CN110889077A - Kendall correlation coefficient-based consistency inspection method for degraded data of accelerated storage and natural storage - Google Patents
Kendall correlation coefficient-based consistency inspection method for degraded data of accelerated storage and natural storage Download PDFInfo
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Abstract
The invention provides a Kendall correlation coefficient-based consistency test method for degraded data of accelerated storage and natural storage. The method is to perform regression fitting on the data from accelerated storage tests to obtain a test time series required to be experienced at a level of degradation such as natural storage data. And judging the correlation between the two groups of sequences by calculating Kendall correlation coefficients of each acceleration stress level and the corresponding test time interval sequence under natural storage, thereby deducing whether the failure mechanism under the acceleration storage and the natural storage is consistent. The consistency test method verifies the implementation scheme of the accelerated test and the validity of test data thereof so as to ensure the validity of product life prediction and verification.
Description
One, the technical field
The invention relates to a method for testing consistency of degradation data of a product under different test stress levels, in particular to a method for testing consistency of degradation data of accelerated storage and natural storage based on Kendall correlation coefficients, belongs to the field of reliability modeling technology and life prediction analysis, and is used for verifying the implementation scheme of an accelerated test and the effectiveness of test data of the accelerated test so as to ensure the effectiveness of product life prediction and verification.
Second, background Art
For long-term storage products, their effective storage life is one of the important design and use criteria. However, the state of the long-storage product changes very slowly under normal storage stress, and in order to obtain the storage failure rule of the product as soon as possible and predict the storage life, the storage failure of the product is accelerated by adopting a stress increasing mode. For some long-storage products, failure life data are difficult to observe even under accelerated stress, and the storage life of the product under normal stress can be predicted only by monitoring the degradation failure rule of some key performance parameters of the product. To ensure the credibility of this statistical inference, it must be demonstrated that the products have the same failure mechanism when stored under normal stress and accelerated stress, i.e. increasing the stress level only increases the failure rate without changing the failure mechanism. The method is an important premise for carrying out accelerated storage degradation test design and also solves the key problem and the basic problem of predicting the storage life of long-storage products. At present, the research on the consistency test method of the failure mechanism of the accelerated test in domestic and foreign documents is mainly divided into three categories: the first type is consistency test of failure mechanism of burst failure products, such as consistency of normal distribution variance; the second type is a degraded failure product with a clear failure mechanism, and a parameter method is generally adopted to test whether the degraded tracks under two stresses belong to the same family and have random processes with different parameters; the third category is a degenerate failure product with an undefined failure mechanism, and is generally judged qualitatively by expert experience, and the conclusion has certain subjectivity and is difficult to popularize and apply. On one hand, the difficulty of determining a product degradation failure mechanism is correspondingly increased due to the improvement of the process complexity of modern long-storage products, and on the other hand, the types and the quantity of collected product detection data are relatively sufficient due to the improvement of the product detection level. Therefore, the non-parametric inspection method based on data driving can effectively improve the level of test data consistency inspection. The Kendall correlation coefficient test is a nonparametric test method for binary overall correlation. The consistency test of the accelerated storage and natural storage degradation data is carried out based on Kendall correlation coefficients, and the implementation scheme of an accelerated test and the validity of the test degradation data can be verified.
Third, the invention
Object (a)
The invention aims to carry out consistency check on accelerated storage degradation data and natural storage degradation data, and the consistency check can check the effectiveness of the accelerated storage degradation data: on one hand, the degradation mechanism of the product is ensured to be consistent in the test process, and the effectiveness of the accelerated test is verified; on the other hand, the reliability and the precision of product life prediction and verification are improved.
(II) technical scheme
The invention discloses a consistency inspection method for degraded data of accelerated storage and natural storage based on Kendall correlation coefficients, which is a method for inspecting the effectiveness of accelerated storage data by a data-driven nonparametric inspection method.
In the invention, considering that the failure mechanism under accelerated storage and natural storage is consistent, test time interval sequences corresponding to the same degradation increment sequence are respectively calculated under two stresses, and the two groups of time interval sequences have cooperative correlation. That is, if a certain degradation increment interval is elapsed for a long time in a natural storage environment, the elapsed time of the degradation increment interval is also relatively long in an accelerated storage environment. The method comprises the following steps:
step 1, collecting basic information of a natural storage degradation test and an accelerated storage degradation test, and respectively collecting natural storage degradation data and accelerated storage degradation data, wherein the collection mode of the natural storage degradation data is usually a special natural storage test or product field detection, and the accelerated storage degradation data is collected in degradation data of different levels under the same stress (usually temperature, humidity, salt spray and the like) in the accelerated storage test.
And 2, performing regression analysis on the degradation data to obtain a regression equation representing the relationship between the degradation quantity and the storage time, wherein the regression equation under the natural storage environment can be obtained by naturally storing the degradation data, and the regression equations under different stress levels can be obtained by using the degradation data under different accelerated stress levels.
And 3, obtaining the time required by the product to reach the equal-interval degradation amount under each stress level by using regression equations under different acceleration stress levels, wherein the equal-interval degradation amount is divided on the premise that the initial degradation amount (namely, the degradation amount is 0) of the product and the failure degradation amount (namely, the failure threshold value) of the product are determined.
And 4, calculating time intervals corresponding to the equal degradation increments of the products at all stress levels, namely, utilizing the time length required by the adjacent equal degradation increments at the same level of stress obtained in the step 3 to make a difference.
And 5, calculating Kendall cooperative correlation coefficients under natural storage and each stress level by using the equal degeneration increment time interval sequence.
And 6, judging the degradation failure process under the natural storage and the corresponding stress level by utilizing Kendall cooperative correlation coefficients, wherein the judgment rule generally comprises the following three types: the method has no correlation, certain positive correlation and certain negative correlation, wherein the more the absolute value of the Kendall collaborative correlation coefficient is close to 1, the stronger the characterization correlation is.
In the selection of the accelerated test, the accelerated storage test conducted on the product was a constant stress accelerated degradation test. The constant stress accelerated degradation test is the most common accelerated test type which is most conveniently carried out in engineering, and if the actually carried accelerated test is step stress or sequential stress, a certain statistical method is adopted to equivalently convert the data into the data under the constant stress accelerated test.
Wherein, the "basic information" in step 1 means that the method of the present invention is performed on the basis of the following basic information, and the basic information includes:
(1) and (4) selecting a test object. The products of the invention are long-storage degradation failure type products, long-time continuous working degradation failure type products and discontinuous working degradation failure type products.
(2) And (4) selecting the type of the accelerated test. The accelerated storage test carried out on the product is a constant stress accelerated degradation test. The constant stress accelerated degradation test is the most common accelerated test type which is most conveniently carried out in engineering, and if the actually carried accelerated test is step stress or sequential stress, a certain statistical method is adopted to equivalently convert the data into the data under the constant stress accelerated test.
(3) Accelerating the setting of the amount of the sample to be tested in the storage test. The common engineering practice is to put one or more samples under each accelerated storage stress level for performance testing and to obtain performance monitoring data of each sample.
(4) And (5) acquiring test data. And at least one performance monitoring data of the same type of product is obtained under the natural storage environment. Under the natural storage environment, if performance monitoring data of a plurality of products of the same type are obtained at the same time, firstly, interpolation is carried out on the performance data by adopting an interpolation method according to the monitoring time point of each product, and the testing time of each product is aligned; then obtaining the sample mean value of each test moment; and then the sequence of the sample mean value changing along with the storage time is regarded as single sample performance change data, so that the multi-sample data under the natural storage environment is converted into single sample degradation sequence data. And at least obtaining performance monitoring data of the same type of product under the accelerated storage environment. Under the accelerated storage environment, if performance monitoring data of a plurality of products of the same type are obtained at the same time, firstly, interpolation is carried out on the performance data by adopting an interpolation method according to the monitoring time point of each product, and the testing time of each product is aligned; then obtaining the sample mean value of each test moment; and then the sequence of the sample mean value changing along with the storage time is regarded as single sample performance change data, so that the multi-sample data under the accelerated storage stress is converted into single sample degradation sequence data.
(III) the invention has the advantages that:
(1) according to the invention, on the basis of considering the principles of sufficiency, necessity, conformity with engineering habits, testability, designability and verifiability, a method for checking the consistency of the natural degradation data is designed according to the data characteristics of the accelerated degradation test of the product, so that the validity of the accelerated degradation test of the product and the validity of the accelerated degradation test data are verified;
(2) the method can be used for verifying the consistency of failure mechanisms of the product in an accelerated storage test and a natural storage test so as to ensure the reliability and the precision of the product life prediction analysis.
Description of the drawings
FIG. 1 is a flow chart of a data consistency checking method of the present invention;
fig. 2 is a schematic diagram of a sequence of equal degeneration delta time intervals. Wherein, the abscissa represents the test time, and the ordinate represents the performance degradation test result;
to a failure threshold value；
The representation is based on natural storage (stress level of
) Regression equations of the data;
presentation is based on accelerated storage (stress level of
) Regression equations of the data;
a division point representing equally spaced degradation increments;
expressed in natural storage stress
Lower degradation increment from
Is degraded to
The length of time elapsed;
indicating storage stress at accelerated speed
Lower degradation increment from
Is degraded to
The length of time elapsed;
fifth, detailed description of the invention
The invention discloses a consistency inspection method for degraded data of accelerated storage and natural storage based on Kendall correlation coefficients, which is a method for inspecting the effectiveness of accelerated storage data by a data-driven nonparametric inspection method. The method is based on the basic information of natural storage test and accelerated storage test of long-storage products. The basic information comprises a test object, an accelerated test type, a reference sample amount setting and test data acquisition. The content of each aspect of information is specifically as follows:
(1) the test objects are long-storage degradation failure type products, long-time continuous working degradation failure type products and discontinuous working degradation failure type products;
(2) the accelerated storage test carried out on the product is a constant stress accelerated degradation test. The test type is the most common accelerated test type which is most conveniently developed in engineering, and if the product which needs to verify the consistency does not meet the test type, namely the actually-performed accelerated test is step stress or sequence stress, a certain statistical method is adopted to equivalently convert the data into the data under the constant stress accelerated test;
(3) description of the amount of the reference sample for accelerated storage test. The common engineering practice is to put in a few products at each stress level, i.e. one or more samples at each accelerated storage stress level for performance testing, and to obtain performance monitoring data of each sample.
(4) For a description of data collection in the experiment. And at least obtaining performance monitoring data of the same type of product under the natural storage environment and the accelerated storage environment. Under the natural storage environment, if performance monitoring data of a plurality of products of the same type are obtained at the same time, firstly, interpolation is carried out on the performance data by adopting an interpolation method according to the monitoring time point of each product, and the testing time of each product is aligned; then obtaining the sample mean value of each test moment; and then the sequence of the sample mean value changing along with the storage time is regarded as single sample performance change data, so that the multi-sample data under the natural storage environment is converted into single sample degradation sequence data. Similar processing is also performed for multi-sample data under accelerated storage testing.
As shown in FIG. 1, the consistency test method of degraded data of accelerated storage and natural storage based on Kendall correlation coefficient comprises the following steps:
step 1, collecting basic information of a natural storage degradation test and an accelerated storage degradation test, and respectively collecting natural storage degradation data and accelerated storage degradation data, wherein the collection mode of the natural storage degradation data is usually a special natural storage test or product field detection, and the accelerated storage degradation data is collected in degradation data of different levels under the same stress (usually temperature, humidity, salt spray and the like) in the accelerated storage test.
Step 2, carrying out regression analysis according to test data under natural storage to obtain a regression equation representing the relationship between the degradation amount and the storage time under the natural storage environment
(ii) a According to stress level
Performing regression analysis on the test data to obtain the characterization stress level
Regression equation of lower degradation quantity and storage time relation
，
Number of stress levels for constant stress accelerated degradation testing.
Step 3, assuming that the degradation amount of the new product is 0, according to the failure threshold value
Will be
Is divided into
A sequence of equally spaced degenerate increments, order
，Specifying
，
，…，
，…
,. Order to
. Solving the regression equation to obtain the stress level
Reach a given level of degradation
Required elapsed test time
I.e. by
Wherein
Indicating the natural storage stress level.
And 4, calculating time intervals corresponding to the equal-spacing degradation increments under different stress levels. Order to
Wherein, in the step (A),
representing a natural storage environment.
Step 5, storing the data of the equal-spacing degeneration increment time interval sequence under the stress level in a natural way and cooperating with the correlation coefficient
I.e. by
Wherein sgn is a sign function,
sgn reflects the synergy between pairs of numbers. sgn =1, the pair of expression numbers is a pair of cooperation numbers, and the number of the pair of cooperation numbers is recorded as
(ii) a sgn = -1, the number pair is represented as uncoordinated number pair, and the number of uncoordinated number pair is recorded as
. Stress level
Data co-correlation coefficient of
Can also be expressed as
And 6, judging the rule. The judgment result includes the following three types: has no correlation, a certain positive correlation and a certain negative correlation, wherein
The closer the absolute value of (d) is to 1, the stronger the correlation is characterized. The specific judgment rule is as follows: given a
Calculating a standard normal distribution
Quantile
If, if
Then the natural storage can be preliminarily determined
And stress level
The lower degradation failure process has no correlation; on the contrary, if
Then the natural storage can be preliminarily determined
And stress level
The underlying degenerative failure processes have some correlation (positive or negative).
The following embodiments are given:
in this case, an XX type propellant is taken as an example to show the application of the method for checking the consistency of the degradation data of the accelerated storage and the natural storage.
The basic information situation of the present case is as follows:
(1) test subjects:
subject type XX propellant is a typical long-storage degenerative failure product.
(2) The type of accelerated test:
the test is an accelerated degradation test under constant high temperature stress.
(3) Sample amount of the samples:
one part of the propellant which is newly delivered from a factory is arranged under the stress of five temperatures.
(4) Data acquisition:
the test times were measured for the remaining contents of different active ingredients in the propellant powder.
And (4) performing the consistency check work of the degradation data of the XX type propellant powder accelerated storage and the natural storage on the basis of the basic information of the XX type propellant powder.
The case implementation flow is the above five steps. For the case, basic information of the XX type propellant is obtained in the first step, and the acquired data are shown in table 1; after the second step, the third step and the fourth step, time intervals corresponding to the equal-spacing degradation increments under different stress levels are calculated and are shown in table 2; after statistics in the fifth step, Kendall correlation coefficients are obtained and are shown in Table 3; therefore, through the calculation of the step six, the consistency test result of the accelerated storage test data and the natural storage test data is obtained:
when the temperature of the water is higher than the set temperature,
,
。
therefore, it is considered that the storage failure mechanism under 5 accelerated stresses is consistent with the failure mechanism in natural storage and is not changed. The accelerated storage test data and the natural storage test data pass consistency check.
TABLE 1 test times at different temperature stress levels
TABLE 2 time intervals corresponding to equidistant degradation increments
TABLE 3 data collaborative correlation coefficient table
| Temperature/. degree.C |
 |
 |
 |
| 50℃ | 39 | 6 | 0.733 |
| 60℃ | 44 | 1 | 0.956 |
| 70℃ | 44 | 1 | 0.956 |
| 80℃ | 44 | 1 | 0.956 |
| 90℃ | 44 | 1 | 0.956 |
The symbols in table 3 illustrate:
the number of the cooperative number pairs;
the number of uncoordinated pairs;
the data is co-correlated with the coefficient.
Claims (7)
1. A consistency test method of degradation data of accelerated storage and natural storage based on Kendall correlation coefficient is based on the premise of basic information of accelerated degradation test of products, the basic information comprises a test object, an accelerated test type, a sample amount setting for participating in the test and a test data acquisition method,
the method comprises the following specific steps:
step 1, collecting basic information of a natural storage degradation test and an accelerated storage degradation test, and respectively collecting natural storage degradation data and accelerated storage degradation data, wherein the collection mode of the natural storage degradation data is usually a special natural storage test or product field detection, and the accelerated storage degradation data is collected in degradation data of different levels under the same stress (usually temperature, humidity, salt spray and the like) in the accelerated storage test;
step 2, regression analysis is carried out on the degradation data to obtain a regression equation representing the relation between the degradation quantity and the storage time, wherein the regression equation under the natural storage environment can be obtained by naturally storing the degradation data, and the regression equations under different stress levels can be obtained by using the degradation data under different accelerated stress levels;
step 3, obtaining the time length required by the product to reach the equal-interval degradation amount under each stress level by using regression equations under different acceleration stress levels, wherein the equal-interval degradation amount is divided on the premise that the initial degradation amount (namely, the degradation amount is 0) of the product and the failure degradation amount (namely, the failure threshold value) of the product are determined;
step 4, calculating time intervals corresponding to the equal degradation increments of the products under each stress level, namely, utilizing the time length required by the adjacent equal degradation increments under the same level of stress obtained in the step 3 to make a difference;
step 5, calculating Kendall cooperative correlation coefficients of natural storage and each stress level by using the equal degeneration increment time interval sequence;
and 6, judging the degradation failure process under the natural storage and the corresponding stress level by utilizing Kendall cooperative correlation coefficients, wherein the judgment rule generally comprises the following three types: the method has no correlation, certain positive correlation and certain negative correlation, wherein the more the absolute value of the Kendall collaborative correlation coefficient is close to 1, the stronger the characterization correlation is.
2. The method for checking consistency of degraded data in accelerated storage and natural storage based on Kendall correlation coefficients as claimed in claim 1, wherein the "basic information" comprises:
(1) the selection of the subject to be tested is carried out,
the products in the invention are long-storage degradation failure type products, long-time continuous working degradation failure type products and discontinuous working degradation failure type products;
(2) the selection of the type of the accelerated test,
the accelerated storage test carried out on the product is a constant stress accelerated degradation test,
the constant stress accelerated degradation test is the most common accelerated test type which is most conveniently carried out in engineering, and if the actually carried accelerated test is step stress or sequential stress, a certain statistical method is adopted to equivalently convert the data into the data under the constant stress accelerated test;
(3) the setting of the amount of the sample to be tested in the storage test is accelerated,
the common method in engineering is that one or more samples are respectively put into each accelerated storage stress level to carry out performance test, and performance monitoring data of each sample is obtained;
(4) the principle of collecting the test data is that,
at least one performance monitoring data of the same type product is obtained under the natural storage environment,
under the natural storage environment, if performance monitoring data of a plurality of products of the same type are obtained at the same time, firstly, interpolation is carried out on the performance data by adopting an interpolation method according to the monitoring time point of each product, and the testing time of each product is aligned; then obtaining the sample mean value of each test moment; then the sequence of the sample mean value changing along with the storage time is regarded as the single sample performance change data, thus converting the multi-sample data under the natural storage environment into the single sample degradation sequence data,
at least one performance monitoring data of the same type product is obtained under the accelerated storage environment,
under the accelerated storage environment, if performance monitoring data of a plurality of products of the same type are obtained at the same time, firstly, interpolation is carried out on the performance data by adopting an interpolation method according to the monitoring time point of each product, and the testing time of each product is aligned; then obtaining the sample mean value of each test moment; and then the sequence of the sample mean value changing along with the storage time is regarded as single sample performance change data, so that the multi-sample data under the accelerated storage stress is converted into single sample degradation sequence data.
3. The Kendall correlation coefficient-based consistency test method for the degraded data of accelerated storage and natural storage according to claim 2, wherein the step of obtaining a regression equation which characterizes the degradation amount and the storage time relation is as follows: performing regression analysis according to test data under natural storage to obtain regression equation representing relationship between degradation amount and storage time under natural storage environment
(ii) a According to stress level
Performing regression analysis on the test data to obtain the characterization stress level
Regression equation of lower degradation quantity and storage time relation
，
Number of stress levels for constant stress accelerated degradation testing.
4. The Kendall correlation coefficient-based consistency verification method for degradation data of accelerated storage and natural storage according to claim 3, wherein the step of obtaining the time length required for the product to reach the degradation amount at equal intervals at each stress level comprises the following steps: assuming that the degradation amount of the new product is 0, the new product is determined according to the failure threshold
Will be
Is divided into
A sequence of equally spaced degenerate increments, order
，Specifying
，
，…，
，…，
Order to
，
Solving the regression equation to obtain the stress level
Reach a given level of degradation
Required elapsed test time
I.e. by
Wherein
Indicating the natural storage stress level.
5. The Kendall correlation coefficient-based consistency verification method for degraded data in accelerated storage and natural storage according to claim 4, wherein the time interval corresponding to equal degradation increment refers to: calculating the time intervals corresponding to the equally spaced degradation increments at different stress levels,
order to
Wherein, in the step (A),
representing a natural storage environment.
6. The Kendall correlation coefficient-based method for testing consistency of degraded data in accelerated storage and natural storage according to claim 5, wherein the Kendall co-correlation coefficient is: natural storage and cooperative correlation coefficient of data of equal-spacing degradation increment time interval under stress level
I.e. by
Wherein the content of the first and second substances,
in order to be a function of the sign,
Stress level
Data co-correlation coefficient of
Can also be expressed as
7. The Kendall correlation coefficient-based consistency verification method for degraded data in accelerated storage and natural storage according to claim 5, wherein the "decision rule" refers to: given a
Calculating a standard normal distribution
Quantile
If, if
Then the natural storage can be preliminarily determined
And stress levelThe lower degradation failure process has no correlation; on the contrary, if
Then the natural storage can be preliminarily determined
And stress level
The underlying degenerative failure processes have some correlation (positive or negative).
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