CN112784414A - Multi-component complete machine storage life confidence lower limit evaluation method - Google Patents

Multi-component complete machine storage life confidence lower limit evaluation method Download PDF

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CN112784414A
CN112784414A CN202110085614.4A CN202110085614A CN112784414A CN 112784414 A CN112784414 A CN 112784414A CN 202110085614 A CN202110085614 A CN 202110085614A CN 112784414 A CN112784414 A CN 112784414A
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马小兵
张远朦
王晗
王艳艳
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Beihang University
No 59 Research Institute of China Ordnance Industry
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Abstract

The invention provides a multi-component complete machine storage life confidence lower limit evaluation method, which comprises the following steps: firstly, the method comprises the following steps: calculating parameter estimation values of all parts by using an overall maximum likelihood theory; II, secondly: calculating the mean and variance of the acceleration factors of the components; thirdly, the method comprises the following steps: calculating the characteristic life and the acceleration factor lower confidence limit of the whole machine product under high stress based on a competitive failure model; fourthly, the method comprises the following steps: and calculating the lower limit of the reliable service life of the whole product under the given storage condition. The invention adopts a competitive failure model to integrate the test results of the component-level products, thereby giving the estimated value of the storage life of the whole product which is difficult to directly carry out the accelerated test; the method adopts an integral maximum likelihood estimation method, has low requirement on the initial value of parameters, and has quick and simple iteration and strong operability; the method can improve the service life prediction precision, and has the advantages of scientific method, good manufacturability and wide popularization and application value.

Description

Multi-component complete machine storage life confidence lower limit evaluation method
Technical Field
The invention relates to a multi-component complete machine storage life confidence lower limit evaluation method, which is based on acceleration factor dispersion quantification. The method utilizes the accelerated storage life test data of each component level product in the multi-component complete machine to carry out overall maximum likelihood estimation on the distribution parameters of the total accumulated failure function of the component products, quantizes the dispersibility of the acceleration factors, estimates the acceleration factors of the complete machine and the confidence lower limit thereof by adopting a competitive failure model, and finally evaluates the storage reliable life and the storage life lower limit of the complete machine product. The method is suitable for the field of evaluation of the storage life of multi-component complete machine products.
Background
Typically, military products need to be stored in warehouses for a period of time after being mass produced, referred to as the product's shelf life. During the storage period, the reliability index of the product is reduced due to the function of the storage environment. In order to quickly verify or evaluate whether the storage period and the storage reliability of a product meet the specified index requirements, an accelerated storage test is widely adopted at present, the storage information of the product under the long-term action of storage stress is acquired in a short time, and reference is provided for the work of designing the storage reliability, fixing the life and prolonging the life, storing and maintaining spare parts and the like. However, for the whole machine grade product, the accelerated storage test is difficult to develop due to the influence of factors such as time, economy and the like, so that the outstanding problems of low evaluation precision of the whole machine storage life, limited application range and the like are caused. Component grade products, by contrast, are more amenable to accelerated shelf life testing, obtaining sufficient test data to estimate acceleration factors and shelf life for specific sensitive stress and failure modes. Therefore, it is considered to establish a multi-component complete machine storage life evaluation method based on component product information.
At present, a whole machine storage life evaluation method based on component information in engineering starts from component acceleration factor evaluation, based on a short-plate principle, an acceleration factor of the weakest link stored in a whole machine is selected as a whole machine acceleration factor or an average principle, and an arithmetic average value or a weighted average value of the acceleration factors of the weak links in the whole machine is used as the acceleration factor of the whole machine. And then deducing the storage life and the lower limit thereof through the estimation value of the acceleration factor of the whole machine.
However, in practical situations, the whole machine product does not necessarily have obvious weak links, and quantization and weight distribution of the weak links have large subjective factors. Thus, both methods have difficulty giving accurate estimates of overall shelf life. In research, the complete machine acceleration factor evaluation method based on the competitive failure is found, namely, the acceleration factors of the complete machine product when the units obey specific distribution are given according to the addition criterion of the failure rate of the competitive failure product on the assumption that various failure modes of the complete machine product are mutually independent, and the complete machine acceleration factor evaluation method has advantages in the aspects of feasibility, accuracy and the like compared with the short plate principle and the average principle.
The invention provides a method for quantifying the dispersibility of an acceleration factor, and an accelerated evaluation method of the storage life of the whole machine by using a competitive failure model method, comprehensively considers the accelerated life test data of each part product, and combines the acceleration factor to provide a lower limit evaluation method of the reliable storage life of the whole machine product.
Disclosure of Invention
(1) The purpose of the invention is as follows: aiming at the situation that test data are difficult to obtain in an acceleration test of a complete machine product and corresponding test data of a component-level product are sufficient, a multi-component complete machine accelerated storage life confidence lower limit evaluation method is provided, namely, the multi-component complete machine storage life confidence lower limit evaluation method based on acceleration factor dispersion quantification is provided, and the method is an evaluation method of the complete machine product storage life and the lower limit thereof, wherein the evaluation method comprises component-level product life estimation, component-level acceleration factor quantification and component product life conversion into the complete machine product life. And processing test data through integral maximum likelihood estimation, estimating parameters of the component product, integrating component-level estimation results by utilizing quantized acceleration factor dispersibility and a competitive failure model, and finally evaluating the lower limit of the reliable service life of the whole product under a given storage condition.
(2) The technical scheme is as follows:
the invention needs to establish the following basic settings:
1, setting the failure of parts in the whole machine product to be independent from each other, wherein the parts are connected in series;
setting 2 that the storage life t of each part in the whole machine product obeys one of exponential distribution and Weibull distribution, wherein the cumulative failure functions of the distributions are respectively as follows:
distribution of indexes:
F(t)＝1-exp(-λt) (1)
(vii) weibull distribution:
Figure BDA0002910700390000021
wherein, λ is failure rate of exponential distribution, η and m are scale parameter and shape parameter of Weibull distribution respectively;
setting 3 a characteristic life-stress of the part to obey an Arrhenius model, wherein the expression is as follows:
ln(θ)＝a0+a1x (3)
wherein θ is the characteristic lifetime and x is a function of the acceleration stress;
the method provided by the invention mainly aims at accelerated storage life test data of each component product in the whole machine, integrates the accelerated life test data of the components according to a competitive failure model, estimates the distribution parameters of the total accumulated failure function of the whole machine product, quantifies the dispersibility of acceleration factors, and evaluates the reliability life confidence lower limit of the whole machine product;
based on the hypothesis, the invention provides a multi-component complete machine accelerated storage life confidence lower limit evaluation method, namely a multi-component complete machine storage life confidence lower limit evaluation method based on acceleration factor dispersibility quantification, which is realized by the following steps:
the method comprises the following steps: calculating parameter estimation values of all parts by using an overall maximum likelihood theory;
determining a service life distribution model obeyed by components in the whole machine, and solving parameter estimation values of an acceleration model and the service life distribution model of each component through integral maximum likelihood estimation;
the method comprises the following specific steps:
I. combining an Arrhenius model with a service life distribution model to form an accelerated service life test model; when the service life distribution model is in exponential distribution, the reciprocal 1/lambda of the failure rate is equal to the characteristic service life theta and is a function of the acceleration stress; when the service life distribution model is Weibull distribution, the scale parameter eta of the service life distribution model does not change along with the stress, and the shape parameter beta is equal to the characteristic service life theta and is a function of the acceleration stress;
II, assuming psi as a parameter vector to be estimated of the accelerated life test model; the number of stress level groups in the accelerated life test is m, and each group of tests comprises niFor each sample, the accelerated life test data is one of full data, constant number truncation and timing truncation, the log likelihood function ln (Ψ) can be expressed as:
complete data:
Figure BDA0002910700390000031
determining number of truncated data:
Figure BDA0002910700390000032
timing and truncating data:
Figure BDA0002910700390000033
wherein, ti,jThe failure time of the jth sample under the ith group of stress combinations is obtained; f (t) is a probability density function of product life, and F (t) is a cumulative failure function of product life; for constant truncated data, riThe failure number of the ith group of test products is shown;
Figure BDA0002910700390000047
is the riThe time to failure of an individual product; for timed tail-biting data, t0The tail-cutting time of the timing tail-cutting;
obtaining an estimate of the unknown model parameters by maximizing the log-likelihood function lnL (Ψ), i.e.
Figure BDA0002910700390000041
Step two: calculating the mean and variance of the acceleration factors of the components;
solving the mean variance and the confidence lower limit of the acceleration factor of the component according to the overall maximum likelihood estimation condition obtained in the step one;
the method comprises the following specific steps:
I. the life of the part obeys an exponential or Weibull distribution, stress level SiRelative to stress level SjThe acceleration factor of (a) is:
Figure BDA0002910700390000042
wherein, thetaiAnd thetajRespectively stress level SiAnd SjCharacteristic life of the following;
obeying the characteristic life and stress of the part to an Arrhenius model, and applying an acceleration factor AFijUsing the parameter a ═ in the Arrhenius model (a)0,a1) Expressed as:
Figure BDA0002910700390000043
wherein x isiAnd xjRespectively stress level SiAnd SjA function of lower acceleration stress;
according to the parameter a obtained in the step one1Mean value of (a)1Sum variance
Figure BDA0002910700390000044
The mean, variance and confidence of the acceleration factor can be obtainedThe limit is as follows:
parameter a1Obey a normal distribution:
Figure BDA0002910700390000045
Figure BDA0002910700390000046
AFL＝μAF-σAFΦ-1(1-p) (11)
wherein f (-) is a1P is confidence, AFLIs an acceleration factor lower confidence limit;
parameter a1Obeying a lognormal distribution:
Figure BDA0002910700390000051
Figure BDA0002910700390000052
AFL＝μAF-σAFΦ-1(1-p) (14)
wherein f (-) is a1P is confidence, AFLIs an acceleration factor lower confidence limit;
step three: calculating the characteristic life and the acceleration factor lower confidence limit of the whole machine product under high stress based on a competitive failure model;
based on the acceleration factor and the dispersion estimation result of the component-level product, calculating the characteristic life and the acceleration factor of the whole product under high stress and the lower confidence limit of the characteristic life and the acceleration factor under high stress by using a competitive failure model and considering the conditions of component life obeying exponential distribution and Weibull distribution;
part life follows an exponential distribution:
assuming that the storage life of each component unit of the whole machine follows exponential distribution, the reliability of the whole machine can be obtained through a competition failure model as follows:
Figure BDA0002910700390000053
wherein R (t) is a reliability function, λiFailure rate of the ith component;
suppose the characteristic lifetime of the ith component is θiThen, the characteristic life of the whole machine is as follows:
Figure BDA0002910700390000054
the whole machine is at normal stress level S0Relative to stress level SjAccelerated life factor AF ofjCan be expressed as:
Figure BDA0002910700390000055
wherein, AFijFor the i-th component under an accelerating stress SjAn acceleration factor of lower;
the whole machine is at normal stress level S0Relative to stress level SjAccelerated life factor AF ofjMean value of
Figure BDA0002910700390000056
Variance (variance)
Figure BDA0002910700390000057
And a lower confidence limit AFLCan be expressed as:
Figure BDA0002910700390000061
Figure BDA0002910700390000062
AFL＝μAF-σAFΦ-1(1-p) (20)
wherein the content of the first and second substances,
Figure BDA0002910700390000063
and
Figure BDA0002910700390000064
respectively the i-th component under an acceleration stress SjMean and variance of the lower acceleration factors, and p is confidence;
unit life obeying Weibull distribution
Assuming that the storage life of each part of the whole machine is subject to Weibull distribution, the reliability of the whole machine can be obtained through a competition failure model as follows:
Figure BDA0002910700390000065
assuming that the position parameters of the Weibull distributions of the components are the same, i.e. miAnd m, the reliability of the whole machine is as follows:
Figure BDA0002910700390000066
suppose the characteristic lifetime of the ith component is θiThe characteristic storage life of the whole machine is as follows:
Figure BDA0002910700390000067
the whole machine is at the normal stress level S0Relative to stress level SjAccelerated life factor AF ofjCan be expressed as:
Figure BDA0002910700390000068
wherein, AFijFor the i-th component under an accelerating stress SjAn acceleration factor of lower;
assuming that the acceleration factor of the component follows normal distribution, the whole machine is at a normal stress level S0Relative to stress level SjAccelerated life factor AF ofjMean value of
Figure BDA0002910700390000069
Variance (variance)
Figure BDA00029107003900000610
And a lower confidence limit AFLCan be expressed as:
Figure BDA0002910700390000071
Figure BDA0002910700390000072
AFL＝μAF-σAFΦ-1(1-p) (27)
wherein the content of the first and second substances,
Figure BDA0002910700390000073
and
Figure BDA0002910700390000074
respectively the i-th component under an acceleration stress SjMean and variance of the lower acceleration factors, and p is confidence;
step four: calculating the lower limit of the reliable service life of the whole product under a given storage condition;
obtaining an accumulated failure function F (t, theta) according to the characteristic life theta of the whole product calculated in the third step, giving a reliability R, and calculating a corresponding reliable life tR：
Figure BDA0002910700390000075
Wherein, F-1(. is an inverse of the total cumulative failure function;
acceleration incorporating step three calculationsFactor confidence lower bound AFLCalculating confidence lower limit t of reliable service lifeRL：
tRL＝tRAFL (29)
Wherein, the "arrhenius model" in the first and second steps refers to:
the relationship among the reaction rate, the temperature and the activation energy is obtained by analyzing a large amount of data by Arrhenius; the expression pattern of the arrhenius model is as follows:
Figure BDA0002910700390000076
wherein the content of the first and second substances,
Figure BDA0002910700390000077
indicating a characteristic life of the product, such as average life, median life, etc.; eaRepresents activation energy, also called activation energy; k is Boltzmann constant, k is 8.6117 × 10-5eV/K; t is the thermodynamic temperature, and the unit is generally K; a is a constant and A > 0;
logarithmic transformation is performed on two sides of the model to obtain:
Figure BDA0002910700390000078
wherein, a0＝lnA，
Figure BDA0002910700390000079
Is a parameter to be determined; thus, the logarithmic form of the characteristic lifetime has a linear relationship with the reciprocal function of the kelvin temperature.
Wherein, the "competition failure model" in step three refers to:
assuming that the overall machine has n failure modes, each failure mode being independent of the other, the storage life of the overall machine can be expressed as:
T＝min{T1,T2,…,Tn} (32)
wherein the content of the first and second substances,t is the overall storage life, Ti(i ═ 1, … n) for shelf life in failure mode i;
let Fi(T) is TiThe cumulative failure distribution function f (t) of the whole machine is:
Figure BDA0002910700390000081
and (3) setting the influence of the ith failure mode on the reliability of the whole machine:
Figure BDA0002910700390000082
wherein λ isi(x) Is a failure rate function;
the reliability function of the whole machine is:
Figure BDA0002910700390000083
(3) the advantages and the effects are as follows: the invention relates to a complete machine storage life accelerated evaluation method based on a competitive failure model method and considering the dispersibility of an acceleration factor, which has the advantages that:
the method utilizes acceleration test data of the component-level product with large data volume, adopts a competitive failure model, integrates test results of the component-level product, and further provides a storage life estimation value of the whole product which is difficult to directly carry out the acceleration test.
The invention adopts the whole maximum likelihood estimation method, the requirement on the initial value of the parameter is lower in the method, the method is quick and simple in iteration and strong in operability.
The invention considers the dispersivity of the acceleration factor, estimates the lower limit of the confidence of the whole machine product and can improve the service life prediction precision. The method is scientific, has good manufacturability and has wide popularization and application values.
Drawings
FIG. 1 is a flow chart of the method of the present invention
FIG. 2 evaluation results of storage reliability under normal stress of pilot operated safety valve
Detailed Description
The present invention will be described in further detail with reference to examples.
A pilot operated safety valve is a typical multi-part complete machine with multiple failure modes coexisting. The components of the device comprise a pilot valve spring, a main valve spring and an O-shaped ring, each part has a failure mode, the stress causing the product failure is temperature stress, and the natural storage temperature of the product is 293 k. The accelerated storage life test was performed on three components of the pilot operated safety valve, and the test data are shown in tables 1, 2, and 3:
TABLE 1 accelerated storage test data for pilot valve spring units
Experiment 1(353K) Experiment 2(393K) Experiment 3(423K) Experiment 4(473K)
1 66.51 6.89 6.33 0.87
2 74.95 10.79 9.95 3.58
3 170.73 17.89 12.19 5.09
4 197.21 27.86 13.84 9.67
5 225.05 33.82 37.21 17.18
TABLE 2 accelerated storage test data for main valve spring assembly
Experiment 1(353K) Experiment 2(393K) Experiment 3(423K) Experiment 4(473K)
1 12.90 2.81 1.12 0.15
2 28.79 7.91 1.44 0.23
3 51.43 11.81 1.81 0.39
4 66.03 14.54 2.81 1.01
5 83.36 18.92 7.54 1.49
TABLE 3 accelerated storage test data for O-ring parts
Figure BDA0002910700390000091
Figure BDA0002910700390000101
Note: the lifetime unit is hundred hours.
The storage life of the three components of the pilot operated safety valve product is assumed to follow the weibull distribution and the position parameters of the three are equal. According to the accelerated storage life evaluation method for the whole machine product, the accelerated life test data of the components are used for evaluating the total accumulated failure function parameters of the whole machine product, and the lower limit of the reliable storage life is evaluated.
The invention discloses a multi-component complete machine accelerated storage life confidence lower limit evaluation method, namely a multi-component complete machine storage life confidence lower limit evaluation method based on acceleration factor dispersion quantization, which is shown in figure 1 and is realized by the following steps:
the method comprises the following steps: calculating parameter estimation values of all parts by using an overall maximum likelihood theory;
firstly, since the service life t of the component product obeys Weibull distribution and the test is a complete data test, parameter estimation results of three components can be obtained through overall maximum likelihood estimation respectively, as shown in Table 4:
TABLE 4 analysis results of accelerated test data of pilot operated safety valve
Figure BDA0002910700390000102
Wherein, ai0，ai1Arrhenius model parameter, m, for the ith component1、m2、m3The respective position parameters of the weibull distribution to which the three components are subjected. Since the three component position parameters are similar, the average value thereof is taken as the assumed value that the position parameters are equal.
Step two: calculating the mean and variance of the acceleration factors of the components;
firstly, through the overall maximum likelihood estimation in the step one, the parameter a can be obtainedi1Mean and variance of (a), as shown in table 5. Due to parameter complianceNormal distribution, which can be calculated to obtain the normal stress level S of the component0Relative to stress level SjAccelerated life factor AF ofijThe results are shown in table 6:
TABLE 5 parameter ai1Mean and variance of
Figure BDA0002910700390000103
Figure BDA0002910700390000111
TABLE 6 acceleration factor AFijMean and variance of
Figure BDA0002910700390000112
Step three: calculating the characteristic life and the acceleration factor lower confidence limit of the whole machine product under high stress based on a competitive failure model; according to the calculation result of the step two, calculating the whole acceleration factor AF through a formulajThe results are shown in table 7:
TABLE 7 acceleration factor AFjMean and variance of
Figure BDA0002910700390000113
Then, when the given confidence p is 0.1, the lower confidence limit of the acceleration factor of the whole machine can be obtained as AFL＝1.39×103. And obtaining the characteristic service life theta of the whole machine at 473k acceleration stress which is 0.4989 according to calculation.
Step four: calculating the lower limit of the reliable service life of the whole product under a given storage condition;
according to the characteristic life theta of the whole machine product under high stress calculated in the third step, giving out the cumulative failure function of the whole machine product and recording the cumulative failure function as
Figure BDA0002910700390000114
The reliability degrees are respectively given as 0.95, 0.90, 0.85 and 0.80, when the confidence degree p is given as 0.1, the corresponding storage reliability life lower limit is respectively calculated, and the calculation results are shown in table 8. By using the characteristic life calculated in the third step, a reliability curve of the pilot safety valve product and the components thereof can be obtained, as shown in fig. 2.
TABLE 8 lower limit of reliable storage life of pilot operated safety valve
t0.95 t0.90 t0.85 t0.80
103.95 164.75 217.39 266.27
Note: the lifetime unit is hundred hours.
The lower limit of 95% reliable shelf life of the pilot safety valve product evaluated at a given confidence p of 0.1 is 103.95 hundred hours, which is about 433 days.
The results show that the method of the invention can accurately evaluate the storage life of the product and achieve the expected purpose.
In conclusion, the invention relates to a complete machine product accelerated storage life evaluation method considering the acceleration factor dispersity and the competitive failure model. Aiming at the accelerated storage life test of components in the whole machine, the method integrates the accelerated life test data of the components through a competitive failure model, estimates the distribution parameters of the total accumulated failure function of the whole machine product, considers the dispersibility of acceleration factors and evaluates the confidence lower limit of the reliable life of the whole machine product. The method comprises the following specific steps: firstly, estimating parameters of a component product by using a maximum likelihood estimation method, then respectively calculating the mean value and the variance of the acceleration factor of each component, further adopting a competition failure model to calculate the acceleration characteristic life and the acceleration factor confidence limit of the whole product, and finally calculating the reliable life and the storage life confidence limit of the product under a given storage condition. The method is suitable for the field of insufficient acceleration data of the whole machine product and sufficient component acceleration data, and has strong operability.

Claims (3)

1. A multi-component complete machine storage life confidence lower limit evaluation method needs to be set as follows:
setting 1: the failures of parts in the whole machine product are mutually independent, and the parts are connected in series;
setting 2: the storage life t of each part in the whole machine product is subjected to one of exponential distribution and Weibull distribution, and the cumulative failure function of each distribution is as follows:
distribution of indexes:
F(t)＝1-exp(-λt) (1)
(vii) weibull distribution:
Figure FDA0002910700380000011
wherein, λ is failure rate of exponential distribution, η and m are scale parameter and shape parameter of Weibull distribution respectively;
setting 3: the characteristic life-stress of the component obeys an Arrhenius model, and the expression is as follows:
ln(θ)＝a0+a1x (3)
wherein θ is the characteristic lifetime and x is a function of the acceleration stress;
the method is characterized in that: the method is realized by the following steps:
the method comprises the following steps: calculating parameter estimation values of all parts by using an overall maximum likelihood theory;
determining a service life distribution model obeyed by components in the whole machine, and solving parameter estimation values of an acceleration model and the service life distribution model of each component through integral maximum likelihood estimation;
the method comprises the following specific steps:
1.1, combining an Arrhenius model with a service life distribution model to form an accelerated service life test model; when the service life distribution model is in exponential distribution, the reciprocal 1/lambda of the failure rate is equal to the characteristic service life theta and is a function of the acceleration stress; when the service life distribution model is Weibull distribution, the scale parameter eta of the service life distribution model does not change along with the stress, and the shape parameter beta is equal to the characteristic service life theta and is a function of the acceleration stress;
1.2 setting psi as a parameter vector to be estimated of the accelerated life test model; the number of stress level groups in the accelerated life test is m, and each group of tests comprises niFor each sample, the accelerated life test data is one of complete data, constant number truncation and timing truncation, and the log likelihood function ln (Ψ) is expressed as:
complete data:
Figure FDA0002910700380000021
determining number of truncated data:
Figure FDA0002910700380000022
timing and truncating data:
Figure FDA0002910700380000023
wherein, ti,jThe failure time of the jth sample under the ith group of stress combinations is obtained; f (t) is the probability density of product lifeThe function, F (t), is the cumulative failure function of the product life; for constant truncated data, riThe failure number of the ith group of test products is shown; t is triIs the riThe time to failure of an individual product; for timed tail-biting data, t0The tail-cutting time of the timing tail-cutting;
estimate of unknown model parameters by maximizing the log-likelihood function lnL (Ψ),
namely, it is
Figure FDA0002910700380000024
Step two: calculating the mean and variance of the acceleration factors of the components;
solving the mean variance and the confidence lower limit of the acceleration factor of the component according to the overall maximum likelihood estimation condition obtained in the step one;
the method comprises the following specific steps:
2.1 the life of the part follows an exponential or Weibull distribution, stress level SiRelative to stress level SjThe acceleration factor of (a) is:
Figure FDA0002910700380000025
wherein, thetaiAnd thetajRespectively stress level SiAnd SjCharacteristic life of the following;
2.2 the acceleration factor AF is given by the characteristic life and stress of the part following the Arrhenius modelijUsing the parameter a ═ in the Arrhenius model (a)0,a1) Expressed as:
Figure FDA0002910700380000026
wherein x isiAnd xjRespectively stress level SiAnd SjA function of lower acceleration stress;
2.3 according to the parameter a solved in step one1Mean value of (a)1Hezhong FangDifference (D)
Figure FDA0002910700380000027
The mean, variance and confidence lower limit of the obtained acceleration factor are as follows:
parameter a1Obey a normal distribution:
Figure FDA0002910700380000031
Figure FDA0002910700380000032
AFL＝μAF-σAFΦ-1(1-p) (11)
wherein f (-) is a1P is confidence, AFLIs an acceleration factor lower confidence limit;
parameter a1Obeying a lognormal distribution:
Figure FDA0002910700380000033
Figure FDA0002910700380000034
AFL＝μAF-σAFΦ-1(1-p) (14)
wherein f (-) is a1P is confidence, AFLIs an acceleration factor lower confidence limit;
step three: calculating the characteristic life and the acceleration factor lower confidence limit of the whole machine product under high stress based on a competitive failure model;
based on the acceleration factor and the dispersion estimation result of the component-level product, calculating the characteristic life and the acceleration factor of the whole product under high stress and the lower confidence limit of the characteristic life and the acceleration factor under high stress by using a competitive failure model and considering the conditions of component life obeying exponential distribution and Weibull distribution;
3.1 part life obeys an exponential distribution:
if the storage life of each component unit of the complete machine follows exponential distribution, the reliability of the complete machine is obtained through a competition failure model as follows:
Figure FDA0002910700380000035
wherein R (t) is a reliability function, λiFailure rate of the ith component;
let the characteristic lifetime of the i-th component be θiThen, the characteristic life of the whole machine is as follows:
Figure FDA0002910700380000036
the whole machine is at normal stress level S0Relative to stress level SjAccelerated life factor AF ofjExpressed as:
Figure FDA0002910700380000041
wherein, AFijFor the i-th component under an accelerating stress SjAn acceleration factor of lower;
the whole machine is at normal stress level S0Relative to stress level SjAccelerated life factor AF ofjMean value of
Figure FDA0002910700380000042
Variance (variance)
Figure FDA0002910700380000043
And a lower confidence limit AFLExpressed as:
Figure FDA0002910700380000044
Figure FDA0002910700380000045
AFL＝μAF-σAFΦ-1(1-p) (20)
wherein the content of the first and second substances,
Figure FDA0002910700380000046
and
Figure FDA0002910700380000047
respectively the i-th component under an acceleration stress SjMean and variance of the lower acceleration factors, and p is confidence;
3.2 cell Life compliance with Weibull distribution
If the storage life of each part of the whole machine is subject to Weibull distribution, the reliability of the whole machine is obtained through a competition failure model as follows:
Figure FDA0002910700380000048
assuming that the position parameters of the Weibull distribution of the parts are the same, i.e. miAnd m, the reliability of the whole machine is as follows:
Figure FDA0002910700380000049
suppose the characteristic lifetime of the ith component is θiThe characteristic storage life of the whole machine is as follows:
Figure FDA00029107003800000410
the whole machine is at the normal stress level S0Relative to stress levelSjAccelerated life factor AF ofjExpressed as:
Figure FDA0002910700380000051
wherein, AFijFor the i-th component under an accelerating stress SjAn acceleration factor of lower;
if the acceleration factor of the part follows normal distribution, the whole machine is at the normal stress level S0Relative to stress level SjAccelerated life factor AF ofjMean value of
Figure FDA0002910700380000052
Variance (variance)
Figure FDA0002910700380000053
And a lower confidence limit AFLExpressed as:
Figure FDA0002910700380000054
Figure FDA0002910700380000055
AFL＝μAF-σAFΦ-1(1-p) (27)
wherein the content of the first and second substances,
Figure FDA0002910700380000056
and
Figure FDA0002910700380000057
respectively the i-th component under an acceleration stress SjMean and variance of the lower acceleration factors, and p is confidence;
step four: calculating the lower limit of the reliable service life of the whole product under a given storage condition;
according to the stepsCalculating the characteristic life theta of the whole product in the third step to obtain an accumulated failure function F (t, theta), giving a reliability R, and calculating a corresponding reliable life tR：
Figure FDA0002910700380000058
Wherein, F-1(. is an inverse of the total cumulative failure function;
acceleration factor confidence lower limit AF calculated in combination with step threeLCalculating confidence lower limit t of reliable service lifeRL：
tRL＝tRAFL (29)。
2. The method of claim 1 for evaluating the confidence lower limit of the storage life of a multi-component complete machine, wherein: the "arrhenius model" described in steps one and two refers to:
the relationship among the reaction rate, the temperature and the activation energy is obtained by analyzing a large amount of data by Arrhenius; the expression pattern of the arrhenius model is as follows:
Figure FDA0002910700380000059
wherein the content of the first and second substances,
Figure FDA0002910700380000061
indicating a characteristic life of the product; eaRepresents activation energy, also called activation energy; k is Boltzmann constant, k is 8.6117 × 10-5eV/K; t is thermodynamic temperature and is expressed in K; a is a constant and A > 0;
logarithmic transformation is performed on two sides of the model to obtain:
Figure FDA0002910700380000062
wherein, a0＝ln A，
Figure FDA0002910700380000063
Is a parameter to be determined; thus, the logarithmic form of the characteristic lifetime has a linear relationship with the reciprocal function of the kelvin temperature.
3. The method of claim 1 for evaluating the confidence lower limit of the storage life of a multi-component complete machine, wherein: the "competitive failure model" described in step three refers to:
if the whole machine has n failure modes, and each failure mode is independent, the storage life of the whole machine is expressed as follows:
T＝min{T1,T2,…,Tn} (32)
wherein T is the storage life of the whole machinei(i ═ 1, … n) for shelf life in failure mode i;
let Fi(T) is TiThe cumulative failure distribution function f (t) of the whole machine is:
Figure FDA0002910700380000064
and (3) setting the influence of the ith failure mode on the reliability of the whole machine:
Figure FDA0002910700380000065
wherein λ isi(x) Is a failure rate function;
the reliability function of the whole machine is:
Figure FDA0002910700380000066
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