CN105184413A - Product optimal aging test time estimation method of considering manufacture quality deviation loss - Google Patents

Abstract

The present invention relates to a product optimal aging test time estimation method of considering manufacture quality deviation loss. The method comprises the steps of 1, quantifying the deviation effects of representing the quality deviation Type-I type and Type-II type manufacture defects; 2, establishing a fateful Type-I type manufacture defect correlated factory yield loss cost model Y0; 3, quantifying the truncated novel defect size distribution s1(x); 4, determining the novel size characteristic distribution s2 (x); 5, establishing a non-fatal Type-II type manufacture defect correlated warranty cost model W0; 6, determining the novel size characteristic distribution s3 (x) according to a size growth rule; 7, establishing an aging cost model Cb and a failure cost model Wb within an aging duration b; 8, quantifying the truncated novel defect size distribution s4 (x) after an aging test; 9, determining the novel size characteristic distribution s5 (x) according to the size growth rule; 10, establishing a warranty cost model W1 within a warranty period w; 11, quantifying the aging cost delta 1 added by the aging test; 12, quantifying an aging test environment to reduce the quality deviation loss delta 2; 13, establishing a target function g(b), and solving a formula to determine the optimal aging time.

Description

A kind of product optimum ageing test duration evaluation method considering workmanship deviation loss

Technical field

The invention provides a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss, belong to electronic product reliability test and administrative skill field.

Background technology

Electronic product is widely used in all trades and professions of national economy, and all types of industries and consumer products mostly have electronic module.The quality of electronic product and technical merit are the concentrated reflections of contemporary new and high technology, day by day fierce along with market competition, and its reliability level has become the focus of the common concern of terminal user and manufacturing enterprise.The important supplement that the fail-test of electronic product and administrative skill manage as traditional quality, is more and more subject to the attention of vast Electronic products manufacturing enterprise and becomes the emphasis of reliability system engineering technical research.

In Electronic products manufacturing process, after the testing experiment that dispatches from the factory, the number of faults that the product of batch production occurs in the initial stage come into operation and the order of severity are that customers' perception product quality is good and bad and form the key that consumption trusts.In the electronic product early application stage, product exposes the initial failure caused by series of problems such as design defect, manufacturing defect, faults in material gradually, present higher failure rate, and have rapid downward trend feature, its reliability level presents tub curve shape.After the early stage break-in of certain hour, product reliability level constantly approaches designed reliability target, and the failure rate impact of Changing Pattern on electronic product serviceability limit stage of infant mortality is great.A large amount of engineering practice shows, the potential manufacturing defect that the initial failure of product is mainly caused by fabrication phase mass property deviation causes, these potential manufacturing defect not easily detect in traditional quality inspection link, to flow in consumer hand with the form of " up-to-standard product " and using initial stage to cause and time, fault that stress is relevant, bring serious quality and reliability problem.Intrinsic uncertainty in production run determines the existence of workmanship deviation, affects the stability of production run, makes the difficult quality guarantee manufactured a product, and the careless omission of quality inspection links is degrading the quality and reliability level that client uses perception further.Visible, for ensureing the product reliability level of batch production, consider that the link such as certificate authenticity, screening of manufacture process workmanship deviation information appropriate design production end is that prevention product occurs that relatively high infant mortality is crucial.

Ageing test (Burn-intesting) engineering is commonly used to reject initial failure product, improves the method for system reliability.For reducing infant mortality, aging test is used to screening and rejecting has mass defect, and wherein the length of burning-in period directly decides the usefulness of ageing test, and the determination of optimum burning-in period is the key of effectively carrying out electronic product shaker test.Present stage, about the research of the seasoned test period of the best, in different constraints as specific average remaining lifetime, specific Task Reliability, specific failure rate, under maximum seasoned test capabilities etc. limit, pay close attention to the structure of cost model on the one hand, pay close attention to the warranty policy type of product on the other hand.For with the optimum ageing analysis that to eliminate fault features be ultimate aim more based on aging test to the reliability achievement of guarantee or maintenance or the improvement of benefit afterwards, prior art scheme have ignored the prior imformations such as the mass deviation of a large amount of fabrication phase preciousness, is also unfavorable for helping Corporate Identity to cause the Critical to quality of the fabrication phase of initial failure, eliminate initial failure from root.Along with the increasingly stringent that people require product reliability, how will the workmanship deviation loss of the higher infant mortality of product be caused to incorporate seasoned test period optimization, and domination sign workmanship deviation loss model reflects underlying quality fluctuation impact, becomes seasoned test period and optimizes the new difficult problem in field.This patent is from the hidden loss of manufacture process quality fluctuation, definition workmanship deviation loss is the extra cost that manufacturing defect that quality fluctuation causes is brought production cost, and it comprises warranty charges 2 part of good devices under the yields failure costs of the test failure device that dispatches from the factory and specific warranty policy.Meanwhile, select the size of flaw size as the qualitative character portraying manufacturing defect, with the effect of time stress, think that flaw size meets certain increasing law and makes nonfatal manufacturing defect can develop into mortality defect with high costs.And then, lost by the mass deviation of the ageing cost and minimizing that add rear increase of weighing aging test, launch the analysis of more comprehensive optimum burning-in period from economy point, with fundamentally make up in traditional sense passive used by product before break-in and screening expose defect and make hazard rate be reduced to the deficiency of the post of normal condition.The invalid characteristic of used for products life cycle management, client, to the susceptibility of initial failure, determines the importance and urgency of carrying out initial failure stage failure mechanism and law study and the estimation of optimum burning-in period in traditional tub curve.For this reason, The present invention gives a kind of method considering the optimum ageing test duration estimation of the product of workmanship deviation loss, for assessment of the interact relation of manufacture process mass deviation loss to the product optimum ageing test duration.

Summary of the invention

(1) object of the present invention: the optimizing research for traditional infant mortality focuses mostly under set warranty policy and minimum cost to the narrow sense optimization of aging test time, existing method does not take into full account the impact of the workmanship deviation loss causing the higher infant mortality of product, make the optimization of seasoned time independent of the source cost of fabrication phase, fundamentally can not instruct the prioritization scheme reduced for infant mortality, manufacture process Quality Control And Reliability is caused to verify the problem disconnected, the invention provides the optimum burning-in period evaluation method of a kind of new product---a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss.It with the obviate of defect pipelines for visual angle, take into full account and pay attention to the information fusion of manufacture process mass deviation information and convectional reliability data, this new ageing criterion of workmanship deviation loss model is characterized by domination, on the one hand in order to reflect underlying quality fluctuation, on the other hand in order to support carrying out of analysis of optimum ageing test duration.Based on the different deflection effects of manufacturing defect, set up dependent deviation loss analysis model, and then considering that the interpolation of ageing testing experiment is on the basis of the impact of constructed mass loss model, the growth discussing flaw size to the regulating and controlling effect of invalidation reports and maintenance cost, and launches the Optimization analyses of the burning-in period of cost control guiding.The deviation loss effect of pay abundant attention manufacture process defect of the present invention, compensate for the vacancy of traditional infant mortality optimization to the preventative monitoring of manufacturing defect caused by underlying fluctuation, can promote that vast manufacturing enterprise is to the objective cognition of optimum ageing test duration and assessment.

(2) technical scheme:

The present invention is a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss, and the basic assumption of proposition is as follows:

Suppose that 1 electron device can not be repaiied.

Suppose that 2 warranty policies are freely change guarantee in the guarantee period.

Suppose that the ageing environment of 3 devices is approximate consistent with normal line environment.

Suppose that 4 aging tests can not cause other any new failure modes.

Suppose that the brand loss that 5 device performance degenerations bring is not considered.

The qualitative character supposing 6 electron devices is flaw size, belongs to prestige compact nature.

When supposing that 7 manufacturing defect sizes are greater than a certain specific critical size x °, think component failure.

Suppose that negative binomial distribution is obeyed in 8 per device defect concentration distributions.

Based on above-mentioned hypothesis, the present invention proposes a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss, its step is as follows:

The Type-I type of step 1 quantization signifying mass deviation and two class deflection effects of Type-II type manufacturing defect;

Step 2 builds the relevant yields failure costs model Y that dispatches from the factory of mortality Type-I type manufacturing defect ₀;

Step 3 quantizes the novel flaw size distribution s of truncation after factory testing ₁(x);

Step 4 determine according to the novel size characteristic distribution s of size increasing law ₂(x);

Step 5 builds the relevant warranty charges model W of non-lethal Type-II type manufacturing defect ₀;

Step 6 determine according to the novel size characteristic distribution s of size increasing law ₃(x);

Step 7 builds the ageing cost model C under ageing effect _band the inefficacy cost model W in ageing duration b _b;

Step 8 quantizes the novel flaw size distribution s of truncation after aging test ₄(x);

Step 9 determine according to the novel size characteristic distribution s of size increasing law ₅(x);

Step 10 builds the warranty charges model W used in guarantee period w ₁;

The ageing expense Δ that step 11 increases under quantizing the plan of ageing testing experiment ₁;

The mass deviation loss Δ that step 12 reduces under quantizing ageing test environment ₂;

Step 13 sets up objective function g (b), considers from economical angle, by solving determine the optimum ageing test duration.

Wherein, the Type-I type of the quantization signifying mass deviation described in step 1 and two class deflection effects of Type-II type manufacturing defect, refer to when describing the qualitative character of manufacturing defect with size characteristic x, givenly causing product failure and underproof manufacturing defect critical size threshold value x °, there is different deflection effects in the different manufacturing defect of size.If existing defects size x > is x °, be the large scale feature model defect of Type-I type depending on such defect, corresponding defect effect is: affect device manufacturing processes yields level; If existing defects size x≤x °, be the small size features manufacturing defect of Type-II type depending on such defect, corresponding defect effect is: affect device reliability level; The cost angle of mass deviation, the unit that there is large scale feature mortality defect is disallowable, cause the yields failure costs that test of dispatching from the factory is relevant, and the unit that there is small size features non-lethal defect causes recessive cost equally, through flaw size growth and concentrate in early days failure phase manifest, bring the warranty charges under specific warranty policy.

Wherein, the yields failure costs model Y that dispatches from the factory that the structure mortality Type-I type manufacturing defect described in step 2 is relevant ₀refer to based on set flaw size feature distribution s ₀(x) and exceed the Probability p that critical size x ° causes component failure because flaw size is excessive ₁=Pr (x > x ° | s ₀(x)), by the impact of mortality defect effect, electron device is judged to the underproof yields failure costs that dispatches from the factory and is here, c ₀for the selling price of unit device, N refers to the manufacturing defect number that per-unit electronics device comprises.

Wherein, the novel flaw size distribution s of truncation after the quantification factory testing described in step 3 ₁x () refers to that the test due to factory inspection eliminates the mortality defect exceeding critical size x °, Initial Flaw Size feature distribution s ₀x () changes, refining is the Size Distribution s of truncation ₁x (), its flaw size size meets x ₁≤ x °.

Wherein, the determination described in step 4 according to the novel size characteristic distribution s of size increasing law ₂x () refers to that flaw size increasing law meets RULE-1: flaw size is with coefficient k ₁ratio is in present defect size size x ₁(x ₁~ s ₁(x)) speed increase, namely there is relation: dx, t=k ₁x ₁, given warranty duration w, the flaw size x after increasing accordingly ₂for $x_2=x_1{e}^{k_{1}w}.$

Wherein, the warranty charges model W that the non-lethal Type-II type manufacturing defect built in step 5 is relevant ₀refer to and exceed based on the increase because of non-lethal defect or reliability defect size the Probability p that critical size x ° causes component failure ₂, by the impact that non-lethal flaw size increases, the warranty charges in the use guarantee period is here, c ₁for the invalidation reports of unit device in guarantee period w.

Wherein, step 6 determination according to the novel size characteristic distribution s of size increasing law ₃x () refers to that flaw size increasing law meets RULE-2: flaw size is with coefficient k ₂ratio is in present defect size size x ₁(x ₁~ s ₁(x)) rate of rise increase.Namely there is relation: dx/dt=k ₂x ₁, in ageing duration b, the flaw size x after increasing accordingly ₃for

Wherein, the ageing cost model C under ageing effect is built in step 7 _band the inefficacy cost model W in ageing duration b _brefer to C respectively _b=c ₂+ c ₃* b, wherein, c ₃for the unit interval ageing cost of time correlation, c ₄for the invalidation reports of unit device in ageing duration b.

Wherein, the novel flaw size distribution s of truncation after aging test is quantized in step 8 ₄x () eliminates size in non-lethal defect through the test of aging test to increase and exceed the segmental defect sample of critical size x °, ageing flaw size feature distribution s ₃x () changes, refining is the Size Distribution s of truncation ₄x (), its flaw size size meets x ₄≤ x °.

Wherein, in step 9 according to size increasing law obtains novel size characteristic distribution s ₅(x).

Wherein, the warranty charges model W in the use guarantee period w built in step 10 ₁for wherein, p ₄for exceeding the probability that critical size x ° causes component failure due to the increase of non-lethal defect or reliability defect size, (1-p ₁) N (1-p ₃) be the number (1-p of non-lethal defect undersized after aging test ₁) N (1-p ₃).

Wherein, the ageing expense Δ increased under aging test plan in step 11 ₁comprise following two parts: fixing aging test environmental preparation expense c ₂, the aging test expense c of time correlation ₃* b, is the ageing expense C in ageing duration _b, i.e. Δ ₁=C _b=c ₂+ c ₃* b.

Wherein, the mass deviation loss Δ reduced under ageing environment in step 12 ₂the loss L of poor quality by per device under measurement home ₀=Y ₀+ W ₀with the mass deviation loss L based on per device under aging test plan ₁=Y ₀+ W ₁+ W _bbetween difference determined, i.e. Δ ₂=L ₀-L ₁.

Wherein, objective function g (b) set up in step 13 is g (b)=Δ ₂-Δ ₁.In theory, g (b) is greater than to equal 0, carries out ageing test and is only significant.In concrete operations, with quadratic distribution f (.)=Ax ²+ Bx+C carries out matching to objective function g (b), namely decomposes g (b) for g (b)=Ab ²+ Bb+C, thus determine Eco-power optimum burning-in period b ^*and best g (b ^*) analytic solution.

(3) a kind of method considering the optimum ageing test duration estimation of the product of workmanship deviation loss of the present invention, it uses step as follows:

Step 1 is based on set flaw size feature distribution s ₀x (), determines to exceed because flaw size is excessive the Probability p that critical size x ° causes component failure ₁, computing formula is as follows,

Here, initial flaw size feature distribution s ₀x the expression formula of () is as follows,

$s_0\left(x\right)=\left\{\begin{array}{cc}\frac{x}{x^{*2}},& 0<x\&le;x^{*}\\ \frac{x^{*2}}{x^3},& x^{*}<x<\mathrm{\&infin;}\end{array}\right.$

The selling price c of the given per device of step 2 ₀, determine that electron device is judged to the underproof yields failure costs that dispatches from the factory through electric performance test and functional test

Here, N refers to the manufacturing defect number that per-unit electronics device comprises, and the defect concentration distribution of having merged the negative binomial distribution definition of defect buildup effect of available classics is portrayed.That is,

$\begin{array}{c}\mathrm{Pr}\left(N=n\right)={\&Integral;}_0^{\mathrm{\&infin;}}\frac{e^{-\mathrm{\&Lambda;}}{\mathrm{\&Lambda;}}^n}{n!}\frac{1}{\mathrm{\&Gamma;}\left(\mathrm{\&alpha;}\right){\mathrm{\&lambda;}}^{\mathrm{\&alpha;}}}{\mathrm{\&Lambda;}}^{\mathrm{\&alpha;}-1}{e}^{-\mathrm{\&Lambda;}/\mathrm{\&gamma;}}d\mathrm{\&Lambda;}\\ =\frac{\left(n+\mathrm{\&alpha;}-1\right)!}{n!(\mathrm{\&alpha;}-1)!}{\left(\frac{\mathrm{\&lambda;}/\mathrm{\&alpha;}}{1+\mathrm{\&lambda;}/\mathrm{\&alpha;}}\right)}^n{\left(1+\mathrm{\&lambda;}/\mathrm{\&alpha;}\right)}^{\mathrm{\&alpha;}}\end{array}$

Wherein, λ=α γ.α is the defect buildup effect factor, and span is between 0.5 to 5, and α value is less, and corresponding buildup effect is larger.Correspondingly, the expectation value of N

Step 3 is measured by initial size distribution s ₀distribution s after (x) truncation ₁x () is in process flaw size propagation process after new size characteristic distribution s ₂x (), has following form,

$s_2\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-p_1}\frac{x}{e^{k_{1}w}{\left(x^{*}\right)}^2},& 0<x\&le;x^{*}{e}^{k_{1}w}\\ \frac{1}{1-p_1}\frac{{\left(x^{*}\right)}^2{\left(e^{k_{1}w}\right)}^3}{x^3},& x^{*}{e}^{k_{1}w}<x\&le;x^0{e}^{k_{1}w}\end{array}\right.$

Wherein, w is the Size Distribution s of given warranty duration, truncation ₁x () has following form:

$s_1\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-p_1}\frac{x}{x^{*2}},& 0<x\&le;x^{*}\\ \frac{1}{1-p_1}\frac{x^{*2}}{x^3},& x^{*}<x\&le;x^0\end{array}\right.$

Step 4 is based on set flaw size feature distribution s ₂x (), determines to exceed because flaw size is excessive the Probability p that critical size x ° causes component failure ₂, formula is as follows,

The invalidation reports c of the given per device of step 5 in guarantee period w ₁, determine to use the warranty charges in the guarantee period $W_0=c_1*\&lsqb;1-{(1-p_2)}^{(1-p_1){\mathrm{Np}}_2}\&rsqb;.$

Step 6 measures the distribution s after truncation ₁x () is in process flaw size propagation process after new size characteristic degree distribution s ₃x (), has following form,

$s_3\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-p_1}\frac{x}{e^{k_{2}b}\left(x^{*}\right)},& 0<x\&le;x^{*}{e}^{k_{2}b}\\ \frac{1}{1-p_1}\frac{{\left(x^{*}\right)}^2{\left(e^{k_{2}b}\right)}^3}{x^3},& x^{*}{e}^{k_{2}b}<x\&le;x^0{e}^{k_{2}b}\end{array}\right.$

Step 7 is based on set flaw size feature distribution s ₃x (), determines to exceed because flaw size is excessive the Probability p that critical size x ° causes component failure ₃, Computing Principle is as follows,

The unit interval ageing cost c that step 8 preset time is relevant ₃and the invalidation reports c of per device in ageing duration b ₄, determine the ageing expense C in ageing duration _b=c ₂+ c ₃* b and the interior relevant inefficacy expense of ageing duration $W_b=c_4*\&lsqb;1-{(1-p_3)}^{(1-p_1){\mathrm{Np}}_3}\&rsqb;.$

Step 9 is measured by Size Distribution s ₃distribution s after (x) truncation ₄x () is in process flaw size propagation process after new size characteristic distribution s ₅x (), has following form,

$s_5\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-p_3}\frac{1}{1-p_1}\frac{x}{e^{k_{2}b+k_{1}w}{\left(x^{*}\right)}^2},& 0<x\&le;\min \left(x^{*}{e}^{k_{2}b+k_{1}w},x^0,e^{k_{1}w}\right)\\ \frac{1}{1-p_3}\frac{1}{1-p_1}\frac{{\left(x^{*}\right)}^2{\left(e^{k_{2}b+k_{1}w}\right)}^3}{x^3},& \min \left(x^{*}{e}^{k_{2}b+k_{1}w},x^0,e^{k_{1}w}\right)<x\&le;x^0{e}^{k_{1}w}\end{array}\right.$

Here, the distribution s of truncation ₄x the distribution of () is as follows:

$s_4\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-p_3}\frac{1}{1-p_1}\frac{x}{e^{k_{2}b}{\left(x^{*}\right)}^2},& 0<x\&le;x^{*}{e}^{k_{2}b}\\ \frac{1}{1-p_3}\frac{1}{1-p_1}\frac{{\left(x^{*}\right)}^2{\left(e^{k_{2}b}\right)}^3}{x^3},& x^{*}{e}^{k_{2}b}<x\&le;x^0\end{array}\right.$

Step 10 is based on set flaw size feature distribution s ₅x (), the increase due to non-lethal defect or reliability defect size exceeds the Probability p that critical size x ° causes component failure ₄, computation process is as follows,

If $min\left(x^{*}{e}^{k_{2}b+k_{1}w},x^0{e}^{k_{1}w}\right)=x^0{e}^{k_{1}w},$ Namely exist $b\&GreaterEqual;\frac{{\mathrm{lnx}}^0-{\mathrm{lnx}}^{*}}{k_2},$ Namely $x_5=x^0{e}^{k_{1}w}$ There is contradiction.

If $\min \left(x^{*}{e}^{k_{2}b+k_{1}w},x^0{e}^{k_{1}w}\right)=x^{*}{e}^{k_{2}b+k_{1}w},$ Namely exist $b<\frac{{\mathrm{lnx}}^0-{\mathrm{lnx}}^{*}}{k_2},$ Now s ₅x () has following form:

$s_5\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-p_3}\frac{1}{1-p_1}\frac{x}{e^{k_{2}b+k_{1}w}{\left(x^{*}\right)}^2},& 0<x\&le;x^{*}{e}^{k_{2}b+k_{1}w}\\ \frac{1}{1-p_3}\frac{1}{1-p_1}\frac{{\left(x^{*}\right)}^2{\left(e^{k_{2}b+k_{1}w}\right)}^3}{x^3},& x^{*}{e}^{k_{2}b+k_{1}w}<x\&le;x^0{e}^{k_{1}w}\end{array}\right.$

If $w<\frac{{\mathrm{lnx}}^0-{\mathrm{lnx}}^{*}-k_{2}b}{k_1},$ Then

If $w\&GreaterEqual;\frac{{\mathrm{lnx}}^0-{\mathrm{lnx}}^{*}-k_{2}b}{k_1},$ Then

Step 11 is determined to use the warranty charges in the guarantee period $W_1=c_1*\&lsqb;1-{(1-p_4)}^{(1-p_1)N(1-p_3)p_4}\&rsqb;.$

The ageing expense Δ that step 12 increases under determining ageing effect ₁=C _b=c ₂+ c ₃* the mass deviation loss of b and minimizing is Δ ₂=(Y ₀+ W) ₀-(Y ₀+ W ₁+ W _b).

Step 13 quadratic fit g (b)=Δ ₂-Δ ₁, determine optimum burning-in period b ^*and best g (b ^*) analytic solution.

(4) advantage and effect:

The present invention is a kind of method considering the optimum ageing test duration estimation of the product of workmanship deviation loss, and its advantage is:

I. the workmanship deviation loss of the present invention's proposition, from the hidden loss that manufacture process quality fluctuation causes, highlight the extra cost that the manufacturing defect that caused by quality fluctuation is brought production cost, and be applied to the optimization of ageing test duration as a brand-new constraint criterion.

Ii. the estimation of the optimum burning-in period of the product of workmanship deviation loss is considered, the prior imformation of the fabrication phase that pay abundant attention causes defect pipelines to occur, weigh with the deflection effect of defect and manufactured the potential impact of fluctuation for initial failure, achieve the ageing optimization based on production run prior imformation, the ageing test duration can be avoided to optimize independent of the source cost of fabrication phase, make up the deficiency that traditional ageing test optimization ignores the workmanship deviation information forming initial failure, can promote that the Prevention and controls of initial failure is just carried out in manufacturing enterprise's attention from the fabrication phase, help they break away from a large amount of initial failure formed after can only by the embarrassment of ageing testing experiment post.

Accompanying drawing explanation

Fig. 1 is four stage evolution process schematic diagram of manufacturing defect size characteristic under ageing environment.

Fig. 2 is flaw size x in different burning-in period b next stage I-stage II ₃evolutionary process.

Fig. 3 be in different burning-in period b next stage III-stage IV different flaw size increasing law size characteristic is distributed affect comparison diagram.

Fig. 4 is L under different defect buildup effect ₁and L ₀variation characteristic figure.

Fig. 5 is the variation characteristic figure of ageing income g (b) under different warranty duration.

Fig. 6 is FB(flow block) of the present invention.

In figure, symbol description is as follows:

X, x ₁, x ₃, x ₄, x ₅refer to the size characteristic value of different phase manufacturing defect respectively

FAT refers to the abbreviation of FactoryAcceptanceTest, i.e. factory inspection and acceptance test

B refer to ageing test the duration that continues

W refers to the warranty duration of device

L ₁refer to the workmanship deviation loss under ageing effect

L ₀refer to the workmanship deviation loss under normal environment for use

G (b) refers to set up objective function, sign be ageing income

Embodiment

Below in conjunction with accompanying drawing and example, the present invention is described in further details.

The present invention is a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss, and its step is as follows:

Collect relevant manufacturing information and the reliability information of certain model computer board.The basic cost data being given computer board reality by computer board design and managerial personnel are c ₀=850 (selling prices), c ₁=2000 (in the guarantee period invalidation reports), c ₂=18 (aging test environmental preparation expenses), c ₄=60 (ageing invalidation reports); Pass through the analysis to computer board fault by Reliability Engineer and maintenance technician, the parameter providing the negative binomial distribution that manufacturing defect sum N obeys is λ=3, and threshold value crucial x °=450 of flaw size, the mode of flaw size is x ^*=220, the growth of defect scale-up factor k under normal operating condition ₁=2.5E-05/hour, and the growth of defect scale-up factor k under ageing environment ₂=0.01.These information are optimize the optimum ageing test duration of certain model computer board to provide abundant basic data.

See Fig. 6, the present invention is a kind of considers the optimum ageing test duration evaluation method of the product of workmanship deviation loss, and the method concrete steps are as follows:

Step 1 determines to exceed because flaw size is excessive the Probability p that critical size x ° causes component failure ₁=Pr (x > 450|s ₀(x)).Based on given basic data, number determines four stage flaw size feature evolution processes of the manufacturing defect caused by manufacture deviation, as shown in Figure 1.Namely flaw size x is determined, x ₁, x ₃, x ₄, x ₅feature distribution.Wherein, for flaw size x in different burning-in period b, stage I-stage II ₃evolutionary process and III-stage, IV stage in different flaw size increasing law respectively Fig. 2 and Fig. 3 is shown in the impact that size characteristic distributes.

Step 2 determines that electron device is judged to the underproof yields failure costs that dispatches from the factory through electric performance test and functional test

$Y_0=c_0*\&lsqb;1-{(1-p_1)}^{{\mathrm{Np}}_1}\&rsqb;=850*\&lsqb;1-{(1-0.1195)}^{0.1195N}\&rsqb;.$

Wherein $E\left(N\right)=\underset{0}{\&Sigma;}n*\mathrm{Pr}(N=n).$

Step 3 measures new size characteristic distribution s ₂x (), has following form,

$s_2\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-0.1195}\frac{x}{e^{(2.5E-05)w}{\left(220\right)}^2},& 0<x\&le;220e^{(2.5E-05)w}\\ \frac{1}{1-0.1195}\frac{{\left(220\right)}^2{\left(e^{(2.5E-05)w}\right)}^3}{x^3},& 220e^{(2.5E-05)w}<x\&le;450e^{(2.5E-05)w}\end{array}\right.$

Step 4 determines to exceed because flaw size is excessive the Probability p that critical size x ° causes component failure ₂as follows:

For $w<\frac{ln450-ln220}{(2.5E-05)}$ Situation,

$p_2=\underset{450}{\overset{450e^{(2.5E-05)w}}{\&Integral;}}\frac{1}{1-0.1195}\frac{{\left(220\right)}^2{\left(e^{(2.5E-05)w}\right)}^3}{x^3}dx;$

For $w\&GreaterEqual;\frac{ln450-ln220}{(2.5E-05)}$ Situation,

$p_2=\underset{450}{\overset{220e^{(2.5E-05)w}}{\&Integral;}}\frac{1}{1-0.1195}\frac{x}{e^{(2.5E-05)w}{\left(220\right)}^2}dx+\underset{220e^{(2.5E-05)w}}{\overset{450e^{(2.5E-05)w}}{\&Integral;}}\frac{1}{1-0.1195}\frac{{\left(220\right)}^2{\left(e^{(2.5E-05)w}\right)}^3}{x^3}dx$

Step 5 is determined to use the warranty charges in the guarantee period $W_0=2000*\&lsqb;1-{(1-p_2)}^{(1-0.1195){\mathrm{Np}}_2}\&rsqb;.$

Step 6 measures new size characteristic degree distribution s ₃x (), has following result:

$s_3\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1-0.1195}\frac{x}{e^{0.01b}{\left(220\right)}^2},& 0<x\&le;220e^{0.01b}\\ \frac{1}{1-0.1195}\frac{{\left(220\right)}^2{\left(e^{0.01b}\right)}^3}{x^3},& 220e^{0.01b}<x\&le;450e^{0.01b}\end{array}\right.$

Step 7 determines to exceed because flaw size is excessive the Probability p that critical size x ° causes component failure ₃as follows:

For $b<\frac{ln450-ln220}{0.01}$ Situation,

$p_3=\underset{450}{\overset{450e^{0.01b}}{\&Integral;}}\frac{1}{1-0.1195}\frac{{\left(220\right)}^2{\left(e^{0.01b}\right)}^3}{x^3}dx$

For $b\&GreaterEqual;\frac{ln450-ln220}{0.01}$ Situation,

$\underset{450}{\overset{220e^{0.01b}}{\&Integral;}}\frac{1}{1-0.1195}\frac{x}{e^{0.01b}{\left(220\right)}^2}dx+\underset{220e^{0.01b}}{\overset{450e^{0.01b}}{\&Integral;}}\frac{1}{1-0.1195}\frac{{\left(220\right)}^2{\left(e^{0.01b}\right)}^3}{x^3}dx$

Step 8 determines the ageing expense C in ageing duration _b=18+5*b, and inefficacy expense relevant in ageing duration $W_b=60*\&lsqb;1-{(1-p_3)}^{(1-0.1195){\mathrm{Np}}_3}\&rsqb;.$

Step 9 measures new size characteristic distribution s ₅(x).Form is as follows,

For $0<x\&le;\min (220e^{0.01b+(2.5E-05)w},450e^{(2.5E-05)w})s$ Situation,

$s_5\left(x\right)=\frac{1}{1-p_3}\frac{1}{1-0.1195}\frac{x}{e^{0.01b+(2.5E-05)w}{\left(220\right)}^2}$

For $min(220e^{0.01b+(2.5E-05)w},450e^{(2.5E-05)w})<x\&le;450e^{(2.5E-05)w}$ Situation,

$s_5\left(x\right)=\frac{1}{1-p_3}\frac{1}{1-0.1195}\frac{{\left(220\right)}^2{\left(e^{0.01b+(2.5E-05)w}\right)}^3}{x^3}$

Step 10 determines the Probability p that the increase of non-lethal flaw size exceeds critical size x ° and causes component failure ₄.It is as follows,

If $w<\frac{ln450-ln220-0.01b}{(2.5E-05)},$ Then

$\begin{array}{c}{p}_4=\mathrm{Pr}\left(x_5>450|s_5\left(x\right)\right)\\ =\underset{450}{\overset{450e^{(2.5E-05w)}}{\&Integral;}}\frac{1}{1-p_3}\frac{1}{0.1195}\frac{{\left(220\right)}^2\left(e^{0.01b+(2.5E-05)w}\right)}{x^3}dx\end{array}$

If $w\&GreaterEqual;\frac{ln450-ln220-0.01b}{(2.5E-05)},$ Then

$\begin{array}{c}{p}_4=\mathrm{Pr}\left(x_5>450|s_5\left(x\right)\right)=\underset{450}{\overset{220e^{0.01b+(2.5E-05)w}}{\&Integral;}}\frac{1}{1-p_3}\frac{1}{1-0.1195}\frac{x}{e^{0.01b+(2.5E-05)w}{\left(220\right)}^2}dx\\ +\underset{220e^{0.01b+(2.5E-05)w}}{\overset{450e^{(2.5E-05)w}}{\&Integral;}}\frac{1}{1-p_3}\frac{1}{1-0.1195}\frac{{\left(220\right)}^2\left(e^{0.01b+(2.5E-05)w}\right)}{x^3}dx\end{array}$

Step 11 is determined to use the warranty charges in the guarantee period $W_1=850*\&lsqb;1-{(1-p_4)}^{(1-0.1195)N(1-p_3)p_4}\&rsqb;.$

Step 12 determines the deviation loss L under ageing effect ₁and L ₀(as follows), discusses L under different defect buildup effect ₁and L ₀variation characteristic, determine the interact relation arranged workmanship deviation loss of defect buildup effect parameter, see Fig. 4.Then the mass deviation loss reduced under obtaining ageing effect is Δ ₂=L ₀-L ₁, and determine increase ageing expense and Δ ₁=C _b=18+5*b.

$\begin{array}{c}{L}_1=Y_0+W_1+W_b\\ =850*\&lsqb;1-{\left(1-0.1195\right)}^{N0.1195}\&rsqb;\\ +2000*\&lsqb;1-{(1-p_4)}^{(1-0.1195)N(1-p_3)p_4}\&rsqb;\\ +60*\&lsqb;1-{(1-p_3)}^{(1-0.1195){\mathrm{Np}}_3}\&rsqb;\end{array}$

$\begin{array}{c}{L}_0=Y_0+W_0\\ =850*\&lsqb;1-{\left(1-0.1195\right)}^{N0.1195}\&rsqb;\\ +2000*\&lsqb;1-{(1-p_2)}^{(1-0.1195){\mathrm{Np}}_2}\&rsqb;\end{array}$

Step 13 quadratic fit objective function g (b)=Δ ₂-Δ ₁.Determine the variation characteristic of ageing income g (b) under different warranty duration, see Fig. 5.Wherein, the quadratic fit process of objective function g (b) and result as shown in table 1.

The quadratic fit process of table 1 objective function g (b) and result

As can be seen from Table 1, g (b ^*) warranty duration be w=15*30*24 hour namely 15 months time, its ageing income reaches and is g (b to the maximum ^*)=2051.86, simultaneously the ageing duration b of corresponding length rather moderate ^*=18.21, the fail-test of certain the model computer board discussed for this patent has certain guidance and practice significance.In addition, in table 1, at optimum ageing duration b ^*the both sides of=18.21, ageing income g (b ^*) show different variation characteristics.B ^*the left side of=18.21, along with the increase of ageing duration, ageing income increases gradually, but at b ^*the right side of=18.21, along with the increase of ageing duration, ageing income reduces on the contrary.How to set the accepted warranty duration of enterprises for product, determine the burning-in period duration that enterprise can bear.Simultaneously, by in step 12 for the discussion arranging the interact relation to workmanship deviation loss of defect buildup effect parameter, can find out, answer the effect of objective measure defect buildup effect when mass deviation loss modeling, determine optimum ageing length of testing speech with objective.

Claims (10)

1. consider the optimum ageing test duration evaluation method of the product of workmanship deviation loss, it is characterized in that: the method concrete steps are as follows:

The Type-I type of step 1 quantization signifying mass deviation and two class deflection effects of Type-II type manufacturing defect;

Step 2 builds the relevant yields failure costs model Y that dispatches from the factory of mortality Type-I type manufacturing defect ₀;

Step 3 quantizes the novel flaw size distribution s of truncation after factory testing ₁(x);

Step 4 determine according to the novel size characteristic distribution s of size increasing law ₂(x);

Step 5 builds the relevant warranty charges model W of non-lethal Type-II type manufacturing defect ₀;

Step 6 determine according to the novel size characteristic distribution s of size increasing law ₃(x);

Step 7 builds the ageing cost model C under ageing effect _band the inefficacy cost model W in ageing duration b _b;

Step 8 quantizes the novel flaw size distribution s of truncation after aging test ₄(x);

Step 9 determine according to the novel size characteristic distribution s of size increasing law ₅(x);

Step 10 builds the warranty charges model W used in guarantee period w ₁;

The ageing expense Δ that step 11 increases under quantizing the plan of ageing testing experiment ₁;

The mass deviation loss Δ that step 12 reduces under quantizing ageing test environment ₂;

Step 13 sets up objective function g (b), considers from economical angle, by solving determine the optimum ageing test duration;

Wherein, the Type-I type of the quantization signifying mass deviation described in step 1 and two class deflection effects of Type-II type manufacturing defect, refer to when describing the qualitative character of manufacturing defect with size characteristic x, givenly causing product failure and underproof manufacturing defect critical size threshold value x °, there is different deflection effects in the different manufacturing defect of size; If existing defects size x > is x °, be the large scale feature model defect of Type-I type depending on such defect, corresponding defect effect is: affect device manufacturing processes yields level; If existing defects size x≤x °, be the small size features manufacturing defect of Type-II type depending on such defect, corresponding defect effect is: affect device reliability level; The cost angle of mass deviation, the unit that there is large scale feature mortality defect is disallowable, cause the yields failure costs that test of dispatching from the factory is relevant, and the unit that there is small size features non-lethal defect causes recessive cost equally, through flaw size growth and concentrate in early days failure phase manifest, bring the warranty charges under specific warranty policy;

Wherein, the yields failure costs model Y that dispatches from the factory that the structure mortality Type-I type manufacturing defect described in step 2 is relevant ₀refer to based on set flaw size feature distribution s ₀(x) and exceed the Probability p that critical size x ° causes component failure because flaw size is excessive ₁=Pr (x > x ° | s ₀(x)), by the impact of mortality defect effect, electron device is judged to the underproof yields failure costs that dispatches from the factory and is in formula, c ₀for the selling price of unit device, N refers to the manufacturing defect number that per-unit electronics device comprises;

Wherein, the novel flaw size distribution s of truncation after the quantification factory testing described in step 3 ₁x () refers to that the test due to factory inspection eliminates the mortality defect exceeding critical size x °, Initial Flaw Size feature distribution s ₀x () changes, refining is the Size Distribution s of truncation ₁x (), its flaw size size meets x ₁≤ x °;

Wherein, the determination described in step 4 according to the novel size characteristic distribution s of size increasing law ₂x () refers to that flaw size increasing law meets RULE-1: flaw size is with coefficient k ₁ratio is in present defect size size x ₁(x ₁~ s ₁(x)) speed increase, namely there is relation: dx/dt=k ₁x ₁, given warranty duration w, the flaw size x after increasing accordingly ₂for

2. a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss according to claim 1, is characterized in that: the warranty charges model W that the non-lethal Type-II type manufacturing defect built in step 5 is relevant ₀refer to and exceed based on the increase because of non-lethal defect or reliability defect size the Probability p that critical size x ° causes component failure ₂, by the impact that non-lethal flaw size increases, the warranty charges in the use guarantee period is in formula, c ₁for the invalidation reports of unit device in guarantee period w.

3. the optimum ageing test duration evaluation method of a kind of product considering workmanship deviation loss according to claim 1, is characterized in that: determine in step 6 according to the novel size characteristic distribution s of size increasing law ₃x () refers to that flaw size increasing law meets RULE-2: flaw size is with coefficient k ₂ratio is in present defect size size x ₁(x ₁~ s ₁(x)) rate of rise increase, namely there is relation: dx/dt=k ₂x ₁, in ageing duration b, the flaw size x after increasing accordingly ₃for

4. a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss according to claim 1, is characterized in that: build the ageing cost model C under ageing effect in step 7 _band the inefficacy cost model W in ageing duration b _brefer to C respectively _b=c ₂+ c ₃* b, wherein, c ₃for the unit interval ageing cost of time correlation, c ₄for the invalidation reports of unit device in ageing duration b.

5. the optimum ageing test duration evaluation method of a kind of product considering workmanship deviation loss according to claim 1, is characterized in that: the novel flaw size distribution s quantizing truncation after aging test in step 8 ₄x () eliminates size in non-lethal defect through the test of aging test to increase and exceed the segmental defect sample of critical size x °, ageing flaw size feature distribution s ₃x () changes, refining is the Size Distribution s of truncation ₄x (), its flaw size size meets x ₄≤ x °.

6. the optimum ageing test duration evaluation method of a kind of product considering workmanship deviation loss according to claim 1, is characterized in that: in step 9 according to size increasing law obtains novel size characteristic distribution s ₅(x).

7. a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss according to claim 1, is characterized in that: the warranty charges model W in the use guarantee period w built in step 10 ₁for wherein, p ₄for exceeding the probability that critical size x ° causes component failure due to the increase of non-lethal defect or reliability defect size, (1-p ₁) N (1-p ₃) be the number (1-p of non-lethal defect undersized after aging test ₁) N (1-p ₃).

8. a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss according to claim 1, is characterized in that: the ageing expense Δ increased under aging test plan in step 11 ₁comprise following two parts: fixing aging test environmental preparation expense c ₂, the aging test expense c of time correlation ₃* b, is the ageing expense C in ageing duration _b, i.e. Δ ₁=C _b=c ₂+ c ₃* b.

9. a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss according to claim 1, is characterized in that: the mass deviation loss Δ reduced under ageing environment in step 12 ₂the loss L of poor quality by per device under measurement home ₀=Y ₀+ W ₀with the mass deviation loss L based on per device under aging test plan ₁=Y ₀+ W ₁+ W _bbetween difference determined, i.e. Δ ₂=L ₀-L ₁.

10. a kind of product optimum ageing test duration evaluation method considering workmanship deviation loss according to claim 1, is characterized in that: objective function g (b) set up in step 13 is g (b)=Δ ₂-Δ ₁, in theory, g (b) is greater than to equal 0, carries out ageing test and is only significant; In concrete operations, with quadratic distribution f (.)=Ax ²+ Bx+C carries out matching to objective function g (b), namely decomposes g (b) for g (b)=Ab ²+ Bb+C, thus determine Eco-power optimum burning-in period b ^*and best g (b ^*) analytic solution.