CN114266006B - A method for evaluating measurement uncertainty in accelerated degradation tests - Google Patents
A method for evaluating measurement uncertainty in accelerated degradation tests Download PDFInfo
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Abstract
本发明涉及一种加速退化试验不确定性评价方法，基于现有加速退化模型，以及模型参数的估计过程，得到加速退化模型参数的测量不确定度、可靠度的测量不确定度，用于综合评价加速退化试验的整体测量不确定度，包括：步骤一：加速退化试验性能参数的测量不确定的评价，包括重复测量过程中的A类不确定度以及机器精度影响的B类不确定度；步骤二：加速退化模型参数的测量不确定度评定；步骤三：加速退化试验可靠度的测量不确定度评定；基于所述加速退化模型参数的估计结果的测量不确定度，以及正常应力下试验的可靠度R(t)估计结果；得到加速退化试验可靠度估计结果的测量不确定度uc(R(t))。本发明能够对加速退化试验的测量不确定度进行综合评价，更精准。
The present invention relates to an accelerated degradation test uncertainty evaluation method. Based on an existing accelerated degradation model and an estimation process of model parameters, the measurement uncertainty of the accelerated degradation model parameters and the measurement uncertainty of the reliability are obtained, which is used to comprehensively evaluate the overall measurement uncertainty of the accelerated degradation test, including: step one: evaluation of the measurement uncertainty of the performance parameters of the accelerated degradation test, including the Class A uncertainty in the repeated measurement process and the Class B uncertainty affected by the machine precision; step two: evaluation of the measurement uncertainty of the accelerated degradation model parameters; step three: evaluation of the measurement uncertainty of the reliability of the accelerated degradation test; based on the measurement uncertainty of the estimation result of the accelerated degradation model parameters and the reliability R(t) estimation result of the test under normal stress; the measurement uncertainty u c (R(t)) of the reliability estimation result of the accelerated degradation test is obtained. The present invention can comprehensively evaluate the measurement uncertainty of the accelerated degradation test, which is more accurate.
Description
Technical Field
The invention belongs to the technical field of reliability analysis, and particularly relates to uncertainty evaluation of an accelerated degradation test.
Background
The uncertainty of the accelerated degradation test (ACCELERATING DEGRADATION TESTING, ADT) comes from three aspects: uncertainty of measurement in measurement and uncertainty of random change of state of the product along with time; uncertainty introduced by manufacturing errors, assembly errors and the like of products in the production and manufacturing processes; cognitive uncertainty for the accelerated degradation model. For uncertainty in the production and manufacturing process, the accelerated degradation test cannot be evaluated and reduced; for the cognitive uncertainty, the control can be performed through the optimal design of an accelerated degradation test; for measurement uncertainty, control can be performed by selecting a measuring instrument with higher precision.
The measurement uncertainty has important reference significance on the accuracy of the accelerated degradation test, is particularly important to the research of the product performance index, but has less related research on how to comprehensively evaluate the measurement uncertainty of the accelerated degradation test. The invention provides a comprehensive evaluation method for measuring uncertainty of an accelerated degradation test aiming at the gap.
Disclosure of Invention
The technical problems to be solved are as follows:
in view of the technical blank in the prior art, the comprehensive evaluation method of the measurement uncertainty of the accelerated degradation test is finally obtained based on the evaluation method given by the measurement uncertainty expression guide (Guide to the expression of Uncertainty in Measurement, GUM for short) in combination with the measurement of the performance parameters in the accelerated degradation test, the construction of the accelerated degradation test model and the influence caused by the propagation of the measurement uncertainty in the estimation process of the target structure such as the model parameters, the reliability and the like.
The technical scheme adopted is as follows:
The method is characterized in that based on a known accelerated degradation model and an estimation process of model parameters, the measurement uncertainty of measurement quantity of performance parameters of the accelerated degradation test, the measurement uncertainty of the parameters of the accelerated degradation model and the measurement uncertainty of reliability of the accelerated degradation test are calculated by combining the estimation process of the measurement uncertainty, and the comprehensive evaluation of the measurement uncertainty of the accelerated degradation test is realized, and specifically comprises the following steps:
step one: evaluation of measurement uncertainty of the performance parameters directly measured by the accelerated degradation test:
(1) Calculation of class a uncertainty u A: the measurement value of the performance parameter Y, which satisfies the repetitive measurement condition, is recorded as Y i;, n is a natural number, i=1,..n, and the performance value obtained by repeatedly measuring the measurement value Y can be used for evaluating class A, and the calculation method comprises Bessel formula method, range method and maximum error method;
(2) Calculation of class B uncertainty u B: class B uncertainty refers to a measure uncertainty assessment using a different method than the class a uncertainty calculation method; the sources of the calibration certificate comprise the magnitude issued by an authority, the magnitude of a certified standard substance, a calibration certificate, the measurement precision of a measuring instrument and the accuracy grade of the verified measuring instrument;
(3) The measurement certainty u (Y i) of the performance parameter measurement quantity Y is obtained as follows:
In the accelerated degradation test, the performance parameter measurement quantity is known information, and measurement uncertainty of the performance parameter measurement quantity can be obtained according to the formula;
step two: the measurement uncertainty of the accelerated degradation model parameters is assessed;
Assuming that the accelerated degradation model parameters are θ= { a, E a, C, σ }, wherein the model parameters A, E a, C are constants, σ is a diffusion coefficient, and each parameter is calculated by a known model parameter estimation process in the modeling process; obtaining measurement uncertainty u (A), u (E a), u (C) and u (sigma) of each model parameter based on the estimation process of the model parameters A, E a, C and sigma, and then calculating measurement uncertainty u (mu 0) of the degradation rate mu 0 of the accelerated degradation model under the normal stress level according to the relationship between the degradation rate mu 0 of the accelerated degradation model under the normal stress level and the model parameters;
Step three: the measurement uncertainty assessment of the reliability of the accelerated degradation test;
An estimation process based on the accelerated degradation model parameters, and a reliability R (t) estimation process of the accelerated degradation test at normal stress levels; and obtaining a measurement uncertainty u c (R (t)) of the reliability of the accelerated degradation test, wherein R (t) is the reliability of the accelerated degradation test under normal stress level and is a function of time t.
In step one, calculating the class a uncertainty of the measurement data using a bessel formula, the class a uncertainty of the measurement quantity Y being obtained as follows:
Where u A(yi) is the standard uncertainty of the single measurement, Is the standard uncertainty of the average of n measurements,Is the mean of n duplicate measurements.
In step one, the class B uncertainty u B is calculated from the measurement accuracy known to the measuring instrument, specifically by: obtaining a possible value interval half width a B of the measured value, selecting a proper factor k B, and finally calculating the class B uncertainty of the measured value as follows:
In the second or third step, if the estimation process of a target amount is calculated by a plurality of correlation amounts, it is necessary to calculate the resultant measurement uncertainty u c of the target amount based on the measurement uncertainties of the plurality of correlation amounts; assuming that a relation between the target amount f and n correlation amounts x i is f=f (x 1,x2,...,xn); the general formula for the resultant measurement uncertainty u c for the target quantity f is:
Where ρ ij denotes the correlation coefficient between the measurement uncertainties u (x i) and u (x j) of different correlation quantities, typically a value between 0 and 1, The transmission coefficient of the measurement uncertainty u (x i) is represented, where n is a natural number equal to or greater than 2, i, j=1.
In the second step, when the accelerated degradation model is a Peck model, a binary linear regression uncertainty assessment method may be used to calculate the estimation process of each parameter, and a calculation formula of the synthesized measurement uncertainty is combined to finally obtain the values of the measurement uncertainties u (a), u (E a), u (C) of the parameters A, E a, C.
In the second step, the accelerated degradation model is selected as a Peck model, at this time, the degradation rate of the Peck model is μ 0＝exp(A-Ea/k0T0+C ln(H0)),Ea as the activation energy, H 0 is the relative humidity value of the normal humidity level, the unit is% RH, T 0 is the kelvin temperature of the normal temperature level, the unit is K, K 0 is the boltzmann constant, assuming that the parameters of the accelerated degradation model are strongly correlated, the correlation coefficient between every two parameters is 1, and the uncertainty of the degradation rate μ 0 of the accelerated degradation model under normal stress can be obtained by the formula (11) of the degradation rate of the accelerated degradation model and the calculation formula (5) of the uncertainty of the composite measurement:
In the third step, the reliability (R (t) is calculated by the diffusion coefficient estimation process with the degradation rate μ 0 and σ, and the uncertainty of the reliability is a synthesized measurement uncertainty, specifically:
The normal stress level is preferably the case when the normal humidity level H 0 is 50% rh and the normal temperature level T 0 is 298.15K.
The invention has the beneficial effects that:
1. the measurement uncertainty of the accelerated degradation test is comprehensively evaluated, the obtained measurement uncertainty is closer to the real situation, the reliability of the test can be known more accurately, and the performance of each parameter of the product can be analyzed more accurately.
2. The existing measurement uncertainty evaluation method is applied to different models of the accelerated degradation test, the propagation of measurement uncertainty is combined with the estimation process of model parameters, the synthesized measurement uncertainty evaluation result is calculated, the measurement uncertainty of the final test reliability can be evaluated more accurately, and the comprehensive and comprehensive measurement uncertainty evaluation result of the accelerated degradation test is obtained.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a simplified illustration of the method steps for evaluating the uncertainty of accelerated degradation usage of the present invention;
FIG. 2 (a) is an observation under group 1 stress levels of the present invention;
FIG. 2 (b) is an observation under group 2 stress levels of the present invention;
FIG. 2 (c) is an observation of the invention at group 3 stress levels;
FIG. 2 (d) is the observation data for group 4 stress levels of the present invention;
FIG. 3 is a graph of the reliability estimation results and the upper and lower limits of the corresponding uncertainty intervals of the accelerated degradation test of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
The assessment method given by the measurement uncertainty expression guide (Guide to the expression of Uncertainty in Measurement, abbreviated as GUM) is the most commonly used method for assessing measurement uncertainty, and is also a universal measurement uncertainty assessment standard in the world. The basic principle of this method is to use uncertainty propagation law to obtain measured estimation value, so as to evaluate measurement uncertainty. The standard of the method in China is JJF1059-2012 measurement uncertainty assessment and representation. The invention is based on the assessment method given by the measurement uncertainty expression guide (Guide to the expression of Uncertainty in Measurement, GUM for short), combines the modeling and parameter estimation process of the accelerated degradation test, takes the accelerated degradation test of a certain electronic product as a case, selects the index of measurement uncertainty, and evaluates the measurement uncertainty of the accelerated degradation test. The accelerated degradation model and the model parameter estimation process are both the prior art, and the improvement is to evaluate how to evaluate the measurement uncertainty of each parameter involved in the accelerated degradation test, so as to obtain the integral and comprehensive evaluation of the measurement uncertainty of the accelerated degradation test of the product.
For a specific accelerated degradation test, first, the uncertainty of the measured value of the performance parameter of the accelerated degradation test is determined, and assuming that the direct measured value Y in the performance parameter of the test, the i-th measured value in n repeated measurements that satisfy the condition of the repeated measurement is denoted as Y i. The performance values from repeated measurements may be used for class a assessment. And by using the related information, such as the measurement precision of a given measuring instrument, etc., the class B evaluation result of the measured quantity can be given. And combining the two assessment methods to finally obtain an uncertainty assessment result of the direct measurement quantity. The method comprises the following steps:
(1) Calculation method for uncertainty of class A measurement
Common class A assessment methods of standard uncertainty include Bessel formula method, extremely bad method, maximum error method and the like. Here we choose the bessel formula to calculate the class a uncertainty of the measurement data. For n repeated measurements meeting the repeatability measurement condition, the Bessel formula is as follows:
Where u A(yi) is the standard uncertainty of the single measurement, Is the standard uncertainty of the average of n measurements,Is the mean of n duplicate measurements. Obviously,As a measurement result more reliable than any single measurement result.
(2) Method for calculating class B uncertainty
Class B uncertainty refers to a measurement uncertainty assessment using a calculation method other than the class a uncertainty calculation method, and any uncertainty calculated by a calculation method other than class a uncertainty for evaluating measurement uncertainty may be classified as class B uncertainty; according to the relevant records in the standard JF1059-2012 measurement uncertainty assessment and representation, the source of class B uncertainty has the magnitude issued by an authority; the amount of the certified standard; calibrating the certificate; the measurement accuracy of the instrument; a level of accuracy of the verified measuring instrument; limit values deduced from personnel experience, etc. Through the information given above, the half width a B of the possible value interval of the measured value can be obtained, and then a proper factor k B is selected, so that the finally obtained measured class B uncertainty is:
When the extension uncertainty is known to be a multiple of the synthesis standard uncertainty, the multiple is k B. During normal distribution, k B is obtained by looking up table 1 according to the required probability.
TABLE 1 probability p versus k B for normal distribution
| p | 0.50 | 0.68 | 0.90 | 0.95 | 0.9545 | 0.99 | 0.9973 |
| kB | 0.675 | 1 | 1.645 | 1.96 | 2 | 2.576 | 3 |
For accelerated degradation test performance parameters, a B is mainly affected by the measuring instrument. A B can be obtained according to the instrument precision given by the manufacturer. Let p be 0.95 assuming that the distribution of uncertainty of the performance parameter measurement is a normal distribution. Finally, the evaluation result of the class B uncertainty is:
Finally, the evaluation result of the measurement uncertainty u (Y i) of the performance parameter measurement value Y is:
For accelerated degradation testing, the known information is a measurement of a performance parameter. The measurement uncertainty u (y i) corresponding to the measurement result can be obtained by using the above process.
Based on this, further, from the previous analysis, it is necessary to determine the resultant measurement uncertainty of the parameters and reliability involved in the accelerated degradation model.
The calculation method of the estimation process is the existing method and formula, and the estimation process is the propagation of measurement uncertainty which can cause the measurement value, and finally the measurement uncertainty can influence the target structure such as reliability. Thus, an assessment of the effect of measuring uncertainty on reliability under normal stress is obtained by synthesis of uncertainty.
That is, if the estimation process of one target amount is calculated by a plurality of correlation amounts, it is necessary to calculate the resultant measurement uncertainty u c of the target amount based on the measurement uncertainties of the plurality of correlation amounts; assuming that a relation between the target amount f and n correlation amounts x i is f=f (x 1,x2,...,xn); the general formula for the target amount of resultant measurement uncertainty u c is:
Where ρ ij denotes the correlation coefficient between the measurement uncertainties u (x i) and u (x j) of different correlation quantities, typically a value between 0 and 1, A transmission coefficient representing measurement uncertainty u (x i), where n is a natural number equal to or greater than 2, i, j=1,..;
Order the Formula (5) can be simplified as:
Obviously, when calculating the uncertainty of the synthesis standard, the correlation coefficient ρ ij between the input quantities must be obtained first. If it cannot be clearly assumed that the components are completely uncorrelated, a conservative estimate is to assume ρ ij =1, i.e. it is considered to have a strong correlation. A greater uncertainty of the synthesis criteria is obtained at this time.
When ρ ij =1, formula (6) can be expressed asWhen ρ ij =0, formula (6) can be expressed as If there are q uncertainty components with strong correlation and p uncertainty components with no correlation in the model, the synthesis standard uncertainty is calculated as follows:
Therefore, the uncertainty synthesis can be performed according to the parameter estimation process of the accelerated degradation model in the accelerated degradation test, the propagation of the uncertainty in the parameter estimation process is researched, and the influence of the uncertainty on the reliability estimation result is evaluated.
For accelerated degradation test data, to evaluate the reliability of the data, the most critical point is to determine an accelerated degradation model of a product. How to build the most appropriate degradation model to fit the degradation data is the most fundamental problem faced by accelerated degradation testing techniques. The current degradation model mainly adopts a mathematical model to describe a performance degradation track, and the most mainstream performance degradation models are degradation track models and can be mainly divided into two main categories: one class is a generalized trajectory model and the other class is a stochastic process model. Typical stochastic processes commonly used for degradation modeling are: wiener process, gamma process, inverse gaussian process, etc. The present invention is discussed with respect to existing wiener processes.
The Wiener process is an important independent incremental process, often referred to as brownian motion. For most products, the incremental degradation over an infinitesimal time interval can be seen as a superposition of a large number of tiny external variables. These degradation increments approximately follow a normal distribution according to the central limit theorem. The external variables are typically independent, as are the resulting degradation increments (over disjoint time intervals). The normal distribution of the delta provides many good properties for the Wiener process. Model { Y (t); t.gtoreq.0 } is generally expressed as:
Y(t)＝μΛ(t)+σB(Λ(t)) (8)
Wherein μ is a drift parameter reflecting the rate of product degradation; σ is the diffusion coefficient and B () is the standard brownian motion. Λ (t) =t r is a time transfer function representing the nonlinear case of the degradation trajectory. The present invention employs the linear assumption, i.e. r=1. Y (t) is typically used to represent system performance degradation, and sometimes also post-conversion system degradation.
The Wiener process satisfies the following properties:
(i) The degradation increment obeys a normal distribution, namely, deltay (t) =y (t+deltat) -Y (t) to N (mu deltat, sigma 2 deltat);
(ii) For any two time intervals without intersections [ t 1,t2],[t3,t4 ], it is assumed that t 1＜t2≤t3＜t4, the degradation increment of the random variable Y (t 4)-Y(t3) and Y (t 2)-Y(t1) are independent of each other;
(iii) Initial value Y (0) =0 and Y (t) continues at t=0.
For the linear Wiener process model, if the failure threshold is known to be a (a > 0), then the lifetime L of the product is generally expressed as the time the cumulative distribution function first reaches the failure threshold, i.e
L＝inf{t|Y(t)＝D1，t≥0} (9)
The probability density function of the wiener process Y (t) first crossing the boundary a is:
The distribution of probability density functions having a form like (10) is commonly referred to as an inverse gaussian distribution. Thus, it can be determined that the pseudo-lifetime distribution of the degradation trajectory model established using the wiener process is an inverse gaussian distribution.
Accelerated degradation analysis of the product under study is based on temperature and humidity combined stress development. For this stress combination, an existing model Peck model may be employed as the accelerated degradation model for the accelerated degradation test of the product. The drift coefficient μ in the wiener process degradation model can be expressed as:
μ＝A′HC exp[-Ea/k0T]＝exp(A+B/T+C ln(H)) (11)
Wherein E a is activation energy; t is absolute temperature; h is relative humidity (unit:% RH), and k 0 is Boltzmann constant; a', A, E a, C are constants.
Based on the above process, an accelerated degradation model based on the wiener process can be constructed. The parameters of the model can be identified by a least square method, a maximum likelihood estimation method and the like. On the basis, given failure threshold value a of parameter drift of the product under study, the reliability function of the product under study under normal use conditions can be extrapolated:
Where Φ (·) represents the cumulative probability distribution function of the standard normal distribution, μ 0 is the degradation rate at normal stress levels.
N samples were randomly divided into k groups and a constant stress acceleration degradation test of k stress levels was performed. S 0 is the normal stress level and S 1＜S2＜...＜Sk is the acceleration stress level. At the acceleration stress level S l, n l samples were taken, i.e
The test was terminated after each sample had been tested for performance m l times, so the test was a "constant" truncated accelerated degradation test. Co-detection in the test m times, i.e
The time for monitoring the product performance at the same time is t lij(l＝1,...,k;i＝1,...,nl;j＝1,...,ml each time), then in the test timeIn the interior, the monitoring time is in turn
The monitored performance value is noted as y lij. The maximum likelihood function of ADT at this time is
Assuming Δy lij＝yli(j+1)-ylij, the monitoring time interval is Δt lij＝tli(j+1)-tlij, and the accelerated degradation model is substituted, the log likelihood function of the above equation is
In general, the bias of equation (16) results in maximum likelihood estimates for each parameter. However, when the parameters a, E a and C to be estimated are biased and made zero, only one equation can be obtained:
From equation (17), it is difficult to determine the unknown parameters A, E a and C by an equation. Since the performance data monitored in the test and the corresponding monitoring times constitute a data pair (t lij,ylij),l＝1,...,K;i＝1,...,nl, j=1., M, the product performance degradation process at the first stress level can be fitted by a least squares method, regression was performed according to the regression equation with Y (t) =μt+y 0, and the performance degradation rates μ l, l=1, k at k accelerating stress levels were obtained.
When obtaining least square estimation of performance degradation rateThen, according to the accelerated degradation model lnμ=A-E a/k0 T+ C lnH, the estimated values/>, of the parameters A, E a and C can be obtained by fitting analysis under the least square criterion on the two-dimensional plane formed by the stress level (T l,Hl) and the performance degradation rate μ l
Performing bias derivation on the parameter sigma in the (16) to obtain
Order theObtaining the product
At this time, the maximum likelihood estimation value of σ is written as formula (20):
Will be AndSubstituting (12) can predict the life and reliability of the product at normal stress level S 0.
Through the analysis, in the process of estimating the reliability of the accelerated degradation test of the product, the class B uncertainty u B of the test mainly comes from the aspect of measuring instruments used in the accelerated degradation test, and can be obtained by calculating the measurement accuracy of the measuring instruments given by manufacturers, and the class A uncertainty u A is reflected in the repeated measurement process of the measurement quantity. The uncertainty u (θ) of the model parameters θ= { a, E a, C, σ } needs to be synthesized by combining the uncertainty u of the measurement quantity with the process of parameter estimation. And finally, obtaining u c (R (f)) of the synthesized uncertainty of the reliability as an evaluation result according to the parameter estimation process of the accelerated degradation model and the propagation of the measurement uncertainty in the reliability calculation process.
The accelerated degradation model in the test was the Peck model, i.e., μ=exp (a-E a/k0 t+cln (H)), and the following uncertainty evaluation method using the existing binary linear regression (reference: uncertainty evaluation method of binary linear regression [ J ]. Instructions of construction science and technology university (Nature science edition), 2000 (03): 304-306. Feng Xiaojuan), and uncertainty synthesis calculation formula adopted in each parameter estimation process and the invention, and uncertainty calculation of each parameter.
Logarithm of the above formula gives lnμ=a-E a/k0 t+ C lnH. After setting p groups of stress levels and obtaining u A (mu) under different stress levels, the corresponding u A (ln (mu)) can be obtained by taking the logarithm. Let z=μ, a 0＝A,a1＝Ea,a2＝C,x1＝-1/k0T,x2 =ln (H), then for the binary linear regression equation: z=a 0+a1x1+a2x2, the estimated value of the coefficient a 0、a1、a2 is:
Wherein,
The deviation value of z i from the regression result z for the argument (x 1,x2) is:
Zi＝zi-z＝zi-a0-a1x1i-a2x2i (22)
the variance S 2 of z i can be expressed as:
Wherein p-3 is the degree of freedom.
The uncertainty of the independent variable x 1,x2 is u x1,ux2, and then the measured uncertainty u z of z can be obtained by combining the variance of the uncertainty with the uncertainty component of the independent variable through a synthetic uncertainty calculation formula:
To simplify the calculation, the independent variable x 1,x2 may be a value obtained by converting the set temperature and humidity value, i.e., u x1,ux2 is 0.
Based on a binary linear regression equation in combination with a synthetic calculation formula that measures uncertainty, uncertainty u a0、ua1、ua2 may be calculated by:
According to the calculation results, estimation results u (A), u (E a) and u (C) of uncertainty of the accelerated degradation model parameters can be obtained. And (3) taking in normal stress level values in the Peck model, and taking in u (A), u (E a) and u (C) to obtain the synthetic uncertainty u (mu 0) of the degradation rate under the normal stress level.
Assuming that the parameters of the accelerated degradation model are strongly correlated, the correlation coefficient between every two parameters is 1. From the formula (11) of the accelerated degradation model and the synthetic calculation formula (5) for measuring uncertainty, the uncertainty of the degradation rate of the accelerated degradation model under normal stress can be obtained as follows:
Wherein μ 0＝exp(A-Ea/k0T0+C ln(H0)),H0 is the normal humidity level in% RH, T 0 is the normal temperature level in K.
Equation (20) is an estimation process of the parameter σ, and since the condition of the repeatability measurement is satisfied, it can be considered that the measurement uncertainty of the measurement values are independent of each other, and the correlation coefficient is 0. According to the synthesis formula (5) of uncertainty, the uncertainty of the obtainable parameter σ is:
Considering the above uncertainties as independent of each other, the resulting uncertainty u c (R (t)) of the model is:
wherein the reliability R (t) is the reliability of the accelerated degradation test at normal stress level, is a function of time t, and is obtained by the formula (12).
Example 1
The effectiveness of the proposed measurement uncertainty assessment method is discussed by adopting a certain electronic product accelerated degradation test case
In the test, three samples are set at each group of stress level for the accelerated degradation test, and twelve samples are used. At the same time point, three repeated measurements of the performance parameter values were respectively performed for each sample, and recorded, and finally, the obtained degradation data are shown in fig. 1.
Step one: calculation of measurement uncertainty
Calculation of class A uncertainty
The uncertainty of class a of the measured values calculated using the above bezier formula is shown in table 2:
TABLE 2D value class A uncertainty calculation
Calculation of class B uncertainty
In the test, the performance parameters of the sample are measured and read by a ZL5 intelligent LCR measuring instrument of Nanjing Su detection instrument equipment Co., ltd. The measurement accuracy of the instrument is calibrated to be 0.05%, and according to the calculation method, the confidence coefficient is selected to be 95% under the assumption of normal distribution, and the confidence factor k B corresponding to the class B uncertainty is 2.
Thus, the experimentally measured class B uncertainty is
Step two: measurement uncertainty assessment of accelerated degradation model parameters
Using equation (11), uncertainty u (μ k) of accelerated degradation model μ k at 4 stress levels can be calculated, respectively:
TABLE 3 accelerated degradation model uncertainty calculation results
According to (21) to (27), uncertainty u (μ 0) of degradation rate μ 0 and uncertainty u (σ) of degradation model parameter σ of accelerated degradation model under normal stress (this test was selected at normal temperature level 25 ℃ and normal humidity level 50% RH) at normal stress level were finally obtained, as shown in Table 4
TABLE 4 estimation results of the uncertainty of the accelerated degradation model parameters
| u(μ0) | u(σ) |
| 7.416×10-4 | 0.1367 |
Step three: uncertainty assessment of accelerated degradation test reliability
By substituting the above results into the equation (28), the measurement uncertainty u c (R (t)) of the reliability estimation result of the accelerated degradation test at each time t can be obtained, corresponding to the upper and lower limits of the uncertainty section in which the reliability estimation result can be obtained. The upper limit is R U, the lower limit is R L, and the following are included:
RU＝R(t)+uc(R(t));RL＝R(t)-uc(R(t)) (30)
Meanwhile, the uncertainty evaluation results obtained finally are shown in the interval [0,1] of the R U and the confidence lower limit R L.
The above-described embodiments are merely preferred embodiments of the present invention, and are not intended to limit the present invention in any way. Any person skilled in the art, using the disclosure above, may make many more possible variations and modifications of the technical solution of the present invention, or make many more modifications of the equivalent embodiments of the present invention without departing from the scope of the technical solution of the present invention. Therefore, the equivalent changes according to the inventive concept should be covered in the protection scope of the present invention without departing from the technical scheme of the present invention.
Claims (4)
1. The method is characterized in that based on a known accelerated degradation model and an estimation process of model parameters, the measurement uncertainty of measurement quantity of performance parameters of the accelerated degradation test, the measurement uncertainty of the parameters of the accelerated degradation model and the measurement uncertainty of reliability of the accelerated degradation test are calculated by combining the estimation process of the measurement uncertainty, and the comprehensive evaluation of the measurement uncertainty of the accelerated degradation test is realized, and specifically comprises the following steps:
step one: evaluation of measurement uncertainty of the performance parameters directly measured by the accelerated degradation test:
(1) Calculation of class a uncertainty u A: the i-th measured value in n repeated measurements meeting the repeated measurement condition is recorded as Y i, n is a natural number, i=1, … and n, the performance value obtained by repeatedly measuring the measured value Y can be used for evaluating class A, and the calculation method comprises a Bessel formula method, a range method and a maximum error method;
(2) Calculation of class B uncertainty u B: class B uncertainty refers to a measure uncertainty assessment using a different method than the class a uncertainty calculation method; the sources of the calibration certificate comprise the magnitude issued by an authority, the magnitude of a certified standard substance, a calibration certificate, the measurement precision of a measuring instrument and the accuracy grade of the verified measuring instrument;
(3) The measurement certainty u (Y i) of the performance parameter measurement quantity Y is obtained as follows:
In the accelerated degradation test, the performance parameter measurement quantity is known information, and measurement uncertainty of the performance parameter measurement quantity can be obtained according to the formula;
step two: the measurement uncertainty of the accelerated degradation model parameters is assessed;
Assuming that the accelerated degradation model parameters are θ= { a, E a, C, σ }, wherein the model parameters A, E a, C are constants, σ is a diffusion coefficient, and each parameter is calculated by a known model parameter estimation process in the modeling process; obtaining measurement uncertainty u (A), u (E a), u (C) and u (sigma) of each model parameter based on the estimation process of the model parameters A, E a, C and sigma, and then calculating measurement uncertainty u (mu 0) of the degradation rate mu 0 of the accelerated degradation model under the normal stress level according to the relationship between the degradation rate mu 0 of the accelerated degradation model under the normal stress level and the model parameters;
Step three: the measurement uncertainty assessment of the reliability of the accelerated degradation test;
An estimation process based on the accelerated degradation model parameters, and a reliability R (t) estimation process of the accelerated degradation test at normal stress levels; obtaining a measurement uncertainty u c (R (t)) of the reliability of the accelerated degradation test, wherein R (t) is the reliability of the accelerated degradation test at a normal stress level and is a function of time t;
In the second or third step, if the estimation process of a target amount is calculated by a plurality of correlation amounts, it is necessary to calculate the resultant measurement uncertainty u c of the target amount based on the measurement uncertainties of the plurality of correlation amounts; assuming that a relation between the target amount f and n correlation amounts x i is f=f (x 1,x2,…,xn); the formula for the combined measurement uncertainty u c for the target quantity f is:
Wherein ρ ij represents the correlation coefficient between the measurement uncertainties u (x i) and u (x j) of different correlation amounts, which is a value between 0 and 1, A transfer coefficient representing measurement uncertainty u (x i), where n is a natural number equal to or greater than 2, i, j=1, …, n, j is a natural number different from i;
In the second step, when the accelerated degradation model is a Peck model, calculating an estimation process of each parameter by adopting a binary linear regression uncertainty evaluation method, and combining a calculation formula of the synthesized measurement uncertainty to finally obtain values of measurement uncertainties u (a), u (E a) and u (C) of the parameters A, E a and C;
In the second step, the accelerated degradation model is selected as a Peck model, at this time, the degradation rate of the Peck model is μ 0＝exp(A-Ea/k0T0+C ln(H0)),Ea as the activation energy, H 0 is the relative humidity value of the normal humidity level, the unit is% RH, T 0 is the kelvin temperature of the normal temperature level, the unit is K, K 0 is the boltzmann constant, assuming that the parameters of the accelerated degradation model are strongly correlated, the correlation coefficient between every two parameters is 1, and the uncertainty of the degradation rate μ 0 of the accelerated degradation model under normal stress is obtained by the formula of the degradation rate of the accelerated degradation model and the calculation formula of the uncertainty of the composite measurement:
in the third step, the reliability R (t) is calculated by the process of estimating the degradation rate μ 0 and the diffusion coefficient σ, and the uncertainty of the reliability is a synthesized measurement uncertainty, specifically:
2. the method for evaluating measurement uncertainty in an accelerated degradation test of claim 1 wherein in step one, said class a uncertainty of measurement data is calculated using a bessel formula to obtain said class a uncertainty of measurement quantity Y as follows:
Where u A(yi) is the standard uncertainty of the single measurement, Is the standard uncertainty of the average of n measurements,Is the mean of n duplicate measurements.
3. The method for evaluating measurement uncertainty of accelerated degradation testing of claim 1, wherein in step one, class B uncertainty u B is calculated from the measurement accuracy known to the measuring instrument, specifically by: obtaining a possible value interval half width a B of the measured value, selecting a proper factor k B, and finally calculating the class B uncertainty of the measured value as follows:
4. The method of claim 1, wherein the normal stress level is selected to be at a normal humidity level H 0 of 50% rh and a normal temperature level T 0 of 298.15K.
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