CN114036463A - Product failure rate consistency inspection method based on exponential distribution - Google Patents

Product failure rate consistency inspection method based on exponential distribution Download PDF

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CN114036463A
CN114036463A CN202111320970.6A CN202111320970A CN114036463A CN 114036463 A CN114036463 A CN 114036463A CN 202111320970 A CN202111320970 A CN 202111320970A CN 114036463 A CN114036463 A CN 114036463A
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failure rate
products
consistency
ratio
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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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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention provides a product failure rate consistency inspection method based on exponential distribution, which comprises the following steps: obtaining failure rate estimation value vectors of two groups of products, wherein the failure rate estimation value vectors of the two groups of products have the same dimension; according to the failure rate estimation value vectors of the two groups of products, obtaining consistency parameters and failure rate ratios of corresponding dimensions of each element in the failure rate estimation value vectors of the two groups of products; obtaining a fitting function of the ratio of the consistency parameter to the failure rate according to the ratio of the consistency parameter to the failure rate; acquiring measurement data samples of any two groups of products to be measured, wherein the two groups of measurement data samples are subjected to exponential distribution to obtain failure rates and failure rate ratios of the two groups of products to be measured; obtaining consistency parameter estimation values of the two groups of products to be detected according to the fitting function and the failure rate ratio of the two groups of products to be detected; and judging whether the two groups of data have consistency or not according to the consistency parameter estimation value and a preset significance level or confidence coefficient.

Description

Product failure rate consistency inspection method based on exponential distribution
Technical Field
The invention relates to the technical field of product performance consistency inspection methods, in particular to a product failure rate consistency inspection method based on exponential distribution.
Background
In some engineering fields, it is often necessary to determine whether two sets of measurement data that are subjected to exponential distribution obey the same overall, i.e., the consistency check problem of the exponential distribution data, so as to further determine whether the data sources are the same. The exponential distribution is a distribution form often used in theoretical analysis and engineering practice, and particularly in the field of life distribution, two groups of different measurement data which are subjected to the exponential distribution are obtained in the engineering practice, such as the lives of two batches of same electronic components, the time for two same machines to fail for the first time, the time intervals for passengers to arrive at airports in different time periods and the like, and the theoretical analysis and the actual measurement data show that the two groups of measurement data are subjected to the exponential distribution. For two sets of samples that obey an exponential distribution (referred to as measured data in the aforementioned practice), a consistency check is required on the two sets of samples to determine whether the two sets of samples obey the same distribution at a given confidence level or significance level. At present, for consistency test of exponential distribution, test statistic is generally required to be constructed. The index distribution consistency inspection method usually adopts a classical Gamma distribution inspection method, the Gamma distribution is used for carrying out consistency inspection on the failure rates of two groups of data under a given significance level, if the inspection is passed, the two groups of data are considered to be subjected to the same index distribution, and if the inspection is not passed, the two groups of data are considered not to be subjected to the same index distribution. This method requires constructing statistics of failure rates that follow the Gamma distribution to be implemented.
However, constructing statistics that the failure rate follows the Gamma distribution is cumbersome. Therefore, a new technology of a product failure rate consistency inspection method based on index distribution is urgently needed in the industry.
Disclosure of Invention
The invention aims to provide a product failure rate consistency testing method based on exponential distribution, which is different from a classical consistency testing method, does not need to construct statistics, obtains consistency measurement of two groups of samples directly according to an empirical formula, and judges the consistency of the two groups of samples according to a given significance level or confidence requirement.
The invention provides a product failure rate consistency inspection method based on exponential distribution, which comprises the following steps:
obtaining failure rate estimation value vectors of two groups of products, wherein the failure rate estimation value vectors of the two groups of products have the same dimension;
according to the failure rate estimation value vectors of the two groups of products, obtaining consistency parameters and failure rate ratios of corresponding dimensions of each element in the failure rate estimation value vectors of the two groups of products;
according to the ratio of the consistency parameter to the failure rate, performing piecewise fitting by using a curve fitting method to obtain a fitting function of the ratio of the consistency parameter to the failure rate;
acquiring measurement data samples of any two groups of products to be measured, wherein the two groups of measurement data samples are subjected to exponential distribution to obtain failure rates and failure rate ratios of the two groups of products to be measured;
obtaining consistency parameter estimation values of the two groups of products to be detected according to the fitting function and the failure rate ratio of the two groups of products to be detected;
and judging whether the data of the two groups of products to be detected have consistency or not according to the consistency parameter estimation values of the two groups of products to be detected and a preset significance level or confidence coefficient.
Further, according to the failure rate estimation value vectors of the two groups of products, obtaining consistency parameters and failure rate ratios of corresponding dimensions of each element in the failure rate estimation value vectors of the two groups of products, including:
obtaining an exponential distribution probability density function of each element in the failure rate estimation value vectors of the two groups of products according to the failure rate estimation value vectors of the two groups of products;
according to the exponential distribution probability density function of each element, obtaining the intersection point of two curves of the distribution probability density functions of each element and the corresponding dimension element in the failure rate estimated value vectors of the two groups of products in a coordinate system;
according to the intersection point of two curves of the distribution probability density function of each element and the corresponding dimension element in the coordinate system, the area c of the overlapping part of the curve of the distribution probability density function of each element and the corresponding dimension element in the coordinate system and the area surrounded by the abscissa axis is obtainedr，crThe consistency parameter is obtained;
the ratio of each element and the corresponding dimension element in the failure rate estimation value vectors of the two groups of products is the failure rate ratio k.
Further, according to the ratio of the consistency parameter to the failure rate, a curve fitting method is used for piecewise fitting to obtain a consistency parameter crA fitting function to the failure rate ratio k, the fitting function being:
Figure BDA0003345151290000021
further, according to the ratio of the consistency parameter to the failure rate, a curve fitting method is used for piecewise fitting to obtain a consistency parameter crA fitting function to the failure rate ratio k, comprising:
the dimensionalities of the failure rate estimation value vectors of the two groups of products are the same and are both N, and the consistency parameter is criThe ratio of failure rate is kiWherein i is 1,2, …, N;
(1) when k is more than 0.1 and less than or equal to 1, fitting by using cubic polynomial according to the characteristics of the curve,
cr＝a0+a1k+a2k2+a3k3
will ki(i is 1,2, …, N) satisfying 0.1 < k ≦ 1, and selecting to form a new set k(1)Corresponding to a consistency parameter c of 0.1 < k.ltoreq.1riAre also selected to form a new set
Figure BDA0003345151290000031
Based on k(1)And
Figure BDA0003345151290000032
the polynomial coefficient a can be obtained by using a least square method0,a1,a2,a3Solution of (2)
Figure BDA0003345151290000033
The solution of cubic polynomial coefficient obtained by data calculation is
Figure BDA0003345151290000034
I.e. the fitting function is
cr＝0.71k3-1.79k2+1.94k+0.14
(2) When k is more than 1 and less than 10, the fitting function is directly obtained as
Figure BDA0003345151290000035
(3) When k is more than 0 and less than 0.1 and k is more than 10, the consistency parameter c is obtained by calculationriLess than 0.3, i.e., when 0 < k < 0.1 or k > 10, the two sets of index distribution samples have low agreement.
Further, measurement data samples of any two groups of products to be measured are obtained, and the two groups of measurement data samples are subjected to exponential distribution to obtain failure rates and failure rate ratios of the two groups of products to be measured; obtaining consistency parameter estimation values of two groups of products to be detected according to the fitting function and the failure rate ratio of the two groups of products to be detected, and the consistency parameter estimation values comprise:
the obtained data sample of the first group of products to be tested is X ═ X1,x2,…,xnAnd the data sample of the second group of products to be tested is Y ═ Y1,y2,…,ymN is the number of samples in the sample set X, m is the number of samples in the sample set Y, and both groups of data samples obey exponential distribution;
failure rate of the first set of data samples X according to maximum likelihood estimation
Figure BDA0003345151290000036
Is composed of
Figure BDA0003345151290000041
Failure rate of the second set of data samples Y
Figure BDA0003345151290000042
Is composed of
Figure BDA0003345151290000043
The failure rate ratio k of the two1Is composed of
Figure BDA0003345151290000044
Will k1Substituting the obtained data into the fitting function to obtain the consistency parameter estimated value c of the two groups of datar。
Further, according to the consistency parameter estimation values of the two groups of products to be tested and the preset significance level or confidence, judging whether the data of the two groups of products to be tested have consistency or not, including:
if the preset significance level or confidence is alpha, the judgment rule of whether the two groups of samples are consistent is as follows:
if c isrIf the sample is more than or equal to 1-alpha, the two groups of samples are considered to have consistency under the significance level alpha;
if c isr< 1- α, the two groups of samples were considered to be inconsistent at the significance level α.
The invention has the technical effects that:
the invention establishes the empirical function relationship between the ratio of the estimated failure rates of two groups of index distribution data and the data consistency parameters, calculates the ratio of the estimated failure rates after respectively obtaining the estimated failure rates according to two groups of data samples, and then can quickly calculate the consistency measurement of the two groups of index samples according to the empirical function relationship. The method is different from a classical consistency test method, does not need to construct statistics, directly obtains consistency measurement of two groups of samples according to an empirical formula, and then judges the consistency of the two groups of samples according to a given significance level or confidence degree requirement.
The invention provides the product failure rate consistency inspection method based on the exponential distribution, which is quick and simple in calculation, reasonable and feasible, and provides a feasible method for solving the problem of complex calculation of the existing product failure rate consistency inspection method based on the exponential distribution.
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.
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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 graph with the ratio of two index distribution failure rate parameters as the abscissa and two index distribution data consistency parameters as the ordinate;
FIG. 3 is a comparison of a curve fit plot with raw data when the ratio of two exponential distribution failure rates is 0.1 < k ≦ 1;
FIG. 4 is a graph of a curve fit versus raw data when the ratio of two exponential failure rates is 1 < k < 10;
FIG. 5 is the absolute error of the fit function when 0.1 < k < 10;
FIG. 6 is the relative error of the fit function when 0.1 < k < 10.
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.
As shown in the title 1, the present invention provides a product failure rate consistency checking method based on exponential distribution, which includes the following steps:
step 101: obtaining failure rate estimation value vectors of two groups of products, wherein the failure rate estimation value vectors of the two groups of products have the same dimension;
step 102: according to the failure rate estimation value vectors of the two groups of products, obtaining consistency parameters and failure rate ratios of corresponding dimensions of each element in the failure rate estimation value vectors of the two groups of products;
step 103: according to the ratio of the consistency parameter to the failure rate, performing piecewise fitting by using a curve fitting method to obtain a fitting function of the ratio of the consistency parameter to the failure rate;
step 104: acquiring measurement data samples of any two groups of products to be measured, wherein the two groups of measurement data samples are subjected to exponential distribution to obtain failure rates and failure rate ratios of the two groups of products to be measured;
step 105: obtaining consistency parameter estimation values of the two groups of products to be detected according to the fitting function and the failure rate ratio of the two groups of products to be detected;
step 106: and judging whether the data of the two groups of products to be detected have consistency or not according to the consistency parameter estimation values of the two groups of products to be detected and a preset significance level or confidence coefficient.
The invention establishes the empirical function relationship between the ratio of the estimated failure rates of two groups of index distribution data and the data consistency parameters, calculates the ratio of the estimated failure rates after respectively obtaining the estimated failure rates according to two groups of data samples, and then can quickly calculate the consistency measurement of the two groups of index samples according to the empirical function relationship. The method is different from a classical consistency test method, does not need to construct statistics, directly obtains consistency measurement of two groups of samples according to an empirical formula, and then judges the consistency of the two groups of samples according to a given significance level or confidence degree requirement.
In a specific embodiment, obtaining the consistency parameter and the failure rate ratio of the corresponding dimension of each element in the failure rate estimation value vectors of the two groups of products according to the failure rate estimation value vectors of the two groups of products includes:
obtaining an exponential distribution probability density function of each element in the failure rate estimation value vectors of the two groups of products according to the failure rate estimation value vectors of the two groups of products;
according to the exponential distribution probability density function of each element, obtaining the intersection point of two curves of the distribution probability density functions of each element and the corresponding dimension element in the failure rate estimated value vectors of the two groups of products in a coordinate system;
according to the intersection point of two curves of the distribution probability density function of each element and the corresponding dimension element in the coordinate system, the area c of the overlapping part of the curve of the distribution probability density function of each element and the corresponding dimension element in the coordinate system and the area surrounded by the abscissa axis is obtainedr，crThe consistency parameter is obtained;
the ratio of each element and the corresponding dimension element in the failure rate estimation value vectors of the two groups of products is the failure rate ratio k.
Suppose that a failure rate estimation vector for a product is obtained in some way (simulated, or measured multiple times for the same product), and expressed as
Figure BDA0003345151290000061
In the same way, another set of failure rate estimation vectors for the product is obtained, and expressed as
Figure BDA0003345151290000062
Are all N-dimensional vectors
The exponential distribution probability density function is:
f(t)＝λe-λt t∈(0,∞)
where λ is the distribution parameter of the exponential distribution, also known as the failure rate.
At a given point
Figure BDA0003345151290000063
In this case, each element in the failure rate estimate vector is calculated for both sets of products
Figure BDA0003345151290000064
And its corresponding dimension element
Figure BDA0003345151290000065
C of the consistency parameterri。
Any element in failure rate estimation value vector of two groups of products
Figure BDA0003345151290000066
And its corresponding dimension element
Figure BDA0003345151290000067
The distribution probability density function of (a) is:
Figure BDA0003345151290000068
Figure BDA0003345151290000069
let f1(t)＝f2(t) then
Figure BDA00033451512900000610
When in use
Figure BDA0003345151290000071
The solution of the intersection point is
Figure BDA0003345151290000072
Respectively calculating the cumulative distribution function from 0 to the intersection point of two probability density function curves, and the formula is as follows
Figure BDA0003345151290000073
Figure BDA0003345151290000074
Wherein
Figure BDA0003345151290000075
Is a cumulative distribution function corresponding to the two probability density functions.
Then the area of the overlapping portion of the curve of the two probability density functions in the coordinate system and the region surrounded by the abscissa axis is calculated as follows:
(1) if it is not
Figure BDA0003345151290000076
The integral is calculated as
Figure BDA0003345151290000077
(2) If it is not
Figure BDA0003345151290000078
The integral is calculated as
Figure BDA0003345151290000079
Wherein, criIs the area of the overlapping part of the two probability density function curves and the area enclosed by the abscissa axis, criI.e. the consistency parameter.
Simultaneous calculation k is calculated according toi：
Figure BDA00033451512900000710
In a specific embodiment, according to the ratio of the consistency parameter to the failure rate, a curve fitting method is used for piecewise fitting to obtain a consistency parameter crA fitting function to the failure rate ratio k, comprising:
according to the obtained N consistency parameters criAnd corresponding kiWhere i is 1,2, …, N. With k as the abscissa, crOn the ordinate, a graph is plotted, see fig. 2.
And (4) performing piecewise fitting on the curve according to the characteristics of the curve in the graph.
(1) When k is more than 0.1 and less than or equal to 1, fitting by using a cubic polynomial according to the characteristics of the curve. Namely, it is
cr＝a0+a1k+a2k2+a3k3
Will ki(i is 1,2, …, N) satisfying 0.1 < k ≦ 1, and selecting to form a new set k(1)Corresponding to a consistency parameter c of 0.1 < k.ltoreq.1riAre also selected to form a new set
Figure BDA0003345151290000081
Based on k(1)And
Figure BDA0003345151290000082
the polynomial coefficient a can be obtained by using a least square method0,a1,a2,a3Solution of (2)
Figure BDA0003345151290000083
The solution of cubic polynomial coefficient obtained by data calculation is
Figure BDA0003345151290000084
I.e. a polynomial of
cr＝0.71k3-1.79k2+1.94k+0.14 (5)
The effect of the function fit is shown in figure 3.
(2) When 1 < k < 10, note that
Figure BDA0003345151290000085
And
Figure BDA0003345151290000086
for consistency parameter criThe calculation of (a) has no influence, which is in accordance with engineering practice. So that the fitting function can be directly obtained as
Figure BDA0003345151290000087
The effect of the function fit is shown in figure 4.
(3) When 0 < k < 0.1 and k > 10, the calculated consistency parameter criAnd is less than 0.3, which means that when 0 < k < 0.1 or k > 10, the two sets of samples of the exponential distribution are relatively less consistent, and the two sets of data are considered by engineering to be inconsistent in this case, i.e., not belonging to the same population. The consistency parameter fitting formula in this case is not given here.
The fitting function can be expressed as
Figure BDA0003345151290000088
Define the fitting absolute error as
Figure BDA0003345151290000089
Wherein the content of the first and second substances,
Figure BDA00033451512900000810
to calculate the consistency parameter from the fitting function, criThe consistency parameter is calculated according to the overlapping area of the exponential distribution probability density function curve and the area surrounded by the abscissa axis.
A plot of absolute error d versus failure rate ratio k is plotted, see fig. 5. As can be seen from the figure, the fitting absolute error is less than 0.01, except that the fitting error is slightly larger when k is around 0.1 (in this case, the consistency parameter is about 0.3).
Defining the fitting relative error as
Figure BDA0003345151290000091
A graph of relative error e versus failure rate ratio k is plotted, see fig. 6. As can be seen from fig. 6 and 2, at criIf the absolute value of the relative error is more than 0.4 (corresponding to 0.14 < k < 7.5), the absolute value of the relative error is less than 1 percent. In other cases, the absolute value of the relative error is greater than 1%, but the two sets of samples of exponential distribution are usedThe consistency is already small.
In order to ensure the precision of the fitting formula, 50000 pairs of failure rate samples lambda are respectively generated by using a simulation method(1)And λ(2)And sufficient verification is performed at the same time.
In a specific embodiment, measurement data samples of any two groups of products to be measured are obtained, and the two groups of measurement data samples are subjected to exponential distribution to obtain failure rates and failure rate ratios of the two groups of products to be measured; obtaining consistency parameter estimation values of two groups of products to be detected according to the fitting function and the failure rate ratio of the two groups of products to be detected, and the consistency parameter estimation values comprise:
the obtained data sample of the first group of products to be tested is X ═ X1,x2,…,xnAnd the data sample of the second group of products to be tested is Y ═ Y1,y2,…,ymN is the number of samples in the sample set X, m is the number of samples in the sample set Y, and both groups of data samples obey exponential distribution;
failure rate of the first set of data samples X according to maximum likelihood estimation
Figure BDA0003345151290000092
Is composed of
Figure BDA0003345151290000093
Failure rate of the second set of data samples Y
Figure BDA0003345151290000094
Is composed of
Figure BDA0003345151290000095
The failure rate ratio k of the two1Is composed of
Figure BDA0003345151290000096
Will k1Substituting the obtained data into the fitting function to obtain the consistency parameter estimated value c of the two groups of datar。
In one embodiment, the determining whether the data of the two groups of products to be tested have consistency according to the consistency parameter estimation values of the two groups of products to be tested and a preset significance level or confidence level includes:
if the preset significance level or confidence is alpha, the judgment rule of whether the two groups of samples are consistent is as follows:
if c isrIf the sample is more than or equal to 1-alpha, the two groups of samples are considered to have consistency under the significance level alpha;
if c isr< 1- α, the two groups of samples were considered to be inconsistent at the significance level α.
The invention has the innovation point that an empirical formula of the failure rate estimated value ratio of two exponential distribution samples and the estimated value of the consistency parameter is established, the main model of the empirical formula is a cubic polynomial which can cover the calculation of the consistency parameter between the two exponential distribution samples with the failure rate ratio between 0.1 and 10, and the fitting absolute precision is less than 0.01. The method provides a quick calculation method for the consistency test of the exponential distribution.
In order to better explain the technical scheme provided by the invention, the following description is made in conjunction with specific examples.
(1) Firstly sampling by using a random sampling method to obtain 500 failure rates, wherein the sampling parameter is [0.001,2 ]]Is uniformly sampled, and is recorded as
Figure BDA0003345151290000101
Then, the same method is used for uniformly sampling 500 failure rate data, and the sampling parameter is [0.002,3 ]]Is marked as
Figure BDA0003345151290000102
(2) Calculating two failure rates by using the overlapping part area of the two exponential distribution probability density function curves and the area surrounded by the abscissa axis
Figure BDA0003345151290000103
Corresponding consistency parameter criSimultaneously order
Figure BDA0003345151290000104
N number of k can be obtainedi,criThe data pairs.
(3) And performing segmented fitting according to the obtained failure rate ratio-consistency parameter data pair. Find out that satisfies 0 < kiK is not more than 1iAnd corresponding criIn 336 pairs, fitting is performed using a cubic polynomial to obtain a polynomial
cr＝0.71k3-1.79k2+1.94k+0.14
For ki> 1, and
Figure BDA0003345151290000105
the calculated failure rates are the same, so for ki> 1, fitting function of
Figure BDA0003345151290000106
Thus, a fitting functional relation between the failure rate ratio of the two exponential distribution data and the consistency parameter is obtained:
Figure BDA0003345151290000107
(4) assuming that there are two batches of electronic devices, the first time of failure measured by the first batch of devices is X ═ X1,x2,…,xn17 samples in total, i.e. n is 17. The time of the first failure measured by the second batch of devices is Y ═ Y1,y2,…,ymA total of 14 samples, i.e. m-14. Both sets of data obey an exponential distribution.
Wherein
X＝{10.1 7.0 123.6 45.8 67.4 11.2 42.0 4.7 85.2 66.6 96.4 99.7 7.0 27.3 29.9 96.6 47.3}
Y ═ 50.076.07.469.7153.717.466.099.463.5163.7141.84.23.138.7. The first set of samples X failure rate is estimated as
Figure BDA0003345151290000111
The failure rate of the second set of data samples Y is estimated as
Figure BDA0003345151290000112
The ratio of the two failure rates is
Figure BDA0003345151290000113
Substituted into the fitting function to obtain
cr1＝0.888
(5) Judging whether the two groups of data samples have consistency or not according to a given significance level or confidence;
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.
The invention provides a product failure rate consistency inspection method based on exponential distribution, which respectively calculates failure rates according to two groups of exponential distribution sample data, inputs two failure rate ratios as parameters into a fitting function formula, can obtain consistency parameter calculation results of the two groups of exponential distribution sample data, and provides a judgment criterion for judging whether the two groups of exponential distribution sample data are consistent. The method for checking the consistency of the failure rates of the products based on the exponential distribution is an empirical formula obtained based on analysis of a large amount of data, is quick and simple to calculate, and provides a quick and feasible calculation method for solving the technical problem of the invention.
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 (6)

1. A product failure rate consistency checking method based on index distribution is characterized by comprising the following steps:
obtaining failure rate estimation value vectors of two groups of products, wherein the failure rate estimation value vectors of the two groups of products have the same dimension;
according to the failure rate estimation value vectors of the two groups of products, obtaining consistency parameters and failure rate ratios of corresponding dimensions of each element in the failure rate estimation value vectors of the two groups of products;
according to the ratio of the consistency parameter to the failure rate, performing piecewise fitting by using a curve fitting method to obtain a fitting function of the ratio of the consistency parameter to the failure rate;
acquiring measurement data samples of any two groups of products to be measured, wherein the two groups of measurement data samples are subjected to exponential distribution to obtain failure rates and failure rate ratios of the two groups of products to be measured;
obtaining consistency parameter estimation values of the two groups of products to be detected according to the fitting function and the failure rate ratio of the two groups of products to be detected;
and judging whether the data of the two groups of products to be detected have consistency or not according to the consistency parameter estimation values of the two groups of products to be detected and a preset significance level or confidence coefficient.
2. The method as claimed in claim 1, wherein obtaining the consistency parameter and the failure rate ratio of the corresponding dimension of each element in the failure rate estimation value vectors of the two groups of products according to the failure rate estimation value vectors of the two groups of products comprises:
obtaining an exponential distribution probability density function of each element in the failure rate estimation value vectors of the two groups of products according to the failure rate estimation value vectors of the two groups of products;
according to the exponential distribution probability density function of each element, obtaining the intersection point of two curves of the distribution probability density functions of each element and the corresponding dimension element in the failure rate estimated value vectors of the two groups of products in a coordinate system;
according to the intersection point of two curves of the distribution probability density function of each element and the corresponding dimension element in the coordinate system, the area c of the overlapping part of the curve of the distribution probability density function of each element and the corresponding dimension element in the coordinate system and the area surrounded by the abscissa axis is obtainedr，crThe consistency parameter is obtained;
the ratio of each element and the corresponding dimension element in the failure rate estimation value vectors of the two groups of products is the failure rate ratio k.
3. The method for checking the consistency of the failure rates of products based on exponential distribution as claimed in claim 1, wherein a consistency parameter c is obtained by piecewise fitting according to the ratio of the consistency parameter to the failure rate by a curve fitting methodrA fitting function to the failure rate ratio k, the fitting function being:
Figure FDA0003345151280000021
4. the product failure rate consistency check based on exponential distribution as claimed in claim 3The method is characterized in that according to the ratio of the consistency parameter to the failure rate, a curve fitting method is used for piecewise fitting to obtain a consistency parameter crA fitting function to the failure rate ratio k, comprising:
the dimensionalities of the failure rate estimation value vectors of the two groups of products are the same and are both N, and the consistency parameter is criThe ratio of failure rate is kiWherein i is 1,2, …, N;
(1) when k is more than 0.1 and less than or equal to 1, fitting by using cubic polynomial according to the characteristics of the curve,
cr＝a0+a1k+a2k2+a3k3
will ki(i is 1,2, …, N) satisfying 0.1 < k ≦ 1, and selecting to form a new set k(1)Corresponding to a consistency parameter c of 0.1 < k.ltoreq.1riAre also selected to form a new set
Figure FDA0003345151280000022
Based on k(1)And
Figure FDA0003345151280000023
the polynomial coefficient a can be obtained by using a least square method0,a1,a2,a3Solution of (2)
Figure FDA0003345151280000024
The solution of cubic polynomial coefficient obtained by data calculation is
Figure FDA0003345151280000025
I.e. the fitting function is
cr＝0.71k3-1.79k2+1.94k+0.14
(2) When k is more than 1 and less than 10, the fitting function is directly obtained as
Figure FDA0003345151280000026
(3) When k is more than 0 and less than 0.1 and k is more than 10, the consistency parameter c is obtained by calculationriLess than 0.3, i.e., when 0 < k < 0.1 or k > 10, the two sets of index distribution samples have low agreement.
5. The method for checking the consistency of the failure rates of the products based on the exponential distribution as claimed in claim 3 or 4, wherein measurement data samples of any two groups of products to be tested are obtained, and the two groups of measurement data samples are subjected to the exponential distribution, so that the failure rates and the failure rate ratios of the two groups of products to be tested are obtained; obtaining consistency parameter estimation values of two groups of products to be detected according to the fitting function and the failure rate ratio of the two groups of products to be detected, and the consistency parameter estimation values comprise:
the obtained data sample of the first group of products to be tested is X ═ X1,x2,…,xnAnd the data sample of the second group of products to be tested is Y ═ Y1,y2,…,ymN is the number of samples in the sample set X, m is the number of samples in the sample set Y, and both groups of data samples obey exponential distribution;
failure rate of the first set of data samples X according to maximum likelihood estimation
Figure FDA0003345151280000031
Is composed of
Figure FDA0003345151280000032
Failure rate of the second set of data samples Y
Figure FDA0003345151280000033
Is composed of
Figure FDA0003345151280000034
The failure rate ratio k of the two1Is composed of
Figure FDA0003345151280000035
Will k1Substituting the obtained data into the fitting function to obtain the consistency parameter estimated value c of the two groups of datar。
6. The method as claimed in claim 5, wherein the step of determining whether the data of the two sets of products to be tested have consistency according to the consistency parameter estimation values of the two sets of products to be tested and a preset significance level or confidence level comprises:
if the preset significance level or confidence is alpha, the judgment rule of whether the two groups of samples are consistent is as follows:
if c isrIf the sample is more than or equal to 1-alpha, the two groups of samples are considered to have consistency under the significance level alpha;
if c isr< 1- α, the two groups of samples were considered to be inconsistent at the significance level α.
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