Grey Differential Equation in gray system theory is：
The time response function of albefaction solution of equation is：
It is not difficult to find that formula (24) has identical form with formula (26), it therefore, can be by grey GM (1,1) models to prestige cloth
You are estimated that specific method is as follows at the parameter of distribution：
Firstth, by the lifetime data t of equipment1,t2,…,tnTemporally front and rear order is ranked up；
Secondth, suitable Median rank formula is selected according to the number n of lifetime data, experience distribution is calculated by formula (19) or formula (20)
Function
3rd, willSubstitute into formulaIn, obtain xi(i=1,2 ..., n)；
4th, by (ti,xi) sequence establishes Grey Differential EquationAnd unknown parameter a and u are solved by formula (27)；
[a,u]T=(BTB)-1BTY (27)
Wherein：
After solving a and u, then the relevant parameter of Weibull distribution can be obtained Scale parameterBy mould
The initial value of type can be calculated.
4. the life-span prediction method of low-voltage complete switch equipment according to claim 1, which is characterized in that the reliability
Function R (t) is to obey three-parameter Weibull distribution in the service life of equipment, and the fault time of equipment is represented by stochastic variable T, then
The Reliability Function R (t) of equipment is：
As γ=0, the Reliability Function R (t) that can obtain two parameters of Weibull is：
It is easy to get by formula (2) and formula (30)：R (t)=1-F (t)；
It was found from the expression formula of Reliability Function R (t), the reliability R of equipment is reduced with the increase of usage time；This be because
For with the increase of usage time, wear and aging phenomenon occurs in equipment, the failure rate of equipment increases, and reliability is caused to reduce；
Failure rate estimation
The crash rate of equipment t in a flash in office refers to equipment work to the probability to fail in the unit interval after t moment；It is aobvious
So, crash rate is the function of time t, is thus generically referred to as failure rate estimation, is denoted as：λ(t)；
By formula (32) both sides simultaneously divided by Δ t, limit when and taking Δ t → 0, obtains：
If equipment life obeys three-parameter Weibull distribution, failure rate estimation λ (t) is：
As γ=0, the failure rate estimation λ (t) that can obtain two parameters of Weibull is：
Work as β it can be seen from the expression formula of the failure rate estimation of Weibull distribution<When 1, the crash rate of equipment is successively decreased at any time,
Suitable for the early application stage of equipment, corresponding to the earlier failure period of tub curve；As β=1, the crash rate of equipment is normal
Number, suitable for equipment serviceability limit stage, corresponding to the random failure period of tub curve；Work as β>When 1, the crash rate of equipment is at any time
Between be incremented by, suitable for the service stage in later stage of equipment, corresponding to the wear-out failure period of tub curve；Therefore, Weibull distribution compared with
Other distribution patterns are more vivid, flexible, can describe situation of change of the equipment life in entire life cycle；Tub curve
For equipment typical failure rate curve, as shown in Figure 1；
Q-percentile life
Reliability Function R (t) is the function of working time t, is reduced with the increase of t, Reliability Function is deposited with the working time
In one-to-one relationship；The working time when reliability of equipment being made to be reduced to set-point R (0≤R≤1) is known as reliability for R
Q-percentile life, be denoted as tR, relationship is：
R(tR)=R (36)
Q-percentile life during equipment reliability R=0.5 is known as median life, with t0.5It represents；Reliability R=exp (- 1)=
Q-percentile life when 0.368 is known as characteristics life, with t0.368It represents；Reliability R and Q-percentile life tRBetween relation can use Fig. 2
It represents.
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