CN102651054B - Probability method of electronic product service life model based on Bayesian theory - Google Patents

Abstract

The invention discloses a probability method of an electronic product service life model based on a Bayesian theory. The probability method comprises four steps of: step 1, determining a main failure mechanism and a physical model; step 2, determining the source and a characterization method of each dispersibility in the main failure mechanism; step 3, determining the service life distribution obeyed by the main failure mechanism; and step 4, updating the parameter distribution according to the Bayesian theory, and obtaining the numerical solution of a probability service life model by combining a failure physical model and utilizing a Monte Carlo sampling method. The method disclosed by the invention is used for calculating the failure probability of a highly-reliable and long-service-life electronic product based on a stress damage model; and by analyzing diepersibility and a description method of factors such as the attribute, the size and the stress of each material causing the electronic product failure and considering the dispersibility factors on the basis of the traditional failure physical model, the probability of the failure physical model is realized, and a new approach is provided for describing the failure more accurately and forecasting the product storage life.

Description

A kind of electronic product life model randomization method based on bayesian theory

Technical field

The invention provides a kind of electronic product life model randomization method (PPoF) based on bayesian theory, particularly relate to the Failure Probability Model of the stress damage model of high reliability long life electronic product, belong to the reliability assessment technical field based on the physics of failure.

Background technology

High reliability long life electronic product generally has that performance index are high, reliability is high, long service life and development cost high.These features make traditional reliability engineering technology gradually can not meet its growth requirement.Therefore only in generation rule and the performance rule of heightened awareness product bug, correctly describe the fault behavior of product, analyse in depth product bug mechanism, review on the basis of the basic reason that causes fault, could realize the high reliability long life requirement of product.

In order to overcome above problem, the researcher in reliability field is from fault, thinking has been placed in the basic reason that causes fault, the failure mechanism of research material, part (components and parts) and structure, and the impact on product degradation or fault of analytical work condition, environmental stress and time.Thereby produced the reliability engineering based on the physics of failure.This technology was through the development of more than 40 years, the some research institutions take Univ Maryland-Coll Park USA as core have now been formed, for variety classes products such as electronics, electromechanics, had abundant failure mechanism model bank, these physics model of failures can be given the time or the amount of degradation of performance parameter and the relation of structure, function, material, working stress and environmental baseline etc. that are out of order and occur, can explain why fault of product from failure mechanism level, the problem such as when break down, really realizes product reliability design and optimization.Reliability design based on fault physics and experimental technique have obtained application comparatively widely in the leading commercial electronic company of Japan, Taiwan, Singapore, Malaysia, U.K. Ministry of Defence and the much U.S., in design and analysis, test and the evaluation process of product, are playing the part of gradually key player.

But the method for the physics of failure is not considered the uncertainty of parameter in physical model.The failure physical model of components and parts is set up is the relation of time to failure and component structure, material, stress etc.For single components and parts, the parameters such as its physical dimension, material properties determine, the life-span obtaining is thus a definite value.But for multiple components and parts, due to the impact of crudy, technology controlling and process factor, its physical dimension, material properties have uncertainty, obey certain distribution; Components and parts are in the process of using, and the parameters such as the environmental stress bearing also have randomness, and therefore its life-span should be a distribution.When utilizing failure physical model carry out plate level or Product-level longevity assessment and analyze, if do not consider the dispersiveness of product, will there is larger error in the result obtaining and verification experimental verification or the actual result obtaining.Therefore the dispersiveness of, considering each parameter on the basis of existing failure physical model is necessary.By existing technology being retrieved and looked into newly, still do not have both at home and abroad scholar to provide clearly definition and the concrete implementation step of the randomization physics of failure, also the computing method of the electronic product failure physical model randomization based on bayesian theory not.

Summary of the invention

1, object: the object of the invention is to the deficiency for existing physics of failure method, a kind of electronic product life model randomization method (PPoF) based on bayesian theory is provided, the method is a kind of high reliability long life electronic product Failure Probability Model based on stress damage model, it is by analysis, to cause the dispersiveness of the factors such as the various material properties, size, stress of electronic product fault, and studies these dispersed describing methods; On the basis of existing failure physical model, consider to add these dispersed factors, set up the relation between failure probability and time, stress, structure, material, realize the randomization of failure physical model, for describing more accurately fault, the storage life of prediction product provides a kind of new way.

2, technical scheme: the present invention is achieved by the following technical solutions, first according to the residing environmental baseline of electronic product and condition of work, determine the main failure mechanism of each components and parts, parts, determine stress condition and failure physical model that various mechanism is corresponding; Then analyze source and characterizing method dispersed in failure mechanism, obtain the prior distribution of dispersed parameter, and by monte carlo method, obtain the prior distribution of life-span obedience; Utilize bayesian theory to upgrade dispersed parameter, combine with existing failure physical model, obtain the probability description method in life-span; Finally utilize the method for Monte Carlo simulation to solve the randomization failure physical model in life-span, obtain the probability density distribution of Single Point of Faliure and relevant reliability index.

A kind of electronic product life model randomization method based on bayesian theory of the present invention, its concrete steps are as follows:

Step 1: main failure mechanism and physical model determine.According to the residing environmental baseline of electronic product and condition of work, determine the dominant mechanism that causes product failure, and select appropriate failure physical model.Failure mechanism refers to the physics, chemistry, biological of inefficacy or other the process of causing; Failure physical model refers in reliability physics for a certain specific failure mechanism, on the formula of basic physics, chemistry or other principles and (or) the basis of test regression formula, there is the mathematical function model of the relations such as (or time of origin) and material, structure, stress in the faults quantitatively of setting up, general type is as follows: TTF=f (D, M, E), wherein, TTF is time of failure, D is parameters of structural dimension, M is material parameter, and E is stress parameters.Environmental stress mainly comprises temperature, vibration, humidity, electromagnetism etc.Temperature stress is divided into again constant temperature, temperature cycles, temperature shock, and vibration is divided into again periodic vibration and random vibration.Working stress mainly refers to electric stress.

Step 2: determine source and the characterizing method of various dispersivenesses in main failure mechanism, mainly comprise:

A. because failure physical model is likely structure, stress, the isoparametric implicit function of material, cause the key parameter losing efficacy in model, directly not embody, therefore to carry out disaggregate approach to selected failure physical model, parameter is divided into material properties, physical dimension, the each several part such as defective workmanship and stress, analyze these parameters and whether all there is dispersiveness, dispersed whether directly embodiment with the parameter in model, whether also need further decomposition, between each parameter, whether there is correlativity (between temperature and humidity, correlativity between electric stress and temperature etc.), and by THE PRINCIPAL FACTOR ANALYSIS, determine the dispersiveness source of key parameter in failure physical model.

B. determine the characterizing method of key parameter dispersiveness.Although the uncertainty of various parameters can not represent with a certain occurrence it, its value is not rambling, but fluctuates in certain scope, obeys certain distribution.Therefore need to analyze and obtain the dispersiveness of these parameters characterizing method in engineering by extensive investigation or to existing experimental data, distribution and characteristic parameter thereof that each parameter is obeyed, this distribution is the prior distribution of parameter.Finally set up main failure mechanism, mechanism model, model parameter, main dispersed factor, the dispersed relational matrix that characterizes (distribution pattern) and characteristic parameter thereof of each factor, its form is as shown in table 1.

The relational matrix that table 1 obtains

Step 3: determine that the life-span that failure mechanism is obeyed distributes.The distribution that in the failure physical model that investigation is obtained, the parameter such as material, structure, stress, defective workmanship is obeyed is as the prior distribution of parameter, be designated as π (Θ), Θ represents the parameters such as material, structure, utilize monte carlo method from the prior distribution of parameter, to obtain N group parameter combinations, in conjunction with selected failure physical model, obtain N fail data.Obtained data are carried out to fitting of distribution, obtain the distribution that the life-span obeys under the known condition of parameter prior distribution π (Θ), be designated as f (t| Θ).

Step 4: distribute based on bayesian theory undated parameter, and in conjunction with failure physical model, utilize the method for Monte Carlo sampling to obtain the numerical solution of randomization life model.Mainly comprise:

Distribution f (t| Θ) and the failure physical model of a. according to life-span of obtaining in step 3, obeying, obtain the likelihood function of out-of-service time under the known condition of parameter prior distribution π (Θ)

in conjunction with bayesian theory undated parameter distribute, obtain its posteriority distribution π (Θ | t), Bayesian formula is as follows:

$\mathrm{\π}\left(\mathrm{\Θ}\right|t)=\frac{L\left(\mathrm{\Θ}\right|t)\mathrm{\π}\left(\mathrm{\Θ}\right)}{{\∫}_{\mathrm{\Θ}}L\left(\mathrm{\Θ}\right|t)\mathrm{\π}\left(\mathrm{\Θ}\right)\mathrm{d\Θ}}$

Above formula is generally difficult to directly obtain its convergence solution by the method for resolving, and in engineering, conventionally with Markov chain-Monte Carlo (MCMC), samples and solves Bayesian prior distribution.Existing a lot of ripe special software is if WinBUGS is for Bayesian inference at present.

B. according to the posteriority of the parameter obtaining, distribute, probability model in conjunction with failure physical model initiation life is described, being about to have its posteriority of dispersed parameter in physical model distributes to explain, and utilize Monte Carlo simulation method to carry out numerical solution to this model, the data that obtain are carried out to fitting of distribution and analyze the posteriority distribution that just can obtain life model, be the probability density function of Single Point of Faliure, its process and step 3 are roughly the same.And according to the relation between fiduciary level, failure probability, probability density function, obtain relevant reliability index.

By above four steps, can directly by failure physical model, obtain the probability density distribution of Single Point of Faliure and relevant reliability index, thereby realize the randomization of failure physical model.

3. advantage and effect: a kind of electronic product life model randomization method based on bayesian theory of the present invention, has the following advantages:

A. utilize " time ", " environment ", the relation of " probability " set up, estimate the index such as fiduciary level, failure probability of product, provide product reliability design to improve the relation changing with index.By the failure physical model of randomization, set up the relation between failure probability and time, stress, structure, material, the life-span that can directly obtain product distributes, and obtain its fiduciary level equiprobability index by further analysis, do not need extra test figure or historical data, thereby for design saves time and cost, and provide product reliability design to improve the relation changing with index.

B. for the complex product Reliability modeling based on fault behavior provides Data Source.In traditional fail-safe analysis, the probabilistic information of each trouble spot is mainly derived from statistics, and this method is not reviewed the basic reason that causes product bug, cannot meet the requirement of high reliability long life product.And the physics of failure of randomization is directly started with from the basic reason that causes fault, and consider the dispersed factor of each parameter, set up the relation between failure probability and time, stress, structure, material, thereby provide Data Source for the fail-safe analysis based on fault behavior.

C. for design technology parameter provides information.The information such as physical dimension, defective workmanship due to the failure physical model of randomization, have been considered, so the data that obtain the physics of failure (PPoF) analytical calculation according to randomization can provide information for design technology parameter.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 is temperature cycling test sectional view.

Fig. 3 implements Monte Carlo simulation process flow diagram.

Fig. 4 is the life-span prior distribution schematic diagram of solder joint thermal fatigue failure mechanism.

Fig. 5 (a) is the posteriority distribution schematic diagram of device length.

Fig. 5 (b) is the posteriority distribution schematic diagram of solder joint height

The posteriority distribution schematic diagram of Fig. 5 (c) temperature variation

Only poor posteriority distribution schematic diagram of Fig. 5 (d) thermal expansivity

The posteriority distribution schematic diagram in Fig. 6 life-span.

Fig. 7 is cumulative distribution function curve synoptic diagram.

Fig. 8 is fiduciary level curve synoptic diagram.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Following examples are randomization analyses of the Surface Mount solder joint thermal fatigue failure mechanism to slice component 0805, to implement according to flow process as shown in Figure 1, mainly comprise determine failure mechanism and failure physical model, determine dispersed source and characterizing method thereof in failure mechanism, determine the life-span prior distribution, utilize bayesian theory undated parameter to distribute, use Monte Carlo simulation to realize the numerical solution of randomization physical model.

See Fig. 1, a kind of electronic product life model randomization method based on bayesian theory of the present invention, concrete steps are as follows:

Step 1: failure mechanism and physical model determine.As shown in Figure 2, high temperature is 125 ℃ to the temperature cycles section of this slice component 0805, and low temperature is-55 ℃, and high low temperature respectively stops 12min.The periodicity break-make of circuit and the cyclical variation meeting of environment temperature make solder joint stand temperature cycles process, when temperature variation, not mating of thermal expansivity between electron device and circuit board can cause that solder joint bears cyclic stress strain, when plastic strain is accumulated to a certain degree, will first there is in solder joint stress concentration zones fatigue damage and finally cause solder joint thermal fatigue failure.Solder joint thermal fatigue failure physical model is a lot, and as Coffin-Manson model, Engelmaier model, full strain model etc., table 2 has been listed the usable range of part solder joint lifetimes assessment models.

Table 2 part solder joint lifetimes assessment models and applicability thereof

Wherein, Coffin-Manson model is the most widely used a kind of low-cycle fatigue life model, and it has provided the relation of the range of strain in fatigue lifetime and a circulation, and for elastic model, range of shear strain during stress relaxation is easy to obtain.

Step 2: determine source and the characterizing method of various dispersivenesses in main failure mechanism, mainly comprise:

A. life-span physical model is the mathematical function model that the relations such as (or time of origin) and material, structure, stress occur about fault, may be the relation of implicit function, material properties, physical dimension etc. causes the key parameter losing efficacy not to be embodied directly in model.Therefore need selected model to decompose, obtain the dispersiveness of each parameter.

The expression formula of Coffin-Manson model is:

$N_f=\frac{1}{2}{\left(\frac{\mathrm{\Δ\γ}}{2{\mathrm{\ϵ}}_f}\right)}^{\frac{1}{c}}---\left(1\right)$

Wherein, N _fthe times of thermal cycle that experiences while occurring to destroy for solder joint, i.e. fatigue lifetime, Δ γ is range of strain, relevant with packing forms, physical dimension, material properties, load history, ε _ffor fatigue extension coefficient, for the eutectic solder of extensive employing, ε _f=0.325, c is tired ductility index, is the parameter relevant to temperature cycles section.In model, directly do not embody the parameters such as material properties, physical dimension, stress to the impact of losing efficacy.Therefore need Δ γ and c to decompose.By investigating the research about Surface Mount solder joint both at home and abroad, the expression formula that obtains range of strain Δ γ is as follows:

$\mathrm{\Δ\γ}=F\frac{L_D\mathrm{\Δ\α\ΔT}}{h}---\left(2\right)$

Wherein h is solder joint height, L _dfor device length, Δ α=α _c-α _s, Δ T=T _max-T _min, wherein, α _c, α _sbe respectively the thermal expansivity of device and substrate, Δ T is the temperature variation in Thermal Cycling, and F is experiential modification coefficient, and value is between 0.5～1.5, and classical value is generally 1 left and right.

The formula of tired ductility index is as follows:

$c=-0.442-{0.0006T}_s+0.0174\ln (1+\frac{360}{t_D})---\left(3\right)$

Wherein, T _sthermal cycle medial temperature, t _dfor the maximum temperature residence time in the cycle, unit is min.In real work, T _sand t _ddispersiveness on the impact of fatigue lifetime, be not very large, and can be controlled in more accurate scope, therefore in this example, do not consider T _sand t _ddispersiveness, the value that can obtain tired ductility index according to the section of Fig. 2 is-0.44.

By above-mentioned decomposition analysis, the parameter that obtains affecting solder joint failure mainly contains: physical dimension is as solder joint height, device length; Material properties is as the thermal expansivity of substrate and device; Stress level is as temperature variation in Thermal Cycling etc.Now Coffin-Manson can be expressed as:

$N_f=\frac{1}{2}{\left(\frac{\mathrm{L\Δ\α\ΔT}}{0.65h}\right)}^{\frac{-1}{0.44}}---\left(4\right)$

B. determine the characterizing method of key parameter dispersiveness, obtain the prior distribution of parameter.

Determined and in model, had after dispersed key parameter need research how dispersiveness to be showed and be attached in physical model, i.e. the characterizing method of key parameter dispersiveness, obtains the prior distribution of parameter.By investigating domestic and international material properties, physical dimension, stress, the isoparametric research of defective workmanship, obtain height h, the device length L of Surface Mount solder joint _dnormal Distribution, the ratio range of standard deviation and average, between 0.1～0.3, is now got μ _h=0.3mm, σ/μ=0.15.The temperature range of device work is at-55 ℃～125 ℃, temperature inversion amount Δ T Normal Distribution, μ _{Δ T}=180 ℃, σ _{Δ T}/ μ _{Δ T}=0.1, the dispersiveness of thermal expansivity is difficult to definite, and can be along with temperature variation, according to the viewpoint of bayesian theory, can be regarded as one and be uniformly distributed, the difference Δ α that therefore gets the thermal expansivity of device and substrate obeys and is uniformly distributed, be Δ α～U (6,9).By above-mentioned analysis, the relational matrix that obtains solder joint thermal fatigue failure mechanism is as shown in table 3:

The correlation matrix of table 3 solder joint thermal fatigue failure mechanism

Step 2: the prior distribution that obtains the life-span:

A. isoparametric the difference of the thermal expansivity of device length, solder joint height, temperature variation, device and substrate prior distribution (is designated as to I (μ _i, σ _i), i represents above-mentioned parameter) be updated in Coffin-Manson model, obtain following expression:

$N_f=\frac{1}{2}{\left(\frac{I({\mathrm{\μ}}_{L_D},{\mathrm{\σ}}_{L_D})I({\mathrm{\μ}}_{\mathrm{\Δ\α}},{\mathrm{\σ}}_{\mathrm{\Δ\α}})I({\mathrm{\μ}}_{\mathrm{\ΔT}},{\mathrm{\σ}}_{\mathrm{\ΔT}})}{2\×0.325I({\mathrm{\μ}}_h,{\mathrm{\σ}}_h)}\right)}^{\frac{1}{-0.44}}---\left(5\right)$

B. utilize Monte Carlo to sample to (5) formula, set frequency in sampling be 90000 times, obtain 90000 fatigue lifetime N _f, and these data are carried out to Fitting Analysis, obtain the lognormal distribution that is distributed as that the life-span obeys under the known condition of parameter prior distribution, shown in Fig. 4 is probability density function, i.e. f (N _f| Θ), Θ represents the parameters such as material, structure, and the logarithm average obtaining is 9.69073, and logarithm variance is 0.31357, and mean lifetime is 16981.Wherein Monte Carlo simulation flow process is shown in Fig. 3.The main part of program is as follows:

Step 4: distribute based on bayesian theory undated parameter, and in conjunction with failure physical model, utilize the method for Monte Carlo sampling to obtain the numerical solution of randomization life model.Mainly comprise:

A. according to life-span of obtaining, distribute, obtain fatigue lifetime likelihood function L (Θ | N _i).Concrete steps are as follows:

According to the prior distribution of parameter, obtained thermal fatigue life obeys logarithm normal distribution, that is:

f(N _f)＝Ln(μ，σ) (6)

Wherein, μ, σ are respectively logarithm average and logarithm standard deviation.Theoretical above formula (4) has represented the average level of fatigue lifetime, and therefore the logarithm average in formula (6) can be expressed as:

$\mathrm{\μ}=\mathrm{Ln}\left(\frac{1}{2}{\left(\frac{\mathrm{L\Δ\α\ΔT}}{0.65h}\right)}^{\frac{-1}{0.44}}\right)---\left(7\right)$

Formula (7) is updated in formula (6), can obtains the condition logarithm distribution function of thermal fatigue failure:

$f\left(N_t\right|\mathrm{\Θ})=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}{N}_i}\exp (-\frac{{({\ln N}_i-\mathrm{Ln}\left(\frac{1}{2}{\left(\frac{\mathrm{L\Δ\α\ΔT}}{0.65h}\right)}^{\frac{-1}{0.44}}\right))}^2}{{2\mathrm{\σ}}^2})---\left(8\right)$

Obtain accordingly the likelihood function of fatigue lifetime:

$L\left(\mathrm{\&Theta;}\right|N_i)=\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000151727590000022.png,HDA0000151727590000033.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Pi;}}}\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;N}}_i}\exp (-\frac{{(\ln N_i-\mathrm{Ln}\left(\frac{1}{2}{\left(\frac{\mathrm{L\&Delta;\&alpha;\&Delta;T}}{0.65h}\right)}^{\frac{-1}{0.44}}\right))}^2}{{2\mathrm{\&sigma;}}^2})---\left(9\right)$

B. investigation obtains the thermal fatigue test data of similar (material, size, environment section etc. the same) Surface Mount solder joint, using this as the cycle index N obtaining under the known condition of each parameter prior distribution _i.The experimental data of using is as shown in table 4:

Table 4 calculates the experimental data that likelihood function is used

2224	1627	1842	1209	501	745	1399	906	2141	1411
										1231	2209	1424	1916	2071	562	1143	1123	2162	1574
707	983	1188	1672	1154	766	793	1110	900	2415
										1526	2199	2265	2397	2346	990	1405	759	1011	1531
2113	1194	2054	1844	813	877	951	1810	1953	2151

2208	2376	1976	1173	1726	2171	2196	1635	729	1586
										2312	1269	1740	2034	1171	1786	1394	2099	1239	1248
2216	680	2185	1039	1742	1976	2051	1981	1608	647
										1161	1457	2311	1322	706	938	1455	1063	1778	1693
2090	1851	1974	2196	646	2211	783	937	1766	2352
										2352	1154	2396	2210	1509	838	1816	1470	796	1319
1425	1792	1100	1263	823	2154	1995	1142	1962	1461
										1144	1697	2091	2068	1213	1621	1531	1244	1921	1258
2085	681	2351	1448	977	1537	1944	904	1989	1721
										710	1225	1821	1998	1023	1472	1225	1112	2309	1135
1080	1445	2191	647	608	1829	1231	1474	1041	1752
										1319	1593	2113	1492	1099	1800	2085	2157	938	2001
2208	1034	2020	1068	1685	2053	2327	1898	619	1802
										1013	1329	1815	707	2171	1319	1262	2171	1083	1405
1470	718	1511	1704	1580	1685	782	783	1740	1520
										888	1690	262	1008	1752	1011	334	346	1057	662
976	1469	775	1009	976	472	322	461	1783	1341
										553	404	697	371	1166	529	511	809	802	1835
616	822	444	745	800	797	681	706	445	507
										1519	187	943	423	1579	2287	1098	1387	1209	735
682	858	1618	1334	1723	1723	1789	858	911	1158
										749	1211	501	233	938	444	736	1237	740	529
1236	1403	1249	1698	542	913	1907	1378	2159	971
										1940	1440	2131	1587	820	1613	1876	983	2032	1198
758	999	1013	505	397	521	661	361	1013	900
										786	172	687	1345	421	604	244	528	421	1115
905	940	636	1951	1177	1432	824	615	1885	925
										1407	650	1586	1448	1617	847	1679	728	737	820
1016	998	1013	1509	851	1384	1514	1194	597	1857
										1139	788	950	1763	2116	1061	859	558	2351	900
821	712	1624	667	822	1663	1757	2104	2322	2229
										1251	1509	1016	875	605	758	647	981	1632	2166
1993	1035	1959	1801	812	1714	1982	1204	1171	2147
										2223	1151	1438	1017	1241	1554	2214	2048	1324	1518
1319	2183	2378	1144	1608	1522	2000	1873	1329	1424
										1755	1976	887	2163	2323	951	1512	1348	1990	1509
2052	1530	1735	1509	1969	2353	851	780	2087	2169
										975	1426	1238	2255	1655	1088	1249	2327	1186	1524
1000	1673	1138	857	1146	2173	1945	1779	1628	1046
										652	849	855	2256	639	1336	1098	1584	1043	1324
671	614	1111	1339	1386	1207	983	899	275	1156
										653	531	1263	504	929	353	1364	951	510	710
1087	911	650	1007	1400	1117	840	1394	680	500

C. utilize likelihood function and in conjunction with the test figure that obtains of investigation, utilize the distribution of parameter in bayesian theory Renewal model, the posteriority that obtains parameter distributes, be designated as π (Θ | N _i)=π (h, L _d, Δ T, Δ α, σ | N _f), wherein σ is logarithm standard deviation:

$\mathrm{\&pi;}\left(\mathrm{\&Theta;}\right|N_i)=\frac{L\left(\mathrm{\&Theta;}\right|N_i)I({\mathrm{\&mu;}}_{L_D},{\mathrm{\&sigma;}}_{L_D})I({\mathrm{\&mu;}}_h,{\mathrm{\&sigma;}}_h)I({\mathrm{\&mu;}}_{\mathrm{\&Delta;\&alpha;}},{\mathrm{\&sigma;}}_{\mathrm{\&Delta;\&alpha;}})I({\mathrm{\&mu;}}_{\mathrm{\&Delta;T}},{\mathrm{\&sigma;}}_{\mathrm{\&Delta;T}})}{{\&Integral;}_{L_D}{\&Integral;}_h{\&Integral;}_{\mathrm{\&Delta;T}}{\&Integral;}_{\mathrm{\&Delta;\&alpha;}}L\left(\mathrm{\&Theta;}\right|N_i)I({\mathrm{\&mu;}}_{L_D},{\mathrm{\&sigma;}}_{L_D})I({\mathrm{\&mu;}}_h,{\mathrm{\&sigma;}}_h)I({\mathrm{\&mu;}}_{\mathrm{\&Delta;\&alpha;}},{\mathrm{\&sigma;}}_{\mathrm{\&Delta;\&alpha;}})I({\mathrm{\&mu;}}_{\mathrm{\&Delta;T}},{\mathrm{\&sigma;}}_{\mathrm{\&Delta;T}}){\mathrm{dL}}_D\mathrm{dhd\&Delta;Td\&Delta;\&alpha;}}---\left(10\right)$

By (10) formula, just can upgrade the distribution of each parameter, obtain its posteriority and distribute.Generally be difficult to directly by the method for integration, try to achieve the analytic solution of (10) formula, conventionally with Markov chain-Monte Carlo (MCMC), sample and solve Bayesian prior distribution, used in this example WinBUGS software, it is a special software that utilizes monte carlo method to carry out Bayesian inference, is below the main part of program:

The posteriority that is available each parameter through the continuous sampling iteration of software distributes, and sees Fig. 5 (a), (b), (c), (d), and each characteristic parameter distributing is in Table 5.

The posteriority of the each parameter of table 5 distributes

Parameter name	Device size	Solder joint height	Temperature variation	Thermal expansivity poor
					The distribution of obeying	N(1.4577，0.4696)	N(0.28，0.09324)	N(180，3.3154)	N(7.387，0.327)

D. turn back in above-mentioned steps three, the posteriority that can obtain the life-span distributes, and is designated as f (N _f), see shown in figure 6, now obtain obeys logarithm normal distribution fatigue lifetime, logarithm average is 9.42599, and logarithm variance is 0.223659, and average is 12721.Now according to the posteriority of the parameter obtaining, distribute, corresponding Monte Carlo simulation program also can change to some extent, and changing unit is as follows:

L＝random(′norm′，mu1，sigma1，n1，1)；

h＝random(′norm′，mu2，sigma2，n3，1)；

T＝random(′norm′，mu3，sigma3，n1，1)；

alpha＝random(′norm′，mu4，sigma4，n2，1)；

E. according to the relation between probability density function and fiduciary level, failure probability etc., can obtain corresponding reliable probability index, wherein fiduciary level is:

$R\left(N_f\right)=\underset{N_f}{\overset{\&Proportional;}{\&Integral;}}f\left(N_f\right)d{N}_f---\left(11\right)$

Failure probability is:

$F\left(N_f\right)=1-R\left(N_f\right)=\underset{0}{\overset{N_f}{\&Integral;}}f\left(N_f\right){\mathrm{dN}}_f---\left(12\right)$

Fig. 7～8 are respectively failure probability curve and the fiduciary level curve of solder joint under this section.

The present invention has set up the electronic product life model method for calculating probability based on bayesian theory, utilize the method, can be without any experimental data in the situation that, utilize existing failure physical model, according to investigation or to data analysis in the past, obtain the distribution that Model Parameter is obeyed, use the distribution of parameter in bayesian theory Renewal model, the method of the Monte Carlo simulation extensively using on incorporation engineering, just can directly by failure physical model, obtain relevant reliable probability index, made up the deficiency of traditional reliability engineering technology, for the expectation of reliability and assessment provide new method.

In the present invention, quoting alphabetical physical significance illustrates as following table:

N f	Fatigue lifetime
		Δγ	Range of strain
ε f	Tired ductility coefficient
		c	Tired ductility index
F	Experiential modification coefficient
		Δα	The thermal expansivity of device and substrate poor
ΔT	Temperature variation in Thermal Cycling
		h	Solder joint height
L D	Device length
		T s	Thermal cycle medial temperature
t D	The maximum temperature residence time in semiperiod
		f(N f)	Fatigue lifetime probability density function
F(N f)	Failure probability

R(N f)	Reliability Function
		λ(N f)	Crash rate

Claims (1)

1. the electronic product life model randomization method based on bayesian theory, is characterized in that: the method concrete steps are as follows:

Step 1: the determining of main failure mechanism and physical model: according to the residing environmental stress of electronic product and working stress, determine and cause the dominant mechanism of product failure, and select appropriate failure physical model; Failure mechanism refers to the physics, chemistry, biological of inefficacy or other the process of causing; Failure physical model refers in reliability physics for a certain specific failure mechanism, on the formula of basic physics, chemistry or other principle and the basis of test regression formula, the mathematical function model of the time of origin of faults quantitatively of setting up and material, structure, stress relation, expression-form is as follows: TTF=f (D, M, E), wherein, TTF is time of failure, and D is parameters of structural dimension, M is material parameter, and E is stress parameters; Environmental stress comprises temperature, vibration, humidity, electromagnetism, and temperature stress is divided into again constant temperature, temperature cycles, temperature shock, and vibration is divided into again periodic vibration and random vibration, and working stress refers to electric stress;

Step 2: determine source and the characterizing method of various dispersivenesses in main failure mechanism, comprising:

A. because failure physical model is structure, the implicit function of stress or material parameter, cause the key parameter losing efficacy in model, directly not embody, therefore to carry out disaggregate approach to selected failure physical model, parameter is divided into material properties, physical dimension, defective workmanship and stress each several part, analyze these parameters and whether all there is dispersiveness, dispersed whether directly embodiment with the parameter in model, whether also need further decomposition, between each parameter, whether there is correlativity and by THE PRINCIPAL FACTOR ANALYSIS, determine the dispersiveness source of key parameter in failure physical model,

B. determine the characterizing method of key parameter dispersiveness: although the uncertainty of various parameters can not represent with a certain occurrence it, its value is not rambling, but fluctuates, and obeys certain distribution in certain scope; Therefore need to analyze and obtain the dispersiveness of these parameters characterizing method in engineering by extensive investigation or to existing experimental data, be distribution and the characteristic parameter thereof that each parameter is obeyed, this distribution is the prior distribution of parameter, finally set up the relational matrix of main failure mechanism, mechanism model, model parameter, main dispersed factor, the dispersed sign of each factor and characteristic parameter thereof, shown in the following list 1 of its form:

The relational matrix that table 1 obtains

Step 3: determine the life-span distribution that failure mechanism is obeyed: the distribution that in the failure physical model that investigation is obtained, material, structure, stress, defective workmanship parameter are obeyed is as the prior distribution of parameter, be designated as π (Θ), Θ represents material, structural parameters, utilize monte carlo method from the prior distribution of parameter, to obtain N group parameter combinations, in conjunction with selected failure physical model, obtain N fail data; Obtained data are carried out to fitting of distribution, obtain the distribution that the life-span obeys under the known condition of parameter prior distribution π (Θ), be designated as f (t| Θ);

Step 4: distribute based on bayesian theory undated parameter, and in conjunction with failure physical model, utilize the method for Monte Carlo sampling to obtain the numerical solution of randomization life model, comprising:

Distribution f (t| Θ) and the failure physical model of a. according to life-span of obtaining in step 3, obeying, obtain the likelihood function of out-of-service time under the known condition of parameter prior distribution π (Θ)

in conjunction with bayesian theory undated parameter distribute, obtain its posteriority distribution π (Θ | t), Bayesian formula is as follows:

$\mathrm{\&pi;}\left(\mathrm{\&Theta;}\right|t)=\frac{L\left(\mathrm{\&Theta;}\right|t)\mathrm{\&pi;}\left(\mathrm{\&Theta;}\right)}{{\&Integral;}_{\mathrm{\&Theta;}}L\left(\mathrm{\&Theta;}\right|t)\mathrm{\&pi;}\left(\mathrm{\&Theta;}\right)\mathrm{d\&Theta;}}$

Above formula is generally difficult to directly obtain its convergence solution by the method for resolving, and common in engineering is that MCMC samples and solves Bayesian prior distribution with Markov chain-Monte Carlo;

B. according to the posteriority of the parameter obtaining, distribute, probability model in conjunction with failure physical model initiation life is described, being about to have its posteriority of dispersed parameter in physical model distributes to explain, and utilize Monte Carlo simulation method to carry out numerical solution to this model, to the data that obtain carry out fitting of distribution analysis obtain life model posteriority distribute, be the probability density function of Single Point of Faliure, its process and step 3 are roughly the same, and according to the relation between fiduciary level, failure probability, probability density function, obtain relevant reliability index;

By above four steps, directly by failure physical model, obtain the probability density distribution of Single Point of Faliure and relevant reliability index, thereby realize the randomization of failure physical model.

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