A reliability prediction method for electronic devices based on the fusion of physics of failure and Bayesian

Abstract

The present invention discloses a method for predicting the reliability of electronic devices by fusing physics of failure and Bayesian theory, which relates to the field of reliability prediction of electronic devices. The method includes collecting the physics of failure model parameters of the failure units of each electronic device, and establishing the physics of failure model through failure mechanism analysis; calculating the reliability parameters of the failure units of the electronic device to obtain the physics of failure prediction value; conducting reliability analysis based on the reliability prediction manual of the electronic device to obtain the failure rate of the failure units of the electronic device, and calculating the mean time between failures of each failure unit; using the Bayesian formula to conduct reliability analysis at the system level to obtain the system failure rate and the mean time to system failure, thereby completing the reliability prediction of the electronic device by fusing physics of failure and Bayesian theory. The present invention solves the problems in the prior art that when predicting the reliability of electronic devices, it is difficult to simultaneously consider the physics of failure mechanism and actual test data, and the prediction is inaccurate due to the lack of dynamic correction ability.

Description

Technical Field

[0001] The present invention relates to the field of reliability prediction of electronic devices, and particularly to a method for predicting the reliability of electronic devices by fusing physics of failure and Bayesian methods. Background Art

[0002] Nowadays, electronic devices are widely used in high-reliability fields such as aerospace, automotive industry, and defense equipment. These complex electronic systems usually work in harsh environments such as high temperature, strong vibration, and strong electromagnetic interference, and are highly sensitive to failures. Once a key component of the system fails, it often leads to system-level failures, bringing safety risks and huge maintenance costs. Therefore, reliability prediction technology has received increasing attention. In the design and development stage of electronic devices, traditional reliability prediction methods mostly rely on life models based on statistical experience or large-sample test inferences, and usually have many deficiencies. For example, many traditional methods only calculate the average life based on historical data or failure statistics, and do not consider the specific failure mechanisms of electronic components (such as thermal fatigue, vibration fatigue, material aging, etc.) deeply enough, making it difficult to accurately promote on new technology or new material products; obtaining reliable statistical data usually requires a large amount of long-term experimental samples, resulting in very high experimental cycles and costs; at the same time, once the electronic product is iteratively upgraded or the usage environment is changed, the original statistical model often needs to be reconstructed.

[0003] To overcome the above difficulties, in recent years, there has been a research trend of combining the physics of failure (PoF) method with statistical analysis. The physics of failure model can accurately depict the failure process and perform accelerated life prediction based on in-depth analysis of the material properties, structural characteristics, and load environment of components; while statistical analysis, especially the Bayesian method, can fuse prior knowledge (such as accelerated tests, historical experience, etc.) with actual service data (such as in-service monitoring, failure occurrence time, etc.), so as to gradually correct and update the model parameters under the condition of limited test samples, and obtain a reliability prediction closer to the real environment. However, most current studies still remain at the stage of applying the physics of failure model and Bayesian estimation separately, lacking a systematic and operable fusion method to cope with multiple failure mechanisms, reliability assessment at multiple unit levels, and dynamic prediction requirements of complex electronic device systems in actual engineering. Especially in an environment where multiple failure modes coexist, how to effectively identify key failure units, establish accurate physics of failure equations, and continuously correct the model in combination with actual service data remains a technical challenge faced by both the industry and the academia. Summary of the Invention

[0004] In view of the above deficiencies in the prior art, a method for predicting the reliability of electronic devices based on failure physics Bayesian fusion provided by the present invention solves the problems in the prior art such as the difficulty in simultaneously considering the failure physics mechanism and actual test data, and the inaccurate prediction caused by the lack of dynamic correction ability when predicting the reliability of electronic devices.

[0005] In order to achieve the above invention purpose, the technical solution adopted by the present invention is: A method for predicting the reliability of electronic devices based on failure physics Bayesian fusion, including the following steps:

[0006] S1: Collect the failure physics model parameters of each failure unit of the electronic device, and establish the failure physics model through failure mechanism analysis;

[0007] S2: Calculate the reliability parameters of the failure unit of the electronic device based on the failure physics model to obtain the failure physics prediction value;

[0008] S3: Conduct reliability analysis based on the electronic device reliability prediction manual to obtain the failure rate of the failure unit of the electronic device, and calculate the mean time between failures of each failure unit;

[0009] S4: Based on the failure physics prediction value, failure rate and mean time between failures, use the Bayesian formula to conduct system-level reliability analysis to obtain the system failure rate and system mean time to failure, and complete the reliability prediction of the electronic device based on failure physics Bayesian fusion.

[0010] Further, the S2 includes the following sub-steps:

[0011] S21: Calculate the time to failure of each failure unit of the electronic device under the failure physics model;

[0012] S22: Compare the time to failure under each failure physics model, and select the output value of the failure physics model with the minimum time to failure as the failure physics prediction value.

[0013] Further, when calculating the time to failure of each failure unit of the electronic device under the failure physics model in S21, the formula is:

[0014] The Coffin-Manson model is:

[0015]

[0016]

[0017]

[0018] Among them, is the number of fatigue cycles, is the shear stress applied to the solder joint, is the fatigue ductility coefficient, is the fatigue ductility index, is the encapsulation factor, is the diagonal length, is the height of the solder joint lift, is the coefficient of thermal expansion of the device, is the coefficient of thermal expansion of the substrate, is the temperature difference of the device, is the temperature difference of the substrate, is the cyclic average temperature, is the high-temperature immersion time of the temperature cycle;

[0019] The TDDB model is:

[0020]

[0021] Among them, is the time to failure under the TDDB model, is a constant, is the dipole or polarization coefficient in the dielectric, is the actual electric field strength applied on the dielectric layer, is the activation energy, is the Boltzmann constant, is the absolute temperature;

[0022] The Corrosion model is:

[0023]

[0024] Among them, is the time to failure under the Corrosion model, is a constant, is the relative humidity RH is the corrosion factor related to is the activation energy;

[0025] The EM failure life model is:

[0026]

[0027] Among them, is the time to failure under the EM failure life model, is the proportionality constant, is the applied current density, is the critical current density, is the EM index, is the activation energy;

[0028] The HCI failure model is:

[0029]

[0030] Among them, is the fault occurrence time under the HCI failure model, is a constant related to materials and device structures, is the peak substrate current, is the current exponent, is the activation energy.

[0031] Furthermore, the step S3 includes the following sub-steps:

[0032] S31: Conduct reliability analysis based on the electronic equipment reliability prediction manual to obtain the failure rate of the failure unit of the electronic equipment. The formula is:

[0033]

[0034]

[0035]

[0036] Among them, is the reliability, is the failure rate, is the time, is the failure distribution function, is the failure density function;

[0037] S32: Calculate the mean time between failures of each failure unit based on the failure rate of the failure unit of the electronic equipment. The formula is:

[0038]

[0039] Among them, is the mean time between failures.

[0040] Furthermore, the step S4 includes the following sub-steps:

[0041] S41: Take the failure rate as the mean of the prior information and the failure physics prediction value as the observed data, and calculate the prior distribution of each failure unit;

[0042] S42: Calculate the posterior distribution of each failure unit based on the prior distribution and the likelihood function of each failure unit, and at the same time correct the posterior parameters to obtain the posterior correction parameters, and calculate the posterior mean and the mean time to failure;

[0043] S43: Obtain the system failure rate and the system mean time to failure based on the posterior mean and the mean time to failure.

[0044] Furthermore, the prior distribution of each failure unit in S41 is:

[0045]

[0046]

[0047] Among them, is the failure rate, is the prior information of the number of failures, is the prior information of the failure time, and Gamma is the gamma distribution.

[0048] Furthermore, the likelihood function in S42 is:

[0049]

[0050] Among them, is the likelihood function, is the cumulative operating time, is the failure rate;

[0051] The posterior distribution of each failed unit is:

[0052]

[0053] Among them, is the posterior distribution;

[0054] The posterior correction parameter is:

[0055]

[0056]

[0057] Among them, and are the posterior correction parameters;

[0058] The posterior mean satisfies:

[0059] .

[0060] The beneficial effects of the present invention are as follows: By combining the physics-of-failure (PoF) model with Bayesian statistical methods, the present invention can make full use of the physics-of-failure mechanism. Based on the mechanism models of thermal fatigue, vibration fatigue, material aging, etc. of components and solder joints, life modeling of key failure units is carried out to improve the scientificity and accuracy of prediction. And on the basis of existing accelerated tests and empirical priors, by integrating the failure data in the actual use process, the reliability model is dynamically updated to make the prediction results more in line with the real service environment. In addition, the data utilization efficiency is improved. Even when the test sample size is small or the test cycle is limited, relatively accurate life prediction and failure rate estimation can be obtained through the Bayesian fusion of prior distribution and actual observed data. Finally, system-level reliability analysis is realized. Based on the unit-level failure distribution and combined with the series-parallel or redundant structure inside the electronic device, system-level reliability indicators and the mean time to failure (MTTF), etc. are obtained, providing a basis for design improvement and operation and maintenance decisions. At the same time, it provides an efficient and accurate reliability evaluation method for the development and use of electronic devices in high-reliability fields such as aviation, aerospace, and automotive. Description of the Drawings

[0061] Figure 1 It is a flowchart of a method for predicting the reliability of an electronic device by Bayesian fusion of physics of failure of the present invention. Detailed Embodiments

[0062] The present invention will be further described below in conjunction with the drawings and specific embodiments.

[0063] As Figure 1 shown, a method for predicting the reliability of an electronic device by Bayesian fusion of physics of failure includes the following steps:

[0064] S1: Collect the physics-of-failure model parameters of the failure units of each electronic device, and establish the physics-of-failure model through failure mechanism analysis;

[0065] S2: Calculate the reliability parameters of the failure units of the electronic device based on the physics-of-failure model to obtain the physics-of-failure prediction value;

[0066] S3: Conduct reliability analysis based on the electronic device reliability prediction manual to obtain the failure rate of the failure units of the electronic device, and calculate the mean time to failure of each failure unit;

[0067] S4: Based on the physics-of-failure prediction value, failure rate, and mean time to failure, use the Bayesian formula to conduct system-level reliability analysis to obtain the system failure rate and the system mean time to failure, and complete the reliability prediction of the electronic device by Bayesian fusion of physics of failure.

[0068] In one embodiment of the present invention, physical model parameters of material failure are collected, and the signal processing module is divided into several failure units, including BGA solder joints, MLCC capacitors, metal film resistors, and bonding wires, which are denoted as C1, C2, C3, and C4 for convenience of calculation. As shown in Table 1-5, the parameter values of the four key failure units under the failure physical model are provided.

[0069] Table 1 Coffin-Manson Model Parameters of Four Key Failure Units

[0070]

[0071] Table 2 TDDB Model Parameters of Four Key Failure Units

[0072]

[0073] Table 3 Corrosion Model Parameters of Four Key Failure Units

[0074]

[0075] Table 4 EM Failure Physical Model Parameters of Four Key Failure Units

[0076]

[0077] Table 5 HCI Failure Physical Model Parameters of Four Key Failure Units

[0078]

[0079] The S2 includes the following sub-steps:

[0080] S21: Calculate the failure occurrence time of each failure unit of the electronic device under the failure physical model;

[0081] S22: Compare the failure occurrence times under each failure physical model, and select the output value of the failure physical model with the minimum failure occurrence time as the failure physical prediction value.

[0082] In the S21, when calculating the failure occurrence time of each failure unit of the electronic device under the failure physical model, the formula is:

[0083] The Coffin-Manson model is:

[0084]

[0085]

[0086]

[0087] Where is the number of fatigue cycles, is the shear stress on the solder joint, is the fatigue ductility coefficient, is the fatigue ductility index, is the encapsulation factor, is the diagonal length, is the solder joint lift-off height, is the coefficient of thermal expansion of the device, is the coefficient of thermal expansion of the substrate, is the device temperature difference, is the substrate temperature difference, is the cyclic average temperature, is the high-temperature immersion time of the temperature cycle;

[0088] For ease of calculation, the Coffin-Manson model uses a common simplified form:

[0089]

[0090] and The Coffin-Manson model parameters can all be obtained from experiments or literature. Different devices, packages, and materials will have different typical values; is the temperature, in K. The time of failure can be calculated by the following formula:

[0091]

[0092] where, is the thermal cycle frequency;

[0093] Calculate the number of fatigue cycles and the time of failure , as shown in Table 1. Additionally, during the calculation process, since the calculated number of fatigue cycles is too small, manual parameter adjustment is performed.

[0094] The TDDB model, commonly seen in the breakdown of the dielectric layer within the chip or the degradation of the metal-dielectric interface, can be represented by the following empirical equation:

[0095] The TDDB model is:

[0096]

[0097] where, is the time of failure under the TDDB model, is a constant, is the dipole or polarization coefficient in the dielectric, is the actual electric field strength applied on the dielectric layer, is the activation energy, is the Boltzmann constant, and

[0098] The Corrosion model often occurs in metallization layers, wire bonding areas, etc. The model formula is as follows:

[0099] The Corrosion model is:

[0100]

[0101] where is the time to failure under the Corrosion model, is a constant, is the relative humidity RH and is the activation energy;

[0102] The EM failure life model is:

[0103]

[0104] where is the time to failure under the EM failure life model, is a proportionality constant, is the applied current density, is the critical current density, is the EM exponent, and

[0105] The HCI failure model is:

[0106]

[0107] where is the time to failure under the HCI failure model, is a constant related to the material and device structure, is the peak substrate current, is the current exponent, and

[0108] Table 6 shows the time to failure calculated by each failure physics model.

[0109] Table 6 Time to Failure Calculated by Each Failure Physics Model

[0110]

[0111] In summary, observing the life prediction of the five failure mechanisms of each component, numerically, the TTF calculated by the Coffin-Manson thermal fatigue model is significantly less than that of the other four models. This mechanism will fail first and dominate. Finally, the life calculated by the Coffin-Manson model is selected as the failure physics prediction value.

[0112] The S3 includes the following sub-steps:

[0113] S31: Conduct reliability analysis based on the electronic equipment reliability prediction manual to obtain the failure rate of the failed unit of the electronic equipment. The failure rate can be obtained by looking up the table, as shown in Table 7:

[0114] Table 7 Failure rate of the failed unit obtained by looking up the table

[0115]

[0116] The reliability is calculated as follows:

[0117]

[0118] The failure distribution function is as follows:

[0119]

[0120] The failure density function is as follows:

[0121]

[0122] Among them, is the reliability, is the failure rate, is the time, is the failure distribution function, is the failure density function;

[0123] S32: Based on the failure rate of the failed unit of the electronic equipment, calculate the mean time between failures of each failed unit. The formula is:

[0124]

[0125] Among them, is the mean time between failures.

[0126] As shown in Table 8, it is the mean time between failures of each failed unit:

[0127] Table 8 Mean time between failures of each failed unit ( )

[0128]

[0129] Step S4 includes the following sub - steps:

[0130] S41: Take the failure rate as the mean of the prior information, take the predicted failure physics value as the observed data, and calculate the prior distribution of each failure unit;

[0131] S42: Based on the prior distribution and likelihood function of each failure unit, calculate the posterior distribution of each failure unit. At the same time, correct the posterior parameters to obtain the posterior correction parameters, and calculate the posterior mean and mean time to failure;

[0132] S43: Based on the posterior mean and mean time to failure, obtain the system failure rate and system mean time to failure.

[0133] The prior distribution of each failure unit in S41 is:

[0134]

[0135]

[0136] where, is the failure rate, is the prior information of the number of failures, is the prior information of the failure time, and Gamma is the gamma distribution;

[0137] For numerical simplicity and ease of calculation, let , then:

[0138]

[0139] As shown in Table 9, the prior parameters of each failure unit are:

[0140] Table 9 Prior Parameters of Each Failure Unit

[0141]

[0142] That is, the prior of each device is:

[0143] .

[0144] The likelihood function in S42 is:

[0145]

[0146] where, is the likelihood function, is the cumulative operating time, is the failure rate;

[0147] The posterior distribution of each failure unit is:

[0148]

[0149] Among them, is the posterior distribution;

[0150] The posterior correction parameter is:

[0151]

[0152]

[0153] Among them, and are the posterior correction parameters;

[0154] The posterior mean satisfies:

[0155] .

[0156] Finally, through calculation, the posterior correction parameters and calculation parameters of each failure unit are obtained, as shown in Table 10, where the unit of the posterior mean is , and the unit of the mean time to failure is .

[0157] Table 10 Posterior correction parameters of each failure unit

[0158]

[0159] This system adopts series system analysis, and the system failure rate is:

[0160]

[0161] Then the mean time to failure of the system is:

[0162] .

[0163] Those of ordinary skill in the art will realize that the embodiments described herein are for helping readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations without departing from the essence of the present invention according to these technical revelations disclosed by the present invention, and these deformations and combinations are still within the protection scope of the invention.

Claims

1. A method for electronic device reliability prediction based on failure physics and Bayesian fusion, characterized in that: The following steps are involved: S1: Collect the failure physical model parameters of each electronic equipment failure unit and establish the failure physical model through failure mechanism analysis; S2: Calculate the reliability parameters of the failure unit of the electronic equipment based on the failure physical model to obtain the failure physical prediction value; S3: Perform reliability analysis based on the Electronic Equipment Reliability Prediction Manual to obtain the failure rate of failed units of electronic equipment and calculate the mean trouble-free working time of each failed unit; The S3 includes the following sub-steps: S31: Perform reliability analysis based on the Electronic Equipment Reliability Prediction Manual to obtain the failure rate of electronic equipment failure units. The formula is: in, For reliability, is the failure rate, For time, is the failure distribution function, is the failure density function; S32: Based on the failure rate of the failure unit of the electronic equipment, the average trouble-free working time of each failure unit is calculated, and the formula is: in, The mean time between failures. S4: Based on the failure physics prediction value, failure rate and mean time between failures, the Bayesian formula is used to perform system-level reliability analysis, obtain the system failure rate and system mean time between failures, and complete the reliability prediction of electronic equipment based on failure physics Bayesian fusion; The S4 comprises the following sub-steps: S41: taking the failure rate as the mean of the prior information and the failure physical prediction value as the observation data, the prior distribution of each failure unit is calculated; The prior distribution of each failed unit in S41 is: in, is the failure rate, is the prior information of the number of failures, is the prior information of failure time, Gamma is the gamma distribution; S42: Based on the prior distribution and likelihood function of each failed unit, the posterior distribution of each failed unit is calculated, and the posterior parameters are corrected to obtain the posterior corrected parameters, and the posterior mean and the mean failure time are calculated; The likelihood function in S42 is: in, is the likelihood function, is the cumulative running time, is the failure rate; The posterior distribution of each failure unit is: in, is the posterior distribution; The a posteriori correction parameters are: in, and is the a posteriori correction parameter; The posterior mean satisfies: S43: Based on the posterior mean and the mean failure time, obtain the system failure rate and the system mean failure time.

2. The electronic device reliability prediction method based on failure physics and Bayesian fusion according to claim 1 is characterized in that: The S2 includes the following sub-steps: S21: Calculate the failure occurrence time of each failure unit of the electronic device under the failure physical model; S22: Compare the failure occurrence times under various failure physical models, and select the output value of the failure physical model with the shortest failure occurrence time as the failure physical prediction value.

3. The electronic device reliability prediction method based on failure physics and Bayesian fusion according to claim 2 is characterized in that: In S21, the failure occurrence time of each failure unit of the electronic device under the failure physical model is calculated, and the formula is: The Coffin-Manson model is: in, is the number of fatigue cycles, is the shear stress on the solder joint, is the fatigue ductility coefficient, is the fatigue ductility index, is the packaging factor, is the diagonal length, The height of the solder joint support. is the device thermal expansion coefficient, is the thermal expansion coefficient of the substrate, is the device temperature difference, is the substrate temperature difference, is the average cycle temperature, High temperature immersion time for temperature cycle; The TDDB model is: in, is the fault occurrence time under the TDDB model, is a constant, is the dipole or polarizability coefficient in the medium, is the actual electric field strength applied to the dielectric layer, is the activation energy, is the Boltzmann constant, is the absolute temperature; The Corrosion model is: in, is the failure occurrence time under the Corrosion model, is a constant, Relative humidity RH Related corrosion factors, is the activation energy; The EM failure life model is: in, is the failure occurrence time under the EM failure life model, is the proportionality constant, is the applied current density, is the critical current density, is the EM index, is the activation energy; The HCI failure model is: in, is the failure occurrence time under the HCI failure model, is a constant related to the material and device structure, is the peak substrate current, is the current index, is the activation energy.

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