CN101571891A - Method and device for inspecting abnormal data - Google Patents
Method and device for inspecting abnormal data Download PDFInfo
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- CN101571891A CN101571891A CNA2008101056282A CN200810105628A CN101571891A CN 101571891 A CN101571891 A CN 101571891A CN A2008101056282 A CNA2008101056282 A CN A2008101056282A CN 200810105628 A CN200810105628 A CN 200810105628A CN 101571891 A CN101571891 A CN 101571891A
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Abstract
The invention relates to a method for inspecting abnormal data and an inspection device applying the method. The method comprises the following steps: performing sequencing on unfiltered data samples according to the size; selecting a proper percentile in the data samples, and calculating a percentile value corresponding to the percentile; and taking the calculation result as a numerical screening limit value of the data samples, and taking data, of which the value is more than the upper limit value of numerical screening or less than the lower limit value of numerical screening, in the data samples as abnormal data points. The invention improves the inspection precision by improving the method for inspecting the abnormal data, is favorable for improving the yield of products and reducing waste plates and the production cost, realizes the inspection on abnormally distributed type data which cannot be realized in the prior art, and improves the production efficiency.
Description
Technical field
The present invention relates to a kind of abnormal data method of inspection and device.
Background technology
Semi-conductive manufacturing production run is very complicated, comprises procedures up to a hundred such as oxide-diffused, photoetching, etching, washing, deposit, generally is difficult to set up corresponding modeling.The monitoring that semiconductor is made production run is normally by gathering the data sample of each working procedure parameter, analyzes and monitor that these data samples realize.
When the data sample is analyzed, at first need to check the data sample of being gathered, the exceptional data point (outlier) that just needs to comprise in the data point is rejected away.Exceptional data point may be that (as the data input of the prescription of the maloperation of wafer, mistake, inferior raw material, mistake, system burst error etc.) cause because cause specific in the production of wafer.If the rejecting abnormalities data point is not directly analyzed the data sample, may cause changing process conditions blindly and cause unnecessary waste.
The Tukey method of inspection is adopted in filtration for exceptional data point in the prior art usually, the data that this method at first will need the to analyze series arrangement of successively decreasing by size; The data that wherein account for whole data sample the 25 hundredths are called first quartile Q
1, the data that account for whole data sample the 75 hundredths are called the 3rd quartile Q
3, interquartile range IQR is the difference of the 3rd quartile and first quartile, i.e. IQR=Q
3-Q
1Utilize 1.5 times or 3 times of interquartile range IQR the boundary that abnormity point is filtered is set, be about to be lower than Q
1Below 1.5 IQR or 3 IQR data and be higher than Q
3More than the data of 1.5 IQR or 3 IQR all handle as exceptional value.About adopting the Tukey method to filter abnormity point, the patent No. is also to mention in U.S.'s patent of invention of 7194465.
Yet the same with most of statistical analysis softwares, the Tukey method is to the processing of exceptional value in the data, also is to be based upon on the prerequisite that data itself are the normal distribution type.For the sample data of skewed distribution type in the productive life, the resulting analysis result of existing Tukey method just becomes unreliable.For the processing of abnormity point in the skewed distribution data sample, have only relevant theoretical research at present, but these theoretical algorithms too complex all is not suitable for the production reality of reality.
Summary of the invention
The invention provides a kind of method of inspection and device that exceptional data point in the skewed distribution data sample is filtered.
The invention provides a kind of abnormal data method of inspection, this method may further comprise the steps: the data sample of filtered is sorted according to size order, select the first hundredths P
1With the second hundredths P
2Calculate hundred fractional values corresponding with described data sample and hundredths, will be corresponding to the first hundredths P
1With the second hundredths P
2Hundred fractional computation results as the numerical value of described data sample screening higher limit and data screening lower limit; Numerical value is exceptional data point greater than numerical value screening higher limit or less than the data of numerical value screening lower limit in the described data sample.
Optionally, can adopt hundred mark Percentile formula to calculate described hundred fractional values.
Optionally, the above-mentioned first hundredths P
1, the second hundredths P
2Satisfy relation: P
1+ P
2=1.
Optionally, described first hundredths is 99.9998828%, and described second hundredths is 0.0001172%.
Optionally, described first hundredths is 99.6512%,, described second hundredths is 0.348802%.
Optionally, can adopt linear extrapolation to calculate described hundred fractional values in conjunction with hundred mark formula Percentile formula.
Optionally, described linear extrapolation comprises: the selected linear numerical value screening limit value computing formula that comprises hundredths; Obtain linear coefficient k value in the linear numerical value screening limit value computing formula by standardized normal distribution hundredths formula; Obtain the data value that comprises hundredths correspondence in described data sample in the linear control circle computing formula; Numerical value screening limit value computing formula with the described linearity of data value substitution of linear coefficient k value and hundredths correspondence.
The present invention also provides a kind of device of using the described abnormal data method of inspection, comprising: data sample sequencing unit, hundredths selected cell, data screening limit value computing unit and determining unit.
Described data sample sequencing unit is used for the data sample of filtered is sorted according to size order;
Described hundredths selected cell is used to select the first hundredths P
1With the second hundredths P
2
Described data screening limit value computing unit is used to calculate hundred fractional values corresponding with described data sample and hundredths, will be corresponding to the first hundredths P
1With the second hundredths P
2Result of calculation as the numerical value of described data sample screening higher limit and data screening lower limit;
Described determining unit is used for described data sample numerical value is defined as exceptional data point greater than numerical value screening higher limit or less than the data of numerical value screening lower limit.
Optionally, described data screening limit value computing unit comprises: numerical value screening higher limit computing unit is used to adopt hundred mark Percentile formula to calculate corresponding to the first hundredths P
1Hundred fractional values, as numerical value screening higher limit; Numerical value screening lower limit computing unit is used to adopt hundred mark Percentile formula to calculate corresponding to the first hundredths P
2Hundred fractional values, as numerical value screening lower limit.
Optionally, described data screening limit value computing unit comprises linear extrapolation computing unit and limit value computing unit; Described linear extrapolation computing unit, the pairing data value in described data sample of the hundredths in the linear formula that calculation control circle computing unit is adopted, and linear coefficient k value; The limit value computing unit adopts the corresponding linear formula according to the data value and the linear coefficient k value of hundredths correspondence, calculates the data screening limit value of described skewed distribution categorical data.
The present invention will be applied in the calculating of data screening limit value unconfined hundred branch counting methods of sample data type, changed in the previous methods and can only handle the normal state distributed data, realized and can the exceptional data point in the skewed distribution data sample have been filtered, improved the accuracy of data screening limit value effectively, help to improve the product yield, reduce useless sheet, reduce production costs, enhance productivity.
Description of drawings
Fig. 1 is a kind of embodiment process flow diagram of the abnormal data method of inspection of the present invention;
Fig. 2 is a kind of embodiment process flow diagram of the abnormal data method of inspection of the present invention;
Fig. 3 is a kind of embodiment distribution of data points figure of the abnormal data method of inspection of the present invention;
Fig. 4 is a kind of embodiment distribution of data points figure of the abnormal data method of inspection of the present invention;
Fig. 5 is a kind of embodiment process flow diagram of abnormal data verifying attachment of the present invention;
Fig. 6 is a kind of embodiment that data screening limit value computing unit is formed in the abnormal data verifying attachment of the present invention;
Fig. 7 is a kind of embodiment that data screening limit value computing unit is formed in the abnormal data verifying attachment of the present invention.
Embodiment
With reference to figure 1, the abnormal data method of inspection of the present invention sorts the data sample of filtered (step D1) according to size order, selects the first hundredths P
1With the second hundredths P
2(step D2) calculates hundred fractional values corresponding with described data sample and hundredths, will be corresponding to the first hundredths P
1With the second hundredths P
2Hundred fractional computation results as the numerical value of described data sample screening higher limit and data screening lower limit (step D3), be exceptional data point (step D4) with numerical value in the described data sample greater than numerical value screening higher limit or less than the data of numerical value screening lower limit.
Hundred fractional computation formula can adopt statistical analysis software commonly used, as SAS, SPSS, or hundred mark formula Percentile[(array in the Excel), p].At Percentile[(array), p] in the formula, p is the number percent numeral between 0 to 1, array is the array or the data area of definition relative position, Percentile[(array), p] return the pairing numerical value of number percent p in value region array, this rreturn value has the dimension identical with array simultaneously.For the different weight percentage p in the same data sample, Percentile[(array), p] can be reduced to P (p).In embodiments of the present invention, the first hundredths P
1With the second hundredths P
2Being respectively the p in the formula, i.e. number percent numeral between 0 to 1, the data sample of array, Percentile[(array), p for needing to filter] numerical value that is returned is the numerical value screening limit value of required calculating.
With reference to figure 2, a kind of embodiment of the abnormal data method of inspection of the present invention sorts the data sample of filtered according to size order; Select the first hundredths P
1With the second hundredths P
2With in the described data sample corresponding to hundredths P
1Hundred fractional value Percentile (P
1) as the numerical value of described data sample screening higher limit, with in the described data sample corresponding to hundredths P
2Hundred fractional value Percentile (P
2) screen lower limit, wherein P as the numerical value of described data sample
1+ P
2=1; In the described data sample, numerical value is exceptional data point greater than numerical value screening higher limit or less than the data of numerical value screening lower limit.
Meet at number of samples under the prerequisite of calculation requirement, hundred fraction methods compared to existing Tukey method, and do not require that sample data must meet normal distribution, therefore hundred fraction methods can application type data type more widely, its resulting data screening limit value is also more accurate.Yet need sample size much larger than 100 similar with the Tukey formula, the data bulk that hundred fraction methods are same to require to be used to calculate hundred fractional values must not be less than 1/p or 1/ (1-p).And in real production run, the data sample of a lot of working procedure parameters can not satisfy in process of production to making demands before the sample data quantity, the present invention optionally provides the employing linear extrapolation in this case in conjunction with hundred fractional value Percentile[(array), p] the limit value of method evaluation screening.
In a concrete embodiment, with reference to figure 3, data point has only 1000, and is non-standard normal distribution, if directly use formula Percentile[(array), p] calculate, can only obtain P (0.1%): P (0.1%)=68.8.Simultaneously, think P (0.001%) and P (0.01%) approximately equal, and P (0.01%) can think also and P (0.1%) approximately equal, therefore obtain P (0.001%)～P (0.01%)～P (0.1%)=68.8.
Present embodiment is reasonably supposed raw data, supposes that its lower end is a linear distribution, then can adopt linear extrapolation, has linear relationship for P (0.001%):
P(0.001％)＝P(50％)-k*[P(50％)-P(10％)]，
Wherein linear coefficient k can be tried to achieve by standardized normal distribution percentile formula NORMSINV (p) (formula in the Excel, average is 0, standard variance is 1).There is following linear relationship in NORMSINV (p):
NORMSINV(0.001％)＝NORMSINV(50％)-k*[NORMSINV(50％)-NORMSINV(10％)]，
Wherein, be known quantity, then can draw because NORMSINV (0.001%), NORMSINV (50%) and NORMSINV (10%) all can be tried to achieve by the Excel function
Organize 1000 raw data of non-standard normal distribution for this, P (50%) and the available Percentile[(array of P (10%)), p] try to achieve: P (50%)=100.02 and P (10%)=87.39, so P (0.001%)=100.02-3.328*[100.02-87.39]=57.9.
Compare in conjunction with the data screening lower limit of the resulting non-standard normal distribution data of linear extrapolation and do not adopt the resulting lower limit of this linear extrapolation, the former is less than the latter, this shows, for the data between the former and the latter, adopt the former can more effectively discern abnormal data, that is to say, under the situation of data point deficiency, adopt linear extrapolation the data screening limit value of non-standard normal distribution data can comparatively reasonably be set, isolate abnormity point effectively in conjunction with hundred fractional value methods.
With reference to figure 4, an alternative embodiment of the invention, primary data sample is 596 data points that obviously are skewed distribution, when evaluation screening higher limit, can reasonably suppose equally in the high-end linearity that is extrapolated for, there is linear relationship in hundred fractional value P (99.999%) during therefore for p=99.999%:
P (99.999%)=P (90%)+k*[P (99%)-P (90%)], wherein linear coefficient k goes out from following formula to calculating:
NORMSINV(99.999％)＝NORMSINV(90％)+k*[NORMSINV(99％)-NORMSINV(90％)]。
By obtain in the Excel function NORMSINV (99.999%), NORMSINV (90%) and [NORMSINV (99%) can obtain:
By the P (90%)=255.07 and the P (99%)=482.62 of 596 data points of this skewed distribution, can obtain hundred mark: P (99.999%)=255.07+2.856* (482.62-255.07)=905 of 99.999% of extrapolation.
With reference to figure 5, a kind of embodiment of statistical Process Control device of the present invention comprises:
Data sample sequencing unit M1 is used for the data sample of filtered is sorted according to size order;
Hundredths selected cell M2 is used to select the first hundredths P
1With the second hundredths P
2
Data screening limit value computing unit M3 is used to calculate hundred fractional values corresponding with described data sample and hundredths, will be corresponding to the first hundredths P
1With the second hundredths P
2Hundred fractional computation results as the numerical value of described data sample screening higher limit and data screening lower limit;
Determining unit M4 is used for described data sample numerical value is defined as exceptional data point greater than numerical value screening higher limit or less than the data of numerical value screening lower limit.
In a kind of concrete embodiment, the above data sample sequencing unit M1, hundredths selected cell M2, data screening limit value computing unit M3 and determining unit M4 cooperatively interact as follows and carry out work:
Above-mentioned data sample sequencing unit M1 sorts according to size order to data sample to be analyzed;
Above-mentioned hundredths selected cell M2 selects the first hundredths P
1With the second hundredths P
2
Above-mentioned data screening limit value computing unit M3 receives the data sample through data sample sequencing unit M1 ordering, calculates the first hundredths P that obtains through hundredths selected cell M2
1With the second hundredths P
2Value corresponding screening higher limit and numerical value screen lower limit respectively;
The numerical value screening limit value that above-mentioned determining unit M4 reception calculates through the primary data sample and the data screening limit value computing unit M3 of data sample sequencing unit M1 ordering, the numerical values recited of the data in the comparing data sample and numerical value screening limit value will be screened higher limit or be defined as exceptional data point less than the data of numerical value screening lower limit greater than numerical value.
In concrete embodiment, with reference to figure 6, described data screening limit value unit M3 comprises numerical value screening higher limit computing unit 31 and numerical value screening lower limit computing unit 32.Described numerical value screening higher limit computing unit 31 is used to adopt hundred mark Percentile formula to calculate corresponding to the first hundredths P
1Hundred fractional values, as numerical value screening higher limit; Described numerical value screening lower limit computing unit 32 is used to adopt hundred mark Percentile formula to calculate corresponding to the first hundredths P
2Hundred fractional values, as numerical value screening lower limit.
In one embodiment, can adopt linear extrapolation to calculate its numerical value screening upper lower limit value in conjunction with hundred fractional value methods.With reference to figure 7, data screening limit value computing unit M3 can comprise linear extrapolation computing unit 12 and limit value computing unit 11.Hundredths pairing data value in described data sample in the linear formula that linear extrapolation computing unit 12 calculating limit value computing units 11 are adopted, and linear coefficient k value, limit value computing unit 11 is according to the data value and the linear coefficient k value of hundredths correspondence, adopt the corresponding linear formula, calculate the data screening limit value of described skewed distribution categorical data.
Though the present invention by the preferred embodiment explanation as above, these preferred embodiments are not in order to limit the present invention.Those skilled in the art without departing from the spirit and scope of the present invention, should have the ability various corrections and additional are made in this preferred embodiment, and therefore, protection scope of the present invention is as the criterion with the scope of claims.
Claims (10)
1. an abnormal data method of inspection is characterized in that, comprising:
The data sample of filtered is sorted according to size order;
Select the first hundredths P
1With the second hundredths P
2
Calculate hundred fractional values corresponding with described data sample and hundredths, will be corresponding to the first hundredths P
1With the second hundredths P
2Hundred fractional computation results as the numerical value of described data sample screening higher limit and data screening lower limit;
Numerical value is exceptional data point greater than numerical value screening higher limit or less than the data of numerical value screening lower limit in the described data sample.
2. the abnormal data method of inspection as claimed in claim 1 is characterized in that, adopts hundred mark Percentile formula to calculate described hundred fractional values.
3. the abnormal data method of inspection as claimed in claim 1 is characterized in that, described P
1, P
2Satisfy relation: P
1+ P
2=1.
4. the abnormal data method of inspection as claimed in claim 1 is characterized in that, described first hundredths is 99.9998828%, and described second hundredths is 0.0001172%.
5. the abnormal data method of inspection as claimed in claim 1 is characterized in that, described first hundredths is 99.6512%, and described second hundredths is 0.348802%.
6. the abnormal data method of inspection as claimed in claim 1 is characterized in that, adopts linear extrapolation to calculate described hundred fractional values in conjunction with hundred mark formula Percentile formula.
7. the abnormal data method of inspection as claimed in claim 6 is characterized in that, described linear extrapolation comprises: the selected linear numerical value screening limit value computing formula that comprises hundredths; Obtain linear coefficient k value in the linear numerical value screening limit value computing formula by standardized normal distribution hundredths formula; Obtain the data value that comprises hundredths correspondence in described data sample in the linear control circle computing formula; Numerical value screening limit value computing formula with the described linearity of data value substitution of linear coefficient k value and hundredths correspondence.
8. an abnormal data verifying attachment is characterized in that, comprising:
The data sample sequencing unit is used for the data sample of filtered is sorted according to size order;
The hundredths selected cell is used to select the first hundredths P
1With the second hundredths P
2
Data screening limit value computing unit is used to calculate hundred fractional values corresponding with described data sample and hundredths, will be corresponding to the first hundredths P
1With the second hundredths P
2Hundred fractional computation results as the numerical value of described data sample screening higher limit and data screening lower limit;
Determining unit is used for described data sample numerical value is defined as exceptional data point greater than numerical value screening higher limit or less than the data of numerical value screening lower limit.
9. abnormal data verifying attachment as claimed in claim 8 is characterized in that, described data screening limit value computing unit comprises:
Numerical value screening higher limit computing unit is used to adopt hundred mark Percentile formula to calculate corresponding to the first hundredths P
1Hundred fractional values, as numerical value screening higher limit;
Numerical value screening lower limit computing unit is used to adopt hundred mark Percentile formula to calculate corresponding to the first hundredths P
2Hundred fractional values, as numerical value screening lower limit.
10. abnormal data verifying attachment as claimed in claim 8 is characterized in that, described data screening limit value computing unit comprises linear extrapolation computing unit and limit value computing unit; Described linear extrapolation computing unit, the pairing data value in described data sample of the hundredths in the linear formula that calculation control circle computing unit is adopted, and linear coefficient k value; The limit value computing unit adopts the corresponding linear formula according to hundred fractional values and the linear coefficient k value of hundredths correspondence, calculates the data screening limit value of described skewed distribution categorical data.
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