CN113743707A - Product credibility calculation method based on uniform distribution - Google Patents

Product credibility calculation method based on uniform distribution Download PDF

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CN113743707A
CN113743707A CN202110340402.6A CN202110340402A CN113743707A CN 113743707 A CN113743707 A CN 113743707A CN 202110340402 A CN202110340402 A CN 202110340402A CN 113743707 A CN113743707 A CN 113743707A
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杨华波
白锡斌
张士峰
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National University of Defense Technology
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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; the two groups of data samples are uniformly distributed; 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 relation of two function curves formed by the uniformly distributed probability density functions of the two groups of data samples in a coordinate system according to the relation between the uniformly distributed 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 prior test data samples are mutually staggered, the function curves of the two groups of measurement data samples are partially overlapped with the area enclosed by the abscissa axis, and the area of the overlapped area is the reliability of the product. The method starts with the concept and the 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

Product credibility calculation method based on uniform distribution
Technical Field
The invention relates to a credibility calculation method of product parameter performance data samples which obey uniform distribution in probability statistics.
Background
In the actual engineering, a plurality of batches of measurement data which are subjected to uniform distribution are obtained, for example, the traction load of the electrified railway under the unit length, the analysis shows that the measurement data are subjected to uniform distribution, for example, the seed number in the normal distribution random sampling, the uniformly distributed random number in the neural network deep learning algorithm and the like, and the measurement data are required to be accurately subjected to uniform distribution in the actual calculation so as to keep the good performance of the calculation result. In practice, when a Bayes method is used to perform statistical analysis on multiple batches of measurement data, two or more sets of measurement data cannot be mixed together without distinction, and the difference of the overall distribution obeyed by different measurement data, that is, the reliability of the data, needs to be considered. Data reliability calculation methods generally include two types, one type is provided according to a model, a way and a mode of obtaining data, and is combined with a corresponding calculation method, such as a VV & a (Verification, Verification and identification) technology in a modeling simulation technology, and the method needs to be completely familiar with the model, the test mode, the environmental conditions and the like of obtaining 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 normal distribution can respectively test the mean value and the variance by using a t distribution test and an F distribution test, but for the uniform distribution, no good technical method is available for calculating the reliability of two different samples at present. Therefore, there is a need for a new technology of a product reliability calculation method based on index distribution.
Disclosure of Invention
In order to solve the technical problems in the prior art, 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 sample and the data sample before the test are uniformly distributed;
respectively obtaining the maximum value and the minimum value of the uniformly distributed parameters of the two groups of data samples according to the uniformly distributed probability density function;
obtaining equivalent uniformly distributed probability density functions obeyed by the two groups of data according to the uniformly distributed probability density functions and the maximum values and the minimum values of the uniformly distributed parameters;
obtaining the relation of two function curves formed by the equivalent uniformly distributed probability density functions of the two groups of data samples in a coordinate system according to the relation between the uniformly distributed 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 prior 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 prior data samples, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are not overlapped, and the reliability 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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the reliability of the product.
Further, respectively obtaining the maximum value and the minimum value of the uniformly distributed parameters of the two groups of data samples according to the uniformly distributed probability density function, including:
the uniformly distributed probability density function is:
Figure BDA0002998967110000021
wherein, b1,b2Any two distribution parameters for uniform distribution, b2＞b1；
According to the maximum likelihood estimation method, the estimated values of the two groups of data uniform distribution parameters are respectively
Figure BDA0002998967110000022
Figure BDA0002998967110000023
Wherein the content of the first and second substances,
Figure BDA0002998967110000024
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure BDA0002998967110000025
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure BDA0002998967110000026
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure BDA0002998967110000027
the maximum value of the uniform distribution parameter under the prior data sample; the field test data sample is 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.
Further, obtaining an equivalent uniformly distributed probability density function obeyed by the two groups of data according to the uniformly distributed probability density function and the maximum value and the minimum value of the uniformly distributed parameter, including:
the uniformly distributed probability density functions obeyed by the two sets of data are respectively:
Figure BDA0002998967110000031
Figure BDA0002998967110000032
wherein the content of the first and second substances,
Figure BDA0002998967110000033
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure BDA0002998967110000034
is the most evenly distributed parameter under a field test data sampleThe value of the one or more of the one or,
Figure BDA0002998967110000035
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure BDA0002998967110000036
is the maximum value of the uniform distribution parameter under the prior data sample.
Further, 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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the credibility parameter of the prior samples relative to the test samples, and the method comprises the following steps:
Figure BDA0002998967110000037
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure BDA0002998967110000038
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure BDA0002998967110000039
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure BDA00029989671100000310
the maximum value of the uniform distribution parameter under the prior data sample;
when in use
Figure BDA00029989671100000311
When the two groups of measurement data samples are in time, the uniformly distributed probability density functions of the two groups of measurement data samples are partially overlapped, and an interval is calculated
Figure BDA00029989671100000312
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the region enclosed by the abscissa axisrIs composed of
Figure BDA00029989671100000313
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
Further, when
Figure BDA00029989671100000314
When the two groups of measurement data samples are in time, the uniformly distributed probability density functions of the two groups of measurement data samples are partially overlapped, and an interval is calculated
Figure BDA00029989671100000315
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the region enclosed by the abscissa axisrIs composed of
Figure BDA0002998967110000041
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
Further, when
Figure BDA0002998967110000042
When the two groups of measurement data samples are in time, the uniformly distributed probability density functions of the two groups of measurement data samples are partially overlapped, and an interval is calculated
Figure BDA0002998967110000043
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the area enclosed by the abscissa axisrIs composed of
Figure BDA0002998967110000044
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
Further, when
Figure BDA0002998967110000045
When the two groups of measurement data samples are in time, the uniformly distributed probability density functions of the two groups of measurement data samples are partially overlapped, and an interval is calculated
Figure BDA0002998967110000046
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the area enclosed by the abscissa axisrIs composed of
Figure BDA0002998967110000047
Wherein, crRepresenting the confidence parameter 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 sample and the data sample before the test are uniformly distributed; respectively obtaining the maximum value and the minimum value of the uniformly distributed parameters of the two groups of data samples according to the uniformly distributed probability density function; obtaining equivalent uniformly distributed probability density functions obeyed by the two groups of data according to the uniformly distributed probability density functions and the maximum values and the minimum values of the uniformly distributed parameters; obtaining the relation of two function curves formed by the equivalent uniformly distributed probability density functions of the two groups of data samples in a coordinate system according to the relation between the uniformly distributed parameters of the two groups of data samples; and then calculating the area of the overlapping part of the curve of the uniformly distributed probability density functions of the two groups of measurement data samples in the coordinate system and the region surrounded by the abscissa axis, wherein the area of the overlapping part of the regions is the reliability of the product. The method starts with the concept and the 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 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 drawing showing
Figure BDA0002998967110000051
When the probability density function curves are not overlapped, the two uniformly distributed probability density function curves are not overlapped;
FIG. 3 is a drawing showing
Figure BDA0002998967110000052
When the probability density function curves are not overlapped, the two uniformly distributed probability density function curves are not overlapped;
FIG. 4 is a drawing showing
Figure BDA0002998967110000053
The two uniformly distributed probability density function curves are partially overlapped, and the area of the overlapped part is shaded in the graph, namely the reliability parameter;
FIG. 5 is a schematic view of a process for producing a semiconductor device
Figure BDA0002998967110000054
The two uniformly distributed probability density function curves are partially overlapped, and the shaded part in the figureDividing the area of the overlapped part into the reliability parameter;
FIG. 6 is a drawing showing
Figure BDA0002998967110000055
The two uniformly distributed probability density function curves are partially overlapped, and the area of the overlapped part is shaded in the graph, namely the reliability parameter;
FIG. 7 is a drawing showing
Figure BDA0002998967110000056
And then, the two uniformly distributed probability density function curves are partially overlapped, and the area of the overlapped part is shaded in the graph, namely the reliability parameter.
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.
The uniform distribution is a distribution form commonly used in the engineering field, such as traction load in unit length of the electrified railway, uniformly distributed random numbers in a neural network deep learning algorithm, and the like, and the data are uniformly distributed. 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. The present invention provides a new way to solve this problem.
In order to complete the calculation of the credibility of the uniformly distributed pre-test samples relative to the field samples, firstly, uniformly distributed distribution parameters are respectively estimated according to the pre-test data samples and the field test data samples; and then calculating the overlapping part of the two probability density function curves and the area enclosed by the abscissa axis according to the relation between the two uniformly distributed distribution parameters, and taking the overlapping part as the credibility parameter of the sample before the test for the field sample.
As shown in fig. 1, the present invention provides a method for calculating credibility of a product based on uniform distribution, 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 data sample before the test are uniformly distributed;
respectively obtaining the maximum value and the minimum value of the uniformly distributed parameters of the two groups of data samples according to the uniformly distributed probability density function;
obtaining equivalent uniformly distributed probability density functions obeyed by the two groups of data according to the uniformly distributed probability density functions and the maximum values and the minimum values of the uniformly distributed parameters;
obtaining the relation of two function curves formed by the equivalent uniformly distributed probability density functions of the two groups of data samples in a coordinate system according to the relation between the uniformly distributed 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 prior 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 prior data samples, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are not overlapped, and the reliability 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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the reliability of the product.
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 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 reliability of the corresponding data is better. The innovation point of the method is that the area of the overlapping part of the two groups of uniformly distributed sample empirical probability density function curves and the area surrounded by the abscissa axis is defined as the reliability of uniformly distributed pre-test data relative to field test data, a novel method for calculating the reliability of uniform distribution is provided, a corresponding calculation process is provided, one basic problem in Bayes fusion estimation of the two groups of uniformly distributed samples is solved, and a feasible method is provided for calculating the reliability of uniform distribution.
Further, respectively obtaining the maximum value and the minimum value of the uniformly distributed parameters of the two groups of data samples according to the uniformly distributed probability density function, including:
the uniformly distributed probability density function is:
Figure BDA0002998967110000071
wherein, b1,b2Any two distribution parameters for uniform distribution, b2＞b1；
According to the maximum likelihood estimation method, the estimated values of the two groups of data uniform distribution parameters are respectively
Figure BDA0002998967110000072
Figure BDA0002998967110000073
Wherein the content of the first and second substances,
Figure BDA0002998967110000074
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure BDA0002998967110000075
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure BDA0002998967110000076
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure BDA0002998967110000077
the maximum value of the uniform distribution parameter under the prior data sample; the field test data sample is 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;
further, obtaining an equivalent uniformly distributed probability density function obeyed by the two groups of data according to the uniformly distributed probability density function and the maximum value and the minimum value of the uniformly distributed parameter, including:
the uniformly distributed probability density functions obeyed by the two sets of data are respectively:
Figure BDA0002998967110000078
Figure BDA0002998967110000079
wherein the content of the first and second substances,
Figure BDA00029989671100000710
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure BDA00029989671100000711
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure BDA00029989671100000712
is the minimum of uniformly distributed parameters under the prior data sampleThe value of the one or more of the one,
Figure BDA00029989671100000713
is the maximum value of the uniform distribution parameter under the prior data sample.
Further, 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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the credibility parameter of the prior samples relative to the test samples, and the method comprises the following steps:
Figure BDA0002998967110000081
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure BDA0002998967110000082
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure BDA0002998967110000083
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure BDA0002998967110000084
the maximum value of the uniform distribution parameter under the prior data sample;
when in use
Figure BDA0002998967110000085
Then, the uniformly distributed probability density functions of the two sets of measured data samples are partially overlapped, and as shown in FIG. 4, the interval is calculated
Figure BDA0002998967110000086
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the region enclosed by the abscissa axisrIs composed of
Figure BDA0002998967110000087
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
Further, when
Figure BDA0002998967110000088
Then, the uniformly distributed probability density functions of the two sets of measured data samples are partially overlapped, and as shown in FIG. 5, the interval is calculated
Figure BDA0002998967110000089
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the region enclosed by the abscissa axisrIs composed of
Figure BDA00029989671100000810
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
Further, when
Figure BDA00029989671100000811
Then, the uniformly distributed probability density functions of the two sets of measured data samples are partially overlapped, and as shown in FIG. 6, the interval is calculated
Figure BDA00029989671100000812
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the area enclosed by the abscissa axisrIs composed of
Figure BDA00029989671100000813
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
Further, when
Figure BDA0002998967110000091
Then, the uniformly distributed probability density functions of the two sets of measured data samples are partially overlapped, and as shown in FIG. 7, the interval is calculated
Figure BDA0002998967110000092
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the area enclosed by the abscissa axisrIs composed of
Figure BDA0002998967110000093
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
Further, in the above-mentioned case,
Figure BDA0002998967110000094
or
Figure BDA0002998967110000095
At this time, there is no overlapping part between the two distributions, as shown in fig. 2 and 3, and it is obvious that the two sets of data are inconsistent, i.e., the confidence level cr＝0。
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 in a line upgrade test, the traction load of a certain section of an electrified railway is measured, and a group of measurement data samples are obtained, wherein X is ═ { X ═ respectively1,x2,…,xnAnd taking the data as a field test data sample. Before the line of the electrified railway section is upgraded, the measurement data of the traction load per unit length is Y ═ Y1,y2,…,ymAnd taking the data as the prior data. Both groups of data samples are subjected to uniform distribution, and in practice, the reliability parameter of the sample Y for the sample X needs to be calculated so as to facilitate the subsequent statistical calculation. Wherein the data setX is 20 samples, i.e., n is 20. The data set Y has 18 samples, i.e., m is 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) Respectively estimating the uniformly distributed parameters under two groups of data by utilizing a maximum likelihood estimation method according to the uniformly distributed probability density function
Figure BDA0002998967110000096
And
Figure BDA0002998967110000097
according to the maximum likelihood estimation method in the classical statistical theory, aiming at the first group of data X, the uniformly distributed parameter estimation value is
Figure BDA0002998967110000098
The resulting probability density function is
Figure BDA0002998967110000099
For the second set of data Y, the distribution parameter estimate is
Figure BDA00029989671100000910
The resulting probability density function is
Figure BDA0002998967110000101
(3) Calculating the credibility of the sample Y relative to the sample X;
according to the obtained relationship of the two uniformly distributed distribution parameters, the method can be obtained
Figure BDA0002998967110000102
Then
Figure BDA0002998967110000103
I.e. the reliability c of the test sample Y with respect to the test sample Xr＝0.8205。
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 (7)

1. A product credibility calculation method based on uniform 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 data sample before the test are uniformly distributed;
respectively obtaining the maximum value and the minimum value of the uniformly distributed parameters of the two groups of data samples according to the uniformly distributed probability density function;
obtaining equivalent uniformly distributed probability density functions obeyed by the two groups of data according to the uniformly distributed probability density functions and the maximum values and the minimum values of the uniformly distributed parameters;
obtaining the relation of two function curves formed by the equivalent uniformly distributed probability density functions of the two groups of data samples in a coordinate system according to the relation between the uniformly distributed 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 prior 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 prior data samples, the equivalent uniform distribution probability density function curves of the two groups of measurement data samples are not overlapped, and the reliability 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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the reliability of the product.
2. The method of claim 1, wherein the product credibility calculation method based on uniform distribution,
respectively obtaining the maximum value and the minimum value of the uniformly distributed parameters of the two groups of data samples according to the uniformly distributed probability density function, wherein the method comprises the following steps:
the uniformly distributed probability density function is:
Figure FDA0002998967100000011
wherein, b1,b2Any two distribution parameters for uniform distribution, b2＞b1；
According to the maximum likelihood estimation method, the estimated values of the two groups of data uniform distribution parameters are respectively
Figure FDA0002998967100000012
Figure FDA0002998967100000013
Wherein the content of the first and second substances,
Figure FDA0002998967100000021
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure FDA0002998967100000022
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure FDA0002998967100000023
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure FDA0002998967100000024
the maximum value of the uniform distribution parameter under the prior data sample; the field test data sample is 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.
3. The method of claim 1, wherein the product credibility calculation method based on uniform distribution,
obtaining an equivalent uniformly distributed probability density function obeyed by the two groups of data according to the uniformly distributed probability density function and the maximum value and the minimum value of the uniformly distributed parameters, wherein the equivalent uniformly distributed probability density function comprises the following steps:
the uniformly distributed probability density functions obeyed by the two sets of data are respectively:
Figure FDA0002998967100000025
Figure FDA0002998967100000026
wherein the content of the first and second substances,
Figure FDA0002998967100000027
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure FDA0002998967100000028
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure FDA0002998967100000029
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure FDA00029989671000000210
is the maximum value of the uniform distribution parameter under the prior data sample.
4. The method of claim 1, wherein the product credibility calculation method based on uniform distribution,
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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the credibility parameter of the prior samples relative to the test samples, and the method comprises the following steps:
Figure FDA00029989671000000211
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure FDA00029989671000000212
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure FDA00029989671000000213
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure FDA00029989671000000214
the maximum value of the uniform distribution parameter under the prior data sample;
when in use
Figure FDA00029989671000000215
When the two groups of measurement data samples are in time, the uniformly distributed probability density functions of the two groups of measurement data samples are partially overlapped, and an interval is calculated
Figure FDA00029989671000000216
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the region enclosed by the abscissa axisrIs composed of
Figure FDA0002998967100000031
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
5. The method of claim 1, wherein the product credibility calculation method based on uniform distribution,
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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the credibility parameter of the prior samples relative to the test samples, and the method comprises the following steps:
Figure FDA0002998967100000032
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure FDA0002998967100000033
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure FDA0002998967100000034
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure FDA0002998967100000035
the maximum value of the uniform distribution parameter under the prior data sample;
when in use
Figure FDA0002998967100000036
When the two groups of measured data samples are in time, the uniformly distributed probability density functions of the two groups of measured data samples are partially overlapped and countedCalculation interval
Figure FDA0002998967100000037
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the region enclosed by the abscissa axisrIs composed of
Figure FDA0002998967100000038
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
6. The method of claim 1, wherein the product credibility calculation method based on uniform distribution,
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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the credibility parameter of the prior samples relative to the test samples, and the method comprises the following steps:
Figure FDA0002998967100000039
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure FDA00029989671000000310
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure FDA00029989671000000311
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure FDA00029989671000000312
the maximum value of the uniform distribution parameter under the prior data sample;
when in use
Figure FDA0002998967100000041
When the two groups of measurement data samples are in time, the uniformly distributed probability density functions of the two groups of measurement data samples are partially overlapped, and an interval is calculated
Figure FDA0002998967100000042
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the area enclosed by the abscissa axisrIs composed of
Figure FDA0002998967100000043
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
7. The method of claim 1, wherein the product credibility calculation method based on uniform distribution,
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 prior 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 enclosed 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 enclosed by the abscissa axis is calculated to be the credibility parameter of the prior samples relative to the test samples, and the method comprises the following steps:
Figure FDA0002998967100000044
is the minimum value of the evenly distributed parameters under the field test data sample,
Figure FDA0002998967100000045
is the maximum value of the uniform distribution parameter under the field test data sample,
Figure FDA0002998967100000046
is the minimum value of the uniform distribution parameter under the prior data samples,
Figure FDA0002998967100000047
the maximum value of the uniform distribution parameter under the prior data sample;
when in use
Figure FDA0002998967100000048
When the two groups of measurement data samples are in time, the uniformly distributed probability density functions of the two groups of measurement data samples are partially overlapped, and an interval is calculated
Figure FDA0002998967100000049
Area c of the overlapped part of the uniformly distributed probability density function curves of the next two groups of measurement data samples and the area enclosed by the abscissa axisrIs composed of
Figure FDA00029989671000000410
Wherein, crRepresenting the confidence parameter of the pre-test sample Y relative to the test sample X.
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