A reliability assessment method considering the initial degradation value of carbon film resistors

Abstract

This invention discloses a reliability assessment method that considers the initial degradation value of carbon film resistors. This method is particularly useful in the field of reliability analysis of carbon film resistors, specifically for calculating the pseudo-failure lifetime of carbon film resistors. The randomness of the initial degradation value is introduced into the traditional degradation trajectory model, and the sum of squared residuals of the sample degradation data is calculated. A selection criterion is established to minimize the sum of squared residuals and determine the optimal degradation trajectory model. The pseudo-failure lifetime of this degradation trajectory model is then calculated, improving the estimation accuracy of subsequent reliability analysis.

Description

Technical Field

[0001] The invention belongs to the field of reliability analysis of carbon film resistors, and in particular aims at calculating the pseudo-failure life of carbon film resistors. Background Art

[0002] The performance degradation process of carbon film resistors is very slow, making it difficult to obtain reliability information using traditional evaluation methods. When product performance degradation is unclear, it is impossible to accurately describe the relationship between life and reliability using a model. In this case, regression analysis in mathematics can be used as the primary analysis method. The degradation trajectory model reflects the relationship between product performance changes over time. Usually, the degradation trajectory of carbon film resistors under different stresses can be described using the same type of curve function. However, due to the randomness of product performance, the degradation curve fluctuates. The uncertainty of the product will cause the relevant parameters of the degradation trajectory curve function to vary. This random fluctuation will affect the preset time to reach the failure threshold, making the life assessment of carbon film resistors uncertain. Summary of the Invention

[0003] The present invention addresses the technical deficiencies in the existing field of reliability assessment of accelerated degradation tests for carbon film resistors. Based on the randomness of test samples and the accuracy requirements of the test scheme, a degradation trajectory model that takes into account random initial values ​​is established, and four degradation trajectory models are optimized to finally calculate the reliability of the carbon film resistor.

[0004] The technical solution of the present invention is a reliability evaluation method considering the initial degradation value of carbon film resistors, which includes the following steps:

[0005] Step 1: Assume that the normal environmental effect of carbon film resistors is temperature stress, and conduct accelerated degradation tests to measure the change in resistance value, i.e., performance degradation data. There are i resistor test samples under each set of accelerated stress levels, and the failure threshold is assumed to be l.

[0006] Step 2: Establish four degradation trajectory models considering random initial values. The specific steps are as follows:

[0007] Step 2.1: Consider the randomness of the initial degradation value of the carbon film resistor and establish the degradation trajectory model based on the degradation data as follows:

[0008] (1) Linear degradation: y i =α i t+β i

[0009] (2) Logarithmic degradation: y i =α i lnt+β i

[0010] (3) Exponential degradation: y i=β i exp(α i t)

[0011] (4) Power law degradation:

[0012] In the formula, y i is the performance degradation index of the carbon film resistor of the product, i is the number of carbon film resistor test samples, t is the test time, α i is the degradation model parameter, β i is the degenerate initial value, and it is assumed to obey the normal distribution β i ~N(μ,σ 2 ); so y i The density functions are expressed as follows:

[0013] (1)

[0014] (2)

[0015] (3)

[0016] (4)

[0017] Among them, σ represents the variance of the degenerate initial value, μ represents the mean of the degenerate initial value;

[0018] Assuming the failure threshold of the resistor is l, when the performance y i When ≥l, it means that the carbon film resistor has failed. The characteristic life T of the carbon film resistor is the time when the degradation process first reaches l, which corresponds to:

[0019] (1)

[0020] (2)

[0021] (3)

[0022] (4)

[0023] The characteristic life T also obeys the normal distribution, so the mean is the average life, which is used as the pseudo failure life value;

[0024] Step 3: Real-time selection of degradation trajectory model;

[0025] Calculate the SSE mean of each sample:

[0026]

[0027] In the above formula: h(t i) represents the true degradation of each test sample at the i-th time point, h0(t i ) means that the degradation trajectory model is fitted to the degradation data to obtain unknown parameters, and then the corresponding h(t i ) The fitting degradation of the detection time;

[0028] The calculated pseudo-failure life and reliability R(t) of the carbon film resistor are:

[0029]

[0030] Where x is the pseudo failure life value;

[0031] Calculate the goodness of fit Q,

[0032] Q=2k-2lnL

[0033]

[0034] Where lnL represents the log-likelihood function, L is the number of stress levels, μ is the drift coefficient, ξ is the diffusion coefficient, and y k is the performance degradation measured at the kth stress level;

[0035] After normalizing SSE, R(t), and Q, they are weightedly added together, and the degradation trajectory model corresponding to the maximum value of the addition result is used as the model for real-time calculation of the reliability of carbon film resistors.

[0036] The beneficial effects of the present invention are as follows: through experimental analysis, degradation data is obtained after a performance degradation test is performed on the carbon film resistor, the randomness of the initial degradation value is introduced into the traditional degradation trajectory model, and the sum of squares of the fitting residuals of the sample degradation data is calculated. A selection criterion is formulated to minimize the sum of squares of the fitting residuals to obtain the optimal degradation trajectory model, and then the pseudo-failure life of the degradation trajectory model is calculated, which improves the estimation accuracy of subsequent reliability analysis and provides new ideas for other high-reliability products with random effects.

[0037] Figures in the specification

[0038] Figure 1 This is a diagram of the pseudo-failure life calculation steps.

[0039] Figure 2 This is a comparison chart of the reliability functions of carbon film resistors. DETAILED DESCRIPTION

[0040] Step 1: Set the normal ambient operating temperature of the carbon film resistor to T0 = 50°C. The test is carried out at temperatures of 80°C, 130°C, and 170°C to measure the change data of the resistance value, i.e., the performance degradation data. There are 9-10 test samples under each group of accelerated stress levels, and it is assumed that the failure threshold of the carbon film resistor is 6%.

[0041] Step 2: Establish four degradation trajectory models considering random initial values. The specific steps are as follows:

[0042] Step 2.1: Consider the linear degradation trajectory model with random initial values:

[0043] y i =α i t+β i

[0044] In the formula, y i is the performance degradation index of the product, i is the number of test samples, t is the test time, α i is the degradation model parameter, β i is the degenerate initial value, assuming it obeys the normal distribution β i ~N(μ,σ 2 ). So y i The density function is expressed as:

[0045]

[0046] Assume that the failure threshold is l, when the performance y i When ≥l, it indicates product failure. The characteristic life of the product, T, is the time when the degradation process first reaches l, which can be expressed as:

[0047]

[0048] It can be seen from the above formula that the characteristic life T also obeys the normal distribution, so the mean is the average life, which is used as the pseudo failure life value. The results are as follows:

[0049] Table 1 Pseudo failure life (PFL) of linear degradation trajectory model

[0050]

[0051] Step 2.3: Consider the logarithmic degradation model with random initial values:

[0052] y i =α i lnt+β i

[0053] In the formula, y i is the performance degradation index of the product, i is the number of test samples, t is the test time, α i is the degradation model parameter, β i is the degenerate initial value, assuming it obeys the normal distribution β i ~N(μ,σ 2 ). So y i The density function is expressed as:

[0054]

[0055] Assume that the failure threshold is l, when the performance y i When ≥l, it indicates product failure. The characteristic life of the product, T, is the time when the degradation process first reaches l, which can be expressed as:

[0056] T=inf{t|y i ≥l}=inf{t|α i lnt+β i ≥l}

[0057]

[0058]

[0059] It can be seen from the above formula that the characteristic life T also obeys the normal distribution, so the mean is the average life, which is used as the pseudo failure life value. The results are as follows:

[0060] Table 2 Pseudo failure life (PFL) of logarithmic degradation trajectory model

[0061]

[0062] Step 2.3: Consider the exponential degradation model with random initial values:

[0063] y i =β i exp(α i t)

[0064] In the formula, y i is the performance degradation index of the product, i is the number of test samples, t is the test time, α i is the degradation model parameter, β i is the degenerate initial value, assuming it obeys the lognormal distribution β i ~LN(μ,σ 2 ). So y i The density function is expressed as:

[0065]

[0066] Assume that the failure threshold is l, when the performance y i When ≥l, it indicates product failure. The characteristic life of the product, T, is the time when the degradation process first reaches l, which can be expressed as:

[0067]

[0068] It can be seen from the above formula that the characteristic life T also obeys the normal distribution, so the mean is the average life, which is used as the pseudo failure life value. The results are as follows:

[0069] Table 3 Pseudo failure life (PFL) of exponential degradation trajectory model

[0070]

[0071] Step 2.4: Consider the power-law degradation model with random initial values:

[0072]

[0073] In the formula, y i is the performance degradation index of the product, i is the number of test samples, t is the test time, α i is the degradation model parameter, β i is the degenerate initial value, assuming it obeys the normal distribution β i ~LN(μ,σ 2 ). So y i The density function is expressed as:

[0074]

[0075] Assume that the failure threshold is l, when the performance y i When ≥l, it indicates product failure. The characteristic life of the product, T, is the time when the degradation process first reaches l, which can be expressed as:

[0076]

[0077]

[0078]

[0079] It can be seen from the above formula that the characteristic life T also obeys the normal distribution, so the mean is the average life, which is used as the pseudo failure life value. The results are as follows:

[0080] Table 4 Pseudo failure life (PFL) of power law degradation trajectory model

[0081]

[0082] Step 3: For the optimization problem of pseudo-failure life in the accelerated degradation test of carbon film resistors, calculate the mean SSE of each sample. The model with the smallest SSE is the optimal model. The variance is used to measure the degree of deviation between the random variable and the mathematical expectation (i.e., the mean). When the mean SSE of the samples is the same, the variance can be used as a reference standard to select the optimal model. As shown in the formula:

[0083]

[0084] In the above formula: h(t i) represents the true degradation of each test sample at the i-th time point; h0(t i ) means that the degradation trajectory model is fitted to the degradation data to obtain unknown parameters, and then the corresponding h(t i ) The fitting degradation amount of the detection time. The calculated pseudo failure life of the carbon film resistor, reliability R(t) is:

[0085]

[0086] Where x is the pseudo failure life value;

[0087] Calculate the goodness of fit Q,

[0088] Q=2k-2lnL

[0089]

[0090] Where lnL represents the log-likelihood function, L is the number of stress levels, μ is the drift coefficient, ξ is the diffusion coefficient, and y k is the performance degradation measured at the kth stress level;

[0091] After normalizing SSE, R(t), and Q, they are weightedly added together, and the degradation trajectory model corresponding to the maximum value of the addition result is used as the model for real-time calculation of the reliability of carbon film resistors.

[0092] Table 5 SSE mean and variance of the power-law degradation trajectory model

[0093]

[0094] The calculation shows that the prediction curve of the pseudo-failure life reliability evaluation results of carbon film resistors based on the traditional linear degradation trajectory model and the pseudo-failure life reliability evaluation results of carbon film resistors considering random initial values ​​are shown in the figure below. It can be seen that as time increases, the reliability decline trend of the improved carbon film resistor is smaller than that of the traditional carbon film resistor.

Claims

1. A reliability assessment method considering the initial degradation value of a carbon film resistor, the method comprising: Step 1: Assume that the normal environmental effect of carbon film resistors is temperature stress, and conduct accelerated degradation tests to measure the change in resistance value, i.e., performance degradation data. There are i resistor test samples under each set of accelerated stress levels, and the failure threshold is assumed to be l. Step 2: Establish four degradation trajectory models considering random initial values. The specific steps are as follows: Step 2.1: Consider the randomness of the initial degradation value of the carbon film resistor and establish the degradation trajectory model based on the degradation data as follows: (1) Linear degradation: y i =α i t+β i (2) Logarithmic degradation: y i =α i ln t+β i (3) Exponential degradation: y i =β i exp(α i t) (4) Power law degradation: In the formula, y i is the performance degradation index of the carbon film resistor of the product, i is the number of carbon film resistor test samples, t is the test time, α i is the degradation model parameter, β i is the degenerate initial value, and it is assumed to obey the normal distribution β i ~N(μ,σ 2 ); so y i The density functions of are expressed as follows: (1) (2) (3) (4) in, σ represents the variance of the degenerate initial value, μ represents the mean of the degenerate initial value; Assuming the failure threshold of the resistor is l, when the performance y i When ≥l, it means that the carbon film resistor has failed. The characteristic life T of the carbon film resistor is the time when the degradation process first reaches l, which corresponds to: (1) (2) (3) (4) The characteristic life T also obeys the normal distribution, so the mean is the average life, which is used as the pseudo failure life value; Step 3: Real-time selection of degradation trajectory model; Calculate the SSE mean of each sample: In the above formula: h(t i ) represents the true degradation of each test sample at the i-th time point, h0(t i ) means that the degradation trajectory model is fitted to the degradation data to obtain unknown parameters, and then the corresponding h(t i ) The fitting degradation of the detection time; The calculated pseudo-failure life and reliability R(t) of the carbon film resistor are: Where x is the pseudo failure life value; Calculate the goodness of fit Q, Q=2k-2ln L Where ln L represents the log-likelihood function, L is the number of stress levels, μ is the drift coefficient, ξ is the diffusion coefficient, and y k is the performance degradation measured at the kth stress level; After normalizing SSE, R(t), and Q, they are weightedly added together, and the degradation trajectory model corresponding to the maximum value of the addition result is used as the model for real-time calculation of the reliability of carbon film resistors.

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