CN109446481A - A kind of lognormal type cell life estimation of distribution parameters method - Google Patents
A kind of lognormal type cell life estimation of distribution parameters method Download PDFInfo
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Abstract
The present invention relates to a kind of lognormal type cell life estimation of distribution parameters methods, this method generates the candidate distribution parameter of n group according to lognormal type unit operating life data first, then likelihood score is initialized, at the quantity of intact unit, the quantity of trouble unit and the inspection moment obtained further according to k inspection result, successively update likelihood score；Then the corresponding logarithm normal distribution logarithmic average parameter of updated maximum likelihood degree and logarithm standard deviation parameter are estimated result.The parameter estimation result of this method " can follow " parameter estimation result of theoretical maturation method on the whole, and estimated accuracy is able to satisfy engine request.
Description
Technical field
The present invention relates to product quality detection technique fields, and in particular to a kind of lognormal type cell life distribution parameter
Estimation method.
Background technique
Product reliability is a kind of core attribute for describing product quality, and the distribution pattern and parameter for commonly using life of product are come
Express the reliability of product.The reliability for accurately knowing product is that reliability growth, the maintainability/protection of development product are set
The premise of the work such as meter.In special reliability test, generally energy is real-time, monitors the serviceable condition of product on-line: once it produces
Product, which break down, to be found at once, therefore can obtain the exact value of life of product X.Obtaining sufficient amount of lifetime data
The life distribution type and parameter of product can be analyzed afterwards.But under operative scenario, and it can be not necessarily provided in for product
Line monitoring device, thus it is unable to the serviceable condition of real-time monitoring product.More common way is regular or indefinite under operative scenario
Phase does integrity inspection to product.It is assumed that it is zero moment that product comes into operation constantly, if in inspection moment Tc, Product Status is
It is intact, it means that the service life X of the product is greater than Tc；If Product Status is failure, it means that the production checking moment Tc
The service life X of product is less than Tc.Compared with the X for having service life exact value, [checking moment Tc state (intact or failure)] is to delete mistake
The lifetime data of partial information.Currently, theoretically there are no delete the accurate life expectancy distribution parameter of mistake type data using this
Method.
Relative to the reliability test scene of standard, when working environment, usage mode etc. change, the reality of product
Service life is often possible to change therewith, therefore, even if having grasped life distribution law of the product under reliability test scene,
Also it is still necessary to going to understand the actual life regularity of distribution of the product under operative scenario.
Summary of the invention
The present invention for the technical problems in the prior art, provides a kind of utilization and deletes mistake type data life expectancy point
The approximation method of cloth parameter, estimated accuracy are able to satisfy engine request.
Product is made of various units.Logarithm normal distribution is common service life distribution in reliability, and there are many units (such as
Insulator, semiconductor components and devices, metal fatigue etc.) service life all obey logarithm normal distribution.Lognormal type unit refers to the service life
The unit of logarithm normal distribution is obeyed, service life X obeys logarithm normal distribution and is denoted as X~LN (μ, σ2), wherein μ is logarithmic average ginseng
Number, σ are logarithm standard deviation parameter, and the density function of X isLn (x) is natural logrithm letter in formula
Number.
It is assumed that: unit comes into operation constantly for zero moment, and the unit with batch comes into operation simultaneously, and each batch unit
Operative scenario is similar.When i-th checks, check that the moment is denoted as Tci, in the batch products, the quantity of intact unit is denoted as Nri,
The quantity of trouble unit is denoted as Nfi.K inspection is completed altogether.
Based on above-mentioned it is assumed that the technical scheme to solve the above technical problems is that a kind of lognormal type unit
Service life estimation of distribution parameters method, comprising the following steps:
Step 1, the candidate distribution parameter (μ 2 of n group is generated according to lognormal type unit operating life dataj,σ2j),1≤j
≤ n, wherein μ 2jIndicate the logarithmic average parameter of logarithm normal distribution, σ 2jIndicate the logarithm standard deviation ginseng of logarithm normal distribution
Number, n is positive integer；
Step 2, likelihood score P is initializedj, enable
Step 3, the quantity Nr of the intact unit obtained according to k inspection resulti, trouble unit quantity NfiAnd it checks
Moment Tci, successively update likelihood score Pj；
Step 4, likelihood score P in the updatedjMaximum likelihood degree is found in (1≤j≤n), is denoted as PM, then likelihood score PMIt is right
The μ 2 answeredM、σ2MThe respectively estimated result of logarithm normal distribution logarithmic average parameter and logarithm standard deviation parameter.
Further, the step 1 specifically includes:
Step 1.1, the Mean Parameters μ of logarithm normal distribution is determinedj1=μmin+ (j1-1) d1,1≤j1≤n1, whereinμmaxIndicate the logarithmic average parameter upper limit of lognormal type cell life distribution, μminIndicate lognormal
The logarithmic average parameter lower limit of type cell life distribution, n1 is positive integer, and n1 >=2；
Step 1.2, the logarithm standard deviation parameter σ of logarithm normal distribution is determinedj2=σmin+ (j2-1) d2,1≤j2≤n2,
In,σmaxIndicate the logarithm standard deviation parameter upper limit of lognormal type cell life distribution, σminExpression pair
The logarithm standard deviation parameter lower limit of number Normal Type cell lifes distribution, n2 is positive integer, and n2 >=2；
Step 1.3, n=n1 × n2 is taken, by μj1And σj2Carry out the distribution parameter (μ 2 that traversal combination obtains n group candidatej,σ
2j), 1≤j≤n.
Further, traversal described in the step 1.3 is realized in the following ways:
Enable j=1；
J1=1:n1 is traversed in first layer circulation, traverses j2=1:n2 in second layer circulation,
It enables
μ2j=μj1；σ2j=σj2；J=j+1；
Wherein, μmax≥μj1≥μmin, σmax≥σj2≥σmin。
Further, the step 3 specifically includes:
Step 3.1, i=1, i is enabled to indicate to check number；
Step 3.2, traversal calculates Wj, 1≤j≤n, orderWherein
TciIndicate inspection moment when i-th checks, NriThe quantity of intact unit, Nf when being checked for i-thiFor i-th
The quantity of trouble unit when inspection；
Step 3.3, traversal updates likelihood score Pj, enable
Step 3.4, i=i+1 is enabled, 3.2 are gone to step if i≤k, otherwise going to step 4, k is general inspection number.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart；
Fig. 2 is the simulation result schematic diagram using theoretical maturation method and the method for the present invention.
Specific embodiment
The principle and features of the present invention will be described below with reference to the accompanying drawings, and the given examples are served only to explain the present invention, and
It is non-to be used to limit the scope of the invention.
Product is made of various units.Logarithm normal distribution is common service life distribution in reliability, and there are many units (such as
Insulator, semiconductor components and devices, metal fatigue etc.) service life all obey logarithm normal distribution.Lognormal type unit refers to the service life
The unit of logarithm normal distribution is obeyed, service life X obeys logarithm normal distribution and is denoted as X~LN (μ, σ2), wherein μ is logarithmic average ginseng
Number, σ are logarithm standard deviation parameter, and the density function of X isLn (x) is natural logrithm letter in formula
Number.
It is assumed that: unit comes into operation constantly for zero moment, and the unit with batch comes into operation simultaneously, and each batch unit
Operative scenario is similar.When i-th checks, check that the moment is denoted as Tci, in the batch products, the quantity of intact unit is denoted as Nri,
The quantity of trouble unit is denoted as Nfi.K inspection is completed altogether.
Embodiment 1
A kind of lognormal type cell life estimation of distribution parameters method provided by the invention, comprising the following steps:
Step 1, the candidate distribution parameter (μ 2 of n group is generated according to lognormal type unit operating life dataj,σ2j),1≤j
≤ n, wherein μ 2jIndicate the logarithmic average parameter of logarithm normal distribution, σ 2jIndicate the logarithm standard deviation ginseng of logarithm normal distribution
Number, n is positive integer；
Specifically, the step includes:
Step 1.1, the Mean Parameters μ of logarithm normal distribution is determinedj1=μmin+ (j1-1) d1,1≤j1≤n1, whereinμmaxIndicate the logarithmic average parameter upper limit of lognormal type cell life distribution, μminIndicate lognormal
The logarithmic average parameter lower limit of type cell life distribution, n1 is positive integer, and n1 >=2；
Step 1.2, the logarithm standard deviation parameter σ of logarithm normal distribution is determinedj2=σmin+ (j2-1) d2,1≤j2≤n2,
In,σmaxIndicate the logarithm standard deviation parameter upper limit of lognormal type cell life distribution, σminExpression pair
The logarithm standard deviation parameter lower limit of number Normal Type cell lifes distribution, n2 is positive integer, and n2 >=2；
Step 1.3, n=n1 × n2 is taken, by μj1And σj2Carry out the distribution parameter (μ 2 that traversal combination obtains n group candidatej,σ
2j), 1≤j≤n.
Traversal described in step 1.3 is realized in the following ways:
Enable j=1；
J1=1:n1 is traversed in first layer circulation, traverses j2=1:n2 in second layer circulation,
It enables
μ2j=μj1；σ2j=σj2；J=j+1；
Wherein, μmax≥μj1≥μmin, σmax≥σj2≥σmin。
Step 2, likelihood score P is initializedj, enable
Step 3, the quantity Nr of the intact unit obtained according to k inspection resulti, trouble unit quantity NfiAnd it checks
Moment Tci, successively update likelihood score Pj；
Specifically, the step specifically includes:
Step 3.1, i=1, i is enabled to indicate to check number；
Step 3.2, traversal calculates Wj, 1≤j≤n, orderWherein
TciIndicate inspection moment when i-th checks, NriThe quantity of intact unit, Nf when being checked for i-thiFor i-th
The quantity of trouble unit when inspection；
Step 3.3, traversal updates likelihood score Pj, enable
Step 3.4, i=i+1 is enabled, 3.2 are gone to step if i≤k, otherwise going to step 4, k is general inspection number.
Step 4, likelihood score P in the updatedjMaximum likelihood degree is found in (1≤j≤n), is denoted as PM, then likelihood score PMIt is right
The μ 2 answeredM、σ2MThe respectively estimated result of logarithm normal distribution logarithmic average parameter and logarithm standard deviation parameter.
Embodiment 2
12 next state inspection results of certain lognormal type unit are as shown in table 1, and examination estimates that its service life logarithm of distribution is equal
Value parameter and logarithm standard deviation parameter.
Table 1
| Check serial number | Check moment h | The quantity of trouble unit | The quantity of intact unit |
| 1 | 3930 | 6 | 0 |
| 2 | 790 | 5 | 1 |
| 3 | 1570 | 5 | 1 |
| 4 | 2360 | 6 | 0 |
| 5 | 7870 | 6 | 0 |
| 6 | 9440 | 6 | 0 |
| 7 | 3150 | 6 | 0 |
| 8 | 7080 | 5 | 1 |
| 9 | 6290 | 6 | 0 |
| 10 | 8650 | 6 | 0 |
| 11 | 4720 | 6 | 0 |
| 12 | 5510 | 6 | 0 |
Calculating process is as follows:
1, candidate service life distribution parameter is determined
According to previous experiences, estimate that the logarithmic average parameter of the unit is step-length with 0.5 in 3~6 ranges；Estimation should
The logarithm standard deviation parameter of unit is step-length with 1 in 1~5 range；Symbiosis is at 35 candidate distribution parameter (μ 2j,σ2j),1
≤j≤35。
2, likelihood score is initialized
Initialize likelihood score Pj, 1≤j≤35 enable
3, traversal adjustment likelihood score
3.1 enable i=1
3.2 traversals calculate Wj, 1≤j≤35 enableWherein
3.3 traversals update likelihood score Pj, 1≤j≤35 enable
3.4 update i, enable i=i+1, turn 3.2 if i≤12, otherwise turn 4.Table 2 lists the updated likelihood of i-th
Degree.
4, service life estimation of distribution parameters result is exported
In all likelihood score PjMaximum likelihood degree is P in (1≤j≤35)17, then 2 μ17=4.5, σ 217=2.0 be respectively the longevity
The estimated result of life distribution logarithmic average parameter and logarithm standard deviation parameter.
The updated likelihood score of 2 i-th of table
Embodiment 3
Following simulation model can be established to simulate the checking process to unit.
It is assumed that the actual life of unit obeys logarithm normal distribution LN (μ, σ2), k inspection is carried out altogether, remembers i-th inspection
Moment is Tci, the unit with batch comes into operation simultaneously, and the element number of the i-th batch is Ni。
1) i=1 is enabled
2) N is randomly generatediA random number simTij,1≤j≤Ni, these random numbers obedience logarithm normal distribution LN (μ, σ2)
3) in simTij(1≤j≤Ni) in, it finds greater than TciRandom number, quantity be intact unit quantity be denoted as
Nri, trouble unit quantity NfiFor Ni-Nri。
4) i is updated, i=i+1 is enabled.Turn if i≤k 2), otherwise this k inspection of simulation terminates.
The Tc obtained for the above simulation modeli、Nri、Nfi, point of the method for the present invention for the estimation unit service life can be used
Cloth parameter.
The simT obtained for the above simulation modelij, theoretically mature method can be used for the estimation unit service life
Distribution parameter.
Logarithm normal distribution LN (4.5,2.0 is obeyed with the actual life of unit2) for, 12 inspections are carried out altogether, it is same to criticize
Secondary unit comes into operation simultaneously, and the element number of the i-th batch is 6, carries out Multi simulation running using above-mentioned simulation model, obtains big
Amount mock survey result simultaneously carries out estimation of distribution parameters, and for statistical analysis to multiple estimated result.
Type checking result data Tc is lost for deleting for simulationi、Nri、Nfi, using the lognormal point of the method for the present invention estimation
The mean value of cloth logarithmic average parameter μ is 4.54, standard deviation 0.40, and the mean value of logarithm standard deviation parameter σ is 2.00, standard deviation is
0.38。
For the lifetime data simT of simulationij, using the logarithm normal distribution logarithmic average parameter μ of theoretical method estimation
Mean value is 4.54, standard deviation 0.25, and the mean value of logarithm standard deviation parameter σ is 2.00, standard deviation 0.16.
Fig. 2 shows using 10 simulation results, respectively for Life Type data and it is corresponding delete mistake type data, respectively adopt
The service life estimation of distribution parameters result obtained with theoretical maturation method and the method for the present invention.From the point of view of Fig. 2, the ginseng of the method for the present invention
Number estimated result " can follow " parameter estimation result of theoretical maturation method on the whole.
A large amount of simulation results show that the method for the present invention has preferable estimated accuracy, meet engineer application requirement.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (4)
1. a kind of lognormal type cell life estimation of distribution parameters method, which comprises the following steps:
Step 1, the candidate distribution parameter (μ 2 of n group is generated according to lognormal type unit operating life dataj,σ2j), 1≤j≤n,
Wherein, 2 μjIndicate the logarithmic average parameter of logarithm normal distribution, σ 2jIndicate the logarithm standard deviation parameter of logarithm normal distribution, n is
Positive integer；
Step 2, likelihood score P is initializedj, enable1≤j≤n；
Step 3, the quantity Nr of the intact unit obtained according to k inspection resulti, trouble unit quantity NfiAnd check the moment
Tci, successively update likelihood score Pj；
Step 4, likelihood score P in the updatedjMaximum likelihood degree is found in (1≤j≤n), is denoted as PM, then likelihood score PMCorresponding μ
2M、σ2MRespectively logarithm normal distribution logarithmic average parameter and logarithm standard deviation parameter estimation result.
2. a kind of lognormal type cell life estimation of distribution parameters method according to claim 1, which is characterized in that described
Step 1 specifically includes:
Step 1.1, the Mean Parameters μ of logarithm normal distribution is determinedj1=μmin+ (j1-1) d1,1≤j1≤n1, whereinμmaxIndicate the logarithmic average parameter upper limit of lognormal type cell life distribution, μminIndicate lognormal
The logarithmic average parameter lower limit of type cell life distribution, n1 is positive integer, and n1 >=2；
Step 1.2, the logarithm standard deviation parameter σ of logarithm normal distribution is determinedj2=σmin+ (j2-1) d2,1≤j2≤n2, whereinσmaxIndicate the logarithm standard deviation parameter upper limit of lognormal type cell life distribution, σminIndicate logarithm
The logarithm standard deviation parameter lower limit of Normal Type cell life distribution, n2 is positive integer, and n2 >=2；
Step 1.3, n=n1 × n2 is taken, by μj1And σj2Carry out the distribution parameter (μ 2 that traversal combination obtains n group candidatej,σ2j), 1
≤j≤n。
3. a kind of lognormal type cell life estimation of distribution parameters method according to claim 2, which is characterized in that described
Traversal described in step 1.3 is realized in the following ways:
Enable j=1；
J1=1:n1 is traversed in first layer circulation, traverses j2=1:n2 in second layer circulation,
It enables
μ2j=μj1；σ2j=σj2；J=j+1；
Wherein, μmax≥μj1≥μmin, σmax≥σj2≥σmin。
4. a kind of lognormal type cell life estimation of distribution parameters method according to claim 1, which is characterized in that described
Step 3 specifically includes:
Step 3.1, i=1, i is enabled to indicate to check number；
Step 3.2, traversal calculates Wj, 1≤j≤n, orderWherein
TciIndicate inspection moment when i-th checks, NriThe quantity of intact unit, Nf when being checked for i-thiFor i-th inspection
When trouble unit quantity；
Step 3.3, traversal updates likelihood score Pj, enable
Step 3.4, i=i+1 is enabled, 3.2 are gone to step if i≤k, otherwise going to step 4, k is general inspection number.
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