CN111832151A - Exponential time function-based Wiener accelerated degradation model construction method and system - Google Patents
Exponential time function-based Wiener accelerated degradation model construction method and system Download PDFInfo
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Abstract
The invention provides a method for constructing a Wiener accelerated degradation model based on an exponential time function, which comprises the following steps of 1, establishing the Wiener degradation model based on the exponential time function. And 2, randomly selecting a group of performance degradation data of the target product, and substituting the performance degradation data into the degradation model to estimate parameter values. And 3, performing equivalent conversion on the performance degradation data by using the random acceleration coefficient, substituting the performance degradation data into the degradation model, and estimating the parameter value again. And 4, comparing the estimated values of the parameters obtained by the two estimations, and judging which parameters are related to the acceleration stress. And 5, establishing an acceleration model for the acceleration stress related parameters. 6, constructing a Wiener accelerated degradation model. And 7, fitting the product accelerated degradation data by applying a Wiener accelerated degradation model. And 8, evaluating the reliability of the product under the normal stress level based on a Wiener accelerated degradation model. The method can accurately establish a product accelerated degradation model and reduce the error of the reliability evaluation result.
Description
Technical Field
The invention belongs to the technical field of reliability engineering, and particularly relates to a method and a system for constructing a Wiener accelerated degradation model based on an exponential time function.
Background
With the progress of product failure physical analysis technology and performance test method, the application scenarios of the product reliability assessment method based on performance degradation data analysis are increasing. In order to obtain the product performance degradation data more efficiently, the accelerated degradation test technology is gradually and widely applied. Accelerated degradation testing is the acceleration of the product's degradation failure process without altering the product's failure mechanism by applying more severe stress levels.
At present, random processes such as Wiener, Gamma, Inverse Gaussian and the like are widely used for performance degradation models of products, however, when modeling accelerated degradation test data, an effective method is lacking to accurately judge which parameters of the random processes are related to accelerated stress (temperature, humidity, vibration, electrical stress and the like), and in the prior art, the parameters related to the accelerated stress are mainly specified according to subjective judgment or engineering experience, which easily causes that the accelerated degradation models of the products are established by mistake, and results of reliability evaluation errors are caused.
For non-linear degradation data, a power law time function is typically employed in the performance degradation model, but for some products, the degradation rate may gradually decrease to 0 over time, in which case an exponential time function is suitably employed. However, the existing accelerated degradation modeling method is full of subjective experience colors, and reliability evaluation errors are easily caused.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for constructing a Wiener accelerated degradation model based on an exponential time function, which comprises the following steps:
s1, establishing a Wiener degradation model based on an exponential time function: assuming that the performance degradation process x (t) of the product is compliant with the Wiener process, the Wiener degradation model is established as follows:
X(t)＝μΛ(t)+σB(ψ(t)),
where μ is a drift parameter, σ > 0 is a diffusion parameter, B (·) represents a standard brownian motion, and Λ (t), ψ (t) represent time functions, respectively.
S2, randomly selecting a group of performance degradation data of the target product, and substituting the performance degradation data into the degradation model to estimate parameter values.
And S3, performing equivalent conversion on the performance degradation data by using the random acceleration coefficient, substituting the performance degradation data into the degradation model, and estimating the parameter value again.
And S4, comparing the estimated values of the parameters obtained in the step S2 and the step S3 respectively, and judging which parameters are related to the acceleration stress.
And S5, establishing an acceleration model for the parameters related to the acceleration stress.
And S6, constructing a Wiener accelerated degradation model based on an exponential time function.
And S7, fitting the accelerated degradation data of the product by applying a Wiener accelerated degradation model based on an exponential time function.
And S8, evaluating the reliability of the product under the normal stress level based on the exponential time function Wiener accelerated degradation model.
Further, if x (t) is a linear degradation process, let Λ (t) ═ ψ (t) ═ t, and j ═ 1, 2. Let Λ (t) be an exponential function if x (t) is the non-linear degradation process.
If the degradation locus is convex, let the time function be Λ (t) ═ exp (- η t) -1, Ψ (t) ═ exp (- λ t) -1. If the degradation locus is concave, let the time function be Λ (t) ═ 1-exp (- η t), Ψ (t) ═ 1-exp (- λ t). Where η, λ represent the parameters of the time function, respectively.
Further, step S2 includes:
s2.1: in the performance degradation test data of the product, a certain sample is randomly selected at the measuring time tiPerformance degradation data x ofiAnd i is 1,2, …, and N is the total number of tests.
S2.2: x is to bei,tiSubstituting the exponential time function-based Wiener degradation model to establish the following likelihood equation
In the formula,. DELTA.xi＝xi-xi-1，ΔΛ(ti)＝exp(-ηti-1)-exp(-ηti)，ΔΨ(ti)＝exp(-λti-1)-exp(-λti)，x0＝0， t0＝0。
S2.3: maximization L (mu, sigma, eta, lambda) to obtain maximum likelihood estimation value of degradation model parameter
Further, step S3 includes:
s3.1: the value of the acceleration factor a is randomly chosen using:
A～UNI(5,20)
where UNI (-) is a uniform distribution function.
S3.2: x is converted by using acceleration coefficient Ai,tiEquivalent conversion of yi,τiThe equivalent conversion formula is yi＝xi，τi＝ti/A
S3.3: will yi,τiSubstituting the exponential time function-based Wiener degradation model to establish the following likelihood equation:
in the formula,. DELTA.yi＝yi-yi-1，ΔΛ(τi)＝exp(-η*τi-1)-exp(-η*τi)，ΔΨ(τi)＝exp(-λ*τi-1)-exp(-λ*τi),y0＝0，τ0＝0。
S3.4: maximization of L (. mu.)*,σ*,η*,λ*) Obtaining the parameter estimation value
Further, step S4 includes: respectively judge
Whether it is equal to 1 or not, if the ratio of two estimates of a certain parameter is equal to 1, it indicates that this parameter is independent of the acceleration stress. If not, this parameter is related to the acceleration stress.
Further, step S5 includes: stress level S of the k orderkThe degradation model parameter at (2) is expressed as μ (S)k),σ(Sk),η(Sk),λ(Sk) Assuming that μ, σ is independent of acceleration stress, μ (S)k)＝μ，σ(Sk) σ. Assuming that η is correlated with the acceleration stress, η (S) is obtained by using Arrhenius relation as an acceleration model when the acceleration stress is absolute temperaturek)＝exp(a-b/Sk) And a and b are acceleration model parameters. Then S is convertedkThe following time functions are expressed as:
Λ(t；Sk)＝1-exp(-η(Sk)t)＝1-exp(-exp(a-b/Sk)t)。
further, step S6 includes: mu (S)k),σ(Sk),η(Sk),λ(Sk) Substituting the model into a Wiener degradation model to construct a Wiener accelerated degradation model based on an exponential time function, wherein the model comprises the following steps:
X(t；Sk)＝μ(Sk)Λ(t；Sk)+σ(Sk)B(Ψ(t；Sk))。
further, step S7 includes:
let ti,j,kIs SkTime of ith measurement, x, of next jth producti,j,kΔ Λ (t) for the corresponding performance degradation measurementi,j,k；Sk)＝exp(-η(Sk)ti-1,j,k)-exp(-η(Sk)ti,j,k)，Δψ(ti,j,k；Sk)＝exp(-λ(Sk)ti-1,j,k)-exp(-λ(Sk)ti,j,k) Respectively, in time increments, Δ xi,j,k＝xi,j,k-xi-1,j,kRepresents the performance degradation increment, wherein i ═ 1,2,. cndot., Hk；j＝1,2,···,Nk； k＝1,2,···,M。HkDenotes SkEach lowerNumber of measurements of individual products. N is a radical ofkDenotes SkThe number of the products to be produced. M represents the number of acceleration stress levels.
Fitting x by applying exponential time function-based Wiener accelerated degradation modeli,j,k,ti,j,k,SkAccording to the independent increment characteristic of the Wiener accelerated degradation model, the following likelihood equation is established:
in the formula, Ω represents a vector of unknown parameters in the Wiener accelerated degradation model. L (omega) is maximized to obtain a parameter estimation value vector
Further, step S8 includes: let the normal stress level of the product be S0From
Determining the accelerated degradation model of Wiener at S0The parameter estimates are respectively
The product life xi is defined as the time when X (t) reaches a failure threshold omega for the first time, and for a Wiener accelerated degradation model, xi is a random variable obeying inverse Gaussian distribution, and the product in S is obtained according to the random variable0The following reliability model is:
where Φ (·) is the cumulative distribution function of a standard normal distribution.
In addition, the invention also provides a system for evaluating the reliability of the Wiener accelerated degradation model based on the exponential time function, which comprises the following steps: the device comprises an input module, an analysis module and an output module.
The input module inputs data to the analysis module. The analysis module is used for constructing an accelerated degradation model by adopting any one of the above-mentioned exponential time function-based Wiener accelerated degradation model construction methods based on the data input by the input module, and carrying out reliability evaluation analysis. And the output module outputs and feeds back the analysis result of the analysis module.
The invention has the advantages that: the method can accurately judge which parameters of the random process are related to the acceleration stress, so that an acceleration degradation model of a product can be more accurately established, and the error of a reliability evaluation result is greatly reduced.
Drawings
FIG. 1 shows the reliability curve obtained in example 2 of the present invention.
FIG. 2 is a graph showing the comparison of the reliability curve obtained in example 2 of the present invention and the reliability curve obtained in the prior art.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
A method for constructing a Wiener accelerated degradation model based on an exponential time function comprises the following steps:
s1, establishing a Wiener degradation model based on an exponential time function: assuming that the performance degradation process x (t) of the product is compliant with the Wiener process, the Wiener degradation model is established as follows:
X(t)＝μΛ(t)+σB(ψ(t)),
where μ is a drift parameter, σ > 0 is a diffusion parameter, B (·) represents a standard brownian motion, and Λ (t), ψ (t) represent time functions, respectively.
If x (t) is a linear degeneration process, let Λ (t) ═ ψ (t) ═ t, and j ═ 1, 2. Let Λ (t) be an exponential function if x (t) is the non-linear degradation process.
If the degradation locus is convex, let the time function be Λ (t) ═ exp (- η t) -1, Ψ (t) ═ exp (- λ t) -1. If the degradation locus is concave, let the time function be Λ (t) ═ 1-exp (- η t), Ψ (t) ═ 1-exp (- λ t). Where η, λ represent the parameters of the time function, respectively.
S2, randomly selecting a group of performance degradation data of the target product, and substituting the performance degradation data into the degradation model to estimate parameter values.
And S3, performing equivalent conversion on the performance degradation data by using the random acceleration coefficient, substituting the performance degradation data into the degradation model, and estimating the parameter value again.
And S4, comparing the estimated values of the parameters obtained in the step S2 and the step S3 respectively, and judging which parameters are related to the acceleration stress.
And S5, establishing an acceleration model for the parameters related to the acceleration stress.
And S6, constructing a Wiener accelerated degradation model based on an exponential time function.
And S7, fitting the accelerated degradation data of the product by applying a Wiener accelerated degradation model based on an exponential time function.
And S8, evaluating the reliability of the product under the normal stress level based on the exponential time function Wiener accelerated degradation model.
Step S2 includes:
s2.1: in the performance degradation test data of the product, a certain sample is randomly selected at the measuring time tiPerformance degradation data x ofiAnd i is 1,2, …, and N is the total number of tests.
S2.2: x is to bei,tiSubstituting the exponential time function-based Wiener degradation model to establish the following likelihood equation
In the formula,. DELTA.xi＝xi-xi-1，ΔΛ(ti)＝exp(-ηti-1)-exp(-ηti)，ΔΨ(ti)＝exp(-λti-1)-exp(-λti)，x0＝0， t0＝0。
S2.3: maximization L (mu, sigma, eta, lambda) to obtain maximum likelihood estimation value of degradation model parameter
Step S3 includes:
s3.1: the value of the acceleration factor a is randomly chosen using:
A～UNI(5,20)
where UNI (-) is a uniform distribution function.
S3.2: x is converted by using acceleration coefficient Ai,tiEquivalent conversion of yi,τiThe equivalent conversion formula is yi＝xi，τi＝ti/A
S3.3: will yi,τiSubstituting the exponential time function-based Wiener degradation model to establish the following likelihood equation:
in the formula,. DELTA.yi＝yi-yi-1，ΔΛ(τi)＝exp(-η*τi-1)-exp(-η*τi)，ΔΨ(τi)＝exp(-λ*τi-1)-exp(-λ*τi),y0＝0，τ0＝0。
S3.4: maximization of L (. mu.)*,σ*,η*,λ*) Obtaining the parameter estimation value
Step S4 includes: respectively judge
Whether it is equal to 1 or not, if the ratio of two estimates of a certain parameter is equal to 1, it indicates that this parameter is independent of the acceleration stress. If not, this parameter is related to the acceleration stress.
Step S5 includes: stress level S of the k orderkThe degradation model parameter at (2) is expressed as μ (S)k),σ(Sk),η(Sk),λ(Sk) Assuming that μ, σ is independent of acceleration stress, μ (S)k)＝μ，σ(Sk) σ. Assuming that η is correlated with the acceleration stress, η (S) is obtained by using Arrhenius relation as an acceleration model when the acceleration stress is absolute temperaturek)＝exp(a-b/Sk) And a and b are acceleration model parameters. Then S is convertedkThe following time functions are expressed as:
Λ(t；Sk)＝1-exp(-η(Sk)t)＝1-exp(-exp(a-b/Sk)t)。
step S6 includes: mu (S)k),σ(Sk),η(Sk),λ(Sk) Substituting the model into a Wiener degradation model to construct a Wiener accelerated degradation model based on an exponential time function, wherein the model comprises the following steps:
X(t；Sk)＝μ(Sk)Λ(t；Sk)+σ(Sk)B(Ψ(t；Sk))。
step S7 includes:
let ti,j,kIs SkTime of ith measurement, x, of next jth producti,j,kΔ Λ (t) for the corresponding performance degradation measurementi,j,k；Sk)＝exp(-η(Sk)ti-1,j,k)-exp(-η(Sk)ti,j,k)，Δψ(ti,j,k；Sk)＝exp(-λ(Sk)ti-1,j,k)-exp(-λ(Sk)ti,j,k) Respectively, in time increments, Δ xi,j,k＝xi,j,k-xi-1,j,kRepresents the performance degradation increment, wherein i ═ 1,2,. cndot., Hk；j＝1,2,···,Nk； k＝1,2,···,M。HkDenotes SkNumber of measurements per product. N is a radical ofkDenotes SkThe number of the products to be produced. M represents the number of acceleration stress levels.
Fitting x by applying exponential time function-based Wiener accelerated degradation modeli,j,k,ti,j,k,SkAccording to the independent increment characteristic of the Wiener accelerated degradation model, the following likelihood equation is established:
in the formula (I), the compound is shown in the specification,Ω represents the vector of unknown parameters in the Wiener accelerated degradation model. L (omega) is maximized to obtain a parameter estimation value vector
Step S8 includes: let the normal stress level of the product be S0From
Determining the accelerated degradation model of Wiener at S0The parameter estimates are respectively
The product life xi is defined as the time when X (t) reaches a failure threshold omega for the first time, and for a Wiener accelerated degradation model, xi is a random variable obeying inverse Gaussian distribution, and the product in S is obtained according to the random variable0The following reliability model is:
where Φ (·) is the cumulative distribution function of a standard normal distribution.
Example 2
Based on the method for constructing the exponential-time-function-based Wiener accelerated degradation model in embodiment 1, with the accelerated degradation test data of a certain type of electrical connector, a degradation parameter is a percentage change x of contact resistance, and when x reaches a threshold value ω being 5, a product is considered to be invalid; the accelerated stress is temperature, and the stress levels of 3 temperatures are 323.15K, 338.15K and 358.15K respectively.
TABLE 1 Electrical connector accelerated degradation test data
S1: and establishing a Wiener degradation model based on an exponential time function. From the data in table 1, it can be seen that the degradation locus of the product is concave, the time function is Λ (t) ═ ψ (t) ═ 1-exp (- η t), and the exponential time function-based Wiener degradation model is established as x (t) ═ μ (1-exp (- η t)) + σ B (1-exp (- η t)).
S2: selecting the first line performance degradation data under 323.15K, substituting the data into the degradation model to estimate the parameter value
S3: equivalent conversion is carried out on the performance degradation data by using a random acceleration coefficient A of 8.6,
s4: the two estimates of each parameter are compared,
are all 1, the parameter mu, sigma is independent of the acceleration stress, and
obviously, this parameter is not 1, indicating that it is related to the acceleration stress. In addition, it can be found
Very close to a-8.6.
S5: establishing an acceleration model for acceleration stress related parameters, e.g. η (S)k)＝exp(a-b/Sk) For the parameter not related to the acceleration stress, μ (S) is setk)＝μ，σ(Sk)＝σ。
S6: mu (S)k),σ(Sk),η(Sk) Substituting the model into a Wiener degradation model to construct a Wiener accelerated degradation model based on an exponential time function, wherein the model comprises the following steps:
X(t；Sk)＝μ(1-exp(-exp(a-b/Sk)t))+σB(1-exp(-exp(a-b/Sk)t))。
s7: fitting accelerated degradation data in the table 1 by using a Wiener accelerated degradation model based on an exponential time function, and establishing the following likelihood equation:
maximization of the above formula to obtain maximum likelihood estimation value
S8: evaluating the reliability of a product under a normal stress level by a Wiener accelerated degradation model based on an exponential time function, and firstly obtaining mu (S)0)＝3.691，σ(S0)＝0.589，η(S0) 0.241, then the product is obtained in S0The reliability model at 313.15K is:
a reliability curve is obtained as shown in fig. 1.
In existing Wiener accelerated degradation models, it is generally assumed that only the parameter μ is correlated with the acceleration stress. Establishing a Wiener accelerated degradation model based on an exponential time function according to the assumption, and estimating mu (S)0)＝2.489，σ(S0)＝0.582，η(S0) The obtained reliability curve is shown by a dashed line in fig. 2 at 0.376, and it can be seen that the obtained reliability curve is assumed to be significantly different from the reliability curve obtained by the present invention according to experience, and has a large error. The method can overcome the defects of the traditional accelerated degradation modeling method and improve the accuracy of the product reliability evaluation result.
Example 3
A system for evaluating reliability of a Wiener accelerated degradation model based on an exponential time function comprises: the device comprises an input module, an analysis module and an output module.
The input module inputs data to the analysis module. The analysis module is used for constructing an accelerated degradation model by adopting the method for constructing the Wiener accelerated degradation model based on the exponential time function in the embodiment 1 based on the data input by the input module, and carrying out reliability evaluation analysis. And the output module outputs and feeds back the analysis result of the analysis module.
Taking the accelerated degradation test data of the electric connector of a certain model in embodiment 2 as an example, the data in table 1 is input into the analysis module through the input module, and the input method may be that the system automatically reads the standardized data or the user manually inputs the standardized data. After the analysis module performs the analysis as described in embodiment 2, the obtained data is fed back to the user through the output module. Taking graphical feedback as an example, a graphical result as shown in solid lines in FIG. 1 may be produced.
It is to be noted and understood that various modifications and improvements can be made to the invention described in detail above without departing from the spirit and scope of the invention as claimed. Accordingly, the scope of the claimed subject matter is not limited by any of the specific exemplary teachings provided.
Claims (10)
1. A method for constructing a Wiener accelerated degradation model based on an exponential time function is characterized by comprising the following steps:
s1, establishing a Wiener degradation model based on an exponential time function: assuming that the performance degradation process x (t) of the product is compliant with the Wiener process, the Wiener degradation model is established as follows:
X(t)＝μΛ(t)+σB(ψ(t))
wherein mu is a drift parameter, sigma > 0 is a diffusion parameter, B (-) represents a standard Brownian motion, and Λ (t) and ψ (t) represent time functions respectively;
s2, randomly selecting a group of performance degradation data of the target product, substituting the performance degradation data into a degradation model, and estimating a parameter value;
s3, performing equivalent conversion on the performance degradation data by using a random acceleration coefficient, substituting the performance degradation data into a degradation model, and estimating a parameter value again;
s4, comparing the estimated values of the parameters obtained in the step S2 and the step S3 respectively, and judging which parameters are related to the acceleration stress;
s5, establishing an acceleration model for parameters related to acceleration stress;
s6, constructing a Wiener accelerated degradation model based on an exponential time function;
s7, fitting product accelerated degradation data by using a Wiener accelerated degradation model based on an exponential time function;
and S8, evaluating the reliability of the product under the normal stress level based on the exponential time function Wiener accelerated degradation model.
2. The method for constructing the exponential-time-function-based Wiener accelerated degradation model according to claim 1, wherein if x (t) is a linear degradation process, let Λ (t) ═ ψ (t) ═ t, j ═ 1, 2; if X (t) is a nonlinear degradation process, let Λ (t), ψ (t) be an exponential function;
if the degradation track is convex, setting the time function as Λ (t) ═ exp (- η t) -1, and psi (t) ═ exp (- λ t) -1; if the degradation locus is in a concave shape, setting the time function as Λ (t) ═ 1-exp (- η t), and Ψ (t) ═ 1-exp (- λ t); where η, λ represent the parameters of the time function, respectively.
3. The method for constructing the Wiener accelerated degradation model based on the exponential time function of claim 1, wherein the step S2 includes:
s2.1: in the performance degradation test data of the product, a certain sample is randomly selected at the measuring time tiPerformance degradation data x ofiI is 1,2, …, and N is the total number of tests;
s2.2: x is to bei,tiSubstituting the exponential time function-based Wiener degradation model to establish the following likelihood equation:
in the formula,. DELTA.xi＝xi-xi-1，ΔΛ(ti)＝exp(-ηti-1)-exp(-ηti)，ΔΨ(ti)＝exp(-λti-1)-exp(-λti)，x0＝0，t0＝0；
S2.3: maximization L (mu, sigma, eta, lambda) to obtain maximum likelihood estimation value of degradation model parameter
4. The method for constructing the Wiener accelerated degradation model based on the exponential time function of claim 3, wherein the step S3 comprises:
s3.1: the value of the acceleration factor a is randomly chosen using:
A～UNI(5,20)
wherein UNI (-) is a uniform distribution function;
s3.2: x is converted by using acceleration coefficient Ai,tiEquivalent conversion of yi,τiThe equivalent conversion formula is yi＝xi，τi＝ti/A
S3.3: will yi,τiSubstituting the exponential time function-based Wiener degradation model to establish the following likelihood equation:
in the formula,. DELTA.yi＝yi-yi-1，ΔΛ(τi)＝exp(-η*τi-1)-exp(-η*τi)，ΔΨ(τi)＝exp(-λ*τi-1)-exp(-λ*τi),y0＝0，τ0＝0；
S3.4: maximization of L (. mu.)*,σ*,η*,λ*) Obtaining the parameter estimation value
5. The method for constructing the Wiener accelerated degradation model based on the exponential time function as claimed in claim 4, wherein the step S4 includes: respectively judge
Whether the ratio of two estimated values of a certain parameter is equal to 1 or not, if the ratio of the two estimated values of the certain parameter is equal to 1, the parameter is irrelevant to the acceleration stress; if not close to 1, the parameters and acceleration stress are describedAnd (4) correlating.
6. The method for constructing the Wiener accelerated degradation model based on the exponential time function of claim 1, wherein the step S5 includes: stress level S of the k orderkThe degradation model parameter at (2) is expressed as μ (S)k),σ(Sk),η(Sk),λ(Sk) Assuming that μ, σ is independent of acceleration stress, μ (S)k)＝μ，σ(Sk) σ; assuming that η is correlated with the acceleration stress, η (S) is obtained by using Arrhenius relation as an acceleration model when the acceleration stress is absolute temperaturek)＝exp(a-b/Sk) Wherein a and b are acceleration model parameters; then S is convertedkThe following time functions are expressed as:
Λ(t；Sk)＝1-exp(-η(Sk)t)＝1-exp(-exp(a-b/Sk)t)。
7. the method for constructing the Wiener accelerated degradation model based on the exponential time function of claim 6, wherein the step S6 comprises: mu (S)k),σ(Sk),η(Sk),λ(Sk) Substituting the model into a Wiener degradation model to construct a Wiener accelerated degradation model based on an exponential time function, wherein the model comprises the following steps:
X(t；Sk)＝μ(Sk)Λ(t；Sk)+σ(Sk)B(Ψ(t；Sk))。
8. the method for constructing the Wiener accelerated degradation model based on the exponential time function of claim 1, wherein the step S7 includes:
let ti,j,kIs SkTime of ith measurement, x, of next jth producti,j,kΔ Λ (t) for the corresponding performance degradation measurementi,j,k；Sk)＝exp(-η(Sk)ti-1,j,k)-exp(-η(Sk)ti,j,k)，Δψ(ti,j,k；Sk)＝exp(-λ(Sk)ti-1,j,k)-exp(-λ(Sk)ti,j,k) Respectively, in time increments, Δ xi,j,k＝xi,j,k-xi-1,j,kRepresents the performance degradation increment, wherein i ═ 1,2,. cndot., Hk；j＝1,2,···,Nk；k＝1,2,···,M；HkDenotes SkMeasuring times of each product; n is a radical ofkDenotes SkThe number of the lower products; m represents the number of acceleration stress levels.
Fitting x by applying exponential time function-based Wiener accelerated degradation modeli,j,k,ti,j,k,SkAccording to the independent increment characteristic of the Wiener accelerated degradation model, the following likelihood equation is established:
in the formula, Ω represents a vector of unknown parameters in the Wiener accelerated degradation model. L (omega) is maximized to obtain a parameter estimation value vector
9. The method for constructing the Wiener accelerated degradation model based on the exponential time function of claim 8, wherein the step S8 includes: let the normal stress level of the product be S0From
Determining the accelerated degradation model of Wiener at S0The parameter estimates are respectively
The product life xi is defined as the time when X (t) reaches a failure threshold omega for the first time, and for a Wiener accelerated degradation model, xi is a random variable obeying inverse Gaussian distribution, and the product in S is obtained according to the random variable0The following reliability model is:
where Φ (·) is the cumulative distribution function of a standard normal distribution.
10. A system for evaluating reliability of a Wiener accelerated degradation model based on an exponential time function is characterized by comprising the following components: the device comprises an input module, an analysis module and an output module;
the input module inputs data to the analysis module; the analysis module is used for constructing an accelerated degradation model by adopting the method for constructing a Wiener accelerated degradation model based on an exponential time function in any one of claims 1 to 9 based on the data input by the input module, and carrying out reliability evaluation analysis; and the output module outputs and feeds back the analysis result of the analysis module.
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| CN112611952A (en) * | 2020-11-27 | 2021-04-06 | 成都海光微电子技术有限公司 | Acceleration coefficient determining method and device, electronic equipment and readable storage medium |
| CN112949209A (en) * | 2021-03-26 | 2021-06-11 | 北京航空航天大学 | Degradation rate-fluctuation combined updating method for evaluating storage life of elastic sealing rubber |
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| CN112611952A (en) * | 2020-11-27 | 2021-04-06 | 成都海光微电子技术有限公司 | Acceleration coefficient determining method and device, electronic equipment and readable storage medium |
| CN112949209A (en) * | 2021-03-26 | 2021-06-11 | 北京航空航天大学 | Degradation rate-fluctuation combined updating method for evaluating storage life of elastic sealing rubber |
| CN112949209B (en) * | 2021-03-26 | 2022-05-17 | 北京航空航天大学 | Degradation rate-fluctuation combined updating method for evaluating storage life of elastic sealing rubber |
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