CN102651054A - 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 present invention provides a kind of electronic product life model randomization method (PPoF) based on bayesian theory; The Failure Probability Model that particularly relates to the stress damage model of high reliability long life electronic product belongs to the reliability assessment technical field based on the physics of failure.

Background technology

The high reliability long life electronic product generally has characteristics such as performance index height, reliability height, long service life and development cost height.These characteristics make traditional reliability engineering technology can not satisfy its growth requirement gradually.Therefore only in the generation rule and 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; Be placed on thinking on the basic reason that causes fault, the failure mechanism of research material, part (components and parts) and structure, and analytical work condition, environmental stress and time are to the influence of product degradation or fault.Thereby produced reliability engineering based on the physics of failure.This technology was through the development in surplus 40 years; Formed is the several studies mechanism of core with the Univ Maryland-Coll Park USA at present; To variety classes products such as electronics, electromechanics; Had abundant failure mechanism model bank, these fault physical models can be given time or the amount of degradation of performance parameter and the relation of structure, function, material, working stress and environmental baseline etc. that is out of order and takes place, can be from failure mechanism level explanation product fault why; Problem such as when break down really realizes the product reliability design and optimizes.Reliability design and experimental technique based on fault physics have obtained application comparatively widely in the leading commercial electronic company of Japan, Taiwan, Singapore, Malaysia, U.K. Ministry of Defence and a lot of U.S., in design, analysis, test and the evaluation process of product, are playing the part of important role gradually.

But the method for the physics of failure is not considered the uncertainty of parameter in the physical model.The failure of elements physical model is set up is the relation of time to failure and component structure, material, stress etc.For single components and parts, parameters such as its physical dimension, material properties confirm that the life-span that obtains thus is a definite value.But for a plurality of components and parts, because the influence 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 environmental stress of being born also have randomness, so its life-span should be a distribution.When utilizing physics of failure model to carry out plate level or the evaluation of product life time of the level and analyzing, if do not consider the dispersiveness of product, will there be bigger error in result who obtains and verification experimental verification or the actual result who obtains.Therefore, on existing physics of failure model based, consider that the dispersiveness of each parameter is necessary.Through existing technology being retrieved and is looked into newly, still there is not the scholar to provide the clearly definition and the practical implementation step of the randomization physics of failure both at home and abroad, also there are not computing method based on the electronic product physics of failure model probabilityization of bayesian theory.

Summary of the invention

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

2, technical scheme: the present invention realizes through following technical scheme; At first according to residing environmental baseline of electronic product and condition of work; Confirm the main failure mechanism of each components and parts, parts, confirm stress condition and physics of failure model that various mechanism are corresponding; Analyze source and characterizing method dispersed in the failure mechanism then, obtain the prior distribution of dispersed parameter, and obtain the prior distribution of life-span obedience through monte carlo method; Utilize bayesian theory to upgrade dispersed parameter, combine, obtain the probability describing method in life-span with existing physics of failure model; Utilize the method for Monte Carlo simulation to find the solution the randomization physics of failure model in life-span at last, obtain the probability density distribution and the relevant reliability index of Single Point of Faliure.

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

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

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

A. because physics of failure model might be structure, stress, the isoparametric implicit function of material; The key parameter that causes losing efficacy does not directly embody in model; Therefore to carry out disaggregate approach to selected physics of failure model; Parameter is divided into each several parts such as material properties, physical dimension, defective workmanship and stress; Whether analyze these parameters and whether all have dispersiveness, whether dispersiveness directly embodies with Model parameter, also need further to decompose; Whether have correlativity (like the correlativity between the temperature and humidity, between electric stress and the temperature etc.) between each parameter, and confirm the dispersiveness source of key parameter in the physics of failure model through THE PRINCIPAL FACTOR ANALYSIS.

B. confirm the characterizing method that key parameter is dispersed.Although the uncertainty of various parameters makes it can not represent that its value is not rambling with a certain occurrence, but in certain scope, fluctuates, obey certain distribution.Therefore need analyze the characterizing method of dispersiveness on engineering that obtains these parameters through extensive investigation or to existing experimental data, i.e. each parameter distribution and characteristic parameter thereof of obeying, 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: confirm the Life Distribution that failure mechanism is obeyed.The distribution that parameters such as material, structure, stress, defective workmanship are obeyed in the physics of failure model that investigation is obtained is as the prior distribution of parameter; Be designated as π (Θ); Θ representes parameters such as material, structure; Utilize monte carlo method from the prior distribution of parameter, to obtain N group parameter combinations, the physics of failure model in conjunction with selected obtains N fail data.Resulting data are carried out fitting of distribution, obtain distribution, be designated as f (t| Θ) in the known obedience of following life-span of condition of parameter prior distribution π (Θ).

Step 4: distribute based on the bayesian theory undated parameter, and combine physics of failure model, utilize the numerical solution of the method acquisition randomization life model of Monte Carlo sampling.Mainly comprise:

The distribution f (t| Θ) and the physics of failure model of a. obeying according to the life-span that obtains in the step 3; Obtain combining the bayesian theory undated parameter to distribute at parameter prior distribution π (Θ) likelihood function of known following out-of-service time of condition

; Obtain its posteriority distribution π (Θ | t), Bayesian formula is following:

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

Following formula generally is difficult to directly obtain its convergence solution with the method for resolving, and samples with Markov chain-Monte Carlo (MCMC) usually on the engineering and finds the solution Bayesian prior distribution.Existing at present a lot of ripe special software such as WinBUGS are used for Bayesian inference.

B. the posteriority according to the parameter that obtains distributes; The probability model that forms the life-span in conjunction with physics of failure model is described; The parameter that will soon have dispersiveness in the physical model distributes with its posteriority and explains, and utilizes the Monte Carlo simulation method that this model is carried out numerical solution, the data that obtain is carried out fitting of distribution 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, the probability density function, the reliability index that obtains being correlated with.

Through above four steps, promptly can directly obtain the probability density distribution and the relevant reliability index of Single Point of Faliure, thereby realize the randomization of physics of failure model by physics of failure 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 of setting up ", the relation of " probability ", indexs such as the fiduciary level of expectation product, failure probability, the relation that provides product reliability design improvement and index to change.Physics of failure model through randomization; Set up the relation between failure probability and time, stress, structure, the material; Can directly obtain the Life Distribution of product, and obtain its fiduciary level equiprobability index, not need extra test figure or historical data through further analysis; Thereby for design saves time and cost, and the relation that provides product reliability design improvement and index to change.

B. for complex product Modelling of Reliability Data Source is provided based on the fault behavior.The probabilistic information of each trouble spot is mainly derived from statistics in traditional fail-safe analysis, and this method is not reviewed the basic reason that causes product bug, can't satisfy the high reliability long life requirement of products.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, the material, thereby for based on the fail-safe analysis of fault behavior Data Source being provided.

C. for the design technology parameter information is provided.Because the physics of failure model of randomization has been considered information such as physical dimension, defective workmanship, so the data that get the physics of failure (PPoF) analytical calculation according to randomization can provide information for the design technology parameter.

Description of drawings

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

Fig. 2 is the temperature cycling test sectional view.

Fig. 3 implements the Monte Carlo simulation process flow diagram.

Fig. 4 is the life-span prior distribution synoptic 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

The posteriority distribution schematic diagram that Fig. 5 (d) thermal expansivity is only poor

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

Fig. 7 is the cumulative distribution function curve synoptic diagram.

Fig. 8 is the fiduciary level curve synoptic diagram.

Embodiment

To combine accompanying drawing and embodiment that the present invention is done further detailed description below.

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

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

Step 1: the confirming of failure mechanism and physical model.The temperature cycles section of this slice component 0805 is as shown in Figure 2, and high temperature is 125 ℃, 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 the temperature cycles process; When temperature variation; Mismatch in coefficient of thermal expansion between electron device and the circuit board can cause that solder joint bears the cyclic stress strain; When plastic strain is accumulated to a certain degree, will fatigue damage at first take place and finally cause the solder joint thermal fatigue failure in the solder joint stress concentration zones.Solder joint thermal fatigue failure physical model is a lot, and like 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, the 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 the circulation, and as far as elastic model, the range of shear strain during stress relaxation is easy to obtain.

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

A. the life-span physical model is about fault (or time of origin) and the mathematical function model that material, structure, stress etc. concern to take place, and possibly be the relation of implicit function, and the key parameter that material properties, physical dimension etc. causes losing efficacy is not embodied directly in the model.Therefore need decompose selected model, 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 is experienced when take place destroying for solder joint, i.e. fatigue lifetime, Δ γ is a range of strain, and is 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 with the temperature cycles section.In model, directly do not embody of the influence of parameters such as material properties, physical dimension, stress to losing efficacy.Therefore need decompose Δ γ and c.Through investigating domestic and international research about the Surface Mount solder joint, the expression formula that obtains range of strain Δ γ is following:

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

Wherein h is a solder joint height, L _DBe 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 the thermal cycle process, and F is the experience correction factor, and value is between 0.5～1.5, and classical value is generally about 1.

The formula of tired ductility index is following:

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

Wherein, T _sBe the thermal cycle medial temperature, t _DBe the maximum temperature residence time in the cycle, unit is min.In real work, T _sAnd t _DDispersiveness be not very big to Fatigue Life, and can be controlled in the more accurate scope, so not consider T in this example _sAnd t _DDispersiveness, the value that can get tired ductility index according to the section of Fig. 2 is-0.44.

Through above-mentioned decomposition analysis, the parameter that obtains influencing solder joint failure mainly contains: physical dimension such as solder joint height, device length; The thermal expansivity of material properties such as substrate and device; Temperature variation in stress level such as the thermal cycle process etc.This moment, 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. confirm the characterizing method that key parameter is dispersed, obtain the prior distribution of parameter.

After having confirmed to have in the model dispersed key parameter, need research how dispersiveness to be showed and be attached in the physical model, i.e. the dispersed characterizing method of key parameter obtains the prior distribution of parameter.Through 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 are got μ at present between 0.1～0.3 _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 regard it as and evenly distribute, the difference Δ α that therefore gets the thermal expansivity of device and substrate obeys evenly and distributes; Be Δ α～U (6,9).Through 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. the isoparametric prior distribution of difference with the thermal expansivity of device length, solder joint height, temperature variation, device and substrate (is designated as I (μ _i, σ _i), i represents above-mentioned parameter) be updated in the Coffin-Manson model, obtain following expression formula:

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

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

Step 4: distribute based on the bayesian theory undated parameter, and combine physics of failure model, utilize the numerical solution of the method acquisition randomization life model of Monte Carlo sampling.Mainly comprise:

A. according to the Life Distribution that obtains, obtain fatigue lifetime likelihood function L (Θ | N _i).Concrete steps are following:

Prior distribution according to parameter has obtained the 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 following formula (4) has been represented the average level of fatigue lifetime, so the logarithm average in the 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 the 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 the likelihood function of fatigue lifetime in view of the above:

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

B. investigation obtains the thermal fatigue test data of similar (material, size, environment section etc. the same) Surface Mount solder joint, with this as the cycle index N that under the known condition of each parameter prior distribution, obtains _iThe 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. the test figure of utilizing likelihood function and combining investigation to obtain is utilized more parameter distributions in the new model of bayesian theory, and 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 the logarithm standard deviation:

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

Just can upgrade each parameter distributions through (10) formula, obtain its posteriority and distribute.Be difficult to directly try to achieve the analytic solution of (10) formula generally speaking with the method for integration; Usually sample with Markov chain-Monte Carlo (MCMC) and find the solution Bayesian prior distribution; Used WinBUGS software in this example; It is a special software that utilizes monte carlo method to carry out Bayesian inference, below is the main part of program:

The posteriority of each parameter that the continuous sampling iteration of process software can obtain distributes, and sees Fig. 5 (a) and (b), (c), (d), and each characteristic parameter that distributes is seen table 5.

The posteriority of each parameter of table 5 distributes

The parameter title	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 the above-mentioned steps three, the posteriority that can obtain the life-span distributes, and is designated as f (N _f), see shown in the figure 6, obtain the obeys logarithm normal distribution fatigue lifetime this moment, and the logarithm average is 9.42599, and the logarithm variance is 0.223659, and average is 12721.This moment, the posteriority based on the parameter that obtains distributed, and corresponding Monte Carlo simulation program also can change to some extent, changes part 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 this method, can have no under the situation of experimental data, utilize existing physics of failure model; Obtain the distribution that parameter is obeyed in the model according to investigation or to data analysis in the past; The utilization bayesian theory is parameter distributions in the new model more, the method for the Monte Carlo simulation that combines extensively to use on the engineering, the reliable probability index that just can directly obtained being correlated with by physics of failure model; Remedied the deficiency of traditional reliability engineering technology, for the expectation and the assessment of reliability provides new method.

Quoting the physical significance such as the following table of letter among the present invention explains:

N f	Fatigue lifetime
		Δγ	Range of strain
ε f	Tired ductility coefficient
		c	Tired ductility index
F	The experience correction factor
		Δα	The thermal expansivity of device and substrate poor
ΔT	Temperature variation in the thermal cycle process
		h	Solder joint height
L D	Device length
		T s	The 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. electronic product life model randomization method based on bayesian theory, it is characterized in that: these method concrete steps are following:

Step 1: the confirming of main failure mechanism and physical model; According to residing environmental baseline of electronic product and condition of work, confirm to cause the dominant mechanism of product failure, and select appropriate physics of failure model; Failure mechanism is meant the physics that causes inefficacy, chemistry, biological or other process; Physics of failure model is meant in the reliability physics to a certain specific failure mechanism, on the basis of the formula of basic physics, chemistry or other principle and test regression formula, and the mathematical function model of setting up that reflects time of failure and material, structure, stress relation quantitatively; Expression-form is following: and TTF=f (D, M, E); Wherein, TTF is the fault time of origin, and D is a parameters of structural dimension; M is a material parameter, and E is a stress parameters; Environmental stress comprises temperature, vibration, humidity, electromagnetism, and temperature stress is divided into constant temperature, temperature cycles, temperature shock again, and vibration is divided into periodic vibration and random vibration again, and working stress mainly is meant electric stress;

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

A. because physics of failure model might be structure, stress, the isoparametric implicit function of material; The key parameter that causes losing efficacy does not directly embody in model; Therefore to carry out disaggregate approach to selected physics of failure model; Parameter is divided into material properties, physical dimension, defective workmanship and stress each several part, analyzes these parameters and whether all have dispersiveness, whether dispersiveness directly embodies with Model parameter; Whether also need further to decompose, whether have correlativity between each parameter and confirm the dispersiveness source of key parameter in the physics of failure model through THE PRINCIPAL FACTOR ANALYSIS;

B. confirm the characterizing method that key parameter is dispersed; Although the uncertainty of various parameters makes it can not represent that its value is not rambling with a certain occurrence, but in certain scope, fluctuates, obey certain distribution; Therefore need analyze the characterizing method of dispersiveness on engineering that obtains these parameters through 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 tabulation 1 of its form;

The relational matrix that table 1 obtains

Step 3: confirm the Life Distribution that failure mechanism is obeyed; The distribution that material, structure, stress, defective workmanship parameter are obeyed in the physics of failure model that investigation is obtained is as the prior distribution of parameter; Be designated as π (Θ); Θ representes material, structural parameters; Utilize monte carlo method from the prior distribution of parameter, to obtain N group parameter combinations, the physics of failure model in conjunction with selected obtains N fail data; Resulting data are carried out fitting of distribution, obtain distribution, be designated as f (t| Θ) in the known obedience of following life-span of condition of parameter prior distribution π (Θ);

Step 4: distribute based on the bayesian theory undated parameter, and combine physics of failure model, utilize the numerical solution of the method acquisition randomization life model of Monte Carlo sampling; Comprise:

The distribution f (t| Θ) and the physics of failure model of a. obeying according to the life-span that obtains in the step 3; Obtain combining the bayesian theory undated parameter to distribute at parameter prior distribution π (Θ) likelihood function of known following out-of-service time of condition

; Obtain its posteriority distribution π (Θ | t), Bayesian formula is following:

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

Following formula generally is difficult to directly obtain its convergence solution with the method for resolving, and is that MCMC samples and finds the solution Bayesian prior distribution with Markov chain-Monte Carlo usually on the engineering;

B. the posteriority according to the parameter that obtains distributes; The probability model that forms the life-span in conjunction with physics of failure model is described; The parameter that will soon have dispersiveness in the physical model distributes with its posteriority and explains, and utilizes the Monte Carlo simulation method that this model is carried out numerical solution, the data that obtain is carried out fitting of distribution 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, the probability density function, the reliability index that obtains being correlated with;

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

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