CN106251044B - Buehler method for product shelf life evaluation under multi-batch success-failure test - Google Patents

Buehler method for product shelf life evaluation under multi-batch success-failure test Download PDF

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CN106251044B
CN106251044B CN201610580679.5A CN201610580679A CN106251044B CN 106251044 B CN106251044 B CN 106251044B CN 201610580679 A CN201610580679 A CN 201610580679A CN 106251044 B CN106251044 B CN 106251044B
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于丹
李赵辉
胡庆培
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Abstract

The invention establishes a sample space ordering method for storage reliability and storage period evaluation aiming at success or failure type storage life tests of products under different storage years. The provided method is suitable for the condition that the storage life is subjected to exponential distribution, Weibull distribution and lognormal distribution. And determining a product reliability evaluation result by utilizing multi-batch success-failure type experimental information based on the model. The invention can quickly and accurately utilize incomplete experimental information to evaluate the reliability of the target product.

Description

Buehler method for product shelf life evaluation under multi-batch success-failure test
The technical field is as follows:
the invention designs a reliability evaluation method aiming at multi-batch success-failure test data.
Background
Currently, in the fields of military, aerospace and the like, even in some commercial fields, the requirement on the reliability of products is higher and higher. However, due to the limitation of product properties, only destructive tests can be carried out on certain types of products during storage life tests, and success-failure test data can be obtained. The tests of the products are multi-batch success-failure tests, the contained information amount is small, and the traditional method is difficult to evaluate the data. The product performs more efficient and high-precision evaluation on the reliability of the target product by introducing a sample space sequencing method aiming at the sequencing criteria provided by different models.
Disclosure of Invention
The invention aims to provide a product reliability statistical evaluation method based on multi-batch success-and-failure test data, which is a calculation method for determining a product reliability evaluation result aiming at a specific test data type.
According to the method, the product life test data type is considered, a product life model is determined for multi-batch success-failure test products, a corresponding sorting criterion is established by using a sample space sorting method, and a product reliability evaluation result is determined by using a branch-and-bound algorithm.
The invention relates to a reliability statistical evaluation method for multi-batch success-failure test data, which comprises the following specific steps:
step 1, determining a product life model: the product life model is derived from an analysis of the properties of the product, providing important information for that type of product.
Step 2, determining the ordering methods under different models required by the sample space ordering method: based on multi-batch success-failure test data, aiming at different life models, a proper sequencing criterion is provided. The ranking criterion is an important measure of the reliability parameters of the model, and the selection of the ranking determines the efficiency and accuracy of the method.
Step 3, reliability evaluation algorithm: based on the above life model and the determined sorting criterion, a confidence lower limit of the product storage reliability is obtained by using a branch and bound algorithm.
Wherein the product life model in step 1 is from exponential distribution, log normal distribution, weibull distribution.
Wherein, the sample space sequencing method in the step 2 refers to setting random variables X-F of the storage life of the productθ(x) X is greater than 0, and the distribution parameter theta is equal to theta. What we can observe is type I deletion test data, i.e. (t)1，y1)，…，(tn，yn) Wherein
Figure BDA0001056135660000021
II{.}Is an indicative function, i.e.: xi≥tiWhen y isi1 indicates that the test was successful; xi＜tiWhen y isi0 indicates test failure. Hereinafter, we will refer to the test results as y ═ y1，…，yn) The corresponding sample is denoted as Y ═ Y (Y)1，…，Yn) I.e. the test result Y is the observed value of the sample Y. Defining a sample space as
y＝{(y1，…，yn)：yi0 or 1, i 1, …, n.
It can be seen from the definition of the sample space y that it is a set of all possible test results. Defining a "sequence" in the sample space y, denoted symbolically as
Figure BDA0001056135660000025
(equivalently, it is also possible to use
Figure BDA0001056135660000022
Is shown)
Defining the probability of an event in sample space y
Figure BDA0001056135660000024
Note the book
gL(y)＝inf{g(θ)：G(y，θ)＞α，θ∈Θ}，
Then g isL(y) is the lower confidence limit for the parameter g (θ) given the sample observations (test results) y and the confidence 1- α.
Wherein, the ranking criteria in step 2 propose different ranking criteria for different life models. From above, the sample space is
y＝{(y1，…，yn)：yi0 or 1, i 1, …, n.
It can be seen from the definition of the sample space y that it is a set of all possible test results. Defining a "sequence" in the sample space y, denoted symbolically as
Figure BDA0001056135660000026
(equivalently, it is also possible to use
Figure BDA0001056135660000023
Is shown), if
Figure BDA0001056135660000027
Then call y2"is superior to" y1Or test result y2"better than" y1. In general, we need to define the order in sample space y according to the index to be inferred and the corresponding statistic
Figure BDA00010561356600000310
Therefore, the order
Figure BDA00010561356600000311
There is great flexibility in defining (c). Sequence of steps
Figure BDA00010561356600000312
The different definition of (1) will result in different evaluation results, and therefore the order
Figure BDA00010561356600000313
The statistical nature of (a) determines whether the resulting evaluation has good statistical properties.
Wherein, the step 2 is the sorting criterion aiming at different service life distribution types, and aiming at the index distribution type, the service life of the product obeys distribution X-Fλ(x) 1-exp { - λ x }, x > 0, the ranking criterion being derived from the magnitude relation of a likelihood function defined as:
Figure BDA0001056135660000031
having a log-likelihood function of
Figure BDA0001056135660000032
Let us note λyFor maximum likelihood estimation of the parameter lambda under the test result y, i.e. to satisfy
Figure BDA0001056135660000033
Let us note λYIs a maximum likelihood estimate of the parameter lambda at sample Y.
An order is defined in the sample space y as follows
Figure BDA00010561356600000314
For any y1，y2E.g. y, scale
Figure BDA00010561356600000315
(y2Is superior to y1) If, if
Figure BDA0001056135660000037
About the order
Figure BDA00010561356600000316
Is directly perceivedThe explanation is that if the test result y2Maximum likelihood estimation of corresponding failure rate
Figure BDA0001056135660000038
Less than in test result y1Maximum likelihood estimation of corresponding failure rate
Figure BDA0001056135660000039
We consider the test result y2"is superior to" y1. The engineering context of the order defined in the above manner is very intuitive here based on the order defined by the parameter maximum likelihood estimation. In addition, for any y ∈ y and 0 ≦ x ≦ + ∞, λyThe essential condition of > x is
Figure BDA0001056135660000034
Order to
Figure BDA0001056135660000035
And
Figure BDA0001056135660000036
it is clear that both β and T are constants determined only by the sample observations. Reissue to order
y0＝{y：y∈y，yTβ＞T}，
I.e. the above defined ranking criteria can be translated into solving the above set directly.
Wherein the ranking criteria for different life distribution types in step 2, for Weibull distribution types, the storage life of the product is obeyed
Figure BDA0001056135660000041
(x > 0), where m, η are unknown parameters, m > 0, η > 0, and the same notations as above, the test results are type I erasure data { (t)1，y1)，…，（tn，yn) And y ═ y (y)1，…，yn)。
On y is determined as followsSense sequence. Balance
Figure BDA0001056135660000042
If one of the following conditions is satisfied:
(1)
Figure BDA0001056135660000043
(2)
Figure BDA0001056135660000044
and is
Figure BDA0001056135660000045
Wherein, the sorting criterion aiming at different life distribution types in the step 2 aims at normal distribution and log-normal distribution types and random variables X-F (X | mu, sigma) of the product storage life.
(1) When the shelf life of the product follows a normal distribution,
Figure BDA0001056135660000046
(2) when the shelf life of the product follows a log normal distribution,
Figure BDA0001056135660000047
where Φ is the standard normal distribution function, μ and σ are unknown parameters,
Figure BDA0001056135660000048
Figure BDA0001056135660000049
σ∈[σ1，σ2]let θ be (μ, σ). The test result is expressed as y ═ y (y)1，…，yn) With a sequence of storage times t1，…，tn。
By utilizing the corresponding relation between the lognormal distribution and the normal distribution, only the sorting criterion under the normal distribution condition needs to be given. For the case of log-normal distribution, only the distribution is neededThe test data is transformed accordingly, i.e., { (t)1，y1)，…，(tn，yn) Is transformed into
{(log t1，y1)，…，(log tn，yn)}，
Corresponding storage time t0Transformation to log t0And then, directly applying a calculation formula under the normal distribution condition to obtain a result under the condition of the log-normal distribution.
Sample space y order
Figure BDA00010561356600000415
Is defined as follows for
Figure BDA00010561356600000410
Balance
Figure BDA00010561356600000411
If one of the following conditions is satisfied:
(1)
Figure BDA00010561356600000412
(2)
Figure BDA00010561356600000413
and is
Figure BDA00010561356600000414
Wherein, the reliability evaluation algorithm in step 3 is an algorithm for calculating reliability confidence lower limit for different service life distribution types after the sorting criterion is determined,
the reliability evaluation algorithm in step 3 is specifically implemented as follows for the index distribution type: input β, T, where β is an m-dimensional vector. The algorithm returns a set, denoted as y (β, T). We use the notation x to denote the cartesian product.
(1) When m is 1:
(a) if beta is larger than T, returning to {0, 1 };
(b) if beta is less than or equal to T, returning to {1 }.
(2) When m > 1:
(a) if it is
Figure BDA0001056135660000051
Return to
{0}×y((β2，…，βm)，T)∪{1}×y((β2，…，βm)，T-β1)；
(b) If it is
Figure BDA0001056135660000052
Return to
{1}×y((β2，…，βm)，T-β1)。
The above completes the traversal of y0Design of branch-and-bound algorithm for all elements in (1).
Wherein, the reliability evaluation algorithm in the step 3 obtains y according to the index distribution product type0Then, using the results obtained by the above algorithm, the 1- α confidence upper limit for product failure rate can be obtained by the following calculation: lambda [ alpha ]U＝sup{λ|P(y0) Less than 1-alpha, and obtaining the lower limit of the 1-alpha confidence of the reliability as R according to the relation between the reliability and the efficiency of the productL＝exp(λvτ0)
The reliability evaluation algorithm in the step 3 is the same as the exponential distribution algorithm for the Weibull distribution and the normal/log normal distribution types, and only the discriminant function in the step two is needed
Figure DA00010561356631837420
The following two steps are adopted:
Figure BDA0001056135660000053
the resulting set is
Figure BDA0001056135660000054
By calculation of
Figure BDA0001056135660000055
Obtaining confidence limits for reliability
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention without any inventive step, are within the scope of protection of the invention.
The following provides a more detailed description of the present invention.
The core of the comprehensive evaluation of the reliability of the batch success-or-failure type products lies in how to define a proper sorting criterion, and then a sample space sorting method can be reasonably applied for evaluation. The different experimental results of the product are considered to represent the quality of the product. For a particular product, if two test specimens of the product at the same test time are said to have test results that are successful and the other fails, we consider the successful product to be of better quality than the failed product. Based on this understanding, we intend to establish the sorting criterion of multiple batches of success-or-failure type products under different life distribution types.
The method of the invention comprises the following steps:
step 1, determining a product life model
Step 2, determining ordering method under different models
Step 3, reliability evaluation algorithm
A similar product life model is first determined.
The product life model is derived from an analysis of the properties of the product, providing important information for that type of product.
And 2, determining the sequencing methods under different models.
According to the model established in step 1, a ranking criterion of the sample space now needs to be established. The details of the operation of the sorting criterion will be described in detail in the description of the operation of step three.
Step 3, reliability evaluation algorithm
The multi-batch success-failure type data reliability evaluation algorithm provided by the invention needs to complete the following two steps: (1) inputting a product life model and experimental data; (2) a lower confidence limit for the corresponding product at the specified confidence level is calculated.
The present invention discusses the second step in step 3,
and obtaining a reliability confidence lower limit by adopting a branch-and-bound algorithm given the service life distribution type and the sequencing criterion of the corresponding product. Wherein for data distribution types such as exponential distribution, weibull distribution, lognormal distribution, etc., the sorting criterion can be summarized as a linear function comparison magnitude with respect to the data. Aiming at the exponential distribution, for any y belonging to y and 0-x ≦ infinity, lambdayThe essential condition of > x is
Figure BDA0001056135660000061
Order to
Figure BDA0001056135660000071
And
Figure BDA0001056135660000072
it is clear that both β and T are constants determined only by the sample observations. Reissue to order
y0＝{y：y∈y，yTβ＞T},
The requested set
Figure BDA0001056135660000073
Into the above set. For Weibull distribution and lognormal distribution, the sample space y is ordered
Figure BDA0001056135660000079
Is defined as follows for
Figure BDA0001056135660000074
Balance
Figure BDA0001056135660000075
If one of the following conditions is satisfied:
Figure BDA0001056135660000076
for the branch-and-bound algorithm proposed by the above sorting criterion, for the index distribution type, the specific implementation details of the algorithm are as follows: input β, T, where β is an m-dimensional vector. The algorithm returns a set, denoted as y (β, T). We use the notation x to denote the cartesian product.
(1) When m is 1:
(a) if beta is larger than T, returning to {0, 1 };
(b) if beta is less than or equal to T, returning to {1 }.
(2) When m > 1:
(a) if it is
Figure BDA0001056135660000077
Return to
{0}×y((β2，…，βm)，T)∪{1}×y((β2，…，βm)，T-β1)；
(b) If it is
Figure BDA0001056135660000078
Return to
{1}×y((β2，…，βm)，T-β1)。
The above completes the traversal of y0Design of branch-and-bound algorithm for all elements in (1).
Wherein, the reliability evaluation algorithm in the step 3 obtains y according to the index distribution product type0Then, using the results obtained by the above algorithm, the 1- α confidence upper limit for product failure rate can be obtained by the following calculation: lambda [ alpha ]U＝sup{λ|P(y0) Less than 1-alpha, according to product reliability andthe lower confidence limit of 1-alpha for reliability of relationship to efficiency is RL＝exp(λUt0)
The reliability evaluation algorithm in the step 3 is the same as the exponential distribution algorithm for the Weibull distribution and the normal/log normal distribution types, and only the discriminant function in the step two is needed
Figure DA00010561356631920292
The following two steps are adopted:
Figure BDA0001056135660000081
the resulting set is
Figure BDA0001056135660000082
By calculation of
Figure BDA0001056135660000083
A lower confidence limit for the reliability is obtained.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. And the software modules may be disposed in any form of computer storage media. To clearly illustrate this interchangeability of hardware and software, various illustrative components and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
It should be understood by those skilled in the art that various modifications, combinations, partial combinations and substitutions may be made in the present invention depending on design requirements and other factors as long as they are within the scope of the appended claims and their equivalents.

Claims (8)

1. A reliability assessment method considering multi-lot success-and-failure type products, comprising:
determining a product test data model;
determining a corresponding sorting criterion from a plurality of sorting criteria to evaluate reliability parameters by utilizing multi-batch success-failure type test data of the product and aiming at different product life data models;
evaluating the reliability of the product by utilizing a branch-and-bound method according to the determined sorting criterion;
determining a product test data model comprises determining a product test data form and a product life data model; wherein the product test data form comprises multi-batch success-and-failure test data, the product life data model comprises a model of product obeying exponential distribution, Weibull distribution or lognormal distribution,
wherein, for the input beta, f, beta is n-dimensional vector, T is total time of product test, and aiming at the model of product obeying exponential distribution, the set returned by the branch-and-bound method
Figure FDA0003143406540000011
The calculation steps are as follows:
(1) when n is equal to 1, the compound is,
(a1) if beta is larger than f, returning to {0, 1 };
(b1) if beta is less than or equal to f, returning to {1},
(2) when n is greater than 1, the compound is,
(a2) if it is
Figure FDA0003143406540000012
Return to
Figure FDA0003143406540000013
(b2) If it is
Figure FDA0003143406540000014
Return to
Figure FDA0003143406540000015
Wherein the content of the first and second substances,
Figure FDA0003143406540000016
and
Figure FDA0003143406540000017
n is the number of tests, lambdayFor maximum likelihood estimation of the parameter lambda in the test result y, tiThe test time point of the ith product is shown, symbol x represents the cartesian product,
and wherein the set of branch-and-bound returns for a product subject to a Weibull or lognormal distributed model
Figure FDA0003143406540000018
In the calculating step of (2) a discriminant function
Figure FDA0003143406540000019
The following criteria were substituted:
(I)
Figure FDA0003143406540000021
or
(II)
Figure FDA0003143406540000022
And is
Figure FDA0003143406540000023
The other calculation steps are the same as those for a model in which the product is subject to an exponential distribution.
2. The method of claim 1, wherein the success-failure test is a single product with a life test result of: (t)0Y); wherein，t0In order to obtain the test time of the product,
Figure FDA0003143406540000024
wherein t is the actual life of the product,
Figure FDA0003143406540000025
is an indicative function, i.e.: if t > t0If Y is 1, the test result is successful; otherwise, Y is 0, which represents that the test result is failure; by multi-batch, it is meant that the product testing is conducted over multiple storage times.
3. The method of claim 1, wherein the evaluation of the reliability parameter is a lower confidence limit for determining the reliability of the product within a specified task time using statistical theory and methods.
4. The method of claim 3, wherein the confidence limit for the reliability of the product within the specified task time is that P (R > R) is satisfiedL) R being not less than 1-alphaL(ii) a Wherein R is the reliability of the product in the specified task time, alpha is the confidence coefficient, P is the probability function, RLIs the lower confidence limit.
5. The method of claim 1, wherein the sample spatial ordering method comprises:
random variable X-F for setting storage life of productθ(x) X is larger than 0, and the distribution parameter theta is equal to theta; wherein the distribution function of the random variable X is Fθ(x) (ii) a The success or failure data of multiple batches is recorded as (t)1，y1)，…，(tn，tn) Wherein
Figure FDA0003143406540000026
Wherein the content of the first and second substances,
Figure FDA0003143406540000027
is an indicative function, i.e.: xi≥tiWhen y isi1 denotes the testSuccess is achieved; xi＜tiWhen y isi0 indicates test failure; wherein, tiDenotes the test time point, X, of the ith productiRepresenting the true life of the ith product; y represents a test result, and the test result is denoted by y ═ y (y)1，…，yn) The sample corresponding to the test result is referred to as Y ═ Y (Y)1，…，Yn) I.e. the test result Y is the observed value of the sample Y; wherein Y represents the test result before observation, Y is a random variable, Y represents the exact test result observed in the actual test, and the sample space is defined as
Figure FDA0003143406540000028
The sample space
Figure FDA0003143406540000029
Is a collection of all possible test results.
6. The method of claim 5, further comprising:
in the sample space
Figure FDA00031434065400000210
The above defines a sequence, which is denoted by the symbol
Figure FDA00031434065400000211
Or
Figure FDA00031434065400000212
If it is
Figure FDA00031434065400000213
Then call y2"is superior to" y1Or test result y2"better than" y1(ii) a Defining a sample space according to an index to be inferred and corresponding statistics
Figure FDA00031434065400000214
Sequence of (1) above
Figure FDA00031434065400000215
Said sequence
Figure FDA00031434065400000216
The statistical properties of (a) determine whether the obtained evaluation results have good statistical properties;
sample space
Figure FDA00031434065400000217
Is n-dimensional in itself, but when in sample space
Figure FDA00031434065400000218
Above define the order
Figure FDA00031434065400000219
Then, the sample space
Figure FDA00031434065400000220
Will become one-dimensional in the sample space
Figure FDA00031434065400000221
Probability of the event defined above
Figure FDA00031434065400000222
Wherein, F (y, theta) is defined in the sample space as 1-G (y, theta)
Figure FDA00031434065400000223
A distribution function of;
note the book
gL(y)＝inf{g(θ)：G(y，θ)＞α，θ∈Θ}，
Then g isL(y) is the lower confidence limit for the parameter g (θ) given the test result y and confidence 1- α;
wherein, the solution is realized by using a branch-and-bound method
Figure FDA0003143406540000031
To calculate gL(y) said branch-and-bound traversal is conditioned to all
Figure FDA0003143406540000032
Sample Y of (1).
7. The method of claim 6, wherein the ranking criteria for products subject to lognormal and Weibull distributions are given by the following criteria:
if one of the following conditions is satisfied:
(1)
Figure FDA0003143406540000033
(2)
Figure FDA0003143406540000034
and is
Figure FDA0003143406540000035
Then call
Figure FDA0003143406540000036
8. The method of claim 7, wherein the sorting criterion for the product obeying the exponential distribution is given by comparing the magnitude of the likelihood function of the test results, the life time obeying distribution of the product being X-Fλ(x) 1-exp { - λ x }, x > 0, the ranking criterion being derived from the magnitude relation of a likelihood function defined as:
Figure FDA0003143406540000037
having a log-likelihood function of
Figure FDA0003143406540000038
Let us note λyFor the test results, maximum likelihood estimation of the yarn parameter lambda, i.e. satisfaction
Figure FDA0003143406540000039
Let us note λYIs a maximum likelihood estimate of the parameter λ at sample Y; wherein the parameter lambda refers to a product failure rate parameter;
wherein in the sample space
Figure FDA00031434065400000310
The order is defined as follows
Figure FDA00031434065400000311
For any purpose
Figure FDA00031434065400000312
If λy1≥λy2Balance of
Figure FDA00031434065400000313
I.e. y2Is superior to y1Wherein, the order
Figure FDA00031434065400000314
Shows if in test result y2Maximum likelihood estimate λ of corresponding failure ratey2Less than in test result y1Maximum likelihood estimate λ of the corresponding failure ratey1Then the test result y2"is superior to" y1。
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104133994A (en) * 2014-07-24 2014-11-05 北京航空航天大学 Reliability evaluation method fusing multi-source success or failure data
CN105718722A (en) * 2016-01-18 2016-06-29 中国人民解放军国防科学技术大学 Product reliability estimation method based on time-truncated life testing data
CN106169124A (en) * 2016-07-21 2016-11-30 中国科学院数学与系统科学研究院 Complex Structural System reliability comprehensive estimation confidence inference method

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101847834B (en) * 2010-06-07 2016-02-03 苏州热工研究院有限公司 The reliability estimation method of power station small sample and non-failure data part failure rate
JP6102277B2 (en) * 2013-01-24 2017-03-29 株式会社Sumco Method for evaluating metal contamination of semiconductor wafer and method for manufacturing semiconductor wafer
CN103218534B (en) * 2013-04-22 2017-02-08 北京航空航天大学 Right tail-truncated type lifetime data distribution selection method
US8839180B1 (en) * 2013-05-22 2014-09-16 International Business Machines Corporation Dielectric reliability assessment for advanced semiconductors
CN104268392B (en) * 2014-09-23 2017-06-23 北京航空航天大学 Manufacturing process product reliability downslide risk evaluating method based on mass deviation
CN104899423B (en) * 2015-05-06 2017-12-15 同济大学 A kind of EMUs subsystem critical component serviceability appraisal procedure

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104133994A (en) * 2014-07-24 2014-11-05 北京航空航天大学 Reliability evaluation method fusing multi-source success or failure data
CN105718722A (en) * 2016-01-18 2016-06-29 中国人民解放军国防科学技术大学 Product reliability estimation method based on time-truncated life testing data
CN106169124A (en) * 2016-07-21 2016-11-30 中国科学院数学与系统科学研究院 Complex Structural System reliability comprehensive estimation confidence inference method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
基于样本空间排序法的剩余寿命评估;顾华海 等;《电子设计工程》;20110531;第19卷(第10期);第42-44页 *

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