CN102262188B - Sampling inspection method for workpieces - Google Patents

Abstract

The invention discloses a sampling inspection method for workpieces and a computer program product. In the method, a reliance index value and a reliance index threshold value of a virtual metrology value of one workpiece and a global similarity index (GSI) value and a GSI threshold value of process parameter data of the workpiece are calculated by analyzing the process parameter data of a production machine. When the reliance index value of the workpiece is smaller than the reliance index threshold value or the GSI value of the workpiece is greater than the GSI threshold value, the workpiece can be selected to be measured.

Description

The method of workpiece pick test

Technical field

The invention relates to a kind of method of workpiece pick test, particularly relevant for a kind of method and the computer program thereof that can effectively inspect out bad workpiece by random samples.

Background technology

Present most of semiconductor and TFT-LCD factory take the mode taken a sample test for the quality monitoring method of the product of producing board or workpiece, wherein this workpiece can be the wafer of semiconductor industry or the glass substrate of TFT-LCD industry.Complete the processing processing of several workpiece (Workpiece) when the production board after, these a little workpiece can be placed in card casket or a wafer transfer box (Front Opening Unified Pod; In FOUP, detect the quality of workpiece to be sent to measurement platform.Generally speaking, measurement platform can be selected a workpiece regularly from a plurality of workpiece (for example: 25) of whole card casket be that sample measures, for example: the unit one in the card casket.The processing procedure quality that the method for the pick test that this kind is known hypothesis is produced board is abnormal suddenly not, thereby the product that can be taken a sample test with quilt or the measurement of workpiece be inferred the quality of all products in same card casket or wafer transfer box.Yet the method for known pick test can only be learnt the quality of the workpiece that this reality is taken a sample test, and the workpiece that this reality is taken a sample test might not be the workpiece with potential risk, therefore often can produce Lou detecting (Miss Detection; MD) situation.In addition, if produce board abnormal between taking a sample test for twice, just prior art method can't in time find, thereby cause the generation of many defective productss, and cause considerable cost allowance.

In theory, if can all workpiece in same card casket or wafer transfer box all be measured, can avoid the situation of aforesaid leakage detecting, more can in time find to produce the board abnormal.Yet, each workpiece in same card casket or wafer transfer box is all carried out actual measurement quite spacious day time-consuming, need expend many manpower and materials.Moreover for wafer with hundreds of roads processing procedure or TFT-LCD factory, it is more almost the impossible task of part that wish is carried out actual measurement to each workpiece of every one processing procedure.

Therefore, occur for avoiding the problems referred to above, a kind of method and computer program thereof of workpiece pick test must be provided, measure so as to effectively selecting suitable workpiece, in order to do just in time finding when producing the board abnormal.

Summary of the invention

Therefore, an aspect of the present invention is exactly at a kind of method that workpiece pick test is provided and computer program thereof, by confidence index (the Reliance Index of judgement workpiece; RI) whether value is less than confidence indicator threshold value; Or the GSI of workpiece (Global Similarity Index; The overall similarity index) value whether greater than GSI threshold value (GSIT), is selected out suitable workpiece effectively measuring, and avoids the situation of leak detecting, and it is abnormal in time to find to produce board.

According to above-mentioned purpose of the present invention, a kind of method of workpiece pick test is proposed.In one embodiment of this invention, at first obtain the many groups of historical process parameter data of producing board, and obtain a plurality of historical measuring values from measurement platform, wherein these a little historical measuring values are respectively the measuring value of the workpiece of producing according to historical process parameter data.Then, estimate pattern and a reference model with historical process parameter data and historical measuring value, the foundation that wherein estimates pattern estimates algorithm according to one, and the foundation of reference model with reference to algorithm, estimates algorithm from different with reference to algorithm according to one.Then, input historical process parameter data to estimating pattern and reference model, and calculate a plurality of historical virtual measurement values and a plurality of historical reference predicted value.Then, calculate respectively the overlapping area between the distribution of the distribution (Distribution) of historical virtual measurement value and historical reference predicted value and produce a plurality of historical confidence desired values, wherein work as overlapping area larger, the confidence desired value is higher, represents that the confidence level of the historical virtual measurement value that corresponds to is higher.Then, calculate a confidence indicator threshold value (RI according to historical virtual measurement value, historical reference predicted value and historical measuring value _T).Then, collect to produce the process parameter data of a plurality of workpiece in the card casket that board sends, and the process parameter data of inputting each workpiece are to estimating pattern and reference model, and calculate virtual measurement value and the reference prediction value of each workpiece.Then, calculate the overlapping area between the distribution of the distribution of virtual measurement value of each workpiece and reference prediction value and produce the confidence desired value of each workpiece, wherein work as overlapping area larger, the confidence desired value is higher, represents that the confidence level of its virtual measurement value that corresponds to heals high.Then, choose its confidence desired value less than at least one first workpiece of confidence indicator threshold value in a little workpiece since then, and the first workpiece is delivered to measurement platform to detect.

According to another embodiment of the present invention, in the method for workpiece pick test, at first obtain the many groups of historical process parameter data of producing board.Then, use the historical process parameter data of this a little group, and according to a statistics apart from algorithm, set up a statistics distance mode.Then, with this historical process parameter data of a little group and historical measuring value, and the leaving-one method (Leave-One-Out in application validation-cross (Cross Validation); LOO) principle is rebuild the statistical distance pattern, and calculates corresponding GSI value, to calculate a GSI threshold value (GSI _T).Then, input the process parameter data of each workpiece to the statistical distance pattern, and calculate the GSI value of the corresponding process parameter data of virtual measurement value of each workpiece.Then, choose its GSI value greater than at least one second workpiece of GSI threshold value in a little workpiece since then, and second workpiece is sent to a measurement platform to detect.

According to above-mentioned purpose of the present invention, the computer program that a kind of interior storage is used for the workpiece pick test is separately proposed, after computing machine loads this computer program and carries out, can complete the method for workpiece pick test described above.

Therefore, use the present invention, can assess its quality possibility by the process parameter data of certain workpiece has extremely, measure effectively to select suitable workpiece, and avoid the situation of leak detecting, and it is abnormal in time to find to produce board.

Description of drawings

For above and other objects of the present invention, feature, advantage and embodiment can be become apparent, appended the description of the drawings is as follows:

Fig. 1 is the system architecture schematic diagram that illustrates the method for implementing workpiece pick test of the present invention;

Fig. 2 is the configuration diagram that illustrates the system of AVM according to an embodiment of the invention;

Fig. 3 is the schematic diagram that illustrates the confidence desired value of explanation embodiments of the invention;

Fig. 4 is the schematic diagram that illustrates the confidence indicator threshold value of explanation embodiments of the invention;

Fig. 5 illustrates the schematic flow sheet of workpiece sampling method according to an embodiment of the invention;

Fig. 6 A illustrates the virtual measurement value of application examples of the present invention and the result schematic diagram of actual amount measured value;

Fig. 6 B is the result schematic diagram that illustrates the confidence desired value of application examples of the present invention; Fig. 6 C is the result schematic diagram that illustrates the overall similarity desired value of application examples of the present invention.

[main description of reference numerals]

10: process parameter data pre-processing module 12: metric data pre-processing module

20: produce board 22: the process parameter data

30: measurement platform 40: confidence index module

50: index of similarity module 60: estimate pattern

62: two stage calculation mechanism 80: the card casket

82: workpiece 90:AVM

100: the RI and the GSI that calculate workpiece

Whether 110:RI is less than RI _TOr whether GSI is greater than GSI _T

120: determine whether measure

130: measured by measurement platform

A: overlapping area

Embodiment

Please refer to Fig. 1, it illustrates the system architecture schematic diagram of the method for implementing workpiece pick test of the present invention.The invention provides full-automatic type virtual measurement (Automatic Virtual Metrology; AVM) system 90 in producing between board 20 and measurement platform 30, measures so as to assisting measurement platform 30 to select suitable workpiece with the process parameter data 22 of all workpiece 82 in card casket 80.In one embodiment, AVM system 90 first notifies manufacturing execution system (Manufacturing Execution System; MES) code name of the workpiece selected out of (not shown), manufacturing execution system gives an order to measurement platform 30 according to the code name of this workpiece of being selected out again, so that this workpiece of being selected out is measured.In addition, in one embodiment, AVM system 90 is embedded in measurement platform 30.In another embodiment, AVM system 90 is embedded in and produces in board 20.Certainly, AVM system 90 also can carry out the workpiece sampling method independently, therefore the present invention and not subject to the limits.

Please refer to Fig. 2, it illustrates the configuration diagram of the system of AVM according to an embodiment of the invention.The AVM system 90 of the present embodiment comprises at least: process parameter data pre-processing module 10, metric data pre-processing module 12, estimate pattern 60, confidence index module 40 and index of similarity module 50.Process parameter data pre-processing module 10 is for arranging and standardization from the original process parameter data of producing board 20, and the suppressing exception data also filter out important parameter, inessential parameter is got rid of, and avoiding producing interference effect, and the impact prediction precision.Metric data pre-processing module 12 screens for the metric data from measurement platform 30, to remove exceptional value wherein.Estimating pattern 60 can utilize and estimate the phase one virtual measurement value (VM that algorithm estimates a plurality of workpiece 82 in card casket 80 _I), also optionally utilize two stage calculation mechanism 62 and estimate the subordinate phase virtual measurement value (VM that algorithm estimates a plurality of workpiece 82 in card casket 80 _II).The algorithm that estimates that may select has: return the various prediction algorithms such as algorithm, neural network algorithm.Confidence index module 40 is used for assessing the confidence level of virtual measurement value, and produces confidence index (RI).The process parameter data that index of similarity module 50 is used for assessing present input and the similarity degree that estimates all supplemental characteristics that are used for training modeling in pattern 60, and the index of similarity (GSI) of generation process parameter, this index of similarity judges the confidence degree of virtual measurement system in order to auxiliary confidence index.

Before estimating pattern 60 runnings, must be from producing process parameter data (historical process parameter data) that board 20 obtains and being sent to respectively process parameter data pre-processing module 10 and metric data pre-processing module 12 from the obtained quality metric data of measurement platform 30 (historical measuring value), to carry out data pre-processing.The input data that these process parameter data after pre-treatment and standardization and quality metric data are the pattern of estimating 60.Then, adopt historical process parameter data and corresponding historical quality metric data train (foundation) for example neural network (NN) estimate pattern.Estimate pattern 60 and have two stage calculation mechanism 62, in order to difference phase one virtual measurement value (VM _I) and subordinate phase virtual measurement value (VM _II) confidence desired value (RI) and the overall similarity desired value (GSI) corresponding with it.The confidence index that so-called " subordinate phase " virtual measurement value is followed with it and index of similarity are when obtaining the actual amount measured value of workpiece 82 from measurement platform, process parameter data and the actual amount measured value of workpiece 82 are added historical process parameter data and historical measuring value, again train or adjustment estimates reference model and the index of similarity module 50 statistical distance patterns of pattern 60, confidence index module 40, then recomputate the subordinate phase virtual measurement value (VM of each workpiece in card release casket 80 _II) confidence index and the overall similarity index followed with it.

Below, the pattern of estimating, confidence desired value (reference model) and the relevant theoretical foundation of overall similarity desired value (statistical distance pattern) are described.

Estimate pattern and confidence index (reference model)

As shown in table 1, suppose to collect at present the data that the n group measures, comprise process data (X _i, i=1,2 ..., n) and corresponding actual amount measured value data (y _i, i=1,2 ..., n), wherein every group of process data includes p parameter (autoregressive parameter 1 is to parameter p), i.e. X _i=[x _i,1, x _i,2..., x _i,p] ^TIn addition, process data when also collecting (m-n) actual production, but except y _n+1, there is no actual amount measured value data outward, namely in the workpiece of (m-n) actual production, for example only take a sample test that the first stroke workpiece carries out actual measurement, then with its actual measurement y _n+1Infer the quality of other (m-n-1) workpiece.

Table 1 raw data example

The sample number strong point

Parameter

1

Parameter 2

?

Parameter p

The actual amount measured value

1

x 1,1

x 1,2

…

x 1,p

y 1

2

x 2,1

x 2,2

…

x 2,p

y 2

…	…	…	…	…	…
						n	x n,1	x n,2	…	x n,p	y n
n+1	x n+1,1	x n+1,2	…	x n+1,p	y n+1
						n+2	x n+2,1	x n+2,2	…	x n+2,p	Zip
…	…	…	…	…	…
						m	x m,1	x m,2	…	x m,p	Zip

In table 1, y ₁, y ₂..., y _nBe historical measuring value, y _n+1Actual amount measured value for the unit one in workpiece unit of cargo just aborning.Usually, one group of actual amount measured value (y _i, i=1,2 ..., n) for having average μ, the normality of standard deviation sigma is distributed, i.e. y _i～N (μ, σ ²).

For sample group (y _i, i=1,2 ..., average n) and standard deviation with all actual amount measured value data normalizations after, can obtain

(also being called z mark (z Scores)), wherein the average of each z mark is 0, and standard deviation is 1, namely For actual metric data, if

More near 0, represent that metric data is more near the specification central value.Its standardized formula is as follows:

$Z_{y_i}=\frac{y_i-\stackrel{-}{y}}{{\mathrm{\σ}}_y},i=\mathrm{1,2},\·\·\·,n---\left(1\right)$

$\stackrel{-}{y}=\frac{1}{n}(y_1+y_2+\·\·\·+y_n)---\left(2\right)$

${\mathrm{\σ}}_y=\sqrt{\frac{1}{n-1}[{(y_1-\stackrel{-}{y})}^2+{(y_2-\stackrel{-}{y})}^2+\·\·\·{+(y_n+\stackrel{-}{y})}^2]}---\left(3\right)$

Wherein

y _iBe i group actual amount measured value data;

Be the actual amount measured value data after i group data normalization;

Average for all actual amount measured value data;

σ _yStandard deviation for all actual amount measured value data;

The algorithm that estimates of application neural network (NN) algorithm is herein set up the pattern that estimates of carrying out virtual measurement, and the checking of setting up with the reference prediction algorithm that for example returns algorithm this estimate the reference model of pattern.Yet the present invention also can use other algorithm for estimating algorithm or reference prediction algorithm, as long as the reference prediction algorithm is different from and estimates algorithm, therefore the present invention and not subject to the limits.Of the present inventionly estimate algorithm and the reference prediction algorithm for example can be respectively: back propagation neural network (BackPropagation Neural Network; BPNN), general recurrence neural network (General RegressionNeural Network; GRNN), neural network (Radial Basis Function NeuralNetwork at the bottom of radial basis; RBFNN), simple regression network (Simple Recurrent Network; SRN), Support Vector data description (Support Vector Data Description; SVDD), support vector machine (SupportVector Machine; SVM), multiple regression algorithm (Multiple Regression; MR); Part least square method (Partial Least Squares; PLS), non-linear inclined to one side least square method (the NonlinearIterative Partial Least Squares that substitutes; NIPALS) or generalized linear pattern (Generalized linearmodels; GLMs).

When application class neural network algorithm and multiple regression algorithm, be error sum of squares (Sum of Square Error as its condition of convergence; SSE) under minimum condition, during and n → ∞, this two-mode actual amount measured value after standardization separately is defined as

With

Its all should with real standardization after the actual amount measured value

Identical.In other words, when n → ∞,

All represent the actual amount measured value after standardization, but change its title for the purpose in response to different mode.Therefore

And

Expression

With

Be same allocated, but due to different estimation models, make the mean value of these two kinds prediction algorithms different from the estimated value of standard deviation.That is NN estimates the average estimator after mode standard With the standard deviation estimator

Will with the multiple regression model standardization after the average estimator

With the standard deviation estimator

Different.

The confidence desired value is designed to judge the Reliability of virtual measurement value, so the confidence desired value should be taken into account the statistics distribution of virtual measurement value

Distribute with the statistics of actual amount measured value

Similarity degree between the two.Yet, when applying virtual measures, there is no the Reliability (significantly, if do not needed virtual measurement just obtain the actual amount measured value) that the actual amount measured value can be used for assessing the virtual measurement value.So the present invention adopts the statistics of being estimated by reference prediction algorithm (for example multiple regression algorithm) to distribute

Replace

Statistics distribute.Reference prediction algorithm of the present invention also can be other relevant prediction algorithm, therefore the present invention and not subject to the limits.

Please refer to Fig. 3, it illustrates the schematic diagram of the confidence desired value of explanation embodiments of the invention.Confidence desired value of the present invention is defined as the distribution of calculating the prediction (virtual measurement value) that estimates pattern (for example adopting neural network (NN) algorithm)

Distribution with the prediction (reference quantity measured value) of reference model (for example adopting the multiple regression algorithm)

Common factor area covering value (overlapping area A) between the two.Therefore, the formula of confidence desired value is as follows:

$\mathrm{RI}=2{\∫}_{\frac{Z_{{\hat{y}}_{\mathrm{Ni}}}+Z_{{\hat{y}}_{\mathrm{ri}}}}{2}}^{\∞}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{x-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\mathrm{dx}---\left(4\right)$

Wherein work as $Z_{{\hat{y}}_{\mathrm{Ni}}}<Z_{{\hat{y}}_{\mathrm{ri}}}$ $\mathrm{\&mu;}=Z_{{\hat{y}}_{\mathrm{Ni}}}$

When $Z_{{\hat{y}}_{\mathrm{ri}}}<Z_{{\hat{y}}_{\mathrm{Ni}}}$ $\mathrm{\&mu;}=Z_{{\hat{y}}_{\mathrm{ri}}}$

σ is made as 1

The confidence desired value increases along with the increase of overlapping area A.This phenomenon points out to use result that the pattern of estimating obtains close to the result of using reference model to obtain, thereby corresponding virtual measurement value is more reliable.Otherwise the fiduciary level of corresponding virtual measurement value reduces along with the minimizing of overlapping area A.When by

Estimated distribution

With by

Estimated distribution

Complete when overlapping, according to statistical theory of distribution, its confidence desired value equals 1; And when two distributed almost completely separately, its confidence desired value leveled off to 0.

Below explanation estimates mode computation virtual measurement value

With

The method of distribution.

In estimating pattern, if the condition of convergence is minimum error quadratic sum (SSE), can suppose " given

Under,

The average that is assigned as equal

Variance is

Distribution ", namely given

Under,

And

The NN estimator be

The NN estimator be

Before carrying out NN and estimating the modeling of pattern, need first carry out the standardized step of process data.

It is as follows that NN estimates pattern process data standardization formula:

$Z_{x_{i,j}}=\frac{x_{i,j}-{\stackrel{-}{x}}_j}{{\mathrm{\&sigma;}}_{x_j}},i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n,n+1,\&CenterDot;\&CenterDot;\&CenterDot;,m;j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,p---\left(5\right)$

${\stackrel{-}{x}}_j=\frac{1}{n}(x_{1,j}+x_{2,j}+...+x_{n,j})---\left(6\right)$

${\mathrm{\&sigma;}}_{x_j}=\sqrt{\frac{1}{n-1}[{(x_{1,j}-{\stackrel{-}{x}}_j)}^2+{(x_{2,j}-{\stackrel{-}{x}}_j)}^2+...+{(x_{n,j}-{\stackrel{-}{x}}_j)}^2]}---\left(7\right)$

Wherein

x _i,jBe j process parameter in i group process data;

It is the process parameter after j standardization in i group process data;

Be the mean value of j process parameter;

It is the standard deviation of j process parameter;

Use the process data after this n organizes standardization Actual amount measured value after the standardization of n group therewith

Come construction NN to estimate pattern.Then, the process data after the standardization of input m group Estimate in pattern to NN, to obtain the virtual measurement value after corresponding standardization

Therefore,

(namely

Estimated value and

(namely

Estimated value can be calculated by formula as follows:

${\widehat{\mathrm{\&mu;}}}_{z_{\mathrm{yi}}}=Z_{{\hat{y}}_{\mathrm{Ni}}},i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n,n+1,\&CenterDot;\&CenterDot;\&CenterDot;,m---\left(8\right)$

${\widehat{\mathrm{\&sigma;}}}_{Z_{\hat{y}N}}=\sqrt{\frac{1}{n-1}[{(Z_{{\hat{y}}_{N1}}-{\stackrel{-}{Z}}_{{\hat{y}}_{\text{N}}})}^2+{(Z_{{\hat{y}}_{N2}}-{\stackrel{-}{Z}}_{{\hat{y}}_N})}^2+...+{(Z_{{\hat{y}}_{\mathrm{Nn}}}-{\stackrel{-}{Z}}_{{\hat{y}}_N})}^2]---}\left(9\right)$

${\stackrel{-}{Z}}_{\hat{y}N}=\frac{1}{n}(Z_{{\hat{y}}_{N1}}+Z_{{\hat{y}}_{N2}}+...+Z_{{\hat{y}}_{\mathrm{Nn}}})---\left(10\right)$

Wherein

Mean value for the virtual measurement value after standardization

Below explanation is by multiple regression model computing reference predicted value

With

Method.

The basic assumption of multiple regression algorithm is " given

Under,

The average that is assigned as equal

Variance is

Distribution ", namely given

Under,

And

The multiple regression estimator be

The multiple regression estimator

For trying to achieve the process data after n organizes standardization

Actual amount measured value after the standardization of n group therewith

Between relation, must definition utilizing in multiple regression analysis the corresponding weight of these p parameter is (β _r0, β _r1, β _r2..., β _rp).Construction

With

Relation is as follows:

${\mathrm{\&beta;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000132926700061.png,HSA00000132926700062.png"\; state="\{\{state\}\}">r</figure-callout>}0}+{\mathrm{\&beta;}}_{r1}{X}_{x_{\mathrm{1,1}}}+{\mathrm{\&beta;}}_{r2}{Z}_{x_{\mathrm{1,2}}}+\&CenterDot;\&CenterDot;\&CenterDot;+{\mathrm{\&beta;}}_{\mathrm{rp}}{Z}_{x_{1,p}}={\mathrm{<figure-callout\; id="1"\; label="Z\; y"\; filenames="HSA00000132926700041.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{y_{}}$

${\mathrm{\&beta;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000132926700061.png,HSA00000132926700062.png"\; state="\{\{state\}\}">r</figure-callout>}0}+{\mathrm{\&beta;}}_{r1}{Z}_{x_{\mathrm{2,1}}}+{\mathrm{\&beta;}}_{r2}{Z}_{x_{\mathrm{2,2}}}+\&CenterDot;\&CenterDot;\&CenterDot;+{\mathrm{\&beta;}}_{\mathrm{rp}}{Z}_{x_{2,p}}=Z_{y_2}---\left(11\right)$

L

${\mathrm{\&beta;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000132926700061.png,HSA00000132926700062.png"\; state="\{\{state\}\}">r</figure-callout>}0}+{\mathrm{\&beta;}}_{r1}{Z}_{x_{n,1}}+{\mathrm{\&beta;}}_{r2}{Z}_{x_{n,2}}+\&CenterDot;\&CenterDot;\&CenterDot;+{\mathrm{\&beta;}}_{\mathrm{rp}}{Z}_{x_{n,p}}=Z_{y_n}$

Suppose $Z_y=\left(\begin{array}{c}{Z}_{y_1}\\ Z_{y_2}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ Z_{y_n}\end{array}\right)---\left(12\right)$

Utilize the least square method in statistically multiple regression analysis, can try to achieve parameter beta _rEstimator ${\widehat{\mathrm{\&beta;}}}_r={[{\widehat{\mathrm{\&beta;}}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000132926700061.png,HSA00000132926700062.png"\; state="\{\{state\}\}">r</figure-callout>}0},{\widehat{\mathrm{\&beta;}}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000132926700041.png"\; state="\{\{state\}\}">r</figure-callout>}1},...{\widehat{\mathrm{\&beta;}}}_{\mathrm{rp}}]}^T,$ Namely

${\widehat{\mathrm{\&beta;}}}_r={\left(Z_x^T{Z}_x\right)}^{-1}{Z}_x^T{Z}_y---\left(14\right)$

Then, multiple regression model can obtain:

$Z_{{\hat{y}r}_i}={\widehat{\mathrm{\&beta;}}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000132926700061.png,HSA00000132926700062.png"\; state="\{\{state\}\}">r</figure-callout>}0}+{\widehat{\mathrm{\&beta;}}}_{r1}{Z}_{x_{i,1}}+{\widehat{\mathrm{\&beta;}}}_{r2}{Z}_{x_{i,2}}+...{+\widehat{\mathrm{\&beta;}}}_{\mathrm{rp}}{Z}_{x_{i,p}}$

$i=\mathrm{1,2},...,n,n+1,...,m---\left(15\right)$

Therefore, when estimating the stage, after process data is come in, can obtain its corresponding multiple regression estimated value according to formula (15)

The standard variance

The multiple regression estimator be

Have:

${\widehat{\mathrm{\&sigma;}}}_{Z_{\hat{y}r}}=\sqrt{\frac{1}{n-1}[{(Z_{{\hat{y}}_{r1}}-{\stackrel{-}{Z}}_{{\hat{y}}_{\text{r}}})}^2+{(Z_{{\hat{y}}_{r2}}-{\stackrel{-}{Z}}_{{\hat{y}}_r})}^2+...+{(Z_{{\hat{y}}_{\mathrm{rn}}}-{\stackrel{-}{Z}}_{{\hat{y}}_r})}^2]}---\left(16\right)$

${\stackrel{-}{Z}}_{{\hat{y}}_r}=\frac{1}{n}(Z_{{\hat{y}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000132926700041.png"\; state="\{\{state\}\}">r</figure-callout>}1}}+Z_{{\hat{y}}_{r2}}+...+Z_{{\hat{y}}_{\mathrm{rn}}})---\left(17\right)$

When the estimator of trying to achieve NN and estimate pattern

With

And the estimator of multiple regression model

With

After, can draw normality distribution diagram as shown in Figure 3, calculate to use the distribution common factor area covering value (overlapping area A) between the two of the prediction (reference quantity measured value) of the distribution of the prediction (virtual measurement value) that estimates pattern (for example adopting neural network (NN) algorithm) and reference model (for example adopting the multiple regression algorithm), can obtain the confidence desired value of each virtual measurement value.

After obtaining confidence desired value (RI), must stipulate a confidence indicator threshold value RI _T).If RI＜RI _T, the degree of reliability of virtual measurement value that has this RI workpiece is low, that is have the quality of the workpiece of this RI may be abnormal, therefore need carry out actual measurement.Below describe and determine confidence indicator threshold value (RI _T) method:

Stipulating confidence indicator threshold value (RI _T) before, at first need stipulate out the maximum admissible error upper limit (E _L).The error of virtual measurement value (Error) is actual amount measured value y _iObtain with the pattern that estimated by NN

Difference, then divided by the percent of the absolute value after the mean value of all actual amount measured values, namely

${\mathrm{Error}}_i=\left|\frac{y_i-{\hat{y}}_{\mathrm{Ni}}}{\stackrel{-}{y}}\right|\&times;100\%---\left(18\right)$

Then, can specify the maximum admissible error upper limit (E according to the degree of accuracy specification of the defined error of formula (18) and virtual measurement _L).Therefore, confidence indicator threshold value (RI _T) be defined as corresponding to the maximum admissible error upper limit (E _L) confidence desired value (RI), as shown in 4 figure.That is,

${\mathrm{RI}}_T=2{\&Integral;}_{\mathrm{Center}}^{\&infin;}\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{e}^{-\frac{1}{2}{\left(\frac{x-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\right)}^2}\mathrm{dx}---\left(19\right)$

μ and σ are defined in formula (4); And

$Z_{\mathrm{center}}=Z_{{\hat{y}}_{\mathrm{Ni}}}+[\stackrel{-}{y}\&times;(E_L/2)]/{\mathrm{\&sigma;}}_y---\left(20\right)$

σ wherein _yBe defined in formula (3).

Overall similarity index (GSI)

As mentioned above, when applying virtual measures, there is not the actual amount measured value can obtain to verify the degree of accuracy of virtual measurement value.Therefore, with the multiple regression estimated value after standardization

Actual amount measured value after the replacement standardization

Calculate confidence desired value (RI).Yet this kind replacement may cause the error of confidence desired value (RI), and in order to compensate this situation, the overall similarity index (GSI) that the present invention proposes processing procedure helps judge the degree of reliability of virtual measurement.

The concept of GSI proposed by the invention is that all the history parameters data when adopt at present equipment process data when the input of virtual measurement system with modeling are compared, and obtains a process data of inputting and the similarity degree index of all history parameters data.

The present invention can quantize similarity with various statistical distance algorithm, such as: mahalanobis distance algorithm (Mahalanobis Distance), Euclidean distance algorithm (Euclidean Distance) and center method (Centroid Method) etc.The statistical distance algorithm that mahalanobis distance is introduced 1936 Christian eras by P.C.Mahalanobis.This kind technological means is based on the kenel of the relevance between variable with identification and the different sample groups of analysis.Mahalanobis distance is in order to determine the method for the similarity between unknown sample group and known sample group, and the relevance between the method consideration data group also has yardstick unchangeability (Scale Invariant), and namely the size to measuring value is not relevant.If data have high similarity, the mahalanobis distance that calculates will be less.

The size of the GSI that utilization of the present invention calculates (mahalanobis distance) is differentiated the process data that newly advances whether similar in appearance to all process datas of modeling.If the GSI that calculates is little, represent that the process data that newly advances is similar to the process data of modeling, the virtual measurement value of the process data (high similarity) that therefore newly advances will be more accurate.Otherwise if the GSI that calculates is excessive, some is different for the process data of the process data that newly advances of expression and modeling.Thereby the quality with workpiece of the process data that newly advances (low similarity) may be abnormal, therefore need carry out actual measurement.

Estimate the standardization process parameter of pattern Computing formula suc as formula shown in (5), (6) and (7).At first, definition example edition supplemental characteristic X _M=[x _M,1, x _M,2..., x _M,p] ^T, x wherein _M,jEqual

So, each parameter of the modeling process data after standardization is 0 (that is the modeling parameters Z after standardization _M,jBe 0).In other words, Z _M=[Z _{M, 1,}Z _M,2..., Z _M,p] ^TIn all parameters be 0.Next calculate the related coefficient between modeling parameters after each standardization.

Suppose that the related coefficient between s parameter and t parameter is rst, and k group data are wherein arranged,

$r_{\mathrm{st}}=\frac{1}{k-1}\underset{l=1}{\overset{k}{\mathrm{\&Sigma;}}}{z}_{\mathrm{sl}}\&CenterDot;z_{\mathrm{tl}}=\frac{1}{k-1}(z_{\mathrm{sl}}\&CenterDot;z_{\mathrm{tl}}+z_{s2}\&CenterDot;z_{t2}+...+z_{\mathrm{sk}}\&CenterDot;z_{\mathrm{tk}})---\left(21\right)$

After completing the related coefficient of calculating between each parameter, can obtain correlation matrix as follows:

Suppose the inverse matrix (R of R ^-1) be defined as A,

$A=R^{-1}=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{1p}\\ a_{21}& a_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{2p}\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ a_{p1}& a_{p2}& \&CenterDot;\&CenterDot;& a_{\mathrm{pp}}\end{array}\right]---\left(23\right)$

So, the standardized process parameter (Z of λ pen _λ) and standardized example edition supplemental characteristic (Z _M) between mahalanobis distance Computing formula is as follows:

$D_{\mathrm{\&lambda;}}^2={(Z_{\mathrm{\&lambda;}}-Z_M)}^T{R}^{-1}(Z_{\mathrm{\&lambda;}}-Z_M)$

(24)

$=Z_{\mathrm{\&lambda;}}^T{R}^{-1}{Z}_{\mathrm{\&lambda;}}$

Can get

$D_{\mathrm{\&lambda;}}^2=\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ij}}{z}_{\mathrm{i\&lambda;}}{z}_{\mathrm{j\&lambda;}}---\left(25\right)$

And the GSI value of λ process data is

After obtaining the GSI value, use leaving-one method (Leave-One-Out in validation-cross (Cross Validation); LOO) principle defines GSI threshold value (GSI _T).GSI threshold value (GSI _T) formula as follows:

${\mathrm{GSI}}_T=a*{\stackrel{-}{\mathrm{GSI}}}_{\mathrm{LOO}}---\left(26\right)$

So-called " leaving-one method (Leave-One-Out; LOO) principle " from whole modeling samples; extract a test sample book of reaching the standard grade as emulation; re-use remaining Sample Establishing GSI model, then use the test sample book that this newly-built GSI model reaches the standard grade for this emulation and calculate its GSI value, this is worth with GSI _LOOExpression.Then repeat above-mentioned steps until in modeling sample all each sample standard deviations calculate its corresponding GSI _LOOTherefore, in formula (26)

Representative sees through all GSI that the whole modeling samples of the former reason of LOO calculate _LOOThe for example 90% average Number of truncation (Trimmed Mean).The a value of formula (26) between 2 to 3, what it can be according to actual state fine setting, the default value of a is 3.

Workpiece sampling method of the present invention below is described.

Please refer to Fig. 5, it illustrates the schematic flow sheet of workpiece sampling method according to an embodiment of the invention.Estimate pattern, reference model and statistical distance pattern in foundation; And acquisition confidence indicator threshold value (RI _T) and GSI threshold value (GSI _T) after, the process parameter data of each workpiece in the input card casket are to the above-mentioned pattern that estimates, reference model and statistical distance pattern, to calculate confidence desired value (RI) and the GSI value (step 100) of each workpiece.Then, to each workpiece, carry out step 110, to judge that whether its confidence desired value (RI) is less than confidence indicator threshold value (RI _T); Or whether its GSI value is greater than GSI threshold value (GSI _T), if judgment result is that of step 110 is carry out step 120, the workpiece of the condition that meets step 110 is measured whether determining; Otherwise finish the workpiece sampling method of the present embodiment.If judgment result is that of step 120 is carry out step 120, by measurement platform, this workpiece is measured.In one embodiment, the method for workpiece pick test of the present invention measures the workpiece that all in casket of card meet the condition of step 110.In another embodiment, because the characteristic of each workpiece in same card casket is identical, therefore, only need certainly blocks and select at least one workpiece in the workpiece of the condition that meets step 110 in casket and measure and get final product.If the determination result is NO for step 120, finish the workpiece sampling method of the present embodiment.

Will be understood that, the method for workpiece pick test of the present invention is above-described implementation step, and interior storage of the present invention is used for the computer program of workpiece pick test, in order to complete the method for workpiece pick test described above.

Please refer to Fig. 6 A to Fig. 6 C, Fig. 6 A illustrates the virtual measurement value of application examples of the present invention and the result schematic diagram of actual amount measured value; Fig. 6 B is the result schematic diagram that illustrates the confidence desired value of application examples of the present invention; Fig. 6 C is the result schematic diagram that illustrates the overall similarity desired value of application examples of the present invention.

As shown in Figure 6A, the 1st to 100 data are the historical measuring value of the 1st to 100 workpiece, and it corresponds to respectively the historical process parameter data of many groups, estimates pattern, reference model and statistical distance pattern in order to foundation; And acquisition confidence indicator threshold value (RI _T) and GSI threshold value (GSI _T).The the 101st to 125 data are a plurality of workpiece in the card casket, and wherein the 101st workpiece taken a sample test by known mode, therefore have the actual amount measured value, sets up in order to adjustment pattern, reference model and the statistical distance pattern of estimating.The purpose of workpiece sampling method of the present invention is: effectively select out suitable workpiece measuring in the 102nd to 125 workpiece, and avoid the situation of leak detecting, and it is abnormal in time to find to produce board.

As shown in Fig. 6 B, utilize confidence desired value (RI) to judge which workpiece (representing with which data group) need be sent to measurement platform to detect.Then, as shown in Fig. 6 C, utilize overall similarity desired value (GSI) to judge the similarity degree of workpiece data and modeling data.Wherein, the 114th data group is although its RI is greater than RI _T(0.567), but its GSI greater than GSI _T(5.093), representative needs the 114th workpiece delivered to measurement platform to detect, with the situation generation of pre-leakproof detecting.And the 107th with the 120th data, because of its RI less than RI _TAnd because of its GSI greater than GSI _TTherefore, need the 107th, 120 workpiece delivered to measurement platform to detect, with the situation generation of pre-leakproof detecting.Except the 107th, 114 with 120 data because the RI of all the other workpiece is greater than RI _TAnd its GSI is less than GSI _T, representative need not detect the workpiece except the 107th, 114 and 120 workpiece, thereby uses manpower and material resources sparingly.In another embodiment, the present invention also can only select at least one workpiece and measures in the 107th, 114 and 120 workpiece.

By the invention described above preferred embodiment as can be known, the method for workpiece pick test of the present invention can be selected out suitable workpiece effectively measuring, and avoids the situation of leak detecting, and it is abnormal in time to find to produce board.

Although the present invention discloses as above with embodiment; so it is not to limit the present invention; any those of ordinary skill in this technical field; without departing from the spirit and scope of the present invention; when can be used for a variety of modifications and variations, so protection scope of the present invention is as the criterion when looking accompanying claims institutes confining spectrum.

Claims (7)

1. the method for a workpiece pick test, is characterized in that, comprises:

Obtain many groups of historical process parameter data of producing board;

Obtain a plurality of historical measuring values from a measurement platform, wherein these a plurality of historical measuring values are respectively the measuring value of the workpiece of producing according to the historical process parameter data of this many group;

Estimate pattern with these historical process parameter data of many groups and these a plurality of historical measuring values, wherein this foundation that estimates pattern estimates algorithm according to one;

Set up a reference model with these historical process parameter data of many groups and these a plurality of historical metric data, wherein with reference to algorithm, it is different with reference to algorithm from this that this estimates algorithm according to one in the foundation of this reference model;

Input should the historical process parameter data of many groups estimate pattern to this, and calculated a plurality of historical virtual measurement values;

Input should be organized historical process parameter data to this reference model more, and calculated a plurality of historical reference predicted values;

Calculate respectively the overlapping area between the distribution of the distribution of these a plurality of historical virtual measurement values and these a plurality of historical reference predicted values and produce a plurality of historical confidence desired values, wherein work as overlapping area larger, historical confidence desired value is higher, represents that the confidence level of these a plurality of historical virtual measurement values that correspond to is higher;

Historical virtual measurement values a plurality of according to this, these a plurality of historical reference predicted values and this a plurality of historical measuring values calculate a confidence indicator threshold value;

Collect the process parameter data of blocking a plurality of workpiece in casket that this production board is sent;

The process parameter data of inputting these a plurality of workpiece estimate pattern to this, and calculate a plurality of virtual measurement values of these a plurality of workpiece;

Input the process parameter data of these a plurality of workpiece to this reference model, and calculate a plurality of reference prediction values of these a plurality of workpiece;

Calculate respectively the overlapping area between the distribution of the distribution of these a plurality of virtual measurement values of these a plurality of workpiece and these a plurality of reference prediction values and produce a plurality of confidence desired values of these a plurality of workpiece, wherein work as overlapping area larger, the confidence desired value is higher, represents that the confidence level of these a plurality of virtual measurement values that correspond to is higher;

Choose its confidence desired value less than at least one first workpiece of this confidence indicator threshold value in these a plurality of workpiece; And

This at least one first workpiece of these a plurality of workpiece is delivered to this measurement platform to detect.

2. the method for workpiece pick test according to claim 1, is characterized in that, this estimates algorithm and this and selects respectively with reference to algorithm and freely return the group that algorithm and a neural network algorithm form.

3. the method for workpiece pick test according to claim 1, it is characterized in that, this estimates algorithm and this and selects respectively neural network at the bottom of freely a back propagation neural network, a general recurrence neural network, a radial basis, a simple regression network, a Support Vector data description, a support vector machine, a multiple regression algorithm, a part of least square method, one non-linearly to substitute the group that inclined to one side least square method and a generalized linear pattern form with reference to algorithm.

4. the method for workpiece pick test according to claim 1, is characterized in that, also comprises:

Using should the historical process parameter data of many groups, and according to a statistics apart from algorithm, set up a statistics distance mode;

With these historical process parameter data of many groups and this a plurality of historical measuring values, and the leaving-one method principle in the application validation-cross rebuilds this statistical distance pattern, and calculates corresponding overall similarity desired value, to calculate an overall similarity indicator threshold value;

Input the process parameter data of these a plurality of workpiece to this statistical distance pattern, and calculate the overall similarity desired value of the corresponding process parameter data of these a plurality of virtual measurement values of these a plurality of workpiece;

Choose its overall similarity desired value greater than at least one second workpiece of this overall similarity indicator threshold value in these a plurality of workpiece; And

This at least one second workpiece of these a plurality of workpiece is delivered to this measurement platform to test.

5. the method for workpiece pick test according to claim 4, is characterized in that, the group that the free mahalanobis distance algorithm of this statistical distance algorithm choosing, an Euclidean distance algorithm and a center method form.

6. the method for a workpiece pick test, is characterized in that, comprises:

Obtain many groups of historical process parameter data of producing board;

Obtain a plurality of historical measuring values from a measurement platform, wherein these a plurality of historical measuring values are respectively the measuring value of the workpiece of producing according to the historical process parameter data of this many group;

Estimate pattern with these historical process parameter data of many groups and these a plurality of historical measuring values, wherein this foundation that estimates pattern estimates algorithm according to one;

Collect the process parameter data of blocking a plurality of workpiece in casket that this production board is sent;

The process parameter data of inputting these a plurality of workpiece estimate pattern to this, and calculate a plurality of virtual measurement values of these a plurality of workpiece;

Using should the historical process parameter data of many groups, and according to a statistics apart from algorithm, set up a statistics distance mode;

With these historical process parameter data of many groups and this a plurality of historical measuring values, and the leaving-one method principle in the application validation-cross rebuilds this statistical distance pattern, and calculates corresponding overall similarity desired value, to calculate an overall similarity indicator threshold value;

Input the process parameter data of these a plurality of workpiece to this statistical distance pattern, and calculate the overall similarity desired value of the corresponding process parameter data of these a plurality of virtual measurement values of these a plurality of workpiece;

Choose its overall similarity desired value greater than at least one first workpiece of this overall similarity indicator threshold value in these a plurality of workpiece; And

This at least one first workpiece in these a plurality of workpiece is delivered to a measurement platform to detect.

7. the method for workpiece pick test according to claim 6, is characterized in that, this statistical distance algorithm is the group that the free mahalanobis distance algorithm of choosing, an Euclidean distance algorithm and a center method form.

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