CN113743707B - Product credibility calculation method based on uniform distribution - Google Patents
Product credibility calculation method based on uniform distribution Download PDFInfo
- Publication number
- CN113743707B CN113743707B CN202110340402.6A CN202110340402A CN113743707B CN 113743707 B CN113743707 B CN 113743707B CN 202110340402 A CN202110340402 A CN 202110340402A CN 113743707 B CN113743707 B CN 113743707B
- Authority
- CN
- China
- Prior art keywords
- uniform distribution
- data samples
- probability density
- density function
- groups
- 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.)
- Active
Links
- 238000009827 uniform distribution Methods 0.000 title claims abstract description 140
- 238000004364 calculation method Methods 0.000 title abstract description 23
- 238000012360 testing method Methods 0.000 claims abstract description 121
- 230000006870 function Effects 0.000 claims abstract description 102
- 238000005259 measurement Methods 0.000 claims abstract description 45
- 238000000034 method Methods 0.000 claims abstract description 30
- 238000009826 distribution Methods 0.000 claims description 15
- 238000007476 Maximum Likelihood Methods 0.000 claims description 5
- 238000005516 engineering process Methods 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 238000013528 artificial neural network Methods 0.000 description 2
- 238000004422 calculation algorithm Methods 0.000 description 2
- 238000013135 deep learning Methods 0.000 description 2
- 238000007619 statistical method Methods 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 238000012790 confirmation Methods 0.000 description 1
- 230000001186 cumulative effect Effects 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005315 distribution function Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 230000004927 fusion Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000010200 validation analysis Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
- G06Q10/063—Operations research, analysis or management
- G06Q10/0639—Performance analysis of employees; Performance analysis of enterprise or organisation operations
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
Landscapes
- Business, Economics & Management (AREA)
- Human Resources & Organizations (AREA)
- Engineering & Computer Science (AREA)
- Strategic Management (AREA)
- Development Economics (AREA)
- Economics (AREA)
- Entrepreneurship & Innovation (AREA)
- Educational Administration (AREA)
- Operations Research (AREA)
- Marketing (AREA)
- Game Theory and Decision Science (AREA)
- Quality & Reliability (AREA)
- Tourism & Hospitality (AREA)
- Physics & Mathematics (AREA)
- General Business, Economics & Management (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Complex Calculations (AREA)
Abstract
The invention provides a product credibility calculation method based on uniform 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 uniform distribution; obtaining the maximum value and the minimum value of the uniform distribution parameters of the two groups of data samples according to the uniform distribution probability density function; obtaining the relationship of two function curves formed by the uniform distribution probability density functions of the two groups of data samples in a coordinate system according to the relationship between the uniform distribution parameters of the two groups of data samples; when the uniform distribution parameters of the field test data samples and the uniform distribution parameters of the pre-test data samples are staggered, the function curves of the two groups of measurement data samples are partially overlapped with the area surrounded by the abscissa axis, and the area of the overlapped part is the credibility of the product. The method starts with the concept and mathematical meaning of the probability density function to calculate the credibility parameter, the mathematical concept is clear, and the calculation steps are clear, reasonable and feasible.
Description
Technical Field
The invention relates to a credibility calculation method of product parameter performance data samples subject to uniform distribution in probability statistics.
Background
In engineering practice, measurement data which are subjected to uniform distribution in batches are obtained, for example, traction load under unit length of an electrified railway, analysis shows that the measurement data are subjected to uniform distribution, for example, seed number during random sampling of normal distribution, uniform distribution random number in a neural network deep learning algorithm and the like, and in actual calculation, the measurement data are required to be accurately subjected to uniform distribution so as to maintain good performance of calculation results. In practice, when the Bayes method is used for carrying out statistical analysis on multiple batches of measurement data, two or more groups of measurement data cannot be mixed together for use without distinction, and differences of overall distribution obeyed by different measurement data, namely the credibility of the data, need to be considered. The data reliability calculation methods generally have two types, one type is given by combining corresponding calculation methods according to a model, a way and a mode for obtaining data, such as a VV & A technology (Verification, validation andAccreditation, verification, confirmation and identification) in modeling simulation technology, and the methods need to be fully familiar with the model, the test mode, the environmental condition and the like for obtaining the data, and are complex. The other method is to directly calculate the credibility according to the measured data, and calculate the credibility by using a hypothesis testing method in classical statistics, for example, normal distribution can be tested on the mean value and the variance by using a t distribution test and an F distribution test respectively, but for uniform distribution, no good technical method is available at present to calculate the credibility of two different samples. Therefore, there is an urgent need in the industry for a new technology for a product credibility calculation method based on exponential distribution.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a product credibility calculating method based on uniform 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 samples and the pre-test data samples are uniformly distributed;
respectively obtaining the maximum value and the minimum value of the uniform distribution parameters of the two groups of data samples according to the uniform distribution probability density function;
obtaining an equivalent uniform distribution probability density function obeyed by the two groups of data according to the maximum value and the minimum value of the uniform distribution probability density function and the uniform distribution parameter;
obtaining the relationship of two function curves formed by the equivalent uniform distribution probability density functions of the two groups of data samples in a coordinate system according to the relationship between the uniform distribution parameters of the two groups of data samples;
when the minimum value of the uniform distribution parameters of the field test data samples is larger than the maximum value of the uniform distribution parameters of the pre-test data samples or the maximum value of the uniform distribution parameters of the field test data samples is smaller than the minimum value of the uniform distribution parameters of the pre-test data samples, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples have no overlapping part, and the credibility is 0;
when the minimum value and the maximum value of the uniform distribution parameters of the field test data samples and the minimum value and the maximum value of the uniform distribution parameters of the pre-test data samples are staggered, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are partially overlapped with the area surrounded by the abscissa axis in the coordinate system, and the area of the overlapped part of the two uniform distribution probability density function curves and the area surrounded by the abscissa axis is calculated to be the credibility of the product.
Further, respectively obtaining a maximum value and a minimum value of uniform distribution parameters of two groups of data samples according to the uniform distribution probability density function, wherein the method comprises the following steps:
the probability density function of the uniform distribution is:
wherein b 1 ,b 2 B for any two distribution parameters of uniform distribution 2 ＞b 1 ；
According to the maximum likelihood estimation method, the estimation values of the two groups of data uniform distribution parameters are respectively
Wherein,for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For uniform distribution under pre-test data sampleMinimum value of parameter->The maximum value of the uniformly distributed parameters under the pre-test data sample; the field test data sample is X= { X 1 ,x 2 ,…,x n Pre-test data samples are y= { Y } 1 ,y 2 ,…,y m N is the number of samples of sample set X, and m is the number of samples of sample set Y.
Further, obtaining an equivalent uniform distribution probability density function obeyed by the two sets of data according to the maximum value and the minimum value of the uniform distribution probability density function and the uniform distribution parameter, including:
the probability density functions of the uniform distribution obeyed by the two groups of data are respectively:
wherein,for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For the minimum value of the uniformly distributed parameters under the pre-test data samples +.>Is the maximum value of the uniformly distributed parameter under the pre-test data sample.
Further, when the minimum value and the maximum value of the uniform distribution parameters of the field test data sample and the minimum value and the maximum value of the uniform distribution parameters of the pre-test data sample are staggered, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are partially overlapped with the area surrounded by the abscissa axis in the coordinate system, and then the area of the overlapped part of the two uniform distribution probability density function curves and the area surrounded by the abscissa axis is calculated as the credibility parameter of the pre-test sample relative to the test sample, and the method comprises the following steps:
for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For the minimum value of the uniformly distributed parameters under the pre-test data samples +.>The maximum value of the uniformly distributed parameters under the pre-test data sample;
when (when)When the two groups of measurement data samples are partially overlapped by the uniform distribution probability density function, calculating interval +.>Area c of overlapping part of uniform distribution probability density function curve of the next two groups of measurement data samples and area surrounded by abscissa axis r Is that
Wherein c r Representing the pre-test sample Y relative to the test sampleReliability parameter of X.
Further, whenWhen the two groups of measurement data samples are partially overlapped by the uniform distribution probability density function, calculating interval +.>Area c of overlapping part of uniform distribution probability density function curve of the next two groups of measurement data samples and area surrounded by abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
Further, whenWhen the two groups of measurement data samples are partially overlapped by the uniform distribution probability density function, calculating interval +.>The area c of the overlapping part of the uniform distribution probability density function curve of the next two groups of measurement data samples and the area surrounded by the abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
Further, whenWhen the two groups of measurement data samples are partially overlapped by the uniform distribution probability density function, calculating interval +.>The area c of the overlapping part of the uniform distribution probability density function curve of the next two groups of measurement data samples and the area surrounded by the abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
The invention has the technical effects that:
1. the invention provides a product credibility calculation method based on uniform distribution, which comprises the steps of obtaining a field test data sample and a pre-test data sample of a product; the field test data samples and the pre-test data samples are uniformly distributed; respectively obtaining the maximum value and the minimum value of the uniform distribution parameters of the two groups of data samples according to the uniform distribution probability density function; obtaining an equivalent uniform distribution probability density function obeyed by the two groups of data according to the maximum value and the minimum value of the uniform distribution probability density function and the uniform distribution parameter; obtaining the relationship of two function curves formed by the equivalent uniform distribution probability density functions of the two groups of data samples in a coordinate system according to the relationship between the uniform distribution parameters of the two groups of data samples; and further calculating the area of the overlapping part of the curve of the two groups of measurement data samples in the coordinate system and the area surrounded by the abscissa axis, wherein the area of the overlapping part is the credibility of the product. The method starts with the concept and mathematical meaning of the probability density function to calculate the credibility parameter, the mathematical concept is clear, and the calculation steps are clear, reasonable and feasible.
2. The product reliability calculated by 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 a measure of the consistency of multiple groups of product performance parameters for judging the consistency of multiple batches of data sources or product production processes.
In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail with reference to the drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 is a schematic flow chart of a method according to a preferred embodiment of the present invention;
FIG. 2 is whenWhen the probability density function curves are distributed, the probability density function curves are distributed uniformly;
FIG. 3 is whenWhen the probability density function curves are distributed, the probability density function curves are distributed uniformly;
FIG. 4 is whenWhen the probability density function curves are distributed, the curves of the probability density function curves are distributed uniformly, and the areas of the hatched parts of the curves are overlapped parts, namely the reliability parameters;
FIG. 5 is whenWhen the probability density function curves are distributed, the curves of the probability density function curves are distributed uniformly, and the areas of the hatched parts of the curves are overlapped parts, namely the reliability parameters;
FIG. 6 is whenWhen the probability density function curves are distributed, the curves of the probability density function curves are distributed uniformly, and the areas of the hatched parts of the curves are overlapped parts, namely the reliability parameters;
FIG. 7 is whenAnd when the two uniformly distributed probability density function curves are partially overlapped, the hatched area of the overlapped part in the diagram is the credibility parameter.
Detailed Description
Embodiments of the invention are described in detail below with reference to the attached drawings, but the invention can be implemented in a number of different ways, which are defined and covered by the claims.
The uniform distribution is a distribution form commonly used in the engineering field, such as traction load under unit length of electrified railway, uniform distribution random numbers in a neural network deep learning algorithm, and the like, and all the data are subjected to uniform distribution. When the physical quantities are statistically analyzed, 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 subject to the same distribution, and when the Bayes method is used for statistical analysis, the credibility (if multiple groups of data are adopted, the analysis can be carried out two by two) of one group of data (pre-test data) relative to the other group of data (on-site data) needs to be calculated, so that the subsequent statistical calculation of related parameters is facilitated. The calculation result can also be used as a measure of the consistency of two sets of data samples for judging the consistency of multiple batches of data sources or the production process of products. The present invention provides a new approach to solving this problem.
In order to finish the credibility calculation of the uniformly distributed pre-test sample relative to the field sample, firstly, respectively estimating uniformly distributed distribution parameters according to the pre-test data sample and the field test data sample; and then calculating the superposition part of the areas surrounded by the two probability density function curves and the abscissa axis according to the relation between the two uniformly distributed distribution parameters, and taking the superposition part as the credibility parameter of the pre-test sample to the field sample.
As shown in fig. 1, the invention provides a product credibility calculation method based on uniform 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 samples and the pre-test data samples are uniformly distributed;
respectively obtaining the maximum value and the minimum value of the uniform distribution parameters of the two groups of data samples according to the uniform distribution probability density function;
obtaining an equivalent uniform distribution probability density function obeyed by the two groups of data according to the maximum value and the minimum value of the uniform distribution probability density function and the uniform distribution parameter;
obtaining the relationship of two function curves formed by the equivalent uniform distribution probability density functions of the two groups of data samples in a coordinate system according to the relationship between the uniform distribution parameters of the two groups of data samples;
when the minimum value of the uniform distribution parameters of the field test data samples is larger than the maximum value of the uniform distribution parameters of the pre-test data samples or the maximum value of the uniform distribution parameters of the field test data samples is smaller than the minimum value of the uniform distribution parameters of the pre-test data samples, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples have no overlapping part, and the credibility is 0;
when the minimum value and the maximum value of the uniform distribution parameters of the field test data samples and the minimum value and the maximum value of the uniform distribution parameters of the pre-test data samples are staggered, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are partially overlapped with the area surrounded by the abscissa axis in the coordinate system, and the area of the overlapped part of the two uniform distribution probability density function curves and the area surrounded by the abscissa axis is calculated to be the credibility of the product.
The probability density function and the cumulative distribution function are two basic concepts in statistics, and the integral constant of the probability density function in the whole definition domain of the random variable is equal to 1. According to the concept and meaning of the probability density function, if the area of the overlapping part of the two uniformly distributed 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 invention is that by defining the area of the overlapping part of the two groups of evenly-distributed sample experience probability density function curves and the area surrounded by the abscissa axis as the credibility of the evenly-distributed pre-test data relative to the field test data, a new method for calculating the evenly-distributed credibility is provided, a corresponding calculation process is provided, a basic problem in Bayes fusion estimation of the two groups of evenly-distributed samples is solved, and a feasible method is provided for calculating the evenly-distributed credibility.
Further, respectively obtaining a maximum value and a minimum value of uniform distribution parameters of two groups of data samples according to the uniform distribution probability density function, wherein the method comprises the following steps:
the probability density function of the uniform distribution is:
wherein b 1 ,b 2 B for any two distribution parameters of uniform distribution 2 ＞b 1 ；
According to the maximum likelihood estimation method, the estimation values of the two groups of data uniform distribution parameters are respectively
Wherein,for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For the minimum value of the uniformly distributed parameters under the pre-test data samples +.>The maximum value of the uniformly distributed parameters under the pre-test data sample; the field test data sample is X= { X 1 ,x 2 ,…,x n Pre-test data samples are y= { Y } 1 ,y 2 ,…,y m N is the number of samples of sample set X, m is the number of samples of sample set Y;
further, obtaining an equivalent uniform distribution probability density function obeyed by the two sets of data according to the maximum value and the minimum value of the uniform distribution probability density function and the uniform distribution parameter, including:
the probability density functions of the uniform distribution obeyed by the two groups of data are respectively:
wherein,for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For the minimum value of the uniformly distributed parameters under the pre-test data samples +.>Is the maximum value of the uniformly distributed parameter under the pre-test data sample.
Further, when the minimum value and the maximum value of the uniform distribution parameters of the field test data sample and the minimum value and the maximum value of the uniform distribution parameters of the pre-test data sample are staggered, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are partially overlapped with the area surrounded by the abscissa axis in the coordinate system, and then the area of the overlapped part of the two uniform distribution probability density function curves and the area surrounded by the abscissa axis is calculated as the credibility parameter of the pre-test sample relative to the test sample, and the method comprises the following steps:
for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For the minimum value of the uniformly distributed parameters under the pre-test data samples +.>The maximum value of the uniformly distributed parameters under the pre-test data sample;
when (when)At this time, the uniformly distributed probability density functions of the two sets of measurement data samples partially coincide, as shown in FIG. 4, and the interval +.>Area c of overlapping part of uniform distribution probability density function curve of the next two groups of measurement data samples and area surrounded by abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
Further, whenAt this time, the uniformly distributed probability density functions of the two sets of measurement data samples partially coincide, as shown in FIG. 5, and the interval +.>Area c of overlapping part of uniform distribution probability density function curve of the next two groups of measurement data samples and area surrounded by abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
Further, whenAt this time, the uniformly distributed probability density functions of the two sets of measurement data samples partially coincide, as shown in FIG. 6, and the interval +.>The area c of the overlapping part of the uniform distribution probability density function curve of the next two groups of measurement data samples and the area surrounded by the abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
Further, whenAt this time, the uniformly distributed probability density functions of the two sets of measurement data samples partially coincide, as shown in FIG. 7, and the interval +.>The area c of the overlapping part of the uniform distribution probability density function curve of the next two groups of measurement data samples and the area surrounded by the abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
Further, the method comprises the steps of,or->At this time, there is no overlapping part between the two distributions, as shown in FIGS. 2 and 3, it is obvious that the two sets of data are inconsistent, i.e. credibility c r ＝0。
In order to better illustrate the technical scheme provided by the invention, the following description is made with reference to specific embodiments.
(1) Assume that in a certain line upgrade detection, a traction load per unit length of a certain section of an electrified railway is measured, and a group of measurement data samples are obtained, wherein the measurement data samples are respectively x= { X 1 ,x 2 ,…,x n And the data is taken as a field test data sample. The unit length traction load of the electrified railway section before line upgrading has a certain measurement data of Y= { Y 1 ,y 2 ,…,y m The data was used as pre-test data. Both groups of data samples are subjected to uniform distribution, and in practice, the credibility parameters of the samples Y and X need to be calculated so as to facilitate subsequent statistical calculation. Wherein the data set X has a total of 20 samples, i.e. n=20. The data set Y has 18 samples in total, i.e. m=18.
X＝{8.3 7.2 2.1 9.2 6.7 1.9 3.5 5.9 7.6 9.7 2.4 9.1 3.6 5.4 8.2 2.3 4.8 4.9 8.1 9.6}，
Y＝{7.9 3.3 9.6 7.4 8.1 3.8 8.7 5.5 7.9 4.5 8.4 10.1 4.5 6.4 6.9 9.4 5.3 4.9}
(2) According to probability density functions of uniform distributionNumber, and using maximum likelihood estimation method to estimate the uniform distribution parameters under two groups of data respectivelyAnd->
According to the maximum likelihood estimation method in the classical statistical theory, for the first group of data X, the estimation value of the uniformly distributed parameters is as follows
The probability density function obtained is
For the second set of data Y, the distribution parameter estimation value is
The probability density function obtained is
(3) Calculating the credibility of the sample Y relative to the sample X;
according to the obtained relationship of two uniformly distributed parameters, the method can obtainThen
I.e. test sample Y pairConfidence c in test sample X r ＝0.8205。
According to a given significance level or confidence, whether the two sets of data samples have consistency can be judged;
assuming that given a significance level of α=0.2, the confidence level is 1- α=0.8, since c r > 1- α, i.e., two sets of samples X and Y were considered to be identical at a significance level of 0.2.
In summary, the method calculates the credibility parameter from the concept and mathematical meaning of the probability density function, the mathematical concept is clear, and the calculation steps are clear, reasonable and feasible. The product reliability calculated by the method is greatly convenient for the subsequent statistical calculation of the related parameters of the product. The calculation result can also be used as a measure of the consistency of multiple groups of product performance parameters 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 variations and modifications are possible without deviating from the scope of the invention as defined in the attached claims. While the invention has been illustrated and described in detail in the drawings and the specification, such illustration and description are to be considered illustrative or exemplary only 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 (2)
1. The product credibility calculating method based on uniform distribution is characterized by comprising the following steps of:
acquiring a field test data sample and a pre-test data sample of a product; the field test data samples and the pre-test data samples are uniformly distributed; the product is traction load under unit length of the electrified railway;
respectively obtaining the maximum value and the minimum value of the uniform distribution parameters of the two groups of data samples according to the uniform distribution probability density function;
obtaining an equivalent uniform distribution probability density function obeyed by the two groups of data according to the maximum value and the minimum value of the uniform distribution probability density function and the uniform distribution parameter;
obtaining the relationship of two function curves formed by the equivalent uniform distribution probability density functions of the two groups of data samples in a coordinate system according to the relationship between the uniform distribution parameters of the two groups of data samples;
when the minimum value of the uniform distribution parameters of the field test data samples is larger than the maximum value of the uniform distribution parameters of the pre-test data samples or the maximum value of the uniform distribution parameters of the field test data samples is smaller than the minimum value of the uniform distribution parameters of the pre-test data samples, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples have no overlapping part, and the credibility is 0;
when the minimum value and the maximum value of the uniform distribution parameters of the field test data samples and the minimum value and the maximum value of the uniform distribution parameters of the pre-test data samples are staggered, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are partially overlapped with the area surrounded by the abscissa axis in the coordinate system, and the area of the overlapped part of the two uniform distribution probability density function curves and the area surrounded by the abscissa axis is calculated to be the credibility of the product;
wherein, according to the maximum value and the minimum value of the uniform distribution probability density function and the uniform distribution parameter, obtaining the equivalent uniform distribution probability density function obeyed by the two groups of data comprises:
the probability density functions of the uniform distribution obeyed by the two groups of data are respectively:
wherein,for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For the minimum value of the uniformly distributed parameters under the pre-test data samples +.>The maximum value of the uniformly distributed parameters under the pre-test data sample;
when the minimum value and the maximum value of the uniform distribution parameters of the field test data samples and the minimum value and the maximum value of the uniform distribution parameters of the pre-test data samples are mutually staggered, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are partially overlapped with the area surrounded by the abscissa axis in the coordinate system, and then the area of the overlapped part of the two uniform distribution probability density function curves and the area surrounded by the abscissa axis is calculated to be the credibility parameter of the pre-test samples relative to the test samples, and the method comprises the following steps:
when (when)When the two groups of measurement data samples are partially overlapped by the uniform distribution probability density function, calculating interval +.>The next two sets of measurement data samplesArea c of overlapping part of uniform distribution probability density function curve and area surrounded by abscissa axis r Is that
When (when)When the two groups of measurement data samples are partially overlapped by the uniform distribution probability density function, calculating interval +.>Area c of overlapping part of uniform distribution probability density function curve of the next two groups of measurement data samples and area surrounded by abscissa axis r Is that
When (when)When the two groups of measurement data samples are partially overlapped by the uniform distribution probability density function, calculating interval +.>The area c of the overlapping part of the uniform distribution probability density function curve of the next two groups of measurement data samples and the area surrounded by the abscissa axis r Is that
When (when)At the time, two sets of measurement data samplesIs partially coincident with the uniformly distributed probability density function of (2), calculating interval +.>The area c of the overlapping part of the uniform distribution probability density function curve of the next two groups of measurement data samples and the area surrounded by the abscissa axis r Is that
Wherein c r Indicating the confidence parameters of the pre-test sample Y relative to the test sample X.
2. A method for calculating the reliability of a product based on uniform distribution according to claim 1,
obtaining a maximum value and a minimum value of uniform distribution parameters of two groups of data samples respectively according to the uniform distribution probability density function, wherein the method comprises the following steps:
the probability density function of the uniform distribution is:
wherein b 1 ,b 2 B for any two distribution parameters of uniform distribution 2 ＞b 1 ；
According to the maximum likelihood estimation method, the estimation values of the two groups of data uniform distribution parameters are respectively
Wherein,for the minimum value of the uniformly distributed parameters under the field test data samples, +.>For the maximum value of the uniformly distributed parameters under the field test data sample, +.>For the minimum value of the uniformly distributed parameters under the pre-test data samples +.>The maximum value of the uniformly distributed parameters under the pre-test data sample; the field test data sample is X= { X 1 ,x 2 ,…,x n Pre-test data samples are y= { Y } 1 ,y 2 ,…,y m N is the number of samples of sample set X, and m is the number of samples of sample set Y.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110340402.6A CN113743707B (en) | 2021-03-30 | 2021-03-30 | Product credibility calculation method based on uniform distribution |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110340402.6A CN113743707B (en) | 2021-03-30 | 2021-03-30 | Product credibility calculation method based on uniform distribution |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113743707A CN113743707A (en) | 2021-12-03 |
| CN113743707B true CN113743707B (en) | 2024-03-01 |
Family
ID=78728239
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110340402.6A Active CN113743707B (en) | 2021-03-30 | 2021-03-30 | Product credibility calculation method based on uniform distribution |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113743707B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115602323B (en) * | 2022-09-07 | 2023-06-06 | 浙江一山智慧医疗研究有限公司 | Combined risk assessment model, method and application applicable to disease risk assessment |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102968556A (en) * | 2012-11-08 | 2013-03-13 | 重庆大学 | Probability distribution-based distribution network reliability judgment method |
| CN110033046A (en) * | 2019-04-17 | 2019-07-19 | 成都信息工程大学 | A kind of quantization method calculating characteristic matching point distribution confidence level |
| CN111177851A (en) * | 2019-12-27 | 2020-05-19 | 北航（四川）西部国际创新港科技有限公司 | Method for evaluating ground risks in unmanned aerial vehicle operation safety risk evaluation |
| 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 |
-
2021
- 2021-03-30 CN CN202110340402.6A patent/CN113743707B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102968556A (en) * | 2012-11-08 | 2013-03-13 | 重庆大学 | Probability distribution-based distribution network reliability judgment method |
| CN110033046A (en) * | 2019-04-17 | 2019-07-19 | 成都信息工程大学 | A kind of quantization method calculating characteristic matching point distribution confidence level |
| CN111177851A (en) * | 2019-12-27 | 2020-05-19 | 北航（四川）西部国际创新港科技有限公司 | Method for evaluating ground risks in unmanned aerial vehicle operation safety risk evaluation |
| 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 |
Non-Patent Citations (3)
| Title |
|---|
| 张士峰.小样本成败型设备可靠性评估方法.《核动力工程》.2006,第2006年第27卷卷(第第5期期),第79-83页. * |
| 彭建康.磁悬浮弹性支承结构机电***全局模型修正与灵敏度分析.《中国优秀硕士学位论文全文数据库信息科技辑》.2017,第1-74页. * |
| 牛杰.基于模型确认的桥梁结构概率损伤识别方法研究.《中国优秀硕士学位论文全文数据库信息科技辑》.2019,第1-124页. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113743707A (en) | 2021-12-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| WO2021120788A1 (en) | Machine learning-based hydrologic forecasting precision evaluation method and system | |
| CN110851980B (en) | Method and system for predicting residual life of equipment | |
| Venkatraman | A permutation test to compare receiver operating characteristic curves | |
| CN110197020B (en) | Method for analyzing influence of environmental change on hydrological drought | |
| CN111612048B (en) | Unsupervised clustering anomaly detection method | |
| CN112651119B (en) | Multi-performance parameter acceleration degradation test evaluation method for space harmonic reducer | |
| CN107515965A (en) | A kind of acceleration degeneration modelling evaluation method based on uncertain course | |
| CN105571645A (en) | Automatic dam monitoring method | |
| CN109979529A (en) | CNV detection device | |
| CN113743707B (en) | Product credibility calculation method based on uniform distribution | |
| CN106599367A (en) | Method for detecting abnormal state of spacecraft | |
| CN111811827B (en) | Product performance consistency inspection method based on Rayleigh distribution | |
| Akkerhuis et al. | The statistical evaluation of binary tests without gold standard: Robustness of latent variable approaches | |
| CN110850358A (en) | Electric energy meter comprehensive verification method and system based on stepwise regression algorithm | |
| CN111914424B (en) | Design wind speed value taking method and system based on short-term wind measurement data | |
| CN106779354B (en) | Bayes data fusion evaluation method for aircraft performance evaluation | |
| CN114266006B (en) | Evaluation method for measurement uncertainty of accelerated degradation test | |
| CN112329283A (en) | Ballastless track CA mortar adjustment layer damage identification method and system | |
| CN113762981B (en) | Product credibility calculation method based on index distribution | |
| CN109523129A (en) | A kind of method of unmanned vehicle multi-sensor information real time fusion | |
| CN107506824B (en) | Method and device for detecting bad observation data of power distribution network | |
| CN114002574A (en) | Method for testing semiconductor structure | |
| CN111753427A (en) | Method for improving precision of electromechanical product simulation model based on evidence theory | |
| Levine et al. | Crimestat version 3.3 update notes: Part 2: Regression modeling | |
| CN111369091A (en) | Method, apparatus, device and medium for user perceptual portrait analysis |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |