CN101174149A - Methodology for establishing control specification boundaries - Google Patents

Abstract

The present invention provides a method for formulating control specification limits of statistical process control (SPC), comprising the following steps: a) providing a sample population; b) selecting k groups of bootstrap samples from the sample population by bootstrap resampling; c) respectively calculating the mean values and relative standard deviations of the k groups of bootstrap samples from the k groups of bootstrap resampling sample populations; and d) calculating a control mean value and a control standard deviation from the mean values and relative standard deviations of the k groups of samples, wherein the control specification limits are functions of the control mean value and the control standard deviation.

Description

Methodology for establishing control specification boundaries

technical field

The invention relates to a method applied to statistical process control, in particular to a method for formulating control specification limits applied to statistical process control.

Background technique

Statistical Quality Control (SQC) is a technology to maintain and improve product quality, and Statistical Process Control (SPC) is one of the main tools, which focuses on the analysis of data in the manufacturing process , to determine the cause of product variation. Therefore, statistical quality management consists of two main parts, statistical process control and sampling acceptance criteria. Statistical process control (SPC) is the use of process operating variables to predictively monitor production variables or product quality variables. Therefore, the use of statistical process control can be said to start from detecting process abnormalities, accurately grasping the process status, avoiding abnormal occurrences, and the ultimate goal is to ensure that the quality of products meets specifications.

For wafer fabs that are extremely concerned about the rate of good quality, the importance of statistical process control is of course even more important. However, in the initial introduction and mass production of new products, if it is still necessary to establish an abnormal monitoring mechanism, it is often due to the insufficient amount of initial imported data, and the distribution of wafer test data (such as good rate or defective rate) does not belong to the normal distribution (Normal Distribution), so it is not easy to establish sampling acceptance restrictions for test data. On the other hand, when the data in statistical process control are data with abnormal distribution, it is possible to define the control specification limit by four times the standard deviation (4σ) obtained from the statistics instead of six times the standard deviation (6σ), but this practice often uses The control specification limit is set too strictly, so that when the control is actually carried out according to the control specification limit, the phenomenon of overkill (Overkill) occurs, thereby increasing the rate of Out-of-Control (OOC). In addition, low sensitivity (Low sensitivity) may also occur in the established control specification boundaries, that is, the established control specification boundaries are too loose to screen out abnormal data.

In order to solve the above problems, the prior art used a Box-Cox transformation method to distinguish the noise that affects the target value and the variation value. The corresponding data between the normal distribution can be obtained through the Box-Kacks data conversion of the abnormally distributed data, so that a more reasonable control specification limit can be obtained. However, using the Box-Cax data transformation, the six standard deviations (6σ) obtained by the inverse transformation (inverse) after the power transformation (power transformation) may exceed the original data domain (Domain) and obtain an unreasonable Upper Control Limit (UCL). And a reasonable control upper limit UCL can only be obtained by spending considerable time and effort on trial and error. And there is a risk of human judgment.

Therefore, how to develop a method for establishing control specification limits for statistical process control, to establish reasonable control specification limits with the most streamlined steps and procedures, and at the same time avoid the phenomenon of over-inspection or failure to screen out abnormal data. Indeed, it is the goal of actively developing research that is currently needed in related fields. The inventors of the present invention have studied carefully, and based on their many years of experience in this research field, they have proposed the method of the present invention for establishing control specification limits for statistical process control, by introducing Bootstrap Resampling (Bootstrap Resampling) means , can effectively solve the problems of the prior art, and is a rare invention.

Contents of the invention

The main purpose of the present invention is to provide a method for establishing control specification limits for statistical process control. By introducing bootstrap re-sampling, a reasonable control can be established with a small number of samples with the most streamlined steps. Specification limits, while avoiding the phenomenon of over-inspection or failure to screen out abnormal data, and solve the problems of the existing technology.

In order to achieve the above-mentioned purpose, a broader embodiment of the present invention provides a method for formulating control specification limits for statistical process control, comprising the following steps: a) providing a mother population; b) selecting a sample population from the mother population; c) from the sample group, select a plurality of samples; d) according to the plurality of samples, find a sample mean and relative standard deviation; e) repeat step c) and step d) until obtaining k groups of sample mean and relative standard deviation standard deviation; and f) obtaining the mean value of the sample mean value and the relative standard deviation of the k groups respectively to obtain a control mean value and a control standard deviation, wherein the control specification limit is the control mean value and the control mean value function of the standard deviation.

According to the concept of the present invention, the control specification limit is used for semiconductor wafer production process control.

According to the conception of the present invention, the step c) is performed by bootstrap resampling.

According to the conception of the present invention, wherein the bootstrap re-sampling is completed by the VBA application program (VisualBasic for Applications) of the spreadsheet.

According to the concept of the present invention, the control specification limit is the control mean plus six times the control standard deviation.

According to the concept of the present invention, the sample population is a specific wafer test data population.

According to the conception of the present invention, the sample group is a data sample obtained by a test system module.

According to the conception of the present invention, wherein the parent population is a non-normal distribution (Non Normal Distribution) population.

According to the conception of the present invention, the sample population is a population with abnormal distribution.

In order to achieve the above object, another broad embodiment of the present invention is to provide a method for formulating control specification limits for statistical process control, the steps of which include at least a) providing a sample population; b) from the sample population, a The bootstrap re-sampling method selects n groups of bootstrap samples (BootstrapSamples) groups; c) from the n groups of bootstrap re-sampling sample populations, respectively find the n group sample mean and relative standard deviation; and d) from the The mean value and relative standard deviation of n groups of samples are calculated to obtain a control mean value and a control standard deviation, wherein the control specification limit is a function of the control mean value and the control standard deviation.

According to the concept of the present invention, wherein the control specification limit is used for semiconductor wafer production process control.

According to the concept of the present invention, the bootstrap resampling is performed by the VBA application program of the spreadsheet.

According to the concept of the present invention, the control specification limit is the control mean plus six times the control standard deviation.

According to the concept of the present invention, the sample population is a specific wafer test data population.

According to the conception of the present invention, the sample group is a data sample obtained by a test system module.

According to the conception of the present invention, the control mean value is the mean of the mean values of the n groups of samples.

According to the concept of the present invention, the control standard deviation is the average of the relative standard deviations of the n groups.

According to the conception of the present invention, the sample population is taken from a parent population with abnormal distribution.

According to the conception of the present invention, the sample population is a population with abnormal distribution.

In order to achieve the above object, another broad implementation form of the present invention is to provide a method for formulating control specification limits applied to semiconductor statistical process control, the steps of which include: storing the wafer test data obtained after testing by the testing machine in the data Repository; take a sample population from the data repository through the user interface; use the statistical analysis engine to calculate the sample population, wherein the calculation includes the following steps: a) from the sample population, select a bootstrap resampling method Get out n groups of bootstrap resampling sample populations; b) from the n groups of bootstrap resampling sample populations, find n groups of sample averages and relative standard deviations; c) from the n groups of sample averages and relative standard deviations, calculating a control mean value and a control standard deviation; and setting the control mean value plus six times the control standard deviation as the control specification limit.

According to the concept of the present invention, the bootstrap resampling is performed by the VBA application program of the spreadsheet.

According to the concept of the present invention, the sample population is a specific wafer test data population.

According to the conception of the present invention, the control mean value is the mean of the mean values of the n groups of samples.

According to the concept of the present invention, the control standard deviation is the average of the relative standard deviations of the n groups.

Description of drawings

Fig. 1 discloses a flow chart of a method for formulating control specification limits of statistical process control according to a preferred embodiment of the present invention.

Fig. 2 discloses a schematic diagram of a method for formulating control specification limits according to another embodiment of the present invention.

Fig. 3 discloses a schematic diagram of a method for formulating control specification limits according to yet another embodiment of the present invention.

[Description of main component symbols]

S10～S16: Method steps 20: Parent group

21, 33: Sample group 221~22n: Sample mean and relative standard deviation

31: Data repository X ₁ ～X _n : Bootstrap resampling sample population

32 Testing Machine 34: User Interface

35: Statistical analysis engine 36: System control results

μ: control mean value σ: control standard deviation

Detailed ways

Some typical embodiments embodying the features and advantages of the present invention will be described in detail in the ensuing description. It should be understood that the present invention can have various changes in different forms without departing from the scope of the present invention, and that the descriptions and illustrations therein are illustrative in nature and not intended to limit the present invention. .

Please refer to FIG. 1, which discloses a method for formulating a control specification limit of a statistical process control (Statistical Process Control, SPC) according to a broader implementation form of a preferred embodiment of the present invention, wherein the control specification limit is used for semiconductor wafer production process control. As shown in the flowchart of Figure 1, the following steps are included: a) providing a mother group, as shown in step S11, wherein the mother group is a non-normal distribution (Non Normal Distribution) group; b) selecting the same group from the mother group This group, as shown in step S12, wherein the sample group is the test data group of a specific chip, belongs to a non-normal distribution group; c) from the sample group, select a plurality of samples, as shown in step S13; d) According to the plurality of samples, find a sample mean value and relative standard deviation, as shown in step S14; e) repeat step c) and step d) until it is determined that the k group sample mean value and relative standard deviation have been obtained, Continue to the next step process, as shown in step S15; and f) average the k group sample mean and relative standard deviation respectively to find the mean, and obtain a control mean and a control standard deviation, as in step S16 where the control specification limit is a function of the control mean and control standard deviation.

It should be emphasized that the test data referred to in the embodiment of the present invention is, for example, data such as good rate or bad rate.

In practical applications, the repeated actions from step c) to step e) can be simply constituted as a bootstrap resampling process flow. Through the bootstrap resampling process, as shown in step S10 , enough samples can be selected from the limited sample population to estimate the control specification limit. The operation of the bootstrap resampling can be completed by the VBA application program (Visual Basic for Applications) of the spreadsheet. In addition, in practical applications, the control specification limit may be the control mean plus six times the control standard deviation.

Accordingly, for data that does not conform to the normal distribution, the method of the present invention can be used to calculate a reasonable control specification limit. It solves the long-standing risk that human judgment must be introduced into the calculation of the control specification limit in the known technology. At the same time, a reasonable control specification limit will not be too strict to cause overkill; of course, it will not cause low sensitivity (low sensitivity) because it is too loose, and abnormalities cannot be detected. After actual testing, it is found that the control specification limit estimated by the method of the present invention with a limited sample population can indeed be effectively applied to the production process control of the initial trial production of semiconductor wafers to detect abnormal product batches. If possible high-risk problems can be clearly detected during the trial production stage, it will certainly help to effectively monitor the process during actual mass production and reduce the occurrence of abnormalities.

Please refer to FIG. 2 again, which discloses a method for formulating control specification limits according to another embodiment of the present invention. The method can be applied to the production process control of the initial trial production of the semiconductor chip industry to obtain reasonable control specification limits. Although the number of parent populations is insufficient, this method can effectively estimate the reasonable control specification limit of the parent population with sufficient resampling samples by introducing the bootstrap resampling method for production process control during actual mass production use. As shown in Figure 2, method step of the present invention at first provides a sample population 21, and wherein this sample population 21 is taken from a mother population 20 of abnormal distribution, in the present embodiment, this sample population 21 is the test of specific wafer The data group belongs to abnormal distribution. Next, from the sample population 21, select n groups of bootstrap samples (Bootstrap Samples) groups X ₁ to X _n by bootstrap resampling, and for the n groups of bootstrap samples groups X ₁ to X _n , respectively Calculate the sample mean value and relative standard deviation 221~22n of each boot resampling sample group. Finally, the mean values and relative standard deviations 221~22n of the n groups of samples obtained as mentioned above are summed and averaged respectively, and then the control mean value μ and control standard deviation σ are obtained, where the control specification limit is the control mean value and the control standard deviation σ A function of the control standard deviation, preferably, the control specification limit is the sum of the control mean value μ plus six times the control standard deviation σ (μ+6σ).

Simply put, since bootstrap resampling is a nonparametric technique, bootstrap resampling is usually the only way to help researchers estimate their interest when there is no standard error in the statistics or when the sampling distribution is unknown. The standard error of the statistic or method of sampling variation. Bootstrap resampling uses only a computer to repeatedly sample collected data to estimate the standard error or sampling distribution of a particular statistic. When applying the bootstrap resampling method, the actual collected sample is usually used as the parent group, and random sampling with replacement is performed (random sampling with replacement). Specifically, the first sample is drawn from it, then put back, and the second is drawn Then put the sample back, repeat this step until the Nth sample is drawn, which is called a bootstrap resampling sample, repeat the above steps until the number of bootstrap resampling samples drawn is enough to provide its statistics until a stable estimate.

Likewise, when the embodiment of the present invention is actually applied, the bootstrap resampling operation can be completed by the VBA application program of the spreadsheet.

Please refer to FIG. 3 , which more simply discloses a diagram of an embodiment of a method for formulating control specification limits applied to semiconductor wafer production process control. As shown in the figure, the testing machine (WT test EQP) 32 is used to store the wafer test data obtained after the test in the data storage library 31, and the user can obtain the sample group 33 from the data storage library 31 through the user interface 34 . The sample population 33 is first calculated by the statistical analysis engine 35, and its calculation method is the same as that of the aforementioned embodiment in FIG. After the calculation of the analysis engine 35, the required system control result (SBL Result) 36 can be obtained. As a result, reasonable control specification boundaries can be estimated with a streamlined process and a limited sample population.

To sum up, the present invention provides a method for formulating the control specification limit of statistical process control. By introducing bootstrap re-sampling, a reasonable The control specification limit solves the long-standing risk that human judgment must be introduced into the calculation of the control specification limit in the prior art. At the same time, a reasonable control specification limit will not be too strict to cause overkill; of course, it will not cause low sensitivity (low sensitivity) because it is too loose, and abnormalities cannot be detected. After actual testing, it is found that the control specification limit estimated by the method of the present invention with a limited sample group can indeed be effectively applied in the production process control of the initial trial production of semiconductor wafers to detect abnormal product batches. If possible high-risk problems can be clearly detected during the trial production stage, it will certainly help to effectively monitor the actual mass production process and reduce the occurrence of abnormalities, which is beyond the reach of existing technologies. The technology of the present invention has practicability, novelty and progress, so the application is filed according to law.

Even though the present invention has been described in detail by the above-mentioned embodiments, various modifications can be devised by those skilled in the art without departing from the protection scope of the appended claims.

Claims (24)

1. A method for formulating control specification limits for statistical process control, comprising the following steps: a) provide a parent group; b) Select a sample population from the parent population; c) Select multiple samples from the sample population; d) Calculate the sample mean value and relative standard deviation according to the plurality of samples; e) repeat step c) and step d), until obtaining the k group sample mean and relative standard deviation; and f) Calculate the average value of the sample average value and the relative standard deviation of the k groups of samples to obtain a control average value and a control standard deviation, wherein the control specification limit is a function of the control average value and the control standard deviation. 2. The method for establishing a control specification limit as claimed in claim 1, wherein the control specification limit is used for semiconductor wafer production process control. 3. The method for formulating control specification limits as claimed in claim 1, wherein the step c) is performed by bootstrap sampling. 4. The method for establishing control specification limits as claimed in claim 3, wherein the boot resampling is performed by a VBA application program of a spreadsheet. 5. The method for establishing a control specification limit as claimed in claim 1, wherein the control specification limit is the control mean plus six times the control standard deviation. 6. The method for establishing control specification limits as claimed in claim 1, wherein the sample group is a test data group of a specific wafer. 7. The method for establishing control specification limits as claimed in claim 6, wherein the sample population is a data sample obtained by a test system module. 8. The method for formulating control specification limits as claimed in claim 1, wherein the mother population is an abnormal distribution population. 9. The method for formulating control specification limits as claimed in claim 1, wherein the sample population is an abnormal distribution population. 10. A method for formulating control specification limits for statistical process control, comprising the following steps: a) Provide a sample population; b) From the sample population, select n groups of boot re-sampling sample populations by means of bootstrap resampling; c) From the n groups of bootstrap resampling sample populations, obtain the n groups of sample mean values and relative standard deviations; and d) calculating a control mean value and a control standard deviation from the n groups of sample mean values and relative standard deviations, wherein the control specification limit is a function of the control mean value and the control standard deviation. 11. The method for establishing a control specification limit as claimed in claim 10, wherein the control specification limit is used for semiconductor wafer production process control. 12. The method for establishing control specification limits as claimed in claim 10, wherein the bootstrap resampling is performed by a VBA application program of a spreadsheet. 13. The method for establishing a control specification limit as claimed in claim 10, wherein the control specification limit is the control mean plus six times the control standard deviation. 14. The method for establishing control specification limits as claimed in claim 10, wherein the sample group is a test data group of a specific wafer. 15. The method for establishing control specification limits as claimed in claim 14, wherein the sample population is a data sample obtained by a test system module. 16. The method for formulating control specification limits as claimed in claim 10, wherein the control average is the average of the n groups of sample averages. 17. The method for formulating control specification limits as claimed in claim 10, wherein the control standard deviation is the average of the relative standard deviations of the n groups. 18. The method for formulating control specification limits as claimed in claim 10, wherein the sample population is taken from a parent population with abnormal distribution. 19. The method for formulating control specification limits as claimed in claim 10, wherein the sample population is an abnormal distribution population. 20. A method for formulating control specification limits applied to semiconductor statistical process control, comprising the following steps: Store the wafer data obtained after testing by the testing machine in the data repository; fetching a sample population from the data repository via a user interface; The sample population is calculated using a statistical analysis engine, wherein the calculation includes the following steps: a) From the sample population, select n groups of bootstrap resampling sample populations by means of bootstrap resampling; b) From the n groups of bootstrap re-sampling sample populations, calculate the n groups of sample mean values and relative standard deviations; and c) from the n groups of sample mean values and relative standard deviations, obtain a control mean value and a control standard deviation; and The control specification limit is formulated as the control mean plus six times the control standard deviation. 21. The method of claim 20, wherein the boot resampling is performed by a VBA application of a spreadsheet. 22. The method of claim 20, wherein the sample population is a specific wafer test data population. 23. The method of claim 20, wherein the control average is the average of the n groups of sample averages. 24. The method of claim 20, wherein the control standard deviation is the average of the relative standard deviations of the n groups.

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