A method for reliability evaluation of multi-mode dependent competing failure systems

Abstract

The application provides a kind of multimode dependent competing failure system reliability evaluation method, it is related to product performance degradation and reliability analysis technical field, including: constructing competing failure reliability model;Based on competing failure reliability model, respectively on the degradation failure and sudden failure of product modeling is carried out, and the degradation failure reliability model, sudden failure reliability model is obtained;Based on the parameter of degradation failure reliability model and the parameter of sudden failure reliability model are obtained based on accelerated degradation test data;The parameter of degradation failure reliability model and the parameter of sudden failure reliability model are substituted into competing failure reliability model, and the reliability function and reliability index of product under different stress conditions are obtained.The application can better describe the competing failure relationship of product on the basis of comprehensive utilization of test data, and improve the product reliability evaluation precision.

Description

Technical Field

[0001] This invention relates to the field of product performance degradation and reliability analysis technology, and in particular to a reliability assessment method for multi-mode dependent competing failure systems. Background Technology

[0002] With advancements in material properties and manufacturing processes, product reliability has significantly improved. However, the failure of long-life, high-reliability products is a complex process, influenced by both intrinsic failure mechanisms and various complex external factors. It primarily manifests as a competition between degradation failure and sudden failure, meaning failure is caused by the first failure mode to appear. Furthermore, degradation and sudden failure modes are often correlated, not entirely independent. Moreover, most competing failure modeling studies tend to presuppose the temporal distribution of sudden failures, which may limit the model's applicability and make it difficult to accurately reflect the diverse sudden failure behaviors in complex systems.

[0003] Therefore, a reliability assessment method for multi-mode dependent competing failure systems is proposed. Summary of the Invention

[0004] This specification provides a reliability assessment method for multimode dependent competing failure systems. Based on the comprehensive use of experimental data, it can better describe the competing failure relationships of products and improve the accuracy of product reliability assessment.

[0005] This specification provides a reliability assessment method for multimode dependent competing failure systems, including:

[0006] Construct a competitive failure reliability model;

[0007] Based on the aforementioned competitive failure reliability model, degradation failure and sudden failure of the product are modeled respectively to obtain degradation failure reliability model and sudden failure reliability model;

[0008] Based on accelerated degradation test data, the unknown parameters of the degradation failure reliability model and the unknown parameters of the sudden failure reliability model are solved respectively to obtain the parameters of the degradation failure reliability model and the parameters of the sudden failure reliability model.

[0009] By substituting the parameters of the degradation failure reliability model and the sudden failure reliability model into the competing failure reliability model, the reliability function and reliability index of the product under different stress conditions are obtained.

[0010] Optionally, constructing the competing failure reliability model includes:

[0011] The product's failure time T can be expressed as:

[0012] T = min{Td ,T r}

[0013] Among them, T d T represents the product degradation and failure time. r For the product's sudden failure mode failure time;

[0014] The reliability model R(t) for competing failure modes of degradation failure and sudden failure is:

[0015] R(t)=P(T>t)=P(T r >t,T d >t)=P(T r >t|T d >t)·P(T d >t)=R r (t)·R d (t)

[0016] Among them, R d (t) represents the reliability of the degradation failure mode; R r (t) represents the conditional reliability of the sudden failure mode under the condition that no degradation failure occurs.

[0017] Optionally, the step of modeling the degradation failure of the product based on the competing failure reliability model to obtain the degradation failure reliability model includes:

[0018] Let X(t) represent the product degradation process, then the degradation failure model X(t) can be established as follows:

[0019] X(t) = X(0) + μt + σB(t)

[0020] Where X(0) = 0 is the initial value of degradation, and for ease of analysis, let X(0) = 0; μ is the drift coefficient, which characterizes the rate of product performance degradation; σ is the diffusion coefficient; B(·) is the standard Brownian motion, which characterizes the dynamic characteristics of degradation;

[0021] The probability density function f(X) of the degradation can be expressed as:

[0022]

[0023] Let w be the product's failure threshold. Then, the time when the product degradation process first reaches the failure threshold is the product degradation failure time T. d :

[0024] T d =inf{t:X(t)≥w|X(0)<w}

[0025] When μ is a random variable and follows the order of random variables, When, the probability density function of the product degradation failure time distribution is... and reliability function R d (t) is:

[0026]

[0027] Optionally, the step of modeling the sudden failure of the product based on the competing failure reliability model to obtain the sudden failure reliability model includes:

[0028] At any time t, X can be considered a random variable. To ensure that the product does not fail due to degradation at time t, the burst failure rate λ(t,X(t)) can be expressed as:

[0029]

[0030] Where λ(t,X(t)) is the failure rate of the product in the event of sudden failure without degradation failure, and the upper limit of integration w is used to ensure that the product has not experienced degradation failure by time t;

[0031] Conditional reliability function R for sudden failure time under conditions of no degradation failure r (t) and conditional probability density function f r (t) is:

[0032]

[0033] f r (t)=λ(t,X(t))·R r (t)

[0034] Optionally, the step of solving for the unknown parameters of the degradation failure reliability model and the sudden failure reliability model based on accelerated degradation test data to obtain the parameters of the degradation failure reliability model and the sudden failure reliability model includes:

[0035] The accelerated degradation test data includes degradation failure occurrence test data, sudden failure occurrence test data, and no failure occurrence test data.

[0036] Based on the test data of the degradation failure occurrence, the unknown parameters of the degradation failure reliability model are solved to obtain the parameters of the degradation failure reliability model;

[0037] Based on the test data of sudden failure occurrence and the test data of no failure occurrence, the unknown parameters of the sudden failure reliability model are solved to obtain the parameters of the sudden failure reliability model.

[0038] Optionally, the step of solving for the unknown parameters of the degradation failure reliability model based on the degradation failure occurrence test data to obtain the parameters of the degradation failure reliability model includes:

[0039] There are m products participating in an accelerated degradation test, with a constant applied stress value of s. The performance degradation of the j-th sample in the k-th measurement is denoted as X. jk Assume that the correlation coefficient of the degradation rate of each product is a fixed value, i.e., a1, a2, ..., a m Then we have:

[0040]

[0041] Among them, t k This represents the time of the k-th measurement of the product, where t0 = 0;

[0042] From the above, we can see that ΔX jk It follows a multivariate normal distribution, with the mean and variance as follows:

[0043]

[0044] The unknown parameters of the degradation failure reliability model are estimated using the maximum likelihood estimation method. The log-likelihood function can be obtained from the above equation:

[0045]

[0046] Where, m j This represents the total number of measurements for the j-th product.

[0047] Let the above equation with respect to σ 2 ,a1,a2,...,a m The first partial derivative is zero, so σ is obtained. 2 ,a1,a2,...,a m The restricted maximum likelihood estimate is:

[0048]

[0049] Given σ 2 ,a1,a2,...,a m Under the premise of this, substituting the above equation into the log-likelihood function corresponding to the unknown parameters of the degradation failure reliability model, we can obtain the parameter σ. 2 ,a1,a2,...,a m The cross-sectional surface number likelihood function:

[0050]

[0051] The estimated value of b is obtained by maximizing the facet-number likelihood function of the profile using the fminsearch function in Matlab, and then substituted into σ. 2 ,a1,a2,...,a mConstrained maximum likelihood estimation, and thus σ 2 ,a1,a2,...,a m Maximum likelihood estimate Get μ u and The estimated value:

[0052]

[0053] Optionally, the step of solving for the unknown parameters of the sudden failure reliability model based on the sudden failure occurrence test data and the no-failure occurrence test data to obtain the parameters of the sudden failure reliability model includes:

[0054] The maximum likelihood function for the unknown parameters of sudden failure based on the sudden failure occurrence test data and the no-failure occurrence test data is:

[0055]

[0056] Where I(·) is the indicator function;

[0057] Given the boundary condition β > 0, the parameter estimate of the sudden failure unknown parameter θ2 can be directly obtained by maximizing the above formula using the fminsearch function in Matlab.

[0058] This invention addresses the complex relationships of competing and interdependent failure modes in products, proposing a reliability modeling and evaluation method for multi-mode dependent competing failure systems. It introduces an accelerated model into the degradation failure model, enabling a better description of the complex failure process of long-life, high-reliability products and allowing for corresponding reliability assessments under different usage environments. Recognizing that most competing failure modeling studies often presuppose sudden failure time distributions, making it difficult to accurately reflect the diverse sudden failure behaviors in complex systems, this invention proposes a competing failure reliability modeling method that does not presuppose sudden failure time distributions, improving the accuracy of product reliability assessment. Furthermore, addressing the issue that most competing failure modeling studies neglect failure data from accelerated degradation tests, this invention proposes a competing failure model parameter estimation method that can utilize degradation data, sudden failure data, and no failure data, enabling more accurate reliability assessment and analysis of products using multiple data sources. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 A schematic diagram illustrating the principle of a reliability assessment method for a multi-mode dependent competing failure system provided in the embodiments of this specification;

[0061] Figure 2 This is a schematic diagram of laser performance degradation data provided in the embodiments of this specification;

[0062] Figure 3 This is a schematic diagram of the laser reliability curve provided in the embodiments of this specification. Detailed Implementation

[0063] The following description is intended to disclose the present invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art. The basic principles of the invention defined in the following description can be applied to other embodiments, modifications, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the invention.

[0064] The following is in conjunction with the appendix Figure 1-3 Exemplary embodiments of the invention will be described more fully here. However, exemplary embodiments can be implemented in many forms and should not be construed as limiting the invention to the embodiments set forth herein. Rather, these exemplary embodiments are provided to make the invention more comprehensive and complete, and to facilitate a full communication of the inventive concept to those skilled in the art. The same reference numerals in the figures denote the same or similar elements, components, or parts, and therefore repeated descriptions of them are omitted.

[0065] Subject to the technical concept of this invention, the features, structures, characteristics or other details described in a particular embodiment may be combined in one or more other embodiments in a suitable manner.

[0066] In the description of specific embodiments, the features, structures, characteristics, or other details described in this invention are intended to enable those skilled in the art to fully understand the embodiments. However, it is not excluded that those skilled in the art can practice the technical solutions of this invention without one or more of the specific features, structures, characteristics, or other details.

[0067] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily need to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0068] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0069] The terms “and / or” or “and / or” include all combinations of any one or more of the listed items.

[0070] Figure 1 This is a schematic diagram illustrating the principle of a reliability assessment method for a multi-mode dependent competing failure system provided in the embodiments of this specification. The method may include:

[0071] S110: Construct a competing failure reliability model;

[0072] In the specific embodiments described in this specification, many products simultaneously exhibit multiple degradation failure and sudden failure modes, and their failure is the result of competition among these multiple failure modes. To simplify the description and analysis of the problem, it is assumed that, given a certain level of performance degradation, the product has only one sudden failure mode, and the occurrence of sudden failure depends on the amount of performance degradation of the product's degradation failure mode. Therefore, the product's reliability function is reflected in the product's reliability under degradation failure conditions and the conditional reliability of the product under sudden failure conditions where no degradation failure occurs.

[0073] Optionally, S110 includes:

[0074] The product's failure time T can be expressed as:

[0075] T = min{T d ,T r}

[0076] Among them, T d T represents the product degradation and failure time. r For the product's sudden failure mode failure time;

[0077] The reliability model R(t) for competing failure modes of degradation failure and sudden failure is:

[0078] R(t)=P(T>t)=P(T r >t,T d >t)=P(T r >t|T d >t)·P(T d >t)=R r (t)·R d (t)

[0079] Among them, R d(t) represents the reliability of the degradation failure mode; R r (t) represents the conditional reliability of the sudden failure mode under the condition that no degradation failure occurs.

[0080] In the specific implementation of this specification, it can be seen from the above formula that in order to achieve product reliability estimation, it is necessary to establish a product degradation failure reliability model and a sudden failure reliability model.

[0081] S120: Based on the aforementioned competitive failure reliability model, model the degradation failure and sudden failure of the product respectively to obtain the degradation failure reliability model and the sudden failure reliability model;

[0082] In the specific implementation of this specification, for the degradation failure model, a stochastic process model is used for modeling. The performance degradation process of the product is assumed to be describable using a Wiener process. Simultaneously, unit heterogeneity and an acceleration model are introduced to establish a Wiener accelerated degradation model that can represent the differences in degradation behavior among individuals and the relationship between the product degradation rate and the applied stress. The corresponding degradation failure reliability function model is then derived. For the sudden failure model, no assumptions are made regarding the sudden failure time distribution. Instead, a failure rate function is used to describe sudden failure. It is assumed that the failure rate of sudden failure depends entirely on the amount of performance degradation of the product. Based on the characteristic that the performance degradation amount follows a Wiener process, a sudden failure failure rate model is established, and the corresponding sudden failure reliability function model is derived.

[0083] Optionally, S120 includes:

[0084] Let X(t) represent the product degradation process, then the degradation failure model X(t) can be established as follows:

[0085] X(t) = X(0) + μt + σB(t)

[0086] Where X(0) = 0 is the initial value of degradation, and for ease of analysis, let X(0) = 0; μ is the drift coefficient, which characterizes the rate of product performance degradation; σ is the diffusion coefficient; B(·) is the standard Brownian motion, which characterizes the dynamic characteristics of degradation;

[0087] The probability density function f(X) of the degradation can be expressed as:

[0088]

[0089] Let w be the product's failure threshold. Then, the time when the product degradation process first reaches the failure threshold is the product degradation failure time T. d :

[0090] T d =inf{t:X(t)≥w|X(0)<w}

[0091] When μ is a random variable and follows the order of random variables, When, the probability density function of the product degradation failure time distribution is... and reliability function R d (t) is:

[0092]

[0093] In the specific embodiments described in this specification, accelerated testing can evaluate product reliability and lifespan in a relatively short time and is widely used for reliability evaluation of high-reliability, long-life products. To represent the relationship between product degradation rate and applied stress, a corresponding accelerated model needs to be established. This invention sets the accelerated model as the Arrhenius model, which is mainly applicable to the influence of temperature stress on product degradation, and sets the drift coefficient to be closely related to the stress magnitude. The accelerated model is expressed as follows:

[0094]

[0095] To account for unit heterogeneity in the acceleration model, the parameter 'a' is treated as a random variable that follows a normal distribution. The drift coefficient of the product degradation process follows a special normal distribution as follows:

[0096]

[0097] Optionally, S120 includes:

[0098] At any time t, X can be considered a random variable. To ensure that the product does not fail due to degradation at time t, the burst failure rate λ(t,X(t)) can be expressed as:

[0099]

[0100] Where λ(t,X(t)) is the failure rate of the product in the event of sudden failure without degradation failure, and the upper limit of integration w is used to ensure that the product has not experienced degradation failure by time t;

[0101] Conditional reliability function R for sudden failure time under conditions of no degradation failure r (t) and conditional probability density function f r (t) is:

[0102]

[0103] f r (t)=λ(t,X(t))·R r (t)

[0104] In the specific implementation described in this specification, during the degradation test, the product may experience sudden failure before actual degradation failure. Further complicating matters, there is often some degree of dependency between these two failure modes. Accurate definition of sudden failure modes and corresponding modeling are required to achieve reliability assessment of the product's sudden failure modes.

[0105] The failure rate of a product's sudden failure depends on the amount of performance degradation. Sudden failure is described using a failure rate function, specifically, at time t, the failure rate function is represented as λ(X(t)).

[0106] In most existing studies on sudden failure modeling, a common approach is to assume that the sudden failure time data follows a certain parametric distribution, such as the exponential or Weibull distribution. To generalize from existing research, this paper makes no assumptions about the sudden failure time distribution and instead uses a failure rate function to describe sudden failure, i.e.:

[0107] λ(X(t))=βX v (t)

[0108] For λ(X(t))=βX v In terms of its functional form, the (t) function is applicable to sudden failure modes where the failure rate increases with the amount of performance degradation. Since the amount of product performance degradation follows a stochastic process, that is, at any time t, X can be regarded as a random variable. Therefore, to ensure that the product does not experience degradation failure at time t, the sudden failure rate can be expressed as follows using the probability density function of the degradation amount:

[0109]

[0110] S130: Based on the accelerated degradation test data, solve for the unknown parameters of the degradation failure reliability model and the unknown parameters of the sudden failure reliability model respectively to obtain the parameters of the degradation failure reliability model and the parameters of the sudden failure reliability model.

[0111] In the specific implementation of this specification, for the unknown parameters of the degradation failure model, a two-step maximum likelihood estimation method is adopted. Degradation data is used to solve for the parameters. First, it is assumed that the correlation coefficient of the degradation rate for each product is a fixed value. The maximum likelihood function of the degradation amount and the surface number likelihood function of the profile are derived. The surface number likelihood function is maximized and then substituted into the maximum likelihood function of the degradation amount to solve for the unknown parameters of the degradation failure model. For the unknown parameters of the sudden failure model, the maximum likelihood estimation method is adopted. Sudden failure data and no-failure data are used to solve for the parameters. First, the reliability expressions of the product under sudden failure and no-failure conditions are derived. Based on the expressions, the corresponding maximum likelihood functions are established. After simplification, maximizing the expression yields the unknown parameters of the sudden failure model.

[0112] Optionally, S130 includes:

[0113] The accelerated degradation test data includes degradation failure occurrence test data, sudden failure occurrence test data, and no failure occurrence test data.

[0114] Based on the test data of the degradation failure occurrence, the unknown parameters of the degradation failure reliability model are solved to obtain the parameters of the degradation failure reliability model;

[0115] Based on the test data of sudden failure occurrence and the test data of no failure occurrence, the unknown parameters of the sudden failure reliability model are solved to obtain the parameters of the sudden failure reliability model.

[0116] Optionally, S130 includes:

[0117] There are m products participating in an accelerated degradation test, with a constant applied stress value of s. The performance degradation of the j-th sample in the k-th measurement is denoted as X. jk Assume that the correlation coefficient of the degradation rate of each product is a fixed value, i.e., a1, a2, ..., a m Then we have:

[0118]

[0119] Among them, t k This represents the time of the k-th measurement of the product, where t0 = 0;

[0120] From the above, we can see that ΔX jk It follows a multivariate normal distribution, with the mean and variance as follows:

[0121]

[0122] The unknown parameters of the degradation failure reliability model are estimated using the maximum likelihood estimation method. The log-likelihood function can be obtained from the above equation:

[0123]

[0124] Where, m j This represents the total number of measurements for the j-th product.

[0125] Let the above equation with respect to σ 2 ,a1,a2,...,a m The first partial derivative is zero, so σ is obtained. 2 ,a1,a2,...,a m The restricted maximum likelihood estimate is:

[0126]

[0127] Given σ 2 ,a1,a2,...,a m Under the premise of this, substituting the above equation into the log-likelihood function corresponding to the unknown parameters of the degradation failure reliability model, we can obtain the parameter σ. 2 ,a1,a2,...,a m The cross-sectional surface number likelihood function:

[0128]

[0129] The estimated value of b is obtained by maximizing the facet-number likelihood function of the profile using the fminsearch function in Matlab, and then substituted into σ. 2 ,a1,a2,...,a m Constrained maximum likelihood estimation, and thus σ 2 ,a1,a2,...,a m Maximum likelihood estimate Get μ u and The estimated value:

[0130]

[0131] Optionally, the step of solving for the unknown parameters of the sudden failure reliability model based on the sudden failure occurrence test data and the no-failure occurrence test data to obtain the parameters of the sudden failure reliability model includes:

[0132] The maximum likelihood function for the unknown parameters of sudden failure based on the sudden failure occurrence test data and the no-failure occurrence test data is:

[0133]

[0134] Where I(·) is the indicator function;

[0135] Given the boundary condition β > 0, the parameter estimate of the sudden failure unknown parameter θ2 can be directly obtained by maximizing the above formula using the fminsearch function in Matlab.

[0136] In the specific implementation of this specification, if the j-th sample experiences a sudden failure during the measurement process, the test is stopped, and the time of this test is recorded as the product sudden failure time, i.e., the product lifespan is... Therefore, for product j, we have:

[0137]

[0138] If we construct the maximum likelihood estimation function for the unknown parameters of sudden failure based solely on the above formula, we can find that the estimation process only utilizes the sudden failure data from the degradation test, without considering the data from the no-failure test at the end of the accelerated degradation test. This may reduce the estimation accuracy of the unknown parameters of sudden failure. To improve the reliability estimation accuracy and reflect the relationship between sudden failure and degradation, it is necessary to consider the no-failure data in the parameter estimation process of the unknown parameters of sudden failure.

[0139] If the j-th sample does not fail during the measurement process, then the measured performance degradation parameter of the product is: And product lifespan Therefore, for product j, we have:

[0140]

[0141] Furthermore, the following definition applies:

[0142]

[0143] Therefore, considering both burst failure data and no failure data, the maximum likelihood function for the burst failure unknown parameter is:

[0144]

[0145] S140: Substitute the parameters of the degradation failure reliability model and the parameters of the sudden failure reliability model into the competing failure reliability model to obtain the reliability function and reliability index of the product under different stress conditions.

[0146] In the specific implementation of this specification, the parameter estimation results are substituted into the product competitive failure reliability model to obtain the product reliability function. By taking different stress condition values ​​and time values, the reliability of the product at a certain stress value and a certain time can be obtained. By taking a large number of time values, the product reliability curve at a certain stress value can be obtained, and corresponding reliability analysis can be performed.

[0147] Specifically, an accelerated degradation test was conducted on a certain type of GaAs laser at 80°C. The percentage change in operating current over time was recorded. The laser was considered to have degraded when its operating current increased to 100% of its rated current. A total of 22 samples participated in the test. Degradation values ​​were measured every 500 hours until 4000 hours. Measurements were stopped when a sample experienced degradation or sudden failure before 4000 hours. A total of 10 samples failed; 3 experienced degradation failure and the other 7 experienced sudden failure. Figure 2 As shown.

[0148] The performance degradation monitored for the GaAs laser samples that experienced sudden failures did not exceed the failure threshold. Table 1 shows the sudden failure time and corresponding performance degradation data for the sudden failure samples.

[0149] Table 1. Laser sudden failure time and corresponding degradation amount

[0150] 3 3000 7.05 5 1000 1.81 9 3500 8.35 12 3500 9.21 15 3500 8.02 17 2000 3.97 21 2500 6.33

[0151] Based on the performance degradation data of GaAs lasers, a reliability analysis was conducted. Given an initial value of 1 for parameter b in θ1, the facet-number likelihood function of the profile was maximized to obtain an estimate of parameter b. Substituting this estimate into the equation, the estimates of the remaining unknown parameter θ1 were obtained. The estimation results of the unknown parameter θ1 are shown in Table 2.

[0152] Table 2. Estimated values ​​of unknown parameter θ1 in GaAs laser case studies.

[0153]

[0154] Based on the special normal distribution, substituting μ... a and The estimation results yield the parameter μ. u and The estimated value.

[0155] The initial value of parameter θ2 = (β, v) is randomly generated using the rand function, and then substituted into parameter μ. u , and σ 2 The estimation results are obtained by maximizing equation (26), and the estimation results are shown in Table 3.

[0156] Table 3. Estimated values ​​of unknown parameter θ2 in GaAs laser case studies.

[0157]

[0158] To evaluate the reliability model used in this invention, and to compare it with methods that only consider degradation data, methods that only consider degradation and burst data but do not utilize failure-free data, the effectiveness of the overall method proposed in this paper is demonstrated. The method of this invention is denoted as M1; the method that only considers degradation data is denoted as M2; and the method that only considers degradation data and burst failure data but does not utilize failure-free data is denoted as M3.

[0159] Based on the competing failure reliability model R(t), the estimated results of the unknown parameters are substituted, and the stress value is set to be consistent with the case stress value to obtain the product reliability curve under the method of this invention. For the M2 method, the parameter estimates in Table 2 are used. Sudden failure is not considered, and the reliability curve of the product under the M2 method is obtained from the reliability function of the product degradation failure time distribution. For the M3 method, the parameter estimates in Table 2 are used for the unknown parameters. A maximum likelihood estimation function for the unknown parameters of sudden failure is constructed to obtain the corresponding parameter estimates. Finally, the stress value is set to be consistent with the case stress value, and the reliability curve of the product under the M3 method is obtained from the competing failure reliability model R(t). The reliability curve is shown in the figure below. Figure 3 As shown.

[0160] from Figure 3 It can be observed that the M2 method only considers degradation failure modeling and ignores the sudden failure mode of the product, which will cause the reliability prediction result of the product to be too large. In contrast, the M1 and M3 methods consider competing failures, which will make the reliability curve more conservative and more in line with engineering practices.

[0161] To illustrate the reliability assessment accuracy of each method, the absolute and relative errors of each method are calculated and compared. The formulas for absolute and relative errors are shown below.

[0162] AE = |R * (t)-R(t)|

[0163]

[0164] Where AE is the absolute error; RE is the relative error; R(t) is the true reliability value; R * (t) is the reliability prediction value.

[0165] The true reliability value was estimated using the frequency method, and the results are shown in Table 4.

[0166] Table 4 Product Reliability Assessment Results

[0167] M1 0.0358 0.1668 4004 M2 0.2422 0.0251 4710 M3 0.4413 0.3027 2711

[0168] Table 4 shows that when the M3 method uses only burst failure data, its reliability curve and reliability assessment results are more conservative. While this aligns better with engineering practices, its reliability assessment accuracy is lower and it cannot accurately reflect changes in product reliability. In contrast, the M1 method has higher reliability assessment accuracy and accurately reflects changes in product reliability, most closely resembling the real situation. This demonstrates that the proposed method for modeling and assessing the reliability of competing failure systems, which does not presuppose a time distribution, considers dependencies and the Wiener degradation process, and comprehensively utilizes experimental data, is more accurate in assessing product reliability and its changes.

[0169] By utilizing accelerated degradation test data, the reliability of a product at a specific moment under test conditions can be obtained through the method of this invention. Furthermore, it can be extrapolated to other test conditions to obtain the reliability of the product at a specific moment under different test conditions, thereby completing the product reliability assessment.

[0170] This invention addresses the complex relationships of competing and interdependent failure modes in products, proposing a reliability modeling and evaluation method for multi-mode dependent competing failure systems. It introduces an accelerated model into the degradation failure model, enabling a better description of the complex failure process of long-life, high-reliability products and allowing for corresponding reliability assessments under different usage environments. Recognizing that most competing failure modeling studies often presuppose sudden failure time distributions, making it difficult to accurately reflect the diverse sudden failure behaviors in complex systems, this invention proposes a competing failure reliability modeling method that does not presuppose sudden failure time distributions, improving the accuracy of product reliability assessment. Furthermore, addressing the issue that most competing failure modeling studies neglect failure data from accelerated degradation tests, this invention proposes a competing failure model parameter estimation method that can utilize degradation data, sudden failure data, and no failure data, enabling more accurate reliability assessment and analysis of products using multiple data sources.

[0171] In summary, this invention can be implemented in hardware, or as software modules running on one or more processors, or a combination thereof. Those skilled in the art will understand that in practice, general-purpose data processing devices such as microprocessors or digital signal processors (DSPs) can be used to implement some or all of the functions of some or all of the components according to the embodiments of the invention. The invention can also be implemented as a device or apparatus program (e.g., a computer program and computer program product) for performing part or all of the methods described herein. Such programs implementing the invention can be stored on a computer-readable medium or can take the form of one or more signals. Such signals can be downloaded from an Internet website, provided on a carrier signal, or provided in any other form.

[0172] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the present invention is not inherently related to any specific computer, virtual device, or electronic device, and various general-purpose devices can also implement the present invention. The above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0173] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0174] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A reliability assessment method for a multi-mode dependent competing failure system, characterized in that, include: Construct a competitive failure reliability model; Based on the aforementioned competing failure reliability model, degradation failure and sudden failure of the product are modeled respectively to obtain a degradation failure reliability model and a sudden failure reliability model; wherein, the step of modeling sudden failure of the product based on the aforementioned competing failure reliability model to obtain a sudden failure reliability model includes: At any given moment hour, It can be considered a random variable, to ensure The product must not degrade or fail at any time, and the failure rate should be minimized. This can be expressed as: in, The failure rate of a product in the event of sudden failure without degradation failure; the coefficient β controls the overall level of the failure rate function; In (t), v determines the rate of failure; through the upper limit of integration To ensure product delivery No degradation or failure occurred at any time; The drift coefficient characterizes the rate of product performance degradation. is the diffusion coefficient; where , These represent the mean and variance parameters of the normal distribution that the drift coefficients follow, respectively. Conditional reliability function for sudden failure time under conditions of no degradation failure and conditional probability density function for: ； Based on accelerated degradation test data, the unknown parameters of the degradation failure reliability model and the unknown parameters of the sudden failure reliability model are solved respectively to obtain the parameters of the degradation failure reliability model and the parameters of the sudden failure reliability model. By substituting the parameters of the degradation failure reliability model and the sudden failure reliability model into the competing failure reliability model, the reliability function and reliability index of the product under different stress conditions are obtained.

2. The reliability assessment method for a multi-mode dependent competing failure system as described in claim 1, characterized in that, The construction of the competitive failure reliability model includes: Product Failure Time It can be represented as: in, This refers to the product's degradation and failure time. For the product's sudden failure mode failure time; The reliability model R(t) for competing failure modes of degradation failure and sudden failure is: in, For the reliability of degradation failure modes; This represents the conditional reliability of sudden failure modes under conditions where no degradation failure has occurred.

3. The reliability assessment method for a multi-mode dependent competing failure system as described in claim 2, characterized in that, The degradation failure of the product is modeled based on the competing failure reliability model to obtain the degradation failure reliability model, including: make To represent the product degradation process, the degradation failure model X(t) can be established as follows: in, Let the initial value be a degenerate value. For ease of analysis, let... ; The drift coefficient characterizes the rate of product performance degradation. The diffusion coefficient is denoted as . It is a standard Brownian motion, characterizing the dynamic properties of degradation; The probability density function f(X) of the degradation can be expressed as: in , These represent the mean and variance parameters of the normal distribution that the drift coefficients follow, respectively. Let the product's failure threshold be The time when the product degradation process first reaches the failure threshold is the product degradation failure time. : when Let be a random variable, and follow the rules of random variables. When, the probability density function of the product degradation failure time distribution is... and reliability function for: 。 4. The reliability assessment method for a multi-mode dependent competing failure system as described in claim 1, characterized in that, The process of solving for the unknown parameters of the degradation failure reliability model and the sudden failure reliability model based on accelerated degradation test data to obtain the parameters of the degradation failure reliability model and the sudden failure reliability model includes: The accelerated degradation test data includes degradation failure occurrence test data, sudden failure occurrence test data, and no failure occurrence test data. Based on the test data of the degradation failure occurrence, the unknown parameters of the degradation failure reliability model are solved to obtain the parameters of the degradation failure reliability model; Based on the test data of sudden failure occurrence and the test data of no failure occurrence, the unknown parameters of the sudden failure reliability model are solved to obtain the parameters of the sudden failure reliability model.

5. The reliability assessment method for a multi-mode dependent competing failure system as described in claim 4, characterized in that, The process of solving for the unknown parameters of the degradation failure reliability model based on the degradation failure occurrence test data to obtain the parameters of the degradation failure reliability model includes: existing Each product participated in the accelerated degradation test, and the applied stress value was always [value missing]. , No. The sample at the th The performance degradation of this measurement is denoted as Assuming the correlation coefficient of degradation rate for each product is a fixed value, that is... Then we have: in, Indicates the product number The time of the measurement, and ; From the above, we can see that It follows a multivariate normal distribution, with the mean and variance as follows: The unknown parameters of the degradation failure reliability model are estimated using the maximum likelihood estimation method. The log-likelihood function can be obtained from the above equation: in, For the first The total number of measurements for each product; Here, s is the applied stress value, and b is the parameter to be estimated in the acceleration model; Let each of the above expressions be related to The first-order partial derivative is zero, so we can obtain... The restricted maximum likelihood estimate is: In a given Under the premise of this, substituting the above formula into the log-likelihood function corresponding to the unknown parameters of the degradation failure reliability model, we can obtain information about the parameters. The cross-sectional surface number likelihood function: The facet number likelihood function of the profile is maximized using the fminsearch function in Matlab. After obtaining the estimated value, substitute it into... Restricted maximum likelihood estimation, and thus obtain Maximum likelihood estimate ,get and The estimated value: 。 6. The reliability assessment method for a multi-mode dependent competing failure system as described in claim 5, characterized in that, The process of solving for the unknown parameters of the sudden failure reliability model based on the sudden failure occurrence test data and the no-failure occurrence test data to obtain the parameters of the sudden failure reliability model includes: The maximum likelihood function for the unknown parameters of sudden failure based on the sudden failure occurrence test data and the no-failure occurrence test data is: in, For indicator functions; Given boundary conditions By maximizing the above formula using the fminsearch function in Matlab, the unknown parameters of sudden failure can be directly solved. Parameter estimates .

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