CN110826234A - Simulation-based multi-stress accelerated life test scheme optimization method - Google Patents
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Abstract
The invention discloses a simulation-based multi-stress accelerated life test scheme optimization method, which is characterized in that a Monte-Carlo simulation method is utilized to carry out test scheme optimization design under a test constraint condition, and reasonable sample grouping, stress conditions and test truncation time are determined, so that the purpose of optimizing a test scheme is achieved, reliability verification test and evaluation can be completed under the limits of sample amount, test time and test expenditure, test time and test samples can be saved, and the method has great economic benefit.
Description
Technical Field
The invention belongs to the technical field of reliability, and particularly relates to a simulation-based multi-stress accelerated life test scheme optimization method.
Background
For the reliability problem of military products, a test data evaluation and analysis method is often adopted to evaluate the reliability level of the military products. At present, the reliability evaluation of military products is mainly realized by adopting a single stress accelerated life test, but the key factors of failure of long-life space electronic products are usually multiple due to the complex environmental stress experienced by the whole life cycle of the space electronic products, so the single stress accelerated life test is difficult to meet the requirements of the life and reliability index verification of the space electronic products; secondly, under certain conditions, the acceleration test time of the long-life aerospace electronic product is still relatively long, and the timeliness is poor; finally, the accelerated life test design method in the prior art can only design accelerated life test time, but cannot combine various test influence factors (such as test time, test cost, life and reliability indexes, test stress level, product performance threshold value and the like) together for consideration, so that the test condition is single, and the accuracy of the test result is low.
Disclosure of Invention
In view of this, the invention provides a simulation-based multi-stress accelerated life test scheme optimization method, which can realize selection of an optimal test scheme of a product to be tested by calculating optimization targets of each test scheme under the condition that test stress and test intervals in the test scheme are set.
The invention provides a simulation-based multi-stress accelerated life test scheme optimization method, which specifically comprises the following steps:
step 1, selecting a plurality of products to be tested as test samples in a test scheme I, wherein the reliability of the products to be tested obeys weber distribution, and the performance to be tested of the products to be tested is monotonically degraded along with the test time, I is a positive integer and is less than or equal to I, and I is the total number of the test schemes;
calculating to obtain an acceleration factor AF according to the initial test temperature and the initial test voltage, and calculating to obtain a reliability lower limit R according to the AFLCalculating the confidence coefficient gamma to obtain the minimum test time tminThen from tminAnd tu_iCalculating to obtain the minimum value l of the test timesmin；
Let the current test number be k, k ═ lminThe current test temperature is the initial test temperature; the current test voltage is an initial test voltage;
step 2, traversing all the test samples to obtain the degradation amount of the performance to be tested of each test sample, and taking the number of the test samples of which the degradation amount is larger than the set maximum degradation amount as failure times;
step 3, adopting the failure times, the current test times k and the set test interval tu_iAnd calculating the lower limit R of the reliability of the product to be tested under the current stress conditioni_k；
Ri_kIf the reliability is greater than or equal to the set lower limit of the reliability and the test expense of the product to be tested under the current stress condition is less than or equal to the set budget, recording the current test as an effective test; otherwise, not recording;
step 4, enabling k to be self-added by 1, changing the current test temperature and the current test voltage for multiple times, and executing step 2 to obtain multiple effective tests;
step 5, calculating the lower limit R of the reliability for all effective testsi_kMean square error value MSE ofiAnd testing the expenses TCi_kAverage value TC for the current test number kiAccording to said MSEiAnd TCiCalculating to obtain an optimization target U of the test scheme ii；
Step 6, executing all the test schemes to obtain an optimization target U of each test schemeiAnd the test scheme with the minimum value of the optimization target is the optimal test scheme.
Further, the calculation formula of the optimization objective is as follows:
wherein, wssFor a set weight coefficient, MSE0、TC0According to the ratio of 1: 1, the estimation precision of the benchmark reliability and the expense of the benchmark test.
Further, the step 4 is: adding 1 to k, increasing the set step length for the current test temperature and the current test voltage, and executing the step 2 if the current test temperature and the current test voltage are both smaller than the set maximum value; and if any one of the current test temperature and the current test voltage is greater than or equal to the set maximum value, executing the step 5.
Has the advantages that:
according to the invention, through researching and analyzing the failure mode and the main failure mechanism of the product to be tested under the stress of a complex environment, the service life distribution and the acceleration model are selected and determined, the optimized design of the test scheme is carried out by utilizing a Monte-Carlo simulation method under the test constraint condition, and the reasonable sample grouping, the stress condition and the test truncation time are determined, so that the purpose of optimizing the test scheme is achieved, the reliability verification test and evaluation can be completed under the limits of the sample amount, the test time and the test expenditure, the test time and the test sample can be saved, the economic benefit is greater, the universal applicability to the design of the multi-stress acceleration service life test scheme of the aerospace electronic product is realized, and the significance is also realized for other electronic and mechanical products.
Detailed Description
The present invention is described in detail below.
The invention provides a simulation-based multi-stress accelerated life test scheme optimization method, which adopts the basic idea that the reliability estimation precision and the test cost are taken as optimization targets, the multi-stress accelerated test scheme optimization design is carried out on aerospace electronic products, the test hypothesis is agreed, the design variables, the constraint conditions and the optimization targets are determined, the test cost and the reliability estimation precision of different test schemes are simulated by adopting a numerical simulation method, and the optimal scheme is determined.
The invention provides a simulation-based multi-stress accelerated life test scheme optimization method, which specifically comprises the following steps:
step 1, hypothesis of test protocol
Generally, before the reliability test of the product to be tested, the following assumption conditions are set:
1. the reliability of the product to be tested follows Weber distribution; an equal interval test method is adopted in the test process, and the test interval is tuThe test time t is in direct proportion to the test times l; the test fault (or failure) judgment criterion of the product to be tested is that the degradation condition of the performance to be tested exceeds the set threshold requirement;
2. under different test stress levels, the failure mechanism of the performance to be tested of the product to be tested is unchanged, the performance to be tested is monotonically degraded along with the test time, and the degradation model is as follows:
where k is the number of tests, α is a random variable that follows a reciprocal weibull distribution, β is a fixed known constant that can be fit to available degradation data, and t iskTime corresponding to the kth test, y (t)k) Is at tkThe amount of degradation of the performance to be measured at that moment; epsilon is a random error term, the physical meaning of epsilon is that instruments or people cause inevitable measurement errors in the test process, and generally, epsilon is assumed to be independent of each other and obey normal distribution.
Step 2, design of test scheme
The design of the test scheme is the selection and setting of the test parameters. In general, the following parameters are preset for the test protocol: the method comprises the steps of selecting the number of products to be tested in the test, testing test intervals, initial values and maximum values of all test stresses, test expenditure budget and maximum test time allowed by test cost. In the present invention, the test stress includes temperature and voltage.
Then, according to the above settingThe initial values of the temperature and the voltage are calculated to obtain a test acceleration factor AF, and then the design index of the lower limit of the reliability of the product to be tested is RLCalculating the confidence coefficient design index of the product to be tested as gamma to obtain the minimum test time tminFrom the minimum test time tminAnd calculating the set test interval to obtain the minimum value l of the test timesmin。
In the invention, in order to improve the timeliness of the test, the initial test frequency of the test is set to be the minimum value l obtained by the calculationmin。
Step 3, carrying out simulation test according to the setting of the test scheme
Assuming that I test schemes are determined in total, for test scheme I (wherein I is a positive integer, I is less than or equal to I), N is selectediThe reliability of the product to be tested is subjected to Weber distribution, and the lower limit of the reliability is designed as RLThe design index of the confidence coefficient is gamma, the performance to be tested of the product to be tested is monotonically degraded along with the test time, and the maximum degradation amount of the performance to be tested is set as ydmax。
In test protocol i, a test interval t is setu_iInitial test temperature Ti_0And initial test voltage Vi_0Wherein, Ti_0≤Tmax，TmaxMaximum value of test temperature, Vi_0≤Vmax，VmaxIs the maximum value of the test voltage; the test expenditure budget is C, and the maximum test time allowed by the test cost is tmax(ii) a According to Ti_0、Vi_0And calculating to obtain the acceleration factor AF.
Then according to AF, RLAnd gamma, calculating to obtain the minimum test time t by adopting a calculation method in the prior artminThen from tminAnd tu_iCalculating to obtain the minimum value l of the test timesmin。
Let test scheme i, the current number of tests be k, let k equal to lmin(ii) a The current test temperature is TkLet Tk＝Ti_0(ii) a The current test voltage is VkLet Vk＝Vi_0。
Step 3.1, traversing all the test samples to obtain the degradation amount of the performance to be tested of each test sample, and when the degradation amount of the sample to be tested is larger than ydmaxIf the sample to be detected is invalid, the current invalid times are added by 1; otherwise, the sample to be tested is considered to be not invalid, and the current failure times are kept unchanged;
step 3.2, adopting failure times, current test times k and test interval tu_iCalculating the lower limit R of the reliability of the product to be tested under the current stress conditionn_k；
When R isi_k≥RLThen, calculating the test cost TC of the product to be tested under the current stress conditioni_kWhen TCi_kWhen the test result is less than or equal to C, recording the lower limit R of the reliability of the testi_kTesting the expenses TCi_kAnd stress conditions, executing step 3.3; when TCi_k>C, executing step 3.3;
step 3.3, enabling k to be added by 1, increasing the set step length for the current test temperature and the current test voltage, and executing the step 3.1 if the current test temperature and the current test voltage are both smaller than the set maximum value; if any one of the current test temperature and the current test voltage is greater than or equal to the set maximum value, executing a step 3.4; in the actual test process, the current test temperature and the current test voltage can be randomly changed for testing, and multiple tests are executed according to the set test times;
step 3.4, calculating all reliability lower limits R recorded in the processi_kMean square error value MSE ofiCalculating a test cost TCi_kAverage value TC for current test times kiAccording to MSEiAnd TCiCalculating to obtain an optimization target U of the test scheme iiCalculating by adopting a calculation formula (1); when I is less than or equal to I, enabling I to be added by 1 to execute the step 3;
wherein, wssFor a set weight coefficient, MSE0、TC0According to the ratio of 1: 1, the estimation precision of the benchmark reliability and the expense of the benchmark test.
Step 4, in all the test schemes, selecting an optimization target UiThe test scheme with the minimum value is the optimal test scheme, and comprises test sample grouping, test times, test intervals, test temperature and test voltage.
Example 1:
the embodiment is that a certain type of grid assembly is a product to be tested, and the grid assembly has certain requirements on test time and test cost due to the restriction of conditions such as development period, expenditure and the like, so the method for optimizing the multi-stress accelerated life test scheme based on simulation provided by the invention is adopted to optimize the scheme of the grid assembly.
Degradation test data of the hole, the groove and the small hole aperture in the temperature-voltage acceleration test of the grid assembly are simulated by adopting numerical simulation, and uncertain quantity is introduced to describe test errors; comparing simulation test data to judge whether the product is invalid or not by combining a performance degradation threshold, and statistically analyzing reliability estimation precision and test cost through simulation times of a certain scale; and selecting a reasonable optimization function and an optimal solution evaluation criterion to determine an optimal test design scheme. The accelerated life test is optimized according to the steps provided by the invention.
And step S01, estimating distribution shape parameters and acceleration model parameters of the grid assembly Weibull through historical test data, and fitting to obtain a small hole aperture, pit and groove sputtering depth and performance degradation model. Initial temperature grade T ═ T of grid assembly test0Initial voltage level V ═ V0。
Step S02, randomly generating three performance degradation functions of the ith product sample to be tested according to the performance degradation model, and calculating an acceleration coefficient AF by adopting a stress condition;
calculating the minimum test times: according to the input task time requirement t and the test interval time tuLower limit of reliability index to be verifiedLAnd confidence gamma, using the following formulaThe formula is calculated as:
thus, the minimum test times is calculated as lmin＝tmin/tuThe number of test times k is assigned to an initial value lmin. And setting the simulation scale N (i is 1,2 … N), namely, performing N times of simulation tests on the test sample under the condition of variable stress.
Calculate the ith test sample at kXtuAmount of temporal performance degradation yd(k×tu) Wherein k is the number of times of testing, each simulation in the invention needs to randomly generate simulation data by using a performance degradation model, and the degradation value of the performance to be tested and the threshold value y are calculateddmaxAnd comparing, judging whether the product to be detected is invalid, counting the number r of the invalid if the product to be detected is invalid, and otherwise, keeping the number of the invalid unchanged.
Step S03, calculating the lower limit of the reliability of the test scheme i under the current stress by adopting the following formula, and judging whether the lower limit of the calculated reliability of all test samples is greater than RL；
If the set reliability index requirement is met, the cost of the test scheme i is calculated by adopting the following formula,
TCi_k＝Csk+Ctktu+c0。
judging whether the cost meets the requirement of given budget, if so, recording the stress condition and the lower limit R of the reliability of the testi_kAnd testing the expenses TCi_kThen, changing the stress condition according to the set step size, and repeating the steps S02 and S03 until the stress condition reaches the set maximum stress value; if the budget requirement is not met, the secondary simulation data is not recorded, then the stress condition is changed according to the set step size, and the steps S02 and S03 are repeated until the stress condition reaches the set stress maximum value.
If the set reliability index requirement is not met, the stress condition is changed according to the set step length, and the step S02 and the step S03 are repeated until the stress condition reaches the set maximum stress value.
Step S04, reliability lower limit R recorded according to the above stepsi_kCalculating mean square error value MSE; calculating test cost TCi_kAverage value TC for current test times kiThe optimization objective is calculated using the following formula:
wherein, wssFor a set weight coefficient, MSE0、TC0According to the ratio of 1: 1, the estimation precision of the benchmark reliability and the expense of the benchmark test.
And taking the scheme with the minimum U value as an optimal scheme, wherein the optimal scheme comprises a test interval, a test temperature and a test voltage.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (3)
1. A multi-stress accelerated life test scheme optimization method based on simulation is characterized by specifically comprising the following steps:
step 1, selecting a plurality of products to be tested as test samples in a test scheme I, wherein the reliability of the products to be tested obeys weber distribution, and the performance to be tested of the products to be tested is monotonically degraded along with the test time, I is a positive integer and is less than or equal to I, and I is the total number of the test schemes;
calculating to obtain an acceleration factor AF according to the initial test temperature and the initial test voltage, and calculating to obtain a reliability lower limit R according to the AFLCalculating the confidence coefficient gamma to obtain the minimum test time tminThen from tminAnd tu_iCalculating to obtain the minimum value l of the test timesmin；
Let the current test number be k, k ═ lminThe current test temperature is the initial test temperature; the current test voltage is an initial test voltage;
step 2, traversing all the test samples to obtain the degradation amount of the performance to be tested of each test sample, and taking the number of the test samples of which the degradation amount is larger than the set maximum degradation amount as failure times;
step 3, adopting the failure times, the current test times k and the set test interval tu_iAnd calculating the lower limit R of the reliability of the product to be tested under the current stress conditioni_k；
Ri_kIf the reliability is greater than or equal to the set lower limit of the reliability and the test expense of the product to be tested under the current stress condition is less than or equal to the set budget, recording the current test as an effective test; otherwise, not recording;
step 4, enabling k to be self-added by 1, changing the current test temperature and the current test voltage for multiple times, and executing step 2 to obtain multiple effective tests;
step 5, calculating the lower limit R of the reliability for all effective testsi_kMean square error value MSE ofiAnd testing the expenses TCi_kAverage value TC for the current test number kiAccording to said MSEiAnd TCiCalculating to obtain an optimization target U of the test scheme ii；
Step 6, executing all the test schemes to obtain an optimization target U of each test schemeiAnd the test scheme with the minimum value of the optimization target is the optimal test scheme.
2. The method of claim 1, wherein the optimization objective is calculated as follows:
wherein, wssFor a set weight coefficient, MSE0、TC0According to the ratio of 1: 1 ofThe benchmark reliability estimation precision and the benchmark test cost obtained by the life test.
3. The method according to claim 1, wherein the step 4 is: adding 1 to k, increasing the set step length for the current test temperature and the current test voltage, and executing the step 2 if the current test temperature and the current test voltage are both smaller than the set maximum value; and if any one of the current test temperature and the current test voltage is greater than or equal to the set maximum value, executing the step 5.
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