CN104750982B - A kind of reliability bounds estimate method that resampling is grouped based on ratio - Google Patents
A kind of reliability bounds estimate method that resampling is grouped based on ratio Download PDFInfo
- Publication number
- CN104750982B CN104750982B CN201510122640.4A CN201510122640A CN104750982B CN 104750982 B CN104750982 B CN 104750982B CN 201510122640 A CN201510122640 A CN 201510122640A CN 104750982 B CN104750982 B CN 104750982B
- Authority
- CN
- China
- Prior art keywords
- sample
- resampling
- reliability
- data
- group
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Landscapes
- Complex Calculations (AREA)
Abstract
The present invention gives a kind of reliability bounds estimate method that resampling is grouped based on ratio, 1. testing data of life-span is grouped according to complete data and censored data first, 2. duplicate sampling is carried out according still further to corresponding ratio, 3. so as to provide the point estimation of distributed constant and reliability, 4. resampling is repeated using bootstrap method (Bootstrap methods), and calculate the point estimation of corresponding distributed constant and reliability, 5. obtained reliability point estimation is ranked up, obtains the interval estimation of reliability.This method avoid the appearance of non-failure data during repetition resampling, it is ensured that the normal operation of method, required knowwhy is less, calculates easy, easily realizes, facilitate engineers and technicians to use, with good application value.
Description
Technical field
A kind of reliability bounds estimate method that resampling is grouped based on ratio of the present invention, is related to a kind of based on ratio packet
The high truncation ratio lifetime data reliability bounds estimate method of resampling, it can effectively carry out the distribution ginseng of censored data
Number and reliability bounds estimate, it is adaptable to the correlative technology field such as reliability assessment, medical care statistics.
Background technology
Reliability bounds estimate is a kind of form of reliability parameter estimation, by the sample drawn from product, carries out phase
Reliability test is closed, according to certain correctness and precise requirements, data processing is carried out, constructs appropriate interval, as
The estimation of product totality reliability true value location.
It is general in traditional statistical inference that the interval estimation of reliability is constructed using pivot amount, but be due to this kind of method by
It is limited to the form of overall distribution and the data type of sample, for the sample of multigroup different truncation conditions, it is impossible to use pivot
Measure method construct interval estimation.Therefore, when constructing reliability bounds estimate, frequently with a kind of bootstrap method (i.e. Bootstrap
Method), this method is to replicate observation information according to given original sample, from original sample carry out resampling obtain new samples and
Statistic, statistical inference is carried out to overall parameter, and then provides the interval estimation of reliability, and its basic thought is：Original
Simple random sampling with replacement has been done in sample, in sampling each time, has been pumped to according to the observation of each in original sample data
Probability equal principle, repetition extracts certain number of times, and the reproduction copies of obtained original sample, the process is referred to as
Bootstrap samples, and corresponding reproduction copies are referred to as Bootstrap samples；It can be obtained for each Bootstrap sample
To a point estimation of reliability, Bootstrap sampling several times can be obtained by several reliability point estimation, if by pair
The sequence of dry reliability point estimation, obtains an empirical distribution function of reliability, and then provide reliability bounds estimate.
In practical application of the Bootstrap methods in reliability field, a class often occur has the sample of truncation phenomenon
This, while truncation ratio is higher, for the life test of high reliability long life product, life of product data are generally truncation number
According to a part of sample is the out-of-service time, and another part sample is experiment deadline (truncated time) and the part sample proportion
It is higher, the characteristics of statistics at this moment shows high truncation ratio；In medical care statistics field, for cancer return situation with
Track is investigated, if the follow-up investigation duration is shorter, in fact it could happen that the sample of recurrence is also less, statistics at this moment also compares
The characteristics of example high truncation ratio.Now, interval estimation is carried out to reliability using the Bootstrap methods of simple random sampling
When, non-failure data sample may be obtained during duplicate sampling, cause Bootstrap methods not calculate, can not be normal
Carry out, so as to largely limit the application of Bootstrap methods.
Therefore, the present invention proposes that a kind of high truncation ratio lifetime data reliability interval for being grouped resampling based on ratio is estimated
Meter method.
The content of the invention
(1) purpose of the present invention：The present invention is carrying out high truncation ratio lifetime data reliability for Bootstrap methods
During interval estimation, no-failure sample often occurs during data resampling, causes the imponderable problem of this method, proposes
It is a kind of based on ratio be grouped resampling high truncation ratio lifetime data reliability bounds estimate method, with supplement and it is perfect
Bootstrap methods, are realized to the reliability bounds estimate under high truncation ratio lifetime data.
(2) technical scheme：
The present invention gives a kind of high truncation ratio lifetime data reliability bounds estimate that resampling is grouped based on ratio
Method, specific implementation steps are as follows：
Step one：Provided with the n group samples that F (X | θ) is distributed from the life-span, i-th group of sample isWherein：X is random change
Amount,Represent complete data,Represent censored data, i=1,2 ..., n.F (X | θ) is stochastic variable X cumulative distribution letter
Number, f (X | θ) is stochastic variable X probability density function, θ=(θ1,θ2,…,θm) for distribution F (X | θ) parameter vector, m is
It is distributed the number of parameter in F (X | θ).In i-th group of sample, there is aiIndividual complete data, biIndividual censored data, and ai+bi=ni, ni
For the sample size of i-th group of sample；Production reliability is R=1-F (X | θ)；
Step 2：Resampling is carried out in n group samples, (i=1,2 ..., n) organizing sample data is divided into complete data by i-th
And censored dataWith
Two classes, resampling is carried out to this two class respectively；Middle use has Simple random sampling with replacement to obtain one group of new samples It is middle using have Simple random sampling with replacement obtain one group it is new
SampleObtain two groups of new samples are merged as a ratio
The sample of example packet resampling, the process is referred to as ratio packet resampling, and obtains sample and be referred to as being grouped resampling sampleI.e.
Step 3：List likelihood functionBy very big
Change L(1)(θ), evenθ is solved, so that it is determined that distributed constant θ Maximum-likelihood estimation θ1=(θ11,θ21,…,
θm1), by substitution R=1-F (X | θ),
Obtain the point estimation R of production reliability1=1-F (X | θ1)；
Step 4：Using the method described in step 2 and step 3, to original sampleRepeat N-1
(General N >=1000) secondary ratio packet resampling, and to each packet resampling sample architecture likelihood function, by maximizing seemingly
Right function, determines the Maximum-likelihood estimation θ of parameter θl=(θ1l,θ2l,…,θml), wherein l=2,3 ..., N.So far, obtain
Parameter vector θ N number of estimation θ1,…,θN,
So as to which production reliability R N number of estimation R can be obtained by formula R=1-F (X θ)1,…RN；
Step 5：According to order from small to large to production reliability point estimation R1,…,RNIt is ranked up, obtaining product can
Order statistic R by spending point estimation(1)≤…≤R(N), then the interval estimation that production reliability R confidence levels are α isAnd the confidence lower limit that production reliability R confidence levels are α is, whereinRepresent to be no more than x
Maximum integer,Represent the smallest positive integral not less than x.
Wherein, " F (X θ) n group samples are distributed from the life-span, i-th group of sample is described in step oneBy product can
The data obtained by property experiment or life test, are arranged with censored data according to complete data, can obtain above-mentioned sample.
(3) advantage：
A kind of high truncation ratio lifetime data reliability bounds estimate method that resampling is grouped based on ratio of the present invention, its
Advantage is as follows：
1. the present invention proposes a kind of reliability bounds estimate method of censored data at high proportion that resampling is grouped based on ratio,
Overcome at high proportion censored data be likely to occur non-failure data using in Bootstrap procedures, repeating resampling, cause
Data, are grouped by the imponderable problem of this method according to complete data and censored data first, according still further to corresponding ratio
Example carries out duplicate sampling, it is to avoid the appearance of non-failure data, it is ensured that the normal operations of Bootstrap methods；
2. ratio proposed by the present invention is grouped resampling method, according to complete data in legacy data and the ratio of censored data
Example carries out repeating resampling, the characteristics of at utmost maintaining initial data so that the interval estimation of final reliability has good
Good statistical property；
3. knowwhy needed for method proposed by the present invention is less, calculates easy, easily realizes, facilitate engineers and technicians
Grasp is used.
Brief description of the drawings
Fig. 1 is flow chart of the present invention
Embodiment
A kind of high truncation ratio lifetime data reliability bounds estimate method that resampling is grouped based on ratio of the present invention, its
Flow chart is as shown in Figure 1.
By taking certain type agricultural aircraft flight control computer testing data of life-span as an example, the present invention is described in further details.
Certain type agricultural aircraft flight control computer life test is made up of two parts, respectively laboratory test and outfield examination
Test, experiment is Random Censored Samples experiment, obtains two groups of testing data of life-span, data are as shown in table 1.It is without "+" data in table
The out-of-service time of equipment, band "+" data are censored data.For example：2160+ represents to reach total time on test in field trial
Equipment is not failed at the end of 2160 hours, and 1080+ is represented at the end of total time on test being reached in laboratory test 1080 hours
Equipment does not fail, below with flight control computer exemplified by 200 hours, solution of the confidence level for 0.05 Reliability confidence lower limit,
Illustrate the application method of the present invention.
Certain the type agricultural aircraft flight control computer testing data of life-span of table 1
| Device numbering | Field trial (hour) | Device numbering | Laboratory test (hour) |
| 1 | 1164 | 15 | 806 |
| 2 | 1752+ | 16 | 780+ |
| 3 | 756 | 17 | 1008+ |
| 4 | 534 | 18 | 970+ |
| 5 | 788 | 19 | 731 |
| 6 | 1218 | 20 | 668 |
| 7 | 1562 | 21 | 888+ |
| 8 | 1279 | 22 | 1080+ |
| 9 | 1896+ | 23 | 938 |
| 10 | 1520 | 24 | 816+ |
| 11 | 2160+ | 25 | 1080+ |
| 12 | 1968+ | 26 | 672+ |
| 13 | 2088+ | 27 | 972 |
| 14 | 702 | 28 | 953 |
Step one：Exponential distribution is obeyed in the life-span distribution of electronic product, and certain type agricultural aircraft flight control computer is thought herein
Life-span obey exponential distribution, its life distribution function and density function are respectively F (X | θ)=1-exp (- θ x), f (X | θ)=θ
Exp (- θ x), wherein θ are distributed constant.Test data to table 1 is arranged, and is obtained field trial data and is
{1164,756,534,788,1218,1562,1279,1520,702,1752+,1896+,1968+,2088+,
2160+ }, and test data in lab is
{806,731,668,938,972,953,780+,1008+,970+,888+,1080+,816+,1080+,672+}；
Step 2：
Field data is divided into complete data { 1164,756,534,788,1218,1562,1279,1520,702 } and cut
Mantissa has been done in complete data put back to simple randomization respectively according to { 1752+, 1896+, 1968+, 2088+, 2160+ } two class
Sampling obtains one group of new complete data sample { 1520,702,756,702,1562,1164,534,1218,702 },
Simple random sampling with replacement has been done in censored data and has obtained one group of new censored data sample, 2160+, 1968+,
1896+,2160+,1896+}；Be combined obtain field data packet resampling sample 1520,702,756,702,
1562,1164,534,1218,702,2160+,1968+,1896+,2160+,1896+}；Laboratory data is divided into perfect number
According to { 806,731,668,938,972,953 } and censored data 780+, 1008+, 970+, 888+, 1080+, 816+, 1080+,
672+ } two classes, and done respectively in complete data Simple random sampling with replacement obtain one group of new complete data sample 668,
953,938,938,972,668 }, Simple random sampling with replacement has been done in censored data and has obtained one group of new censored data sample,
{ 888+, 780+, 1008+, 888+, 816+, 1080+, 1008+, 780+ }, is combined and obtains the packets of laboratory's data and take out again
All { 668,953,938,938,972,668,888+, 780+, 1008+, 888+, 816+, 1080+, 1008+, 780+ }；
Step 3：List likelihood function
L(1)(θ)=θ9·exp[-θ(1520+702+756+702+1562+1164+534+1218+702)]
·exp[-θ(2160+1968+1896+2160+1896)]
·θ6·exp[-θ(668+953+938+938+972+668)]
·exp[-θ(780+1008+888+816+1080+1008+780)]
=θ15·exp(-31325·θ)
Maximize L(1)(θ), evenObtain
Solve θ1=0.0004786, reliability R of the product at 200 hours1For
R1=1-F (X | θ1)=1- [1-exp (- θ x)]=exp (- 0.0004786 × 200)=0.9087
Step 4：Using the method described in step 2 and step 3, from field trial data and test data in lab
In repeat 999 repetition resamplings of progress, and calculate distributed constant θ point estimation and product in the case of each group of new samples and exist
200 hours reliability R point estimation, so far, 1000 point estimation and the product for having obtained distributed constant θ are reliable at 200 hours
Spend R 1000 point estimation；
Step 5：1000 point estimation of production reliability are ranked up according to order from small to large, product is obtained
The order statistic of reliability point estimation, then the confidence lower limit that production reliability R confidence levels are 0.05 is
I.e. the 50th order statistic of production reliability point estimation, is computed
Therefore, the type agricultural aircraft flight control computer was at 200 hours, and the Reliability confidence lower limit that confidence level is 0.05 is
0.9041。
In summary, The present invention gives a kind of reliability of censored data at high proportion interval that resampling is grouped based on ratio
Method of estimation.Testing data of life-span is grouped by this method according to complete data and censored data first, then carries out ratio
Resampling is grouped, the point estimation of distributed constant and reliability is provided based on obtained packet resampling sample, finally to obtaining
Reliability point estimation is ranked up, and obtains the interval estimation of reliability.This method avoid Bootstrap repeat resampling when without
The appearance of fail data, it is ensured that the normal operation of this method, required knowwhy is less, calculates easy, easily realizes, convenient
Engineers and technicians use, with good application value.
Claims (2)
1. a kind of reliability bounds estimate method that resampling is grouped based on ratio, it is characterised in that：Specific implementation steps are such as
Under：
Step one：Provided with the n group samples that F (X | θ) is distributed from the life-span, i-th group of sample isWherein：X is random change
Amount,Represent complete data,Represent censored data, i=1,2 ..., n, F (X | θ) is stochastic variable X cumulative distribution letter
Number, f (X | θ) is stochastic variable X probability density function, θ=(θ1,θ2,…,θm) for distribution F (X | θ) parameter vector, m is
The number of parameter in F (X | θ) is distributed, in i-th group of sample, there is aiIndividual complete data, biIndividual censored data, and ai+bi=ni, ni
For the sample size of i-th group of sample；Production reliability is R=1-F (X | θ)；
Step 2：Resampling is carried out in n group samples, i-th group of sample data is divided into complete data and censored dataWithTwo classes, to this two
Class carries out resampling respectively；Middle use has Simple random sampling with replacement to obtain one group of new samples It is middle using have Simple random sampling with replacement obtain one group it is new
SampleObtain two groups of new samples are merged as a ratio
The sample of resampling is grouped, the process is referred to as ratio packet resampling, and obtains sample and be referred to as being grouped resampling sampleI.e.Its
In, i=1,2 ..., n；
Step 3：List likelihood functionPass through the L that maximizes(1)
(θ), evenθ is solved, so that it is determined that distributed constant θ Maximum-likelihood estimation θ1=(θ11,θ21,…,θm1), will
Substitution R=1-F (X | θ), obtain the point estimation R of production reliability1=1-F (X | θ1)；
Step 4：Using the method described in step 2 and step 3, to original sampleRepeat N-1 times
Ratio is grouped resampling, and to each packet resampling sample architecture likelihood function, by the likelihood function that maximizes, determines parameter
θ Maximum-likelihood estimation θl=(θ1l,θ2l,…,θml), wherein l=2,3 ..., N；So far, the N number of of parameter vector θ has been obtained to estimate
Count θ1,…,θN, so that production reliability R N number of estimation R can be obtained by formula R=1-F (X | θ)1,…RN；Wherein, N >=
1000；
Step 5：According to order from small to large to production reliability point estimation R1,…,RNIt is ranked up, obtains production reliability
The order statistic R of point estimation(1)≤…≤R(N), then the interval estimation that production reliability R confidence levels are α isAnd the confidence lower limit that production reliability R confidence levels are α isWhereinRepresent to be no more than x
Maximum integer,Represent the smallest positive integral not less than x.
2. a kind of reliability bounds estimate method that resampling is grouped based on ratio according to claim 1, its feature is existed
In：
" F (X | θ) n group samples are distributed from the life-span, i-th group of sample is described in step onePass through the reliable of product
Property the experiment and obtained data of life test, arranged according to complete data and censored data, above-mentioned sample can be obtained.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510122640.4A CN104750982B (en) | 2015-03-19 | 2015-03-19 | A kind of reliability bounds estimate method that resampling is grouped based on ratio |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510122640.4A CN104750982B (en) | 2015-03-19 | 2015-03-19 | A kind of reliability bounds estimate method that resampling is grouped based on ratio |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104750982A CN104750982A (en) | 2015-07-01 |
| CN104750982B true CN104750982B (en) | 2017-10-31 |
Family
ID=53590658
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510122640.4A Expired - Fee Related CN104750982B (en) | 2015-03-19 | 2015-03-19 | A kind of reliability bounds estimate method that resampling is grouped based on ratio |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104750982B (en) |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105718722B (en) * | 2016-01-18 | 2018-07-06 | 中国人民解放军国防科学技术大学 | Product reliability estimation method based on Fix-Time Censored Test data |
| CN106202636B (en) * | 2016-06-27 | 2019-06-18 | 广东电网有限责任公司电力科学研究院 | A kind of method and system of micro-capacitance sensor electro-magnetic transient real-time simulation |
| CN107132834B (en) * | 2017-04-12 | 2019-03-08 | 北京航空航天大学 | Based on statistic sequence and connection system dependability lower confidence limit estimation method |
| CN108256254B (en) * | 2018-01-30 | 2020-05-29 | 北京航空航天大学 | Unbalanced data multi-dimensional parameter estimation method based on sample expansion |
| CN108647186B (en) * | 2018-04-17 | 2021-05-28 | 大连理工大学 | Small sample test data estimation method based on grey self-help and unknown rational number |
| CN109542747B (en) * | 2018-11-23 | 2023-04-07 | 复旦大学 | Bootstrap-based performance evaluation method for manageable program |
| CN110826022A (en) * | 2019-11-11 | 2020-02-21 | 北京师范大学 | Method for maximum likelihood ranking based on traffic data between entities |
| CN113762981B (en) * | 2021-03-30 | 2023-11-28 | 中国人民解放军国防科技大学 | Product credibility calculation method based on index distribution |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103970990A (en) * | 2014-04-22 | 2014-08-06 | 中国民航大学 | Aircraft route segment fuel consumption range estimation method based on QAR data |
| CN104182603A (en) * | 2013-05-24 | 2014-12-03 | 上海空间电源研究所 | Reliability evaluation method for long-service-life and high-reliability electronic product |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR2979705B1 (en) * | 2011-09-05 | 2014-05-09 | Commissariat Energie Atomique | METHOD AND DEVICE FOR ESTIMATING A MOLECULAR MASS PARAMETER IN A SAMPLE |
-
2015
- 2015-03-19 CN CN201510122640.4A patent/CN104750982B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104182603A (en) * | 2013-05-24 | 2014-12-03 | 上海空间电源研究所 | Reliability evaluation method for long-service-life and high-reliability electronic product |
| CN103970990A (en) * | 2014-04-22 | 2014-08-06 | 中国民航大学 | Aircraft route segment fuel consumption range estimation method based on QAR data |
Non-Patent Citations (3)
| Title |
|---|
| 可靠度区间估计;罗文瑛;《天津医科大学学报》;20040330;第10卷(第1期);第131-133页 * |
| 模糊可靠度的区间估计方法;陈胜军;《机械设计与制造》;20051228(第12期);第10-11页 * |
| 比例Bootstrap及其方差估计的相合性;杨军 等;《中国科学院研究生院学报》;20070515;第24卷(第3期);第273-279页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104750982A (en) | 2015-07-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104750982B (en) | A kind of reliability bounds estimate method that resampling is grouped based on ratio | |
| US11935233B2 (en) | Neural network classification | |
| CN108694390A (en) | A kind of cuckoo search improves the modulated signal sorting technique of grey wolf Support Vector Machines Optimized | |
| CN103942457A (en) | Water quality parameter time series prediction method based on relevance vector machine regression | |
| Hu et al. | Identification of migratory insects from their physical features using a decision-tree support vector machine and its application to radar entomology | |
| Ding et al. | Accelerated life test sampling plans for the Weibull distribution under type I progressive interval censoring with random removals | |
| CN106991090A (en) | The analysis method and device of public sentiment event entity | |
| Essick et al. | Probing Extremal Gravitational-wave Events with Coarse-grained Likelihoods | |
| Pérez-Ortiz et al. | Machine learning techniques to select Be star candidates-An application in the OGLE-IV Gaia south ecliptic pole field | |
| Li et al. | Generative emulation of weather forecast ensembles with diffusion models | |
| Ashour et al. | Bayesian and Non–Bayesian Estimation for Two Generalized Exponential Populations Under Joint Type II Censored Scheme | |
| CN107861965A (en) | Data intelligence recognition methods and system | |
| Ashour et al. | Parameter estimation for multiple Weibull populations under joint type-II censoring | |
| CN106295175B (en) | Station meteorological data missing value fill method based on svd algorithm | |
| CN116244612B (en) | HTTP traffic clustering method and device based on self-learning parameter measurement | |
| Balakrishnan et al. | Inference for a simple step-stress model with Type-I censoring and lognormally distributed lifetimes | |
| CN109766548B (en) | Examination point identification method, examination point identification device, examination point identification equipment and computer storage medium | |
| Li et al. | A transformer fault diagnosis method based on sub-clustering reduction and multiclass multi-kernel support vector machine | |
| Hu et al. | Hypernetwork models based on random hypergraphs | |
| Kim et al. | Identifying aberrant data in structural equation models with IRLS-ADF | |
| Xiong et al. | Fault detection of UHV converter valve based on optimized cost-sensitive extreme random forest | |
| Pang et al. | The Present-day Mass Function of Star Clusters in the Solar Neighborhood | |
| CN104965976A (en) | Sampling method and device | |
| Dong et al. | Empirical likelihood for cumulative hazard ratio estimation with covariate adjustment | |
| Balmert et al. | Nonparametric inference on quantile lost lifespan |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20171031 Termination date: 20190319 |