CN103176077B - The reliability fast assessing method of a kind of numerical control finished circuit board under environment comprehensive effect - Google Patents

Abstract

The invention discloses the reliability fast assessing method of a kind of numerical control finished circuit board under environment comprehensive effect, comprising: (i) select temperature and Dc bias as accelerating stress, for the circuit board of pending test and appraisal builds acceleration model(II) determines acceleration stress level and stress number of combinations, and grouping is carried out accelerated life test and noted down test data simultaneously; (iii) choose Lifetime Distribution Model and carry out parametric solution according to test data, calculate the different characteristics life values of accelerating under stress combination; (iv) according to characteristics life value, circuit board acceleration model is carried out to matching and model coefficient establishment, then carry out reliability test and appraisal, thereby obtain the reliability index of numerical control finished circuit board under environment comprehensive effect. By the present invention, can determine fast, quantitatively and the reliability index of numerical control production board under environment comprehensive effect meet the requirement of system reliability rapid evaluation, and overall flow convenient operation, efficiency is high, meets the requirement of digital control system high reliability.

Description

The reliability fast assessing method of a kind of numerical control finished circuit board under environment comprehensive effect

Technical field

The invention belongs to printed circuit board technology field, more specifically, relate to a kind of numerical control finished product circuitThe reliability fast assessing method of plate under environment comprehensive effect.

Background technology

Printed circuit board is the critical piece in electronic product, is widely used in aviation, numerical control, calculatingThe every field such as machine, self-reacting device. Consider that the capability and performance of printed circuit board and stability are to producingProduct are most important, therefore in manufacture process, often need to carry out environmental testing, establish that it is reliableProperty index. Environmental test roughly can be divided into climatic environment test, mechanical environment test and integrated environmentThe types such as test, wherein climatic environment test refers to printed circuit board finished product to be detected is positioned over notUnder same humiture, pressure, gas, salt fog, wind and rain and solar radiation condition, investigate its inefficacy machineReason and unfailing performance; Mechanical environment test is that printed circuit board finished product to be detected is set to different rushingHit, vibrate, the test condition such as collision, acceleration and high noisy, and carry out test and detect; Integrated environmentTest is that mechanical environment and climatic environment are combined to common set environment stress, and then investigates and surveyFailure mechanism and the unfailing performance of examination circuit board under this environment comprehensive effect.

Numerical control finished circuit board plate is to meet detail of design, relevant specification and purchase requirement, and by oneProduce batch numerical control printed circuit board of producing. Along with Numeric Control Technology is constantly to multifunction and heightThe future developments such as stability, the number of plies of numerical control finished circuit board is more and more higher, and line density is more and more thinnerClose. Meanwhile, often need to be in the integrated environment of the hot and humid bias voltage long-time work of numerical control deviceDo, make circuit board electrochemical migration phenomenon (electrochemicalmigration is called for short ECM)Become a factor that numerical control reliability is produced to considerable influence. So-called ECM phenomenon is on circuit boardMetal such as copper, silver, tin, aluminium etc. under hot and humid environment, there is ionization, and at electric fieldThe growth to the conducting metal filament of another utmost point by insulating barrier under effect, this will cause under insulating propertiesFall, even cause printed circuit board to lose efficacy. This fault is in digital-control circuit plate miniaturization day by day, integratedUnder the development trend of changing, will highlight all the more, and especially extensively adopt for current numerical control printed circuit boardThe copper-clad plate of FR-4 type epoxy prepreg has considerable influence.

At present, exert an influence for reliability and the ECM phenomenon of investigating numerical control finished circuit boardMode be mainly by accelerated life test, short under the stress condition that exceedes environment for use conditionSample was lost efficacy in a short time, to predict the reliability under normal environment for use, but do not change testThe failure mechanism of sample. Carry out accelerated life test and must determine a series of test parameters, for example bagDraw together but be not limited to test time, sample size, accelerated factor, test environment etc., wherein crucialBe to know which kind of distribution test specimens product obey, and understand sample life-span and the proof stress applyingBetween acceleration model (or being referred to as Failure physics equation), like this could be under condition of high ground stressThe life information of numerical control finished circuit board is extrapolated.

In present technology, test sample is carried out to intrinsic the adding adopting in accelerated life test processSpeed model generally includes Arrhenius model, contrary power rate model, Eyring model etc., and these are existingModel can be determined quickly accelerated factor, save time, but has conventionally only considered the impact of single stress,Application is also indefinite and have a diversity, and it is more complicated to lack the assignment of accuracy and model variable.In order further to improve the reliability level of numerical control finished circuit board, first must research numerical control finished productThe reliability index of circuit board under environmental stress comprehensive function, meets the requirement of system reliability design,In order to realize, reliability growth is provided fundamental basis and guidance program. Correspondingly, numerical control finished circuit board existsReliability consideration under high temperature, high humidity and bias voltage integrated environment becomes an important problem, and logarithmThe foundation of the reliability model of control finished circuit board including acceleration model and Lifetime Distribution Model is realExecute the key of accelerated life test design, data statistics and reliability assessment.

Summary of the invention

For above defect and/or the technical need of prior art, the object of the present invention is to provide oneFor numerical control finished circuit board being carried out under combined environment test to reliability fast evaluation method, it is logicalCross numerical control finished circuit board is set up to the reliability statistics model under the integrated environment effect of many stress, energyEnough know more rapidly the reliability index under this production board is under environment comprehensive effect, and entiretyFlow process convenient operation, efficiency is high, and can meet the requirement of numerical control production board rapid evaluation.

For achieving the above object, according to one aspect of the present invention, provide a kind of printed circuit board to existReliability fast assessing method under environment comprehensive effect, is characterized in that, the method comprises following stepRapid:

(a) for building, the printed circuit board of pending reliability test and appraisal is used for characterizing its product feature life-spanAnd the following acceleration model between main acceleration stress, wherein η represents the product feature longevity of circuit board under testLife, S¹And S²Represent to affect the main acceleration stress in printed circuit board life-span, φ₁(S¹)、φ₂(S²) be respectivelyFor characterizing the function expression that main acceleration stress exerted an influence to the circuit board features life-span,Represent the interactive function expression between two main stress, α₀、α₁、α₂And α₃Represent respectively coefficient correlation to be estimated:

lnη=α₀+α₁φ₁(S¹)+α₂φ₂(_S ²)+α₃φ₃(S¹,S²)

(b) accelerate to arrange accelerated life test under stress level combination in difference, thereby obtain correspondingFailure of insulation lifetime data;

(c) choose applicable Lifetime Distribution Model, and the failure of insulation obtaining according to step (b)Lifetime data carries out parametric solution to Lifetime Distribution Model, then failure mechanism under different stress levelsUnder the prerequisite remaining unchanged, calculate the characteristics life of the printed circuit board under each stress level combination;

(d), according to calculated characteristics life, the acceleration model of setting up by step (a) is enteredRow process of fitting treatment is to determine described coefficient correlation α₀、α₁、α₂And α₃, thus according to fixed accelerationModel and life-span distribute the life-span to printed circuit board execution reliability fast assessing, thereby obtain circuit boardReliability index value under home combined stress.

According to another aspect of the present invention, also provide a kind of numerical control finished circuit board to do at environment comprehensiveWith under reliability fast assessing method, numerical control finished circuit board is to meet detail of design, relevant ruleModel and purchase requirement, and produce batch feature board that can realize designing requirement of producing by one.It is characterized in that, the method comprises the following steps:

(i) choose affect the main acceleration stress of numerical control finished circuit board characteristics life be also temperature T andDc bias V, and build numerical control finished circuit board characteristics life and these two acceleration of accelerating between stressModel is as follows:

$\ln \mathrm{\η}={\mathrm{\β}}_0+{\mathrm{\β}}_1\frac{1}{T}+{\mathrm{\β}}_2\ln V+{\mathrm{\β}}_3\frac{\ln V}{T}$

Wherein, η represents the product feature life-span of digital-control circuit plate to be measured,LnV characterizes temperatureThe function expression that degree and Dc bias exert an influence to numerical control finished circuit board characteristics life,BeCharacterize the function expression of interactive relation between temperature and Dc bias stress, β₀、β₁、β₂And β₃PointDo not represent coefficient correlation to be estimated;

(ii) determine the different stress levels of temperature and Dc bias, and in different stress level groupsClose lower arrangement accelerated life test and record failure of insulation lifetime data simultaneously;

(iii) choose Weibull distribution as Lifetime Distribution Model, according to the obtained failure of insulation longevityFate, according to Weibull Lifetime Distribution Model is carried out to parametric solution, then lost efficacy under different stress levelsIt is also under the constant prerequisite of the form parameter of Weibull distribution that mechanism remains unchanged, and calculates each stress waterThe characteristics life of the printed circuit board under flat combination;

(iv) according to calculated characteristics life, the acceleration model of (i) setting up by step is enteredRow process of fitting treatment is to determine described coefficient correlation β₁、β₁、β₂And β₃, thus according to fixed accelerationModel and Weibull distribution model are carried out reliability fast assessing to numerical control finished circuit board, thereby obtainThe reliability index value of this numerical control finished circuit board under home combined stress.

As further preferably, according to machine tool numerical control system general technical specifications and electric and electronic productEnvironmental testing requires to set test parameters, and wherein the number of levels of each stress is set as more than 4, andJust temperature and Dc bias number of combinations is between the two set as more than 5 groups.

As further preferably, the foundation of described acceleration model is to lose based on electrochemical migration (ECM)Effect mechanism.

As further preferably, described numerical control finished circuit board is the copper-clad plate of FR-4 type epoxy prepreg.

As further preferably, described accelerated life test is set to the examination of Censoring accelerated agingTest.

As further preferably, described Lifetime Distribution Model chosen position scale model.

In general, according to circuit board abatement detecting method of the present invention compared with prior art, mainPossess following technological merit:

1, play the main stress condition of key effect and consider that it each other owing to choosing someImpact builds acceleration model, can embody more exactly printed circuit board true or approaching trueFailure procedure under environmental condition, determines its reliability system under environmental stress comprehensive function quantitativelyScore is analysed;

2, by the especially mechanism research of ECM phenomenon of failure procedure with finished circuit board to numerical control,Take into full account that these main stress of environment temperature, relative humidity and bias voltage and correlation thereof are to productThe impact of characteristics life; In addition, by by constructed according to this acceleration model and Weibull distribution modelCombine execution fail-safe analysis, can evaluate quickly and accurately numerical control finished circuit board and combineClose the reliability index under action of environmental stresses;

3, for according to reliability fast assessing method of the present invention, wherein build and accelerate mould by employingThe technological means such as type and Lifetime Distribution Model, execution accelerated life test and failure of insulation detection, canSolve in prior art circuit board under environmental stress comprehensive function, be difficult to carry out reliability design and thenThe technical problem that causes system reliability can not be guaranteed, corresponding can acquisition quantitatively determined and normally canBy property index, be convenient to the technique effect of fast assessing, and be particularly useful for numerical control with finished circuit boardFail-safe analysis process.

Brief description of the drawings

Fig. 1 be according to the present invention for numerical control finished circuit board the fast assessing under environment comprehensive effectThe process chart of method;

Fig. 2 is close according to the probability of two parameters of Weibull that adopt in reliability model of the present inventionDegree function schematic diagram;

Fig. 3 be for to according under environment comprehensive effect of the present invention reliability fast assessing method implementSchematic flow sheet.

Detailed description of the invention

In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawingAnd embodiment, the present invention is further elaborated. Should be appreciated that described herein concreteEmbodiment only, in order to explain the present invention, is not intended to limit the present invention.

In hot and humid environment, printed circuit board usually can be found adjacent in the time applying operating voltageTwo wires and Kong Yukong between insulaion resistance sharply decline to occurring after certain hour, this phenomenonBeing mainly electrochemical migration (ECM) phenomenon causes. Along with people divide printed circuit board failure mechanismThe further investigation of analysing, shows that ECM phenomenon is that printed circuit board is at high temperature-high humidity-bias voltage (T-H-B)The Main Patterns even losing efficacy Deng hydraulic performance decline under integrated environment. The condition that wherein electrochemical migration producesMainly comprise: between conductor, have bias voltage, have ion migration gap, have Ionized liquid desiccant(moisture content etc.), and have ionic material existence etc.

Because numerical control at present generally adopts the copper-clad plate of FR-4 type epoxy prepreg with printed circuit board, researchFind, the attached outstanding power under damp and hot environment between the epoxy resin of the type circuit board and glass is easyOccur deteriorated, for conducting metal filament growth provides passage; Meanwhile, wicking is again ECMGrowth provides the metallics of enough facile hydrolysis, and the of electronic component own is electrochemistry in electriferous stateMigration provides electrical potential difference, thereby makes the growth of conducting metal filament obtain power and easily impel ECMGrowth. Therefore, for the numerical control circuit board including the copper-clad plate of FR-4 type epoxy prepreg,Under condition of work, temperature, relative humidity and bias voltage are to cause that it ECM phenomenon occurs and causes insulationThe integrated environment stress condition having the greatest impact losing efficacy. In general, in air, relative humidity is larger,The easier dewfall in metal surface, the time that lip-deep electrolyte membrane exists is also longer, and corrosion rate is phase alsoShould increase. The researchers such as J.A.Augis propose and have proved that electrochemical migration formation has relatively wetDegree critical value, just can not occur lower than this critical value electrochemical migration phenomenon. The pcb board of different substrate materialsUnder different working environments, relative humidity limit value is also different. The relative humidity of general electronic productsCritical value is between 50%RH～85%RH. Therefore set after relative humidity limit value, just can be rightNumerical control is carried out the accelerated aging examination under the main stress condition such as high temperature, high humidity or bias voltage with finished circuit boardTest.

But, in accelerated life test of the prior art, conventionally only adopt the acceleration mould of single stressType, for example the Arrhenius model of extensive use at present has only been considered Temperature Accelerating Factor in Life Test, therefore mainBe used to the accelerated life test relevant with temperature stress; Contrary power rate model (inversepowerModel) equally only considered the relation that affects between electric stress and life of product, etc. In addition, thoughSo many stress accelerations model is possessed some special knowledge, such as D.S.Peck proposes description humitureAcceleration model Peck model, M.B.Srinivash etc. have proposed to consider electric stress, temperatureThe life model of stress and mechanical stress, but these models all simply think that each accelerates between stressBe separate, and ignored influencing each other between stress; Especially, for numerical control finished product electricityThe accelerated life test of road plate, there is no at present and can describe comparatively accurately, all sidedly temperature, phaseTo humidity and bias voltage, these cause the critical stress condition of ECM phenomenon and the acceleration model of correlation thereof,Thereby can not be applicable to preferably to investigate the failure mechanism of digital-control circuit plate under environment comprehensive effect and canBy performance.

Based on above analysis, in the present invention, expect to be the printing electricity including numerical control finished circuit boardThe accelerated life test of road plate rebuilds new acceleration model, is embodied in thus true or approaches trueUnder real integrated environment state, some play the main stress condition of key effect to digital-control circuit plateThe impact of failure procedure, and reflect the correlation between these critical stress. Through a large amount of realitiesBorder test analysis and theoretical derivation, can build product feature life-span η and two acceleration stress S¹And S²BetweenAcceleration model as follows:

Wherein, wherein η represents the product feature life-span of circuit board under test, S¹And S²Represent impact printingThe main acceleration stress in circuit board life-span, φ₁(S¹)、φ₂(S²) be respectively for characterizing main acceleration stress pairThe function expression that the circuit board features life-span exerts an influence,Represent two main stress itBetween interactive function expression, α₁、α₁、α₂And α₃Represent respectively coefficient correlation to be estimated.

Consider the numerical control circuit board including the copper-clad plate of FR-4 type epoxy prepreg,Under normal running conditions, temperature, relative humidity and bias voltage are to cause that it ECM phenomenon occurs and causes absolutelyThe environmental stress having the greatest impact that edge lost efficacy, there is rh value critical value in circuit board as mentioned above,The impact of electrochemistry being lost efficacy higher than humidity after its critical value is also not obvious, can ignore, and therefore setsAfter humidity critical value, temperature, relative humidity and bias voltage comprehensive function can be simplified the impact of circuit boardFor temperature and two stress of bias voltage. With reference to the temperature of reacting in Arrhenius model and inverse power law modelStress and electric stress be the relation to life of product respectively, and above-mentioned model can further be expressed as:

$\ln \mathrm{\η}={\mathrm{\β}}_0+{\mathrm{\β}}_1\frac{1}{T}+{\mathrm{\β}}_2\ln V+{\mathrm{\β}}_3\frac{\ln V}{T}---\left(2\right)$

Wherein, η represents the product feature life-span of digital-control circuit plate to be measured,LnV characterizes temperatureThe function expression that degree and Dc bias exert an influence to numerical control finished circuit board characteristics life,BeCharacterize the function expression of interactive relation between temperature and Dc bias stress, β₀、β₁、β₂And β₃PointDo not represent coefficient correlation to be estimated. Like this, can be embodied in more exactly true or approach trueUnder real integrated environment state, these play the main stress condition pair of key effect temperature and bias voltageThe failure procedure of finished circuit board for numerical control, the especially impact of ECM phenomenon on failure of insulation process,Thereby reflect rightly the mutual pass between two critical stress by the multiplication relationship of getting both simultaneouslySystem.

After building acceleration model, also need as previously mentioned to determine the Lifetime Distribution Model of test sample,So that the life information to the numerical control finished circuit board under condition of high ground stress is extrapolated. Due to pcb boardBe the supporter of electronic devices and components, from function finished circuit board, the insulation of any conducting wire is lostEffect, all can cause the inefficacy of whole numerical control circuit board, and therefore the inefficacy of numerical control finished circuit board distributesBelong to a minimum extreme-value problem. Suppose that the life-span of i article is T in n bar conducting wire_i(i=1,2 ..., n), the life-span of every conducting wire is separate, and distribution is all F_e(t),The life-span of production board distributes and is T=min{T₁,T₂,…,T_n, its life-span distribution functionCan be expressed asAs shown in the formula (3), wherein F_e(t) represent every conducting wire life-span distribute:

In practice is used, conventionally can adopt exponential distribution, normal distribution, logarithm normal distribution and prestigeThe boolean model and the use that combines according to the constructed acceleration model of the present invention such as distribute, so as to carry out rightThe fail-safe analysis of numerical control finished circuit board. Research shows that n is larger, the distribution function shown in formula (3)More approach two parameter Weibull distribution, as shown in Figure 2. For ease of calculating, preferably use φ₍₁₎(t) graduallyEnter minimum and distribute, two-parameter weibull distribution replaces strict minimum to distribute to represent finished productThe Failure life distribution of plate, its probability-distribution function F (t) can be expressed as formula (4), and wherein t representsLifetime data, η is expressed as scale parameter or characteristics life, and m represents form parameter:

$F\left(t\right)=1-\exp (-{\left(\frac{t}{\mathrm{\η}}\right)}^m)---\left(4\right)$

Like this, by selecting the Lifetime Distribution Model of Weibull distribution as circuit board under test, and with pressAccording to the use that combines of the constructed acceleration model of the present invention, can set up thus numerical control finished circuit board and existReliability statistics model under high temperature, high humidity and the effect of bias voltage multiple environmental stresses, mutually should be able to be fast,Evaluate quantitatively the reliability level of numerical control finished circuit board under integrated environment effect of stress. In realityIn operation, because the corresponding coefficient correlation of dissimilar digital-control circuit plate may be different, therefore firstFirst can carry out the accelerated aging examination under different stress combinations for digital-control circuit plate according to acceleration modelTest, and obtain form parameter and the characteristics life value under each stress combination, ensureing each group of form parameterConstant is also under the constant prerequisite of failure mechanism, utilizes each stack features life value and corresponding stress level,Acceleration model is verified and matching, solved relevant coefficient value simultaneously, finally utilize and determine systemThe acceleration model of number is combined with Weibull distribution model, thereby completes numerical control finished circuit board at ringFail-safe analysis under the comprehensive function of border and assessment.

Fig. 1 be according to the present invention for numerical control finished circuit board the reliability under environment comprehensive effect fastThe process chart of speed assessment method. As shown in fig. 1, according to reliability fast assessing of the present inventionMethod mainly comprises following process steps:

First, for building, the numerical control finished circuit board of pending reliability fast assessing is used for characterizing its productAcceleration model between product characteristics life and main acceleration stress is as follows:

$\ln \mathrm{\η}={\mathrm{\β}}_0+{\mathrm{\β}}_1\frac{1}{T}+{\mathrm{\β}}_2\ln V+{\mathrm{\β}}_3\frac{\ln V}{T}$

Wherein, η represents the product feature life-span of digital-control circuit plate to be measured, and T and V are respectively temperature and inclined to one sideCompression, correspondingWith lnV be respectively for characterizing temperature and Dc bias to product feature life-span instituteThe function expression exerting an influence,To characterize between temperature and these two acceleration stress of Dc bias to hand overThe function expression of mutual relation, β₀、β₁、β₂And β₃Represent respectively coefficient correlation.

Then, can be according to machine tool numerical control system general technical specifications and electric and electronic product environmental testingRequirement, lost efficacy and studied in conjunction with ECM, and the relative humidity limit value of setting in accelerated life test is for example85%RH, the normal stress level of temperature and two stress of Dc bias is respectively T₀And V₀, the most heavily stressedLevel is respectively acceleration stress level and is respectively T_maxAnd V_max, acceleration stress level is setT₀<T₁<...<T_l≤T_maxAnd V₀<V₁<...<V_k≤V_max, wherein l and k are respectively two acceleration stressNumber of levels, generally must not be less than 4. And note i of temperature T by abridging and accelerate stress level and Dc biasJ the horizontal combination of accelerating stress of V is (i, j), i=1, and 2 .., l, j=1,2 .., k,Normal stress horizontal combination is (0,0). Generally accelerate each arrangement longevity under stress level combination at lkLife test, but in practice, for reducing sample number, reduce experimentation cost, the part of horizontal of being everlasting combinationUnder carry out life test, but consider test validity, should not be less than 5 groups, then choose respectively shouldForce level combines under (i, j) n_ijIndividual numerical control production board carries out Fix-Time Censored Test, truncated timeFor τ, gained truncation failure of insulation lifetime data isi=1,…,l,j=1,…,k。

Then, choose Weibull distribution as Lifetime Distribution Model, according to obtained different stress groupsLifetime Distribution Model is carried out to parametric solution to failure of insulation lifetime data under closing or checking is processed, becauseThe variation of the form parameter m of Weibull distribution has reflected the variation of failure mechanism, so will ensure notRemain unchanged with the failure mechanism under stress level, require form parameter constant, calculate and print simultaneouslyThe characteristics life value of circuit board under different stress combinations;

Finally, according to the characteristics life value of asking under the combination of different stress, to the characteristics life of setting up withThe acceleration model of stress carries out process of fitting treatment and checking, asks for model coefficient β to be determined₀、β₁、β₂Withβ₃, then numerical control finished circuit board is carried out to reliability fast assessing, thereby obtains this numerical control finished product electricityThe reliability index of road plate under normal stress.

We verify the model that above testing process is used below, specifically verify flow process asShown in Fig. 3.

One, numerical control is adopted to the checking of choosing Weibull distribution with the Lifetime Distribution Model of finished circuit board

For the matching inspection of position scale model (the extreme value distribution), can use more effective specialThe method of inspection, is commonly referred to Van-Montfort method of inspection. Whether obey for the actual pcb board life-spanWeibull distribution, can be by original lifetime data is taken the logarithm, thereby Weibull distribution is converted toThe extreme value distribution, this just can utilize Van-Montfort method to carry out the extreme value distribution inspection. Be provided with n sampleProduct carry out Fix-Time Censored Test, obtain r fail data t₁≤t₂≤…≤t_r, establish life of productBe distributed as F (t), first suppose that F (t) obeys Weibull distribution, lifetime data is taken the logarithm, evenX=lnt,Above-mentioned null hypothesis is converted to: the position scale that is distributed as of X dividesCloth (the extreme value distribution) or $F\left(x\right)=G\left(\frac{x-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\right)=1-\exp (-e^{\frac{x-\mathrm{\&mu;}}{\mathrm{\&sigma;}}})$ Set up.

Order $l_i=\frac{x_{i+1}-x_i}{E\left(Z_{i+1}\right)-E\left(Z_i\right)},i=\mathrm{1,2},...,r-1$

Z in above formula_iFrom standard the extreme value distribution G i order statistic (x); E (Z_i) be Z_iMathematic expectaion, its value can be looked into " reliability test with table ". VanMontfort proves in hypothesisState under the condition of hypothesis establishment l₁、l₂，…，l_r-1Progressive independent and progressive obedience normal exponential distribution.

Order $W=\frac{\left[\frac{r}{2}\right]\underset{r=(r/2)+1}{\overset{r-1}{\mathrm{\&Sigma;}}}{l}_i}{\left[\frac{r-2}{2}\right]\underset{i=1}{\overset{r/2}{\mathrm{\&Sigma;}}}{l}_i}$

Under the condition of setting up in above-mentioned hypothesis, the approximate obedience of the statistic W free degree is 2[(r-1)/2]And 2[r/2] F distribute. For given level of significance α, ifOrThink that above-mentioned hypothesis is false; Otherwise, can think this truncated sample fromThe extreme value distribution. Therefore can, by structure Van-Montfort method of inspection, can draw numerical control finished productThe life-span of circuit board is distributed in conclusion separate in statistics and that obey Weibull distribution.

Two, use finished circuit board under different stress combination conditions to numerical control, the shape of Weibull distributionThe remain unchanged checking of (equating) of parameter, i.e. the constant inspection of failure mechanism

In the statistical analysis of permanent Accelerated Life, conventionally suppose the calibration parameters of product under each stress levelEquate, Bartlett method of inspection is very effective to the extreme value distribution, and calculates fairly simple. Work as the life-spanWhile obeying Weibull distribution, the inspection that form parameter is equal also can adopt Bartlett method of inspection.

For the Weibull distribution of K group

$F_j\left(t\right)=1-e^{-{(t/{\mathrm{\&eta;}}_j)}^{m_j}},(j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K)$

First suppose m₁＝m₂＝...＝m_K, also suppose K group the extreme value distribution

$F_j\left(x\right)=1-\exp (-e^{\frac{x-{\mathrm{\&mu;}}_j}{{\mathrm{\&sigma;}}_j}}),(j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K)$

In addition suppose σ₁＝σ₂＝...＝σ_K, like this according to K group censored samples, estimate with best linear unbiasMeter obtains σ_jEstimated value(j=1,2 ..., K). Structure Bartlett test statistics,

$B^2=2\left(\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{l}_{r_j{n}_j}^{-1}\right)[\ln \left(\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{l}_{r_j{n}_j}^{-1}{\widehat{\mathrm{\&sigma;}}}_j\right)-\ln \left(\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{l}_{r_j{n}_j}^{-1}\right)]-2\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{l}_{r_j{n}_j}^{-1}\ln {\widehat{\mathrm{\&sigma;}}}_j$

$C=1+\frac{1}{6(K-1)}[\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{l}_{r_j{n}_j}-{\left(\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{l}_{r_j{n}_j}^{-1}\right)}^{-1}]$

Under the condition of setting up in above-mentioned hypothesis, B²/ C obeys the χ that the free degree is (K-1) approx²PointCloth. For given level of significance α, ifThink that hypothesis H0 is vertical; No, can think that the equal supposition of calibration parameters is set up under K group stress level. Therefore, pass throughStructure Bartlett test statistics, can show that numerical control finished circuit board is under different stress combinationsForm parameter equate, i.e. the constant conclusion of failure mechanism.

Three, to according to parameter Estimation and the inspection of the constructed acceleration model of the present invention

The constructed acceleration model according to the present invention, known:

Wherein i=0,1 ..., l;j=0,1,…，k

μ_ijWithout inclined to one side estimation, and coefficient of variation valueLooking into " table for reliability test " can obtain,Get final product variance not wait linear model as follows:

Order

$A=\mathrm{diag}(A_{r_{11},n_{11}},A_{r_{12},n_{12}},\&CenterDot;\&CenterDot;\&CenterDot;,A_{r_{\mathrm{ij}},n_{\mathrm{ij}}})$

The matrix form of above-mentioned expression formula is

$\left\{\begin{array}{c}E\left(\widehat{\mathrm{\&mu;}}\right)=\mathrm{X\&beta;}\\ \mathrm{Var}\left(\widehat{\mathrm{\&mu;}}\right)={\mathrm{\&sigma;}}^{2}A\end{array}\right.$

By Gauss-Markov theorem, can obtain the BLUE(optimum linearity of β without inclined to one side estimation) be estimated as

$\widehat{\mathrm{\&beta;}}={\left(X^{\&prime;}{A}^{-1}X\right)}^{-1}{X}^{\&prime;}{A}^{-1}\widehat{\mathrm{\&mu;}}$

And have $\mathrm{Var}\left(\widehat{\mathrm{\&beta;}}\right)={\left(X^{\&prime;}{A}^{-1}X\right)}^{-1}{\mathrm{\&sigma;}}^2$

To every in the acceleration model building, especially whether interaction item is necessary to stay acceleration mouldIn type, need to do hypothesis testing and confirm one by one, set up accordingly following three hypothesis

H_0i:β_i＝0，i=1,2,3

If H₀₁Set up, accelerate stress S⁽¹⁾Characteristics life is not made a difference, can reject; To H₀₂ClassSeemingly. If H₀₃Set up, illustrate that in acceleration model, interaction item is unnecessary, can reject.

Ask aboveProcess in known

$E\left({\widehat{\mathrm{\&beta;}}}_i\right)={\mathrm{\&beta;}}_i,\mathrm{Var}\left({\widehat{\mathrm{\&beta;}}}_i\right)=C_{\mathrm{ii}}{\mathrm{\&sigma;}}^2,$ Wherein C_ii=(X'A^-1X)^-1

Now can use normal distribution N (β_i，C_iiσ²) conductAPPROXIMATE DISTRIBUTION. If H₀₁Set up,

${\widehat{\mathrm{\&beta;}}}_i~N(0,C_{\mathrm{ii}}{\mathrm{\&sigma;}}^2)$

? $Z_i=\frac{{\widehat{\mathrm{\&beta;}}}_i}{\sqrt{C_{\mathrm{ii}}}\mathrm{\&sigma;}}~N\left(\mathrm{0,1}\right)$

Z_iAs H₀₁Test statistics, to given level of significance α (0 < α < 1), if | Z_i|≥u_α/2，Refuse H_0i, think β_i≠ 0, this should be retained in acceleration model; If | Z_i|<u_α/2, think H_0iSet up β in acceleration model_iItem can be rejected, wherein u_α/2For standardized normal distributionUpside quantile.

Those skilled in the art will readily understand, the foregoing is only preferred embodiment of the present invention,Not in order to limit the present invention, all any amendments of doing within the spirit and principles in the present invention, etc.With replacement and improvement etc., within all should being included in protection scope of the present invention.

Claims (1)

1. the reliability fast assessing method of numerical control finished circuit board under environment comprehensive effect, itsBe characterised in that, this numerical control finished circuit board is the copper-clad plate of FR-4 type epoxy prepreg, and selection temperature,These factors of relative humidity and Dc bias be used as causing this circuit board generation electrochemical migration phenomenon andThree integrated environment stress conditions that cause failure of insulation, the method comprises the following steps:

(i) for building, the numerical control finished circuit board of pending reliability fast assessing is used for characterizing its productAcceleration model between characteristics life and main acceleration stress is as follows:

$ln\mathrm{\&eta;}={\mathrm{\&beta;}}_0+{\mathrm{\&beta;}}_1\frac{1}{T}+{\mathrm{\&beta;}}_2\ln V+{\mathrm{\&beta;}}_3\frac{\ln V}{T}$

Wherein, η represents the product feature life-span of FR-4 type epoxy prepreg copper-clad plate to be measured,LnV is respectively the function representation that sign temperature and Dc bias exerted an influence to this product feature life-spanFormula,The function expression that characterizes interactive relation between temperature and Dc bias, β₀、β₁、β₂Withβ₃Represent respectively coefficient correlation to be estimated;

(ii) combined with electrochemical migration failure mechanism, will speed up relative humidity in life test criticalValue is set as 85%, and the normal stress level of these two stress of temperature and Dc bias is set to respectively T₀WithV₀, high stress level is set to respectively T_maxAnd V_max, accelerate stress level and be set toT₀＜T₁＜...＜T_l≤T_maxAnd V₀＜V₁＜...＜V_k≤V_max, wherein l and k are respectively that above-mentioned two acceleration shouldThe number of levels of power and must not be less than 4;

In addition, the number of combinations by temperature and Dc bias between the two is set as being no less than 5 groups,And accelerate to arrange accelerated aging in the mode of Fix-Time Censored Test under stress level combination at l × kThe failure of insulation lifetime data of corresponding acquisition is recorded in test simultaneously, and wherein truncated time is τ, corresponding instituteThe failure of insulation lifetime data obtaining isI=1 ..., l and j=1 ..., k;

(iii) choose Weibull Lifetime Distribution Model as the copper-clad plate of described FR-4 type epoxy prepregLifetime Distribution Model, and this Lifetime Distribution Model chosen position scale model, then according to step(ii) the described failure of insulation lifetime data that the difference of obtaining is accelerated under stress level combination comes thisWeibull Lifetime Distribution Model carries out parametric solution, accelerates to lose efficacy under stress level combination thus in differenceIt is also under the constant prerequisite of the form parameter of Weibull Lifetime Distribution Model that mechanism remains unchanged, and calculatesEach characteristics life value of accelerating the FR-4 type epoxy prepreg copper-clad plate under stress level combination;

(iv) according to calculated characteristics life value, to the acceleration mould of setting up by step (i)Type carries out process of fitting treatment to determine described coefficient correlation β₀、β₁、β₂And β₃, thus according to fixedDescribed acceleration model and described Weibull Lifetime Distribution Model, cover copper to described FR-4 type epoxy prepregPlate is carried out reliability fast assessing, thereby obtains this FR-4 type epoxy prepreg copper-clad plate in homeReliability index value under combined stress.