CN102495966B - Computing method for quality loss of mechanical product based on service life distribution - Google Patents

Abstract

The invention discloses a computing method for the quality loss of a mechanical product based on service life distribution. The computing method comprises the following steps of: (1) obtaining the discounted value of quality loss fund in a period according to the discounted value of actual loss generated due to the scrapping of the mechanical product caused by reason that the quality characteristic value of the mechanical product exceeds a specialized range after the mechanical product is put into service; (2) calculating the total quality loss in the service life of the mechanical product; (3) comprehensively considering the quality characteristic distribution before the mechanical product is put into service, and the variation of the quality characteristic distribution and the tolerance technical requirements of quality characteristics after the mechanical product is put into service, and obtaining the service life distribution of the mechanical product based on the tolerance requirements of the quality characteristics and a density function of the mechanical product; and (4) introducing the density function into the step (3), and obtaining the quality loss of the mechanical product based on service life distribution. The computing method can be used for reflecting the discounted value of the actual loss generated due to the scrapping of different mechanical products under different tolerance design requirements and different service conditions and environments caused by reason that the mechanical products lose functions as the quality characteristic value of the mechanical product exceeds the specialized range.

Description

The computing method for quality loss of mechanical product distributing based on service life

Technical field

The invention belongs to mechanical product tolerance optimal design, mechanical product quality loss assessment field, say more specifically a kind of computing method for quality loss of mechanical product distributing based on service life.

Background technology

Traditional quality view is thought as long as it is exactly qualified that engineering goods meet technical requirement, does not distinguish quality grades different in qualified engineering goods.And the mass loss of field mouth proposition afterwards refers to the loss causing to society after launch, and weigh product quality loss with quadratic loss function.For the limitation of Taguchi quality loss function, lot of domestic and foreign scholar has carried out a large amount of research around product quality loss modeling.PAN is in < < Optimization of engineering tolerance design using revised loss functions > >, Li Yuebo etc. have proposed to replace field mouth quadratic function as quality loss function with contrary normal distyribution function in < < new loss function > >, solved the unboundedness Wu of Taguchi quality loss function in < < TANG G R.Tolerance design for products with asymmetric quality losses > >, Li is in < < Quality loss function based manufacturing process setting models for unbalanced tolerance design > >, Chen Xiang waits in the quality characteristic value optimization of < < asymmetric loss function and selects > > to propose asymmetric mass loss function model, Zhang Genbao etc. in < < mass loss Extended Model and economic analysis > > thereof, Wang uncle equality adopts piecewise function theory to expand Taguchi quality loss function at the research > of < < Section Curve Quality Loss Function Model >, set up segmentation mass loss model, Cao Yanlong applies fuzzy theory Taguchi's quality loss model is expanded in the foundation of < < fuzzy quality loss model and application > >, has proposed fuzzy quality loss model, the quality loss function of dynamic mass characteristic has been proposed in the < < dynamic perfromance quality loss function research > > such as Zhang Yueyi.For great majority, research concentrates on the quality loss function of single features, Lee has proposed multiple correlation feature total mass loss model in < < Tolerance design for products with correlated characteristics > >, Peng and equality have proposed the unified model of multiple correlation characteristic product in the tolerance optimization design > > based on multiple correlation characteristic mass loss function at < <, Huang etc. have carried out parallel operation tolerance design to multiple correlation fitted position in < < Concurrent process tolerance design based on minimum product manufacturing cost and quality loss > >.Wang Jun equality is set up the method for application percentage conversion and multivariate function Taylor expansion in the mathematical method > > of multiparameter mass loss model mono-kind of < <, the more common form of mass loss model has been proposed, Sun Dihua etc. adopt the quality loss function of contrary Normal Type in the research > > of < < expansion quality loss function model, set up the quality loss function model of multidimensional qualitative attribute under general situation.

No matter the said goods mass loss model is quadratic function loss model and the improved model thereof that field mouth proposes, still afterwards scholar for the use improving the limitation of Taguchi's quality loss model and propose is against normal distyribution function and improved model thereof, fuzzy quality loss model etc., be all hypothesis mass loss by a certain funtcional relationship (as quadratic function, contrary normal distyribution function, ambiguity function) change, predict the loss that society is brought, it has following features: 1) nature static, product is after factory inspection, drop into and be on active service on front timing node, be conceived to the manufacture process segment before product export, and do not consider to meet in the whole service life of product user's demand comprehensively, 2) predictability, represents the loss that product may bring society by the funtcional relationship of hypothesis, and what this root problem does not relate to product quality characteristic is dropping into the Changing Pattern after being on active service and being lost to the end.

The product quality of field mouth see the represented larger loss of the product quality characteristic value value of departing from objectives of lower loss model with regard to larger, depart from more small loss and meet convention with regard to less this relation.But product is processed, assembles, is come into operation after the assay was approved by manufacture, due to reasons such as stressed, motion and wearing and tearing, in product, element size feature constantly changes in-service, thereby causes product military service performance quality changing features, thereby causes that product quality loss changes.A.Teran quotes the cash flow present worth concept in engineering economic analysis principle in < < Present worth of external quality losses for symmetric nominal-is-better quality characteristics > >, on the basis of field mouth quality view, the temporal extension of Taguchi's quality loss is on active service the stage to product, by the mass loss changing in product military service process is discounted, a kind of symmetrical mass loss of hoping order qualitative character model of discounting has been proposed, C.-Y.Chou is in < < Minimum-loss assembly tolerance allocation by considering product degradation and time value of money > >, H.P.Peng applies Teran mass loss model and with processing cost and mass loss present worth summation minimum, carries out tolerance optimization design respectively in < < Optimal tolerance design for products with correlated characteristics by considering the present worth of quality loss > >.

Teran thinks that product quality characteristic x can change along with the time, thereby caused its average μ due to after product comes into operation _xand variances sigma (t) _x(t) constantly change, so the consecutive mean mass loss of product is

$E\left[L_x\left(t\right)\right]=k[{\mathrm{\&sigma;}}_x^2\left(t\right)+{({\mathrm{\&mu;}}_x\left(t\right)-m_x)}^2]=k[{\mathrm{\&sigma;}}_x^2\left(t\right)+{\mathrm{\&delta;}}_x^2\left(t\right)]---\left(1\right)$

In formula: k is the mass loss coefficient in process, k=C _m/ Δ ², Δ is the mobility scale that product quality characteristic is allowed, i.e. technical requirement, is called tolerance; δ _x(t) be the deviation of qualitative character value x (t).

Teran is quality loss function E[L _x(t)] be defined as and occur in the resources flow that product is on active service in phase T, and according to the definition of cash flow present worth, released product quality loss present worth model and be

$L_{\mathrm{PW}}\left(T\right)={\&Integral;}_0^{T}E\left[L_x\left(t\right)\right]e^{-\mathrm{rt}}\mathrm{dt}=k{\&Integral;}_0^T[{\mathrm{\&sigma;}}_x^2\left(t\right)+{\mathrm{\&delta;}}_x{\left(t\right)}^2]e^{-\mathrm{rt}}\mathrm{dt}---\left(2\right)$

In formula: T is product active time, r is annual rate or discount rate.

Teran product quality loss model be exactly by product be on active service the mass loss of T time be transformed to product drop into be on active service before discounting on timing node, its intension is that mass loss is along with active time increases and reduces.Although this model relates to product quality characteristic in the variation dropping into after being on active service, but still on mouth quality view basis, field, put forward, also be to predict society is brought to loss by quadratic function relation, and uselessly relate to loss itself, being lost to the end is any this root problem.And by quality loss function E[L _x(t) it is inappropriate] being considered as resources flow, because quality loss function E[L _x(t)] the loss C defective caused with product _mdimension identical, normally monetary unit, is fund, is not resources flow.The product quality loss present worth unit that formula (2) obtains is not just monetary unit.In addition, Teran mass loss model is that the product active time based on definite is calculated, and the active time of right a collection of product is not certain, but uncertain at random.If regard the service life of product as certain, just do not conform to actual conditions.

Summary of the invention

In order to solve the problems of the technologies described above, the invention provides a kind ofly can reflect that different engineering goods require in different tolerance design, under different service condition and environment because afunction causes scrapping the actual loss producing, mechanical product tolerance design is expanded to product from the product design fabrication phase and be on active service the stage, for the Changing Pattern of research mechanical product quality in the life cycle managements such as design, processing, operation phase provides the computing method for quality loss of mechanical product distributing based on service life of new solution.

The technical scheme that the present invention solves above-mentioned technical matters is: a kind of computing method for quality loss of mechanical product distributing based on service life, comprises the following steps:

1) the qualitative character value of setting certain concrete engineering goods is x (t), qualified during product export, and x (0) meets | x (0)-m _x|≤Δ, m _xfor the true value of product quality characteristic x, after product drop into be on active service, its eigenwert generation random variation, makes at t sometime | x (t)-m _x| > Δ, product is defective scraps, and defective caused loss is C _m, and then show that the loss that this product rejection produces discounts as L (t)=C _m(1+r) ^-t, r is discount rate;

2) establishing ζ (t) is engineering goods service life distribution density function, t Yi Nianwei unit, and within 1 year, being divided into again the m phase, total issue is the tm phase, the time interval of every first phase is dt, therefore show that the loss fund in first phase is C _mζ (t) dt, its present worth is

$\mathrm{dL}\left(t\right)=\underset{m\&RightArrow;+\&infin;}{\lim }{C}_m\mathrm{\&zeta;}\left(t\right)\mathrm{dt}{(1+\frac{r}{m})}^{-\mathrm{tm}}=C_m\mathrm{\&zeta;}\left(t\right)\mathrm{dt}\underset{m\&RightArrow;+\&infin;}{\lim }{(1+\frac{r}{m})}^{-\frac{m}{r}\mathrm{rt}}=C_m\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt};$

3) loss of definition mechanical product quality is the total mass loss in engineering goods service life, can obtain:

$L_{\mathrm{LC}}=C_m{\&Integral;}_0^{+\&infin;}\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt};$

4) before engineering goods drop into and are on active service, the distribution density function of its qualitative character x (0) is f (x (0)), along with the passing of active time is arrived t constantly, the distribution density function of its qualitative character is f (x (t)), draw thus from being on active service, start to t constantly product exceed [L because of qualitative character value _sL, U _sL] and the probability scrapped, namely product service life is less than the probability of t and is in formula: L _sL, U _sLbe respectively lower limit, the higher limit of demand of technical standard, L _sL=m _x-Δ, U _sL=m _x+ Δ; The engineering goods service life distribution density function that therefore can obtain based on qualitative character tolerance is

5) density function $\mathrm{\&zeta;}\left(t\right)=\frac{\mathrm{dP}\left(t\right)}{\mathrm{dt}}$ Be updated to step 3) in $L_{\mathrm{LC}}=C_m{\&Integral;}_0^{+\&infin;}\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt},$ Can draw the mechanical product quality loss distributing based on service life.

Owing to adopting technique scheme, the invention has the beneficial effects as follows: the present invention expands to product by mechanical product tolerance design from the product design fabrication phase and is on active service the stage, for mechanical product quality provides new solution in the Changing Pattern research of the life cycle managements such as design, processing, operation phase.

Accompanying drawing explanation

Fig. 1 is qualitative character changes in distribution figure in product military service process of the present invention.

Fig. 2 is axle sleeve service life distribution density function of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation:

1, the computing method for quality loss of mechanical product distributing based on service life

Qualitative character value for certain concrete engineering goods is x (t), qualified during product export, and x (0) meets | x (0)-m _x|≤Δ (m _xtrue value for product quality characteristic x).After product drop into be on active service, will there is random variation in its eigenwert, at t (year) sometime, make | x (t)-m _x| > Δ, product is defective scraps, and defective caused loss is C _m, getting discount rate is r.So, the loss that this product rejection produces discount into

L(t)＝C _m(1+r) ^-t (3)

Engineering goods life cycle management is a stochastic process, and its qualitative character value is random at each constantly, and its service life is also random.If ζ (t) is engineering goods service life distribution density function.If t Yi Nianwei unit, if within 1 year, being divided into again the m phase, total issue is the tm phase, and the time interval of every first phase is dt, so the loss fund in first phase is C _mζ (t) dt, its present worth is

$\mathrm{dL}\left(t\right)=\underset{m\&RightArrow;+\&infin;}{\lim }{C}_m\mathrm{\&zeta;}\left(t\right)\mathrm{dt}{(1+\frac{r}{m})}^{-\mathrm{tm}}=C_m\mathrm{\&zeta;}\left(t\right)\mathrm{dt}\underset{m\&RightArrow;+\&infin;}{\lim }{(1+\frac{r}{m})}^{-\frac{m}{r}\mathrm{rt}}=C_m\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt}---\left(4\right)$

Mechanical product quality loss (Life Cycle Loss) in this definition is the total mass loss in engineering goods service life, can obtain:

$L_{\mathrm{LC}}=C_m{\&Integral;}_0^{+\&infin;}\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt}---\left(5\right)$

2, after a collection of engineering goods of the computing method of the engineering goods service life distribution density function based on qualitative character tolerance drop into and are on active service, due to reasons such as stressed, distortion, heating, wearing and tearing and fatigues, its quality enters deterioration process, and qualitative character will change.Randomness due to engineering goods self and working environment, whole product quality characteristic distributes and also will change, some of them engineering goods will be scrapped because of qualitative character off technical requirement specialized range, like this, engineering goods service life also presents randomness, and shows certain regularity of distribution.

Before engineering goods drop into and are on active service, the distribution density function of its qualitative character x (0) is f (x (0)).Along with the passing of active time is arrived t constantly, the distribution density function of its qualitative character is f (x (t)), as shown in Figure 1.From scheming, along with product is constantly on active service, due to qualitative character, to exceed the product that technical tolerance requirement scraps more and more, can continue the product of being on active service fewer and feweri, and after certain hour, the product quantity that can be on active service is close to 0.Therefore can draw from being on active service, start to t constantly product exceed [L because of qualitative character value _sL, U _sL] and the probability scrapped, namely product service life is less than the probability of t and is

$P\left(t\right)={\&Integral;}_{L_{\mathrm{SL}}}^{U_{\mathrm{SL}}}(f\left(x\left(0\right)\right)-f\left(x\left(t\right)\right))\mathrm{dx}---\left(6\right)$

In formula: L _sL, U _sLbe respectively lower limit, the higher limit of demand of technical standard, L _sL=m _x-Δ, U _sL=m _x+ Δ.

The engineering goods service life distribution density function that therefore can obtain based on qualitative character tolerance is

$\mathrm{\&zeta;}\left(t\right)=\frac{\mathrm{dP}\left(t\right)}{\mathrm{dt}}---\left(7\right)$

Wushu (7) is updated to formula (5), just can draw the mechanical product quality loss distributing based on service life.Generally, product quality loss inconvenience is directly obtained by analytic method, but can obtain by numerical evaluation.

Embodiment mono-

Take certain model sleeve diameter size characteristic as the mass loss of example calculating axle sleeve.Consider that at axle sleeve, when dispatching from the factory (t=0), its internal diameter size feature x (0) must meet design requirement, | x (0)-m _x|≤Δ, through just coming into operation after the assay was approved, therefore its internal diameter size feature x (0) should Normal Distribution N (μ _x(0), σ _x(0) truncation) distributes, and its probability density function is

In formula: regular constant is $k_n=\mathrm{\&Phi;}\left(\frac{U_{\mathrm{SL}}-{\mathrm{\&mu;}}_x\left(0\right)}{{\mathrm{\&sigma;}}_x\left(0\right)}\right)-\mathrm{\&Phi;}\left(\frac{L_{\mathrm{SL}}-{\mathrm{\&mu;}}_x\left(0\right)}{{\mathrm{\&sigma;}}_x\left(0\right)}\right),$ Φ () is the distribution function of standardized normal distribution N (0,1).

The axle sleeve constantly also Normal Distribution N (μ of its internal diameter size feature of t that is on active service _x(t), σ _x(t) truncation), its probability density function is

In formula: α, β are axle sleeve military service internal diameter size distribution parameter, and mainly in product military service process, each factor determines, as running environment, lubricating condition, be subject to external force situation etc.

The distribution parameter average and the variance that according to the internal diameter size inspection during manufacture data statistics of a collection of axle sleeve of manufacturer, go out internal diameter size feature x (0) are respectively μ _x(0)=100.0mm, σ _x(0)=0.0033mm; And running environment, lubricating condition after being on active service according to axle sleeve, being subject to external force situation etc. to show that axle sleeve military service internal diameter size profile parameter, β are respectively 0.0010mm/, 0.0005mm/, sleeve diameter size and tolerance thereof are so Δ=0.01, m _x=100.0mm, U _sL=100.01mm, L _sL=99.99mm.The loss that axle sleeve is scrapped is taken as the price C of axle sleeve _m=280 yuan, mass loss coefficient k=C _mΔ ²=2.8 * 10 ^{+ 6}unit/mm ², discount rate is got r=10%.

Above-mentioned correlation parameter substitution formula (6)～(9), by calculating, can obtain axle sleeve service life probability distributing density function, as shown in Figure 2.From scheming, axle sleeve service life probability distributing density function is similar to lognormal distribution.In product service life distribution density function and relevant parameters substitution formula (5), the mass loss obtaining in axle sleeve service life is 104.89 yuan.Hence one can see that, and the mass loss that new product quality loss model calculates has the order of magnitude suitable with product price.Identical parameter, by field mouth quadratic function loss model, can obtain axle sleeve mass loss is 31.11 yuan, is 11% of product price.By product service life distribution density function, can show that its life-span average is 22.05, by itself and relevant parameters substitution formula (2), the mass loss that draws Teran model is 3.53 * 10 ³unit, is 12.6 times of product axle sleeve price, and obviously, this is with actual inconsistent.

Claims (1)

1. the computing method for quality loss of mechanical product distributing based on service life, comprises the following steps:

1) the qualitative character value of setting certain concrete engineering goods is x (t), qualified during product export, and x (0) meets | x (0)-m _x|≤Δ, m _xfor the true value of product quality characteristic x, after product drop into be on active service, its eigenwert generation random variation, makes at t sometime | x (t)-m _x| > Δ, product is defective scraps, and defective caused loss is C _m, and then show that the loss that this product rejection produces discounts as L (t)=C _m(1+r) ^-t, r is discount rate;

2) establishing ζ (t) is engineering goods service life distribution density function, t Yi Nianwei unit, and within 1 year, being divided into again the m phase, total issue is the tm phase, the time interval of every first phase is dt, therefore show that the loss fund in first phase is C _mζ (t) dt, its present worth is

$\mathrm{dL}\left(t\right)=\underset{m\&RightArrow;+\&infin;}{\lim }{C}_m\mathrm{\&zeta;}\left(t\right)\mathrm{dt}{(1+\frac{r}{m})}^{-\mathrm{tm}}=C_m\mathrm{\&zeta;}\left(t\right)\mathrm{dt}\underset{m\&RightArrow;+\&infin;}{\lim }{(1+\frac{r}{m})}^{-\frac{m}{r}\mathrm{rt}}=C_m\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt};$

3) loss of definition mechanical product quality is the total mass loss in engineering goods service life, can obtain:

$L_{\mathrm{LC}}=C_m{\&Integral;}_0^{+\&infin;}\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt};$

4) before engineering goods drop into and are on active service, the distribution density function of its qualitative character x (0) is f (x (0)), along with the passing of active time is arrived t constantly, the distribution density function of its qualitative character is f (x (t)), draw thus from being on active service, start to t constantly product exceed [L because of qualitative character value _sL, U _sL] and the probability scrapped, namely product service life is less than the probability of t and is in formula: L _sL, U _sLbe respectively lower limit, the higher limit of demand of technical standard, L _sL=m _x-Δ, U _sL=m _x+ Δ; The engineering goods service life distribution density function that therefore can obtain based on qualitative character tolerance is

5) density function $\mathrm{\&zeta;}\left(t\right)=\frac{\mathrm{dP}\left(t\right)}{\mathrm{dt}}$ Be updated to step 3) in $L_{\mathrm{LC}}=C_m{\&Integral;}_0^{+\&infin;}\mathrm{\&zeta;}\left(t\right)e^{-\mathrm{rt}}\mathrm{dt},$ Can draw the mechanical product quality loss distributing based on service life.