Wiener accelerated degradation model construction method and system based on exponential time function

Abstract

The present invention provides a method for constructing a Wiener accelerated degradation model based on an exponential time function, comprising the following steps: 1. Establishing a Wiener degradation model based on an exponential time function. 2. Randomly selecting a group of performance degradation data of a target product, substituting them into the degradation model to estimate parameter values. 3. Using a random acceleration coefficient to perform equivalent conversion on the performance degradation data, substituting them into the degradation model to estimate parameter values ​​again. 4. Comparing the estimated values ​​of each parameter obtained by the two estimates, and determining which parameters are related to accelerated stress. 5. Establishing an acceleration model for parameters related to accelerated stress. 6. Constructing a Wiener accelerated degradation model. 7. Applying the Wiener accelerated degradation model to fit the accelerated degradation data of the product. 8. Evaluating the reliability of the product under normal stress levels based on the Wiener accelerated degradation model. The present invention can accurately establish a product accelerated degradation model and reduce the error of reliability evaluation results.

Description

Technical Field

[0001] The invention belongs to the technical field of reliability engineering, and in particular relates to a method and system for constructing a Wiener accelerated degradation model based on an exponential time function. Background Art

[0002] With the advancement of product failure physical analysis technology and performance testing methods, the application scenarios of product reliability assessment methods based on performance degradation data analysis are increasing. In order to obtain product performance degradation data more efficiently, accelerated degradation test technology has gradually been widely used. Accelerated degradation testing is to accelerate the degradation failure process of the product without changing the product failure mechanism by applying more severe stress levels.

[0003] So far, random processes such as Wiener, Gamma, and Inverse Gaussian are widely used in product performance degradation models. However, when modeling accelerated degradation test data, there is a lack of effective methods to accurately determine which parameters of the random process are related to accelerated stress (temperature, humidity, vibration, electrical stress, etc.). The existing technology mainly specifies parameters related to accelerated stress based on subjective judgment or engineering experience, which can easily lead to incorrect establishment of accelerated degradation models for products and cause errors in reliability assessment results.

[0004] For nonlinear degradation data, a power law time function is usually used in the performance degradation model. However, for some products, the degradation rate may gradually decrease to 0 over time. In this case, an exponential time function is suitable. However, the existing accelerated degradation modeling method is full of subjective experience and can easily cause reliability assessment errors. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a method for constructing a Wiener accelerated degradation model based on an exponential time function, comprising the following steps:

[0006] S1. Establish a Wiener degradation model based on exponential time function: Assuming that the performance degradation process X(t) of the product obeys the Wiener process, the Wiener degradation model is established as follows:

[0007] X(t)=μΛ(t)+σB(ψ(t)),

[0008] Among them, μ is the drift parameter, σ>0 is the diffusion parameter, B(·) represents the standard Brownian motion, Λ(t) and ψ(t) represent the time function respectively.

[0009] S2. Randomly select a set of performance degradation data of the target product and substitute it into the degradation model to estimate the parameter values.

[0010] S3. Use the random acceleration coefficient to perform equivalent conversion on the performance degradation data, substitute it into the degradation model and estimate the parameter value again.

[0011] S4. Compare the estimated values ​​of the parameters obtained in step S2 and step S3, respectively, and determine which parameters are related to the accelerated stress.

[0012] S5. Establish an accelerated model for parameters related to accelerated stress.

[0013] S6. Construct a Wiener accelerated degradation model based on exponential time function.

[0014] S7. Apply the Wiener accelerated degradation model based on exponential time function to fit the product accelerated degradation data.

[0015] S8. The Wiener accelerated degradation model based on the exponential time function is used to evaluate the reliability of the product under normal stress levels.

[0016] Furthermore, 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 exponential functions.

[0017] If the degradation trajectory is convex, let the time function be Λ(t) = exp(-ηt)-1, Ψ(t) = exp(-λt)-1. If the degradation trajectory is concave, let the time function be Λ(t) = 1-exp(-ηt), Ψ(t) = 1-exp(-λt). Where η and λ represent the parameters of the time function respectively.

[0018] Further, step S2 includes:

[0019] S2.1: In the product performance degradation test data, randomly select a sample at the measurement time t i Performance degradation data of x i , i=1,2,…,N, N is the total number of tests.

[0020] S2.2: x i ,t i Substituting into the Wiener degradation model based on the exponential time function, the following likelihood equation is established:

[0021]

[0022] In the formula, Δx i =x i -x i-1 , ΔΛ(t i )=exp(-ηt i-1 )-exp(-ηt i ), ΔΨ(ti )=exp(-λt i-1 )-exp(-λt i ), x0=0, t0=0.

[0023] S2.3: Maximize L(μ,σ,η,λ) to obtain the maximum likelihood estimate of the degradation model parameters

[0024] Further, step S3 includes:

[0025] S3.1: Randomly select the value of the acceleration factor A using the following formula:

[0026] A~UNI(5,20)

[0027] Among them, UNI(·) is the uniform distribution function.

[0028] S3.2: Use the acceleration factor A to convert x i ,t i Equivalent conversion to y i ,τ i , the equivalent conversion formula is y i =x i , τ i =t i / A

[0029] S3.3: Add y i ,τ i Substituting into the Wiener degradation model based on the exponential time function, the following likelihood equation is established:

[0030]

[0031] In the formula, Δy i =y i -y i-1 , ΔΛ(τ i )=exp(-η * τ i-1 )-exp(-η * τ i ), ΔΨ(τ i )=exp(-λ * τ i-1 )-exp(-λ * τ i ),y0=0,τ0=0.

[0032] S3.4: Maximize L(μ * ,σ * ,η * ,λ * ), and obtain parameter estimates

[0033] Further, step S4 includes: respectively judging Is it approximately equal to 1? If the ratio of the two estimated values ​​of a parameter is approximately equal to 1, it means that this parameter has nothing to do with accelerated stress. If it is not close to 1, it means that this parameter is related to accelerated stress.

[0034] Further, step S5 includes: setting the kth stress level S k The degradation model parameter under k ),σ(S k ),η(S k ),λ(S k ), assuming that μ, σ are independent of the accelerating stress, then μ(S k )=μ,σ(S k )=σ. Assuming that η is related to the accelerating stress, when the accelerating stress is absolute temperature, the Arrhenius relationship is used as the accelerating model, then η(S k )=exp(ab / S k ), where a and b are acceleration model parameters. Then S k The time function is expressed as:

[0035] Λ(t; S k )=1-exp(-η(S k )t)=1-exp(-exp(ab / S k )t).

[0036] Further, step S6 includes: k ),σ(S k ),η(S k ),λ(S k ) is substituted into the Wiener degradation model to construct a Wiener accelerated degradation model based on the exponential time function:

[0037] X(t;S k )=μ(S k )Λ(t;S k )+σ(S k )B(Ψ(t;S k )).

[0038] Further, step S7 includes:

[0039] Assume t i,j,k For S k The i-th measurement time of the j-th product, x i,j,k is the corresponding performance degradation measurement value, ΔΛ(t i,j,k ; S k )=exp(-η(S k )ti-1,j,k )-exp(-η(S k )t i,j,k ), Δψ(t i,j,k ; S k )=exp(-λ(S k )t i-1,j,k )-exp(-λ(S k )t i,j,k ) are time increments, Δx i,j,k =x i,j,k -x i-1,j,k represents the performance degradation increment, where i=1,2,···,H k ; j = 1, 2, ···, N k ; k = 1, 2, ···, M. H k Indicates S k The number of measurements for each product is as follows. N k Indicates S k The number of products under test. M represents the number of accelerated stress levels.

[0040] Apply the Wiener accelerated degradation model based on exponential time function to fit x i,j,k ,t i,j,k ,S k , according to the independent increment characteristics of the Wiener accelerated degradation model, the following likelihood equation is established:

[0041]

[0042] Where Ω represents the vector of unknown parameters in the Wiener accelerated degradation model. Maximizing L(Ω) yields the parameter estimation vector

[0043] Further, step S8 includes: assuming that the normal stress level of the product is S0, The parameter estimates of the Wiener accelerated degradation model under S0 are determined to be The product life ξ is defined as the time when X(t) first reaches the failure threshold ω. For the Wiener accelerated degradation model, ξ is a random variable that obeys the inverse Gaussian distribution. Based on this, the reliability model of the product under S0 is:

[0044]

[0045] Where Φ(·) is the cumulative distribution function of the standard normal distribution.

[0046] In addition, the present invention also provides a Wiener accelerated degradation model reliability evaluation system based on exponential time function, including: an input module, an analysis module and an output module.

[0047] The input module inputs data to the analysis module. Based on the data input by the input module, the analysis module uses any of the above-mentioned Wiener accelerated degradation model construction methods based on the exponential time function to construct an accelerated degradation model and perform reliability evaluation analysis. The output module outputs the analysis result of the analysis module as feedback.

[0048] The advantages of the present invention are that the present invention can accurately determine which parameters of the random process are related to the accelerated stress, thereby being able to more accurately establish an accelerated degradation model for the product, greatly reducing the error of the reliability evaluation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The reliability curve obtained in Example 2 of the present invention is shown.

[0050] Figure 2 The figure shows a comparison between the reliability curve obtained by the second embodiment of the present invention and the reliability curve obtained by the prior art. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0052] Example 1

[0053] A method for constructing a Wiener accelerated degradation model based on an exponential time function comprises the following steps:

[0054] S1. Establish a Wiener degradation model based on exponential time function: Assuming that the performance degradation process X(t) of the product obeys the Wiener process, the Wiener degradation model is established as follows:

[0055] X(t)=μΛ(t)+σB(ψ(t)),

[0056] Among them, μ is the drift parameter, σ>0 is the diffusion parameter, B(·) represents the standard Brownian motion, Λ(t) and ψ(t) represent the time function respectively.

[0057] 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 exponential functions.

[0058] If the degradation trajectory is convex, let the time function be Λ(t) = exp(-ηt)-1, Ψ(t) = exp(-λt)-1. If the degradation trajectory is concave, let the time function be Λ(t) = 1-exp(-ηt), Ψ(t) = 1-exp(-λt). Where η and λ represent the parameters of the time function respectively.

[0059] S2. Randomly select a set of performance degradation data of the target product and substitute it into the degradation model to estimate the parameter values.

[0060] S3. Use the random acceleration coefficient to perform equivalent conversion on the performance degradation data, substitute it into the degradation model and estimate the parameter value again.

[0061] S4. Compare the estimated values ​​of the parameters obtained in step S2 and step S3, respectively, and determine which parameters are related to the accelerated stress.

[0062] S5. Establish an accelerated model for parameters related to accelerated stress.

[0063] S6. Construct a Wiener accelerated degradation model based on exponential time function.

[0064] S7. Apply the Wiener accelerated degradation model based on exponential time function to fit the product accelerated degradation data.

[0065] S8. The Wiener accelerated degradation model based on the exponential time function is used to evaluate the reliability of the product under normal stress levels.

[0066] Step S2 includes:

[0067] S2.1: In the product performance degradation test data, randomly select a sample at the measurement time t i Performance degradation data of x i , i=1,2,…,N, N is the total number of tests.

[0068] S2.2: x i ,t i Substituting into the Wiener degradation model based on the exponential time function, the following likelihood equation is established:

[0069]

[0070] In the formula, Δx i =x i -x i-1 , ΔΛ(t i )=exp(-ηt i-1 )-exp(-ηt i ), ΔΨ(t i )=exp(-λt i-1 )-exp(-λti ), x0=0, t0=0.

[0071] S2.3: Maximize L(μ,σ,η,λ) to obtain the maximum likelihood estimate of the degradation model parameters

[0072] Step S3 includes:

[0073] S3.1: Randomly select the value of the acceleration factor A using the following formula:

[0074] A~UNI(5,20)

[0075] Among them, UNI(·) is the uniform distribution function.

[0076] S3.2: Use the acceleration factor A to convert x i ,t i Equivalent conversion to y i ,τ i , the equivalent conversion formula is y i =x i , τ i =t i / A

[0077] S3.3: Add y i ,τ i Substituting into the Wiener degradation model based on the exponential time function, the following likelihood equation is established:

[0078]

[0079] In the formula, Δy i =y i -y i-1 , ΔΛ(τ i )=exp(-η * τ i-1 )-exp(-η * τ i ), ΔΨ(τ i )=exp(-λ * τ i-1 )-exp(-λ * τ i ),y0=0,τ0=0.

[0080] S3.4: Maximize L(μ * ,σ * ,η * ,λ * ), and obtain parameter estimates

[0081] Step S4 includes: respectively judging Is it approximately equal to 1? If the ratio of the two estimated values ​​of a parameter is approximately equal to 1, it means that this parameter has nothing to do with accelerated stress. If it is not close to 1, it means that this parameter is related to accelerated stress.

[0082] Step S5 includes: setting the kth stress level S k The degradation model parameter under k ),σ(S k ),η(S k ),λ(S k ), assuming that μ, σ are independent of the accelerating stress, then μ(S k )=μ,σ(S k )=σ. Assuming that η is related to the accelerating stress, when the accelerating stress is absolute temperature, the Arrhenius relationship is used as the accelerating model, then η(S k )=exp(ab / S k ), where a and b are acceleration model parameters. Then S k The time function is expressed as:

[0083] Λ(t; S k )=1-exp(-η(S k )t)=1-exp(-exp(ab / S k )t).

[0084] Step S6 includes: k ),σ(S k ),η(S k ),λ(S k ) is substituted into the Wiener degradation model to construct a Wiener accelerated degradation model based on the exponential time function:

[0085] X(t;S k )=μ(S k )Λ(t;S k )+σ(S k )B(Ψ(t;S k )).

[0086] Step S7 includes:

[0087] Assume t i,j,k For S k The i-th measurement time of the j-th product, x i,j,k is the corresponding performance degradation measurement value, ΔΛ(t i,j,k ; S k )=exp(-η(S k )t i-1,j,k )-exp(-η(S k )t i,j,k ), Δψ(ti,j,k ; S k )=exp(-λ(S k )t i-1,j,k )-exp(-λ(S k )t i,j,k ) are time increments, Δx i,j,k =x i,j,k -x i-1,j,k represents the performance degradation increment, where i=1,2,···,H k ; j = 1, 2, ···, N k ; k = 1, 2, ···, M. H k Indicates S k The number of measurements for each product is as follows. N k Indicates S k The number of products under test. M represents the number of accelerated stress levels.

[0088] Apply the Wiener accelerated degradation model based on exponential time function to fit x i,j,k ,t i,j,k ,S k , according to the independent increment characteristics of the Wiener accelerated degradation model, the following likelihood equation is established:

[0089]

[0090] Where Ω represents the vector of unknown parameters in the Wiener accelerated degradation model. Maximizing L(Ω) yields the parameter estimation vector

[0091] Step S8 includes: assuming that the normal stress level of the product is S0, The parameter estimates of the Wiener accelerated degradation model under S0 are determined to be The product life ξ is defined as the time when X(t) first reaches the failure threshold ω. For the Wiener accelerated degradation model, ξ is a random variable that obeys the inverse Gaussian distribution. Based on this, the reliability model of the product under S0 is:

[0092]

[0093] Where Φ(·) is the cumulative distribution function of the standard normal distribution.

[0094] Example 2

[0095] Based on the Wiener accelerated degradation model construction method based on the exponential time function described in Example 1, using the accelerated degradation test data of a certain model of electrical connector, the degradation parameter is the percentage change x of the contact resistance, and the product is considered to have failed when x reaches the threshold value ω=5; the accelerated stress is temperature, and the three temperature stress levels are 323.15K, 338.15K, and 358.15K, respectively.

[0096] Table 1 Accelerated degradation test data of electrical connectors

[0097]

[0098] S1: Establish a Wiener degradation model based on exponential time function. From the data in Table 1, it can be seen that the degradation trajectory of the product is concave. Assuming the time function is Λ(t) = ψ(t) = 1-exp(-ηt), the Wiener degradation model based on the exponential time function is established as X(t) = μ(1-exp(-ηt)) + σB(1-exp(-ηt)).

[0099] S2: Select the first row of performance degradation data at 323.15K and substitute it into the degradation model to estimate the parameter value

[0100] S3: Use the random acceleration factor A=8.6 to perform equivalent conversion on the performance degradation data.

[0101] S4: Compare the two estimated values ​​of each parameter, are all 1, indicating that the parameters μ and σ have nothing to do with the accelerated stress, while It is obviously not 1, indicating that this parameter is related to the accelerated stress. In addition, it can be found that Very close to A=8.6.

[0102] S5: Establish an acceleration model for parameters related to acceleration stress, such as η(S k )=exp(ab / S k ), for parameters that are not related to the acceleration stress, set them to μ(S k )=μ,σ(S k )=σ.

[0103] S6: μ(S k ),σ(S k ),η(S k ) is substituted into the Wiener degradation model to construct a Wiener accelerated degradation model based on the exponential time function:

[0104] X(t;S k )=μ(1-exp(-exp(ab / S k)t))+σB(1-exp(-exp(ab / S k )t)).

[0105] S7: The Wiener accelerated degradation model based on the exponential time function is used to fit the accelerated degradation data in Table 1, and the following likelihood equation is established:

[0106]

[0107] Maximize the above formula to get the maximum likelihood estimate

[0108] S8: Based on the Wiener accelerated degradation model of the exponential time function, the reliability of the product under normal stress level is evaluated. First, μ(S0)=3.691, σ(S0)=0.589, η(S0)=0.241 are obtained, and then the reliability model of the product under S0=313.15K is obtained as follows:

[0109]

[0110] The reliability curve is obtained as Figure 1 shown.

[0111] In the existing Wiener accelerated degradation model, it is usually assumed that only the parameter μ is related to the accelerated stress. Based on this assumption, a Wiener accelerated degradation model based on the exponential time function is established, and μ(S0)=2.489, σ(S0)=0.582, η(S0)=0.376 are estimated. The obtained reliability curve is similar to Figure 2 As shown by the dotted line in , it can be seen that the reliability curve obtained based on the empirical assumption is significantly different from the reliability curve obtained by the present invention, and has a large error. The method of the present invention can overcome the shortcomings of the traditional accelerated degradation modeling method and improve the accuracy of the product reliability evaluation results.

[0112] Example 3

[0113] A reliability evaluation system for a Wiener accelerated degradation model based on an exponential time function comprises an input module, an analysis module and an output module.

[0114] The input module inputs data to the analysis module. Based on the data input by the input module, the analysis module constructs an accelerated degradation model using the Wiener accelerated degradation model construction method based on the exponential time function in Example 1, and performs reliability evaluation analysis. The output module outputs the analysis result of the analysis module for feedback.

[0115] Taking the accelerated degradation test data of a certain type of electrical connector in Example 2 as an example, the data in Table 1 is input into the analysis module through the input module. The input method can be that the system automatically reads the standardized data, or the user manually inputs it. After the analysis module performs the analysis as described in Example 2, the obtained data is fed back to the user through the output module. Taking graphical feedback as an example, the following can be generated: Figure 1 The graphical results are shown as solid lines.

[0116] It should 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 claims of the present invention. Therefore, the scope of the claimed technical solution is not limited by any specific exemplary teaching given.

Claims

1. A method for constructing a Wiener accelerated degradation model based on an exponential time function, characterized in that: The following steps are involved: S1. Establish a Wiener degradation model based on exponential time function: Assuming that the performance degradation process X(t) of the product obeys the Wiener process, the Wiener degradation model is established as follows: X(t)=μΛ(t)+σB(ψ(t)) Where μ is the drift parameter, σ>0 is the diffusion parameter, B(·) represents the standard Brownian motion, Λ(t) and ψ(t) represent the time function respectively; 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 exponential functions; If the degradation trajectory is convex, let the time function be Λ(t) = exp(-ηt)-1, Ψ(t) = exp(-λt)-1; if the degradation trajectory is concave, let the time function be Λ(t) = 1-exp(-ηt), Ψ(t) = 1-exp(-λt); where η and λ represent the parameters of the time function respectively; S2. Randomly select a set of performance degradation data of the target product and substitute it into the degradation model to estimate the parameter values; S3. Use the random acceleration coefficient to perform equivalent conversion on the performance degradation data, substitute it into the degradation model and estimate the parameter value again; S4. Compare the estimated values ​​of the parameters obtained in step S2 and step S3, respectively, to determine which parameters are related to the accelerated stress; S5. Establish an acceleration model for parameters related to accelerated stress; S6. Construct a Wiener accelerated degradation model based on exponential time function; S7. Apply the Wiener accelerated degradation model based on exponential time function to fit the product accelerated degradation data; S8. The Wiener accelerated degradation model based on the exponential time function is used to evaluate the reliability of the product under normal stress levels.

2. The method for constructing a Wiener accelerated degradation model based on an exponential time function according to claim 1, characterized in that: Step S2 includes: S2.1: In the product performance degradation test data, randomly select a sample at the measurement time t i Performance degradation data of x i , i=1,2,…,N, N is the total number of tests; S2.2: x i ,t i Substituting into the Wiener degradation model based on the exponential time function, the following likelihood equation is established: where Δx i = x i - x i-1 , ΔΛ(t i ) = exp(-ηt i-1 ) - exp(-ηt i ), ΔΨ(t i ) = exp(-λt i-1 ) - exp(-λt i ), x0 = 0, t0 = 0; S2.3: Maximize L(μ,σ,η,λ) to obtain the maximum likelihood estimate of the degradation model parameters 3. The method for constructing a Wiener accelerated degradation model based on an exponential time function according to claim 2, characterized in that: Step S3 includes: S3.1: Randomly select the value of the acceleration factor A using the following formula: A~UNI(5,20) Among them, UNI(·) is the uniform distribution function; S3.2: Use the acceleration factor A to convert x i ,t i Equivalent conversion to y i ,τ i , the equivalent conversion formula is y i =x i , τ i =t i / A S3.3: Add y i ,τ i Substituting into the Wiener degradation model based on the exponential time function, the following likelihood equation is established: where Δy i = y i - y i-1 , ΔΛ(τ i ) = exp(-η * τ i-1 ) - exp(-η * τ i ), ΔΨ(τ i ) = exp(-λ * τ i-1 ) - exp(-λ * τ i ), y0 = 0, τ0 = 0; S3.4: Maximize L(μ * ,σ * ,η * ,λ * ), and obtain parameter estimates 4. The method for constructing a Wiener accelerated degradation model based on an exponential time function according to claim 3, characterized in that: Step S4 includes: respectively judging Is it approximately equal to 1? If the ratio of the two estimated values ​​of a parameter is approximately equal to 1, it means that this parameter is not related to the accelerated stress; if it is not close to 1, it means that this parameter is related to the accelerated stress.

5. The method for constructing a Wiener accelerated degradation model based on an exponential time function according to claim 1, characterized in that: Step S5 includes: setting the kth stress level S k The degradation model parameter under k ),σ(S k ),η(S k ),λ(S k ), assuming that μ, σ are independent of the accelerating stress, then μ(S k )=μ,σ(S k )=σ; Assuming that η is related to the accelerating stress, when the accelerating stress is absolute temperature, the Arrhenius relationship is used as the accelerating model, then η(S k )=exp(ab / S k ), where a and b are acceleration model parameters; then S k The time function is expressed as: Λ(t;S k )=1-exp(-η(S k )t)=1-exp(-exp(a-b / S k )t)。 6. The method for constructing a Wiener accelerated degradation model based on an exponential time function according to claim 5, characterized in that: Step S6 includes: k ),σ(S k ),η(S k ),λ(S k ) is substituted into the Wiener degradation model to construct a Wiener accelerated degradation model based on the exponential time function: X(t;S k )=μ(S k )Λ(t;S k )+σ(S k )B(Ψ(t;S k ))。 7. The method for constructing a Wiener accelerated degradation model based on an exponential time function according to claim 1, characterized in that: Step S7 includes: Assume t i,j,k For S k The i-th measurement time of the j-th product, x i,j,k is the corresponding performance degradation measurement value, ΔΛ(t i,j,k ; S k )=exp(-η(S k )t i-1,j,k )-exp(-η(S k )t i,j,k ), Δψ(t i,j,k ; S k )=exp(-λ(S k )t i-1,j,k )-exp(-λ(S k )t i,j,k ) are time increments, Δx i,j,k =x i,j,k -x i-1,j,k represents the performance degradation increment, where i=1,2,…,H k ; j = 1, 2, ..., N k ; k = 1, 2, ..., M; H k Indicates S k The number of measurements for each product; N k Indicates S k The number of products under this condition; M represents the number of accelerated stress levels; Apply the Wiener accelerated degradation model based on exponential time function to fit x i,j,k ,t i,j,k ,S k , according to the independent increment characteristics of the Wiener accelerated degradation model, the following likelihood equation is established: In the formula, Ω represents the vector of unknown parameters in the Wiener accelerated degradation model. Maximizing L(Ω) obtains the parameter estimation vector 8. The method for constructing a Wiener accelerated degradation model based on an exponential time function according to claim 7, characterized in that: Step S8 includes: assuming that the normal stress level of the product is S0, The parameter estimates of the Wiener accelerated degradation model under S0 are determined to be The product life ξ is defined as the time when X(t) first reaches the failure threshold ω. For the Wiener accelerated degradation model, ξ is a random variable that obeys the inverse Gaussian distribution. Based on this, the reliability model of the product under S0 is: Where Φ(·) is the cumulative distribution function of the standard normal distribution.

9. A Wiener accelerated degradation model reliability assessment system based on exponential time function, characterized in that: include: Input module, analysis module and output module; The input module inputs data to the analysis module; The analysis module constructs an accelerated degradation model based on the data input by the input module using any Wiener accelerated degradation model construction method based on exponential time function according to claims 1-8, and performs reliability evaluation analysis; the output module outputs the analysis results of the analysis module as feedback.

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