A reliability assessment method and system based on uncertainty analysis of degradation models

Abstract

In order to address the deficiencies of the prior art, the present invention provides a reliability assessment method based on uncertainty analysis of a degradation model, comprising the following steps: S1. Determine the uncertain distribution of the failure threshold of a product performance parameter. S2. Use a time-varying uncertain distribution function to establish a degradation model for a target product. S3. Establish a reliability model for the product. S4. Establish a performance margin equation for the product, obtain the inverse uncertain distribution function of the performance margin, and perform reliability assessment. Compared with the existing degradation data analysis method based on probability theory, the present invention introduces the uncertainty of the failure threshold in the analysis and evaluation process, and can perform a more accurate assessment for the more critical early stages of a product's life, thereby obtaining a more accurate assessment result. In addition, the present invention also provides a reliability assessment system based on uncertainty analysis of a degradation model, wherein the analysis module uses a reliability assessment method based on uncertainty analysis of a degradation model for analysis.

Description

Technical Field

[0001] The invention belongs to the technical field of reliability engineering, and in particular relates to a reliability evaluation method and system based on uncertainty analysis of degradation models. Background Art

[0002] Traditional product reliability assessment methods are based on modeling and statistical analysis of product failure time data. However, for some high-reliability products, failure time data is difficult to obtain. With the advancement of product failure physical analysis technology and performance testing methods, reliability assessment methods based on performance degradation data analysis are increasingly being used. Based on the tested product performance degradation data, a degradation model of product performance over time can be established. Without the need for product failure, the time it takes for the product to degrade to the failure threshold can be calculated based on the degradation model, thereby achieving efficient reliability assessment.

[0003] So far, most degradation data analysis methods are based on probability theory, which makes it difficult to characterize the cognitive uncertainty in the degradation data analysis process, resulting in unreliable analysis results. Especially for many newly developed products, the failure threshold of the product is often uncertain. In addition, the measured product performance degradation data may not be accurate and inevitably contains uncertainty. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a reliability assessment method based on uncertainty analysis of a degradation model, comprising the following steps:

[0005] S1. Determine the failure threshold P of product performance parameters th The uncertain distribution of .

[0006] S2. Use time-varying uncertain distribution function to establish the degradation model of the target product.

[0007] S3. Establish a reliability model for the product.

[0008] S4. Establish the performance margin equation of the product, obtain the inverse uncertainty distribution function of the performance margin, and conduct reliability evaluation.

[0009] Further, step S1 includes:

[0010] S1-1 Set P th Normal uncertainty distribution Where e1 represents the mean, σ1 represents the standard deviation, and the distribution function Φ1(x) is

[0011]

[0012] S1-2 Based on P th Estimated range: P thValue is less than y1,y2,…,y k The reliability is α1, α2, …, α k , where y1<y2,…,<y k , α1<α2,…,<α k , establish the following least squares estimation model

[0013]

[0014] S1-3 minimizes Q and obtains the least squares estimate The uncertainty distribution of the failure threshold is determined as

[0015] Further, step S2 includes:

[0016] S2-1 Assume P i,j ,t i,j are the jth performance degradation measurement value and test time of the i-th product, i = 1, 2, ..., N1, j = 1, 2, ..., N2, assuming that each measurement time t i,j The corresponding P i,j All follow uncertain distribution It is estimated that i，j The corresponding parameter estimates

[0017] S2-2 Establish a degradation model P(t) based on time-varying uncertain distribution function, expressed as Where e(t) = e0θ1(t), σ(t) = σ0θ2(t), θ1(t), θ2(t) represent time functions, and the time-varying uncertainty distribution function of P(t) is

[0018]

[0019] S2-3: Analyze the estimated values ​​separately Follow i,j If the estimated value changes linearly with time, θ1(t) = t, θ2(t) = t. If it changes nonlinearly, let if Does not change with time, assume θ2(t)=1.

[0020] S2-4 Establish the following likelihood equation

[0021]

[0022] The symbol ∧ means taking the smaller value.

[0023] S2-5 maximizes L, and the optimal solution obtained is the maximum likelihood estimate of the unknown parameters Then the degradation model is determined as

[0024] Furthermore, at each measurement time t under the confidence level β i,j All corresponding P i,j If the following equations are satisfied, then the degradation model precise:

[0025]

[0026] In the formula,

[0027] Further, step S3 includes:

[0028] S3-1 Establish product reliability model:

[0029] R(t)=M (E(t)>0)

[0030] Where M(·) represents the uncertain measure function.

[0031] S3-2 According to the dual axiom of uncertainty theory, we get

[0032] R(t)=M (E(t)>0)=1-M (E(t)≤0)

[0033] S3-3 According to the definition of uncertainty distribution, we have

[0034] R(t)=1-M (E(t)≤0)=1-Ψ t (0).

[0035] Further, step S4 includes:

[0036] S4-1 Determine the performance margin equation E(t) based on whether the P value is expected to be large or small. Expected to be small means that the smaller the P value, the more favorable it is to product performance, and expected to be large means that the larger the P value, the more favorable it is to product performance.

[0037] S4-2 derives Ψ according to the following calculation rules t (x) corresponds to the inverse distribution function

[0038]

[0039] S4-3: According to the inverse distribution function, E(t) should obey the following uncertain distribution: get

[0040]

[0041] S4-4: t (0) Substitute into the reliability model established in step S3, and we get

[0042]

[0043] S4-5: Calculate the reliable life of the product as T(α)={t|R(t)=α}={t|Ψ t (0) = 1-α}.

[0044] Furthermore, the performance margin equation in step S4-1 is:

[0045]

[0046] Where E(t) is the performance margin of the product, P(t) is the performance degradation, and P th is the failure threshold.

[0047] In addition, the present invention also provides a reliability evaluation system based on uncertainty analysis of degradation models, including: an input module, an analysis module and an output module.

[0048] The input module inputs data to the analysis module. The analysis module uses any reliability assessment method based on uncertainty analysis of degradation models to perform reliability assessment analysis based on the data input by the input module. The output module outputs the analysis result of the analysis module as feedback.

[0049] The advantage of the present invention is that compared with the existing degradation data analysis method based on probability theory, the present invention introduces the uncertainty of the failure threshold in the analysis and evaluation process, and can perform more accurate evaluation for the more critical early stage of product life, thereby obtaining more accurate evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Shown are the estimated values ​​of ej at each measurement time of Example 2 of the present invention.

[0051] Figure 2 The figure shows the σ at each measurement time of Example 2 of the present invention. j Estimated value.

[0052] Figure 3 Shown is a schematic diagram of reliability curve comparison of Example 2 of the present invention. DETAILED DESCRIPTION

[0053] 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.

[0054] Example 1

[0055] A reliability assessment method based on uncertainty analysis of degradation models comprises the following steps:

[0056] S1. Determine the failure threshold P of product performance parameters th The uncertain distribution of .

[0057] S2. Use time-varying uncertain distribution function to establish the degradation model of the target product.

[0058] S3. Establish a reliability model for the product.

[0059] S4. Establish the performance margin equation of the product, obtain the inverse uncertainty distribution function of the performance margin, and conduct reliability evaluation.

[0060] Step S1 includes:

[0061] S1-1 Due to differences in materials and manufacturing processes, the failure threshold P of individual product performance parameters th Often there is uncertainty, let P th Subject to uncertain distribution Where e1 represents the mean, σ1 represents the standard deviation, and the distribution function Φ1(x) is

[0062]

[0063] S1-2 Although the failure threshold P of product performance parameters th is uncertain, but product designers can give an approximate range of failure thresholds. For example, product designers give P th Not less than the values ​​y1,y2,…,y k The reliability is α1, α2, …, α k , where y1<y2,…,<y k , α1<α2,…,<α k Based on the information, the following least squares estimation model is established

[0064]

[0065] S1-3 minimizes Q and obtains the least squares estimate The uncertainty distribution of the failure threshold is determined as

[0066] Step S2 includes:

[0067] S2-1 Assume P i,j ,t i,j are the jth performance degradation measurement value and test time of the i-th product, i = 1, 2, ..., N1, j = 1, 2, ..., N2, assuming that each measurement time t i,j The corresponding P i,j All obey uncertain normal distribution It is estimated that i,j The corresponding parameter estimates

[0068] S2-2 establishes a degradation model P(t) based on time-varying uncertain distribution function, expressed as Where e(t) = e0θ1(t), σ(t) = σ0θ2(t), θ1(t), θ2(t) represent time functions, and the time-varying uncertainty distribution function of P(t) is

[0069]

[0070] S2-3: Analyze the estimated values ​​separately Follow i,j If the estimated value changes linearly with time, θ1(t) = t, θ2(t) = t. If it changes nonlinearly, let if Does not change with time, assume θ2(t)=1.

[0071] S2-4 Establish the following likelihood equation

[0072]

[0073] The symbol ∧ means taking the smaller value.

[0074] S2-5 maximizes L, and the optimal solution obtained is the maximum likelihood estimate of the unknown parameters Then the degradation model is determined as

[0075] At each measurement time t under the confidence level β i,j All corresponding P i,j If the following equations are satisfied, then the degradation model precise:

[0076]

[0077] In the formula,

[0078] Step S3 includes:

[0079] S3-1 Establish product reliability model:

[0080] R(t)=M (E(t)>0)

[0081] Where M(·) represents the uncertain measure function.

[0082] S3-2 According to the dual axiom of uncertainty theory, we get

[0083] R(t)=M (E(t)>0)=1-M (E(t)≤0)

[0084] S3-3 According to the definition of uncertainty distribution, we have

[0085] R(t)=1-M (E(t)≤0)=1-Ψ t (0).

[0086] Step S4 includes:

[0087] S4-1 Determine the performance margin equation E(t) based on whether the P value is expected to be large or small. Expected to be small means that the smaller the P value, the more favorable it is to product performance, and expected to be large means that the larger the P value, the more favorable it is to product performance. In order to measure the reliability of the product, it is necessary to establish the product margin equation. A positive margin E(t)>0 means that the product is reliable.

[0088] S4-2 derives Ψ according to the following calculation rules t (x) corresponds to the inverse distribution function

[0089]

[0090] S4-3: According to the inverse distribution function, E(t) should obey the following uncertain normal distribution get

[0091]

[0092] S4-4: t (0) Substitute into the reliability model established in step S3, and we get

[0093]

[0094] S4-5: Calculate the reliable life of the product as T(α)={t|R(t)=α}={t|Ψ t (0) = 1-α}.

[0095] The performance margin equation in step S4-1 is:

[0096]

[0097] Where E(t) is the performance margin of the product, P(t) is the performance degradation, and P th is the failure threshold.

[0098] Example 2

[0099] Based on the reliability assessment method based on uncertainty analysis of the degradation model described in Example 1, taking the degradation experimental data of GaAs laser at 80°C as an example, the performance degradation parameter is the percentage increase of the working current relative to the original value. There are a total of 10 samples with observed degradation data at 16 moments.

[0100] Table 1 Performance parameter degradation value P of GaAs laser i，j

[0101]

[0102] Reliability evaluation of GaAs laser based on the data in Table 1:

[0103] First, based on the information obtained from product design engineers: th The reliability of a value less than 8 is 0.3, the reliability of a value less than 10 is 0.7, and the reliability of a value less than 12 is 0.95. First, assume that P th It obeys the uncertain linear distribution and estimates the parameter value using the least squares method, and we get The residual sum of squares is ∑1=3.7E-3. Then assume that P th It obeys the uncertain normal distribution and estimates the parameter value using the least squares method to obtain P th ~N(8.987, 2.509), the residual sum of squares is ∑2=3.6E-4. Since the ∑2 value is smaller, we believe that P th Better to obey the uncertain normal distribution P th ~N(8.987, 2.509).

[0104] Assume that each measurement time t i，j The corresponding P i，j All obey uncertain normal distribution Based on the performance degradation data at each measurement time in Table 1, the normal uncertainty distribution parameter value of the product at each measurement time is obtained. The changing trends over the measurement time are as follows: Figure 1 and Figure 2 shown.

[0105] visible Both tend to increase with time, and both parameters have an obvious linear relationship with time. Based on this, let the time function be θ1(t) = t, θ2(t) = t, and by maximizing the likelihood equation L, the estimated value is

[0106] After the reliability model is established in step S3, the parameter estimation value is substituted into the formula in step S4-4 to determine the product reliability prediction model as follows:

[0107]

[0108] Reliability curve Figure 3 The solid line in the figure shows that T(0.9)=1.766×10 3 h.

[0109] In contrast, if the uncertainty of the failure threshold is not considered, P th Collapses to a constant but It is still an uncertain variable, and its uncertain distribution function is recorded as Ω(x), and the corresponding inverse distribution function is

[0110]

[0111] By Ω -1 (α) can be derived

[0112]

[0113] Then the reliability prediction model is determined as

[0114]

[0115] In the formula, assume The value is the uncertain variable P th The expected value of Reliability curve Figure 3 The dashed line in the figure shows T(0.9) * =2.668×10 3 h. From R(t) and R * The reliability curve of (t) shows that the reliability assessment results are significantly different depending on whether the uncertainty of the failure threshold is considered. If the uncertainty of the failure threshold is not considered, the reliability assessment results obtained in the more critical early product life are significantly larger, and the obtained reliable life value is also significantly larger, for example, T(0.9) * It is more than 50% larger than T(0.9). Therefore, in order to obtain more accurate reliability evaluation results, the uncertainty of the failure threshold should be fully considered.

[0116] Example 3

[0117] A reliability evaluation system based on uncertainty analysis of degradation models includes an input module, an analysis module and an output module.

[0118] The input module inputs data to the analysis module. The analysis module performs reliability evaluation analysis based on the data input by the input module using the reliability evaluation method based on uncertainty analysis of degradation model in Example 1. The output module outputs the analysis result of the analysis module as feedback.

[0119] Taking the degradation experimental data of GaAs laser at 80°C in Example 2 as an example, the data in Table 1 is input into the analysis module through the input module. 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 3The graphical results are shown as solid lines.

[0120] 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 reliability assessment method based on uncertainty analysis of degradation models, characterized in that: The following steps are involved: S1. Determine the failure threshold P of product performance parameters th The uncertain distribution of includes: S1-1 Set P th Subject to uncertain distribution Where e1 represents the mean, σ1 represents the standard deviation, and the distribution function Φ1(x) is S1-2 Based on P th Estimated range: P th Value is less than y1,y2,…,y k The reliability is α1, α2, …, α k , where y1<y2,…,<y k , α1<α2,…,<α k , establish the following least squares estimation model S1-3 minimizes Q and obtains the least squares estimate The uncertainty distribution of the failure threshold is determined as S2. Use time-varying uncertain distribution function to establish the degradation model of the target product, including: S2-1 Assume P i,j ,t i,j are the jth performance degradation measurement value and measurement time of the i-th product, i = 1, 2, ..., N1, j = 1, 2, ..., N2, assuming that each measurement time t i,j The corresponding P i,j All follow uncertain distribution It is estimated that i,j The corresponding parameter estimates S2-2 Establish a degradation model P(t) based on time-varying uncertain distribution function, expressed as Where e(t) = e0θ1(t), σ(t) = σ0θ2(t), θ1(t), θ2(t) represent time functions, and the time-varying uncertainty distribution function of P(t) is S2-3: Analyze the estimated values ​​separately Follow i,j If the estimated value changes linearly with time, θ1(t) = t, θ2(t) = t; if it changes nonlinearly, if Does not change with time, assuming θ2(t) = 1; S2-4 Establish the following likelihood equation The symbol ^ means taking the smaller value. S2-5 maximizes L, and the optimal solution obtained is the maximum likelihood estimate of the unknown parameters Then the degradation model is determined as S3. Establish a reliability model for the product, including: S3-1 Establish product reliability model: R(t)=M(E(t)>0) Where M(·) represents the uncertain measurement function; S3-2 According to the dual axiom of uncertainty theory, we get R(t)=M(E(t)>0)=1-M(E(t)≤0) S3-3 According to the definition of uncertainty distribution, we have R(t)=1-M(E(t)≤0)=1-Ψ t (0); S4. Establish the product performance margin equation, obtain the inverse uncertainty distribution function of the performance margin, and conduct reliability assessment, including: S4-1 Determine the performance margin equation E(t) according to whether the P value is expected to be large or small; the expected small means that the smaller the P value, the more favorable it is to the product performance, and the expected large means that the larger the P value, the more favorable it is to the product performance; The performance margin equation is: Where E(t) is the performance margin of the product, P(t) is the performance degradation, and P th is the failure threshold; S4-2 derives Ψ according to the following calculation rules t (x) corresponds to the inverse distribution function S4-3: According to the inverse distribution function, E(t) should obey the following uncertain distribution: get S4-4: t (0) Substitute into the reliability model established in step S3, and we get S4-5: Calculate the reliable life of the product as T(α)={t|R(t)=α}={t|Ψ t (0) = 1-α}.

2. The reliability assessment method based on uncertainty analysis of degradation model according to claim 1 is characterized in that: At each measurement time t under the confidence level β i,j All corresponding P i,j If the following equations are satisfied, then the degradation model precise: In the formula, 3. A reliability assessment system based on uncertainty analysis of degradation models, characterized in that: include: Input module, analysis module and output module; The input module inputs data to the analysis module; The analysis module performs reliability assessment analysis based on the data input by the input module using any reliability assessment method based on uncertainty analysis of degradation models in claims 1-2; the output module outputs the analysis result of the analysis module as feedback.

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