CN113762981A - Product credibility calculation method based on exponential distribution - Google Patents
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Abstract
The invention provides a product credibility calculation method based on exponential distribution, which comprises the following steps: acquiring a field test data sample and a pre-test data sample of a product; both sets of data samples obey exponential distribution; respectively estimating the index distribution parameters of the two groups of data samples according to the index distribution probability density function; when the index distribution parameters of the two groups of data samples are different, the two groups of index distribution probability density function curves are intersected, and the intersection point of the two probability density curves is obtained through calculation; respectively calculating cumulative distribution functions from 0 to the intersection points of the two probability density function curves according to the intersection points of the two probability density curves; and obtaining the reliability of the product according to the cumulative distribution function of the two probability density functions. The method does not need to construct statistics, but starts with the concept and the mathematical meaning of the probability density function to calculate the credibility parameter, and the calculation method has clear mathematical concept, clear calculation steps, and is reasonable and feasible.
Description
Technical Field
The invention relates to a reliability calculation method of product parameter performance data samples obeying exponential distribution in probability statistics.
Background
The exponential distribution is a distribution form often used in theoretical analysis and engineering practice, and particularly in the field of service life distribution, such as the service lives of electronic components, the time when a certain machine breaks down for the first time, the time interval when passengers arrive at an airport in different periods, the time interval when two cars pass through the same road intersection before and after, and the like, theoretical analysis and actual measurement data show that the data are subjected to the exponential distribution. In practice, when statistical analysis is performed on product performance parameters by using a Bayes method, the pre-test data and the field test data cannot be mixed together for use without distinction, and the difference of the overall distribution obeyed by the pre-test data and the field test data needs to be considered, namely the reliability of the pre-test data. Data reliability calculation methods generally include two types, one type is given according to a way and a mode of acquiring data and by combining with a corresponding calculation method, such as a VV & a (Verification, Verification and identification) technology in a simulation technology, and the method needs to be completely familiar with a model, a test mode, environmental conditions and the like of acquiring data, and is relatively complicated. The other method is to directly calculate the reliability according to the measured data and calculate by using a hypothesis test method in the classical statistics, for example, the reliability calculation of the index distribution failure rate parameters can adopt a classical Gamma distribution test method, the failure rates of two groups of data are tested by using Gamma distribution under a given significance level, and the reliability parameters are determined according to the test confidence. This method requires constructing statistics of failure rates that follow the Gamma distribution to be implemented. However, it is relatively complicated to construct statistics that failure rate obeys Gamma distribution, and therefore, a new technology of a product reliability calculation method based on exponential distribution is urgently needed in the industry.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a product credibility calculation method based on exponential distribution, which comprises the following steps:
acquiring a field test data sample and a pre-test data sample of a product; the field test data sample and the pre-test data sample are subjected to exponential distribution;
respectively estimating the index distribution parameters of the two groups of data samples according to the index distribution probability density function;
obtaining the relation of two function curves formed by the index distribution probability density functions of the two groups of data samples in a coordinate system according to the relation of the index distribution parameters of the two groups of data samples;
when the index distribution parameters of the two groups of data samples are the same, the two groups of index distribution probability density function curves are superposed, and the reliability parameter is 1;
when the index distribution parameters of the two groups of data samples are different, the two groups of index distribution probability density function curves are intersected, and the intersection point of the two probability density curves is obtained through calculation;
respectively calculating cumulative distribution functions from 0 to the intersection points of the two probability density function curves according to the intersection points of the two probability density curves;
and obtaining the reliability of the product according to the cumulative distribution function of the two probability density functions.
Further, according to the exponential distribution probability density function, respectively estimating the exponential distribution parameters of the two groups of data samples, including:
the exponential distribution probability density function is:
f(t)＝λe-λt t∈(0,∞)
wherein λ is a distribution parameter of exponential distribution, also called failure rate;
according to the maximum likelihood estimation method, the estimated values of the two groups of data exponential distribution parameters are respectively
Wherein, the field test data sample is X ═ { X ═ X1,x2,…,xnY, Y is the sample of the prior data1,y2,…,ymN is the number of samples in the sample set X, and m is the number of samples in the sample set Y;
the exponential distribution probability density functions obeyed by the two sets of data are respectively:
wherein the content of the first and second substances,
is an exponential distribution parameter of a field test data sample,
is an exponential distribution parameter of a prior data sample.
Further, when the index distribution parameters of the two sets of data samples are different, the two sets of index distribution probability density function curves are intersected, and the intersection point of the two probability density curves is obtained through calculation, which includes:
the exponential distribution probability density functions obeyed by the two groups of data are respectively:
wherein the content of the first and second substances,
is an exponential distribution parameter of a field test data sample,
is an exponential distribution parameter of the prior data sample; f. of1(t) represents the probability density function for the field test sample, f2(t) represents the probability density function corresponding to the prior data sample, t represents a variable, and subscripts 1 and 2 are distributed to represent the field test and the prior data sample;
let f1(t)＝f2(t) then
When in use
The solution of the intersection point is
Further, according to the intersection points of the two probability density curves, the cumulative distribution function from 0 to the intersection point of the two probability density function curves is respectively calculated, and the method comprises the following steps:
when in use
Then, the cumulative distribution function from 0 to the intersection of the two probability density function curves is calculated, as follows:
wherein the content of the first and second substances,
is a cumulative distribution function of probability density functions corresponding to field test samples,
is a cumulative distribution function of the probability density functions corresponding to the pre-test samples,
is the intersection of the two probability density curves.
Further, obtaining the reliability of the product according to the cumulative distribution function of the two probability density functions includes: the confidence level is expressed as
Wherein min (-) represents the minimum, crTo assess the reliability of the pre-test sample Y with respect to the test sample X,
is a cumulative distribution function of probability density functions corresponding to field test samples,
is a cumulative distribution function of the probability density functions corresponding to the pre-test samples,
is the intersection of the two probability density curves.
The invention has the technical effects that:
1. the invention provides a product credibility calculation method based on exponential distribution, which comprises the steps of obtaining a field test data sample and a pre-test data sample of a product; both sets of data samples obey exponential distribution; then, respectively estimating the index distribution parameters of the two groups of data samples according to the index distribution probability density function; when the index distribution parameters of the two groups of data samples are different, the two groups of index distribution probability density function curves are intersected, and the intersection point of the two probability density curves is obtained through calculation; respectively calculating cumulative distribution functions from 0 to the intersection points of the two probability density function curves according to the intersection points of the two probability density curves; and obtaining the credibility parameter of the product according to the cumulative distribution function of the two probability density functions. The method does not need to construct statistics, but starts with the concept and the mathematical meaning of the probability density function to calculate the credibility parameter, and the calculation method has clear mathematical concept, clear calculation steps, and is reasonable and feasible.
2. The product credibility obtained by the calculation of the method is greatly convenient for the subsequent statistical calculation of the relevant parameters of the product. The calculation result can also be used as the measure of consistency of multiple groups of product performance parameters and used for judging the consistency of multiple batches of data sources or product production processes.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic flow diagram of a preferred embodiment method of the present invention;
fig. 2 is a schematic diagram of the reliability calculation of the prior sample relative to the field sample in the fractional distribution, and an intersection point of two probability density function curves is given, and the area of a diagonally shaded part in the diagram is recorded as the reliability.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
In some engineering fields, such as the service life of electronic components, the time of first fault of a certain machine, the time interval of a passenger arriving at an airport, the time interval of two automobiles passing through the same road intersection before and after, and the like, the measured data of the electronic components and the time interval obey exponential distribution. When the physical quantities are subjected to statistical analysis, multiple batches of measurement data under different situations and different conditions can be obtained, the multiple batches of data cannot be simply considered to be subjected to the same distribution, and when the Bayes method is used for the statistical analysis, the reliability of one group of data (data before the test) relative to the other group of data (field data) needs to be calculated (if the data are multiple groups of data, two groups of data can be analyzed), so that the subsequent statistical calculation of related parameters is facilitated. The calculated result can also be used as a measure of consistency of two groups of data samples, and is used for judging consistency of multiple batches of data sources or product production processes.
Referring to fig. 1, the present invention provides a product credibility calculation method based on index distribution, including the following steps:
acquiring a field test data sample and a pre-test data sample of a product; the field test data sample and the pre-test data sample are subjected to exponential distribution;
respectively estimating the index distribution parameters of the two groups of data samples according to the index distribution probability density function;
obtaining the relation of two function curves formed by the index distribution probability density functions of the two groups of data samples in a coordinate system according to the relation of the index distribution parameters of the two groups of data samples;
when the index distribution parameters of the two groups of data samples are the same, the two groups of index distribution probability density function curves are superposed, and the reliability parameter is 1;
when the index distribution parameters of the two groups of data samples are different, the two groups of index distribution probability density function curves are intersected, and the intersection point of the two probability density curves is obtained through calculation;
respectively calculating cumulative distribution functions from 0 to the intersection points of the two probability density function curves according to the intersection points of the two probability density curves;
and obtaining the reliability of the product according to the cumulative distribution function of the two probability density functions.
Probability density functions and cumulative distribution functions are two basic concepts in statistics, and the integral of the probability density functions is constantly equal to 1 throughout the domain of the random variables. According to the concept and the meaning of the probability density function, if the overlapping area of the two exponential distribution probability density function curves and the area surrounded by the abscissa axis is larger, the approximation degree of the two probability density functions is larger, and the corresponding data reliability is better. The innovation point of the method is that the area of the overlapping part of the two groups of index distribution sample empirical probability density function curves and the area surrounded by the abscissa axis is defined as the reliability of the test data before the index distribution test relative to the field test data, a novel method for calculating the reliability of the index distribution is provided, the corresponding calculation process is provided, one basic problem in Bayes fusion estimation of the two groups of index distribution samples is solved, and a feasible method is provided for calculating the reliability of the index distribution.
Further, according to the exponential distribution probability density function, respectively estimating the exponential distribution parameters of the two groups of data samples, including:
the exponential distribution probability density function is:
f(t)＝λe-λt t∈(0,∞)
wherein λ is a distribution parameter of exponential distribution, also called failure rate;
according to the maximum likelihood estimation method, the estimated values of the two groups of data exponential distribution parameters are respectively
Wherein, the field test data sample is X ═ { X ═ X1,x2,…,xnY, Y is the sample of the prior data1,y2,…,ymN is the number of samples in the sample set X, and m is the number of samples in the sample set Y;
the exponential distribution probability density functions obeyed by the two sets of data are respectively:
wherein the content of the first and second substances,
is an exponential distribution parameter of a field test data sample,
is an exponential distribution parameter of a prior data sample.
Further, when the index distribution parameters of the two sets of data samples are different, the two sets of index distribution probability density function curves are intersected, and the intersection point of the two probability density curves is obtained through calculation, which includes:
the exponential distribution probability density functions obeyed by the two groups of data are respectively:
wherein the content of the first and second substances,
is an exponential distribution parameter of a field test data sample,
is an exponential distribution parameter of the prior data sample; f. of1(t) represents the probability density function for the field test sample, f2(t) represents the probability density function corresponding to the prior data sample, t represents a variable, and subscripts 1 and 2 are distributed to represent the field test and the prior data sample;
let f1(t)＝f2(t) then
When in use
The solution of the intersection point is
Further, according to the intersection points of the two probability density curves, the cumulative distribution function from 0 to the intersection point of the two probability density function curves is respectively calculated, and the method comprises the following steps:
when in use
Then, the cumulative distribution function from 0 to the intersection of the two probability density function curves is calculated, as follows:
wherein
Is a cumulative distribution function corresponding to the two probability density functions.
Further, obtaining the reliability of the product according to the cumulative distribution function of the two probability density functions includes: the reliability calculation formula is
Where min (-) denotes the minimum, crIs the confidence level of the pre-test sample Y to the test sample X.
In order to better explain the technical scheme provided by the invention, the following description is made in conjunction with specific examples.
(1) Suppose that X ═ X is obtained as the time when a certain electronic device first fails1,x2,…,xn17 samples in total, i.e. n is 17. According to one approach, the time for the electronic device to fail before the improved process is obtained as Y ═ Y1,y2,…,ymA total of 14 samples, i.e., m-14, which is considered as the pre-test information of X samples. Both sets of data samples obeyed an exponential distribution. Wherein
X＝{10.1 7.0 123.6 45.8 67.4 11.2 42.0 4.7 85.2 66.6 96.4 99.7 7.0 27.3 29.9 96.6 47.3}，
Y＝{50.0 76.0 7.4 69.7 153.7 17.4 66.0 99.4 63.5 163.7 141.8 4.2 3.1 38.7}
(2) Respectively estimating the index distribution parameters under two groups of samples by utilizing a maximum likelihood estimation method according to the index distribution probability density function
And
according to the maximum likelihood estimation method in the classical statistical theory, aiming at field test data X, the distribution parameter estimation value of exponential distribution is
The resulting probability density functions are respectively
For the data Y before the test, the distribution parameter estimated value is
The resulting probability density function is
(3) After empirical probability density functions of two groups of data are obtained, the intersection point of two probability density function curves is calculated, and the intersection point of the two empirical probability density functions is
(4) Calculating confidence parameters of sample Y relative to sample X
The confidence level is calculated as follows:
fig. 2 is a schematic diagram of the reliability calculation of the prior sample relative to the field sample in the exponential distribution in this embodiment, and an intersection point of two probability density function curves is given, and the area of the hatched area of the oblique line in fig. 2 is recorded as the reliability size.
According to a given significance level or confidence coefficient, whether the two groups of data samples have consistency can be judged;
given a significance level α of 0.2, the confidence level is 1- α of 0.8, since cr> 1- α, i.e., the two sets of samples X and Y were considered to be consistent at a significance level of 0.2.
In conclusion, the method starts with the concept and the mathematical meaning of the probability density function to calculate the reliability parameter, the mathematical concept is clear, and the calculation steps are clear, reasonable and feasible. Moreover, the reliability of the product obtained by the calculation of the method is greatly convenient for the subsequent statistical calculation of the relevant parameters of the product. The calculation result can also be used as the measure of consistency of multiple groups of product performance parameters and used for judging the consistency of multiple batches of data sources or product production processes.
It will be clear to a person skilled in the art that the scope of the present invention is not limited to the examples discussed in the foregoing, but that several amendments and modifications thereof are possible without deviating from the scope of the present invention as defined in the attached claims. While the invention has been illustrated and described in detail in the drawings and the description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments.
Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the term "comprising" does not exclude other steps or elements, and the indefinite article "a" or "an" does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims shall not be construed as limiting the scope of the invention.
Claims (5)
1. A product credibility calculation method based on index distribution is characterized by comprising the following steps:
acquiring a field test data sample and a pre-test data sample of a product; the field test data sample and the pre-test data sample are subjected to exponential distribution;
respectively estimating the index distribution parameters of the two groups of data samples according to the index distribution probability density function;
obtaining the relation of two function curves formed by the index distribution probability density functions of the two groups of data samples in a coordinate system according to the relation of the index distribution parameters of the two groups of data samples;
when the index distribution parameters of the two groups of data samples are the same, the two groups of index distribution probability density function curves are superposed, and the reliability is 1;
when the index distribution parameters of the two groups of data samples are different, the two groups of index distribution probability density function curves are intersected, and the intersection point of the two probability density curves is obtained through calculation;
respectively calculating cumulative distribution functions from 0 to the intersection points of the two probability density function curves according to the intersection points of the two probability density curves;
and obtaining the reliability of the product according to the cumulative distribution function of the two probability density functions.
2. The method of claim 1, wherein the step of estimating the index distribution parameters of the two groups of data samples according to the index distribution probability density function comprises:
the exponential distribution probability density function is:
f(t)＝λe-λtt∈(0,∞)
wherein λ is a distribution parameter of exponential distribution, also called failure rate;
according to the maximum likelihood estimation method, the estimated values of the two groups of data exponential distribution parameters are respectively
Wherein, the field test data sample is X ═ { X ═ X1,x2,…,xnY, Y is the sample of the prior data1,y2,…,ymN is the number of samples in the sample set X, and m is the number of samples in the sample set Y;
the exponential distribution probability density functions obeyed by the two sets of data are respectively:
wherein the content of the first and second substances,
is an exponential distribution parameter of a field test data sample,
referencing exponential distributions of a prior data sampleAnd (4) counting.
3. The method of claim 1, wherein when the parameters of the exponential distribution of the two sets of data samples are different, the two sets of probability density function curves of the exponential distribution intersect, and an intersection point of the two probability density curves is obtained by calculation, comprising:
the exponential distribution probability density functions obeyed by the two groups of data are respectively:
wherein the content of the first and second substances,
is an exponential distribution parameter of a field test data sample,
is an exponential distribution parameter of the prior data sample; f. of1(t) represents the probability density function for the field test sample, f2(t) represents the probability density function corresponding to the prior data sample, t represents a variable, and subscripts 1 and 2 are distributed to represent the field test and the prior data sample;
let f1(t)＝f2(t) then
When in use
Time, intersection point
Is composed of
4. The method for calculating the credibility of the product based on the exponential distribution as claimed in claim 1, wherein the step of calculating the cumulative distribution function from 0 to the intersection point of the two probability density function curves according to the intersection point of the two probability density curves comprises:
when in use
Then, the cumulative distribution function from 0 to the intersection of the two probability density function curves is calculated, as follows:
wherein the content of the first and second substances,
is a cumulative distribution function of probability density functions corresponding to field test samples,
is a cumulative distribution function of the probability density functions corresponding to the pre-test samples,
is the intersection of the two probability density curves.
5. The method of claim 1, wherein obtaining the credibility of the product according to a cumulative distribution function of two probability density functions comprises:
the confidence level is expressed as
Wherein min (-) represents the minimum, crTo assess the reliability of the pre-test sample Y with respect to the test sample X,
is a cumulative distribution function of probability density functions corresponding to field test samples,
is a cumulative distribution function of the probability density functions corresponding to the pre-test samples,
is the intersection of the two probability density curves.
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Citations (16)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS63273945A (en) * | 1987-05-01 | 1988-11-11 | Ricoh Co Ltd | Check system for adaptation degree of software reliability growth curve |
| US20040117051A1 (en) * | 2000-06-06 | 2004-06-17 | Ford Dean M. | Method of determining a cumulative distribution function confidence bound |
| US20050288892A1 (en) * | 2004-06-07 | 2005-12-29 | Universita' Degli Studi Del Piemonte Orientale'amedeo Avogadro' | Method and system for the statistical control of industrial processes |
| JP2008128698A (en) * | 2006-11-17 | 2008-06-05 | Ntn Corp | Method and apparatus for estimating necessary life difference of significant difference determination in accelerated test |
| US20110010140A1 (en) * | 2009-07-13 | 2011-01-13 | Northrop Grumman Corporation | Probability Distribution Function Mapping Method |
| CN103646138A (en) * | 2013-12-03 | 2014-03-19 | 北京航空航天大学 | Time terminated acceleration acceptance sampling test optimum design method based on Bayesian theory |
| CN104182377A (en) * | 2014-09-02 | 2014-12-03 | 北京航空航天大学 | Parameter estimation method based on beta likelihood function |
| CN104750982A (en) * | 2015-03-19 | 2015-07-01 | 北京航空航天大学 | Reliability interval estimation method based on proportion grouping re-sampling |
| CN106779354A (en) * | 2016-12-01 | 2017-05-31 | 中国人民解放军国防科学技术大学 | Bayes data fusion evaluation methods based on power prior distribation |
| CN107657145A (en) * | 2017-09-15 | 2018-02-02 | 电子科技大学 | Weibull is distributed non-failure data reliability index method of estimation |
| CN107908807A (en) * | 2017-07-21 | 2018-04-13 | 哈尔滨工程大学 | A kind of System in Small Sample Situation Reliability Assessment Method based on bayesian theory |
| CN108564282A (en) * | 2018-04-13 | 2018-09-21 | 东北大学 | A kind of ending lifetime data for reliability assessment accepts or rejects method |
| CN108959178A (en) * | 2018-07-02 | 2018-12-07 | 西南交通大学 | The reliability confidence limit statistical estimation method of non-failure data |
| CN110096753A (en) * | 2019-04-03 | 2019-08-06 | 江苏理工学院 | The Bayes appraisal procedure of lower pair of exponential distribution of two kinds of stochastic variables |
| CN111784193A (en) * | 2020-07-17 | 2020-10-16 | 中国人民解放军国防科技大学 | Product performance consistency inspection method based on normal distribution |
| CN111811827A (en) * | 2020-07-17 | 2020-10-23 | 中国人民解放军国防科技大学 | Product performance consistency inspection method based on Rayleigh distribution |
-
2021
- 2021-03-30 CN CN202110354658.2A patent/CN113762981B/en active Active
Patent Citations (16)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS63273945A (en) * | 1987-05-01 | 1988-11-11 | Ricoh Co Ltd | Check system for adaptation degree of software reliability growth curve |
| US20040117051A1 (en) * | 2000-06-06 | 2004-06-17 | Ford Dean M. | Method of determining a cumulative distribution function confidence bound |
| US20050288892A1 (en) * | 2004-06-07 | 2005-12-29 | Universita' Degli Studi Del Piemonte Orientale'amedeo Avogadro' | Method and system for the statistical control of industrial processes |
| JP2008128698A (en) * | 2006-11-17 | 2008-06-05 | Ntn Corp | Method and apparatus for estimating necessary life difference of significant difference determination in accelerated test |
| US20110010140A1 (en) * | 2009-07-13 | 2011-01-13 | Northrop Grumman Corporation | Probability Distribution Function Mapping Method |
| CN103646138A (en) * | 2013-12-03 | 2014-03-19 | 北京航空航天大学 | Time terminated acceleration acceptance sampling test optimum design method based on Bayesian theory |
| CN104182377A (en) * | 2014-09-02 | 2014-12-03 | 北京航空航天大学 | Parameter estimation method based on beta likelihood function |
| CN104750982A (en) * | 2015-03-19 | 2015-07-01 | 北京航空航天大学 | Reliability interval estimation method based on proportion grouping re-sampling |
| CN106779354A (en) * | 2016-12-01 | 2017-05-31 | 中国人民解放军国防科学技术大学 | Bayes data fusion evaluation methods based on power prior distribation |
| CN107908807A (en) * | 2017-07-21 | 2018-04-13 | 哈尔滨工程大学 | A kind of System in Small Sample Situation Reliability Assessment Method based on bayesian theory |
| CN107657145A (en) * | 2017-09-15 | 2018-02-02 | 电子科技大学 | Weibull is distributed non-failure data reliability index method of estimation |
| CN108564282A (en) * | 2018-04-13 | 2018-09-21 | 东北大学 | A kind of ending lifetime data for reliability assessment accepts or rejects method |
| CN108959178A (en) * | 2018-07-02 | 2018-12-07 | 西南交通大学 | The reliability confidence limit statistical estimation method of non-failure data |
| CN110096753A (en) * | 2019-04-03 | 2019-08-06 | 江苏理工学院 | The Bayes appraisal procedure of lower pair of exponential distribution of two kinds of stochastic variables |
| CN111784193A (en) * | 2020-07-17 | 2020-10-16 | 中国人民解放军国防科技大学 | Product performance consistency inspection method based on normal distribution |
| CN111811827A (en) * | 2020-07-17 | 2020-10-23 | 中国人民解放军国防科技大学 | Product performance consistency inspection method based on Rayleigh distribution |
Non-Patent Citations (3)
| Title |
|---|
| 宫凤强;李夕兵;邓建: "岩土力学参数概率分布的切比雪夫多项式推断", 计算力学学报, no. 006 * |
| 李荣: "指数分布下可靠性参数的样条经验Bayes估计", 国防科技大学学报, no. 06 * |
| 王静;孙权;冯静;: "基于随机继承因子的指数分布Bayes可靠性评估", 质量与可靠性, no. 04 * |
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