JP4616243B2 - FAILURE PROCESS ESTIMATION METHOD, FAILURE PROCESS ESTIMATION DEVICE, PROGRAM, AND RECORDING MEDIUM - Google Patents

Description

  The present invention relates to a defective process estimation method that estimates a manufacturing process that is a cause of defective products from a plurality of manufacturing processes that are sequentially executed to manufacture a manufactured product.

  The present invention also relates to a defective process estimation device used for implementing such a defective process estimation method.

  The present invention also relates to a program for causing a computer to execute such a defective process estimation method.

  The present invention also relates to a computer-readable recording medium on which a program for causing a computer to execute such a defective process estimation method is recorded.

  For example, a manufactured product of a semiconductor or a liquid crystal panel is manufactured by sequentially executing a plurality of manufacturing processes on a substrate. In the inspection process, manufactured products are classified as either good products or defective products. When it is found that the number of manufactured products classified as defective products increases and the yield decreases, it is important to investigate the cause of defective products in the manufacturing process and take countermeasures. However, manufactured products such as semiconductors and liquid crystal panels are produced through tens to hundreds of manufacturing processes and manufacturing apparatuses. Therefore, once a defect occurs in a manufactured product, it is generally very difficult to specify the cause of the defective product.

  In order to specify the defective product generation factor, an inspection process is provided between a plurality of manufacturing processes executed sequentially. If an inspection process is provided for each manufacturing process, if the yield decreases in a certain inspection process, it can be easily understood that the manufacturing process executed immediately before the inspection process is a defective process. However, providing a large number of inspection processes not only requires a large amount of capital investment, but also has the disadvantage of generating maintenance costs for the inspection process or increasing the lead time. For this reason, the minimum number of inspection processes is provided.

  Therefore, in reality, a defective process is estimated from a plurality of manufacturing processes executed immediately before the inspection process using an inspection result of a certain inspection process. As a conventional method for estimating such a defective process, Patent Document 1 (Japanese Patent Application Laid-Open No. 2005-142406) describes a method of examining the deviation of manufacturing apparatus history.

と計算できる。この式中のｆi・×ｆ・j／ｎは、図９の分割表を構成するセル（i，j）の理論度数（あるいは期待度数）と呼ばれ、帰無仮説の下で、予測される（期待される）度数である。また、図９の分割表の自由度νは、（表側の項目数−１）×（表頭の項目数−１）＝２×１＝２である。
有意確率＝１−Ｆ（χ²，ν）＜α
であれば有意水準αで、製造装置と不良品発生率に相関があると推定される。有意水準αは、１％ないしは５％とすることが伝統的に多い。ここで、Ｆ（ｘ，ν）は、自由度νのカイ２乗累積分布関数を表す。また、カイ２乗累積分布関数Ｆ（ｘ，ν）は、カイ２乗確率密度関数ｆ（ｘ，ν）を使って、次式のように表すことができる。

The chi-square test described in Patent Document 1 will be described. First, a quality value representing a certain quality of a manufactured product is obtained from each manufactured product by an inspection process. Each manufactured product is a non-defective product based on the magnitude relationship between the obtained quality value and a predetermined reference value (for example, a binarization threshold value for determining whether the product is a non-defective product or a defective product). / Classified as defective. Next, reference is made to manufacturing history data that records which manufacturing apparatus has processed each manufactured product in each manufacturing process. A case will be described as an example where three manufacturing apparatuses (each of which is capable of executing the manufacturing process independently) 1, 2, and 3 are used in parallel in a certain manufacturing process. It is assumed that the numbers of manufactured products processed by the manufacturing apparatuses 1, 2, and 3 within a certain period are f1, f2, and f3, respectively. In addition, the number of defective products among the manufactured products processed by the manufacturing apparatuses 1, 2, and 3 is assumed to be f11, f21, and f31, respectively. In addition, the number of non-defective products among the manufactured products processed by the manufacturing apparatuses 1, 2, and 3 is set to f12, f22, and f32, respectively. Further, the total number of defective products processed in this manufacturing process is f · 1, and the total number of non-defective products is f · 2. FIG. 9 shows a contingency table listing these numerical values. The front side item of this contingency table is the manufacturing apparatus number, and the number of items is three. The top item of this contingency table is the number of defective / non-defective products, and the number of items is two. Here, the front side is a variable in the vertical direction, and the front is a variable in the horizontal direction. In general, a contingency table in which the number of items on the front side is s and the number of items on the front is t is called an s × t contingency table, and in the case of FIG. 9, it is a 3 × 2 contingency table. If the total number of manufactured products is n,
n = f1,. + f2,. + f3. = f.1 + f.2.
It is. Further, f1, ·, f2, ·, f3 ·, f · 1, f · 2 are frequencies representing the sum in the horizontal direction or the vertical direction, and are called peripheral frequencies. f11, f21, f31, f12, f22, and f32 are called observation frequencies. The statistic χ ² of the chi-square test is

Can be calculated. The fi · × f · j / n in this equation is called the theoretical frequency (or expected frequency) of the cell (i, j) constituting the contingency table of FIG. 9, and is predicted under the null hypothesis. Is the (expected) frequency. Further, the degree of freedom ν of the contingency table of FIG. 9 is (number of front side items−1) × (number of front head items−1) = 2 × 1 = 2.
Significance probability = 1−F (χ ² , ν) <α
If so, it is estimated that there is a correlation between the manufacturing apparatus and the defective product occurrence rate at the significance level α. Traditionally, the significance level α is often 1% or 5%. Here, F (x, ν) represents a chi-square cumulative distribution function with ν degrees of freedom. Further, the chi-square cumulative distribution function F (x, ν) can be expressed as follows using the chi-square probability density function f (x, ν).

  When it is verified that there is a correlation between the manufacturing apparatus and the defective product occurrence rate at the significance level α, between the manufacturing apparatuses (between the three manufacturing apparatuses 1, 2, 3 in the example of FIG. 9), There will be a difference in the rate of defective products. That is, it is possible to find a possibility that a manufacturing apparatus that significantly generates defective products exists in the three manufacturing apparatuses 1, 2, and 3. Furthermore, by performing defective process estimation for each of a plurality of manufacturing processes, it is possible to list manufacturing apparatus candidates that generate defective products.

  However, the chi-square test may give an incorrect test result. That is, an error that rejects a place where the null hypothesis should be adopted (first type error) or an error that adopts a place where the null hypothesis should be rejected (second type error). In order to eliminate the first type error or the second type error, it is known to perform an exact test instead of the chi-square test.

The chi-square test is a parametric method based on the fact that the asymptotic distribution of the statistic χ ² is a chi-square distribution under the null hypothesis. On the other hand, the exact probability test is a nonparametric method that does not assume the distribution of statistics. The exact probability test is also called a direct probability test, and is a method of performing a test by calculating a significance probability based on all combinations of observed frequencies that can occur when the peripheral frequencies of the contingency table are fixed. Here, the significance probability is also called a p-value.

また、ｆ11を確率変数とすれば、この確率分布は超幾何分布となることが知られている。 The exact probability test will be described in detail with reference to FIG. FIG. 10 is an example of a contingency table when n = 100. The number of manufacturing devices is m = 2, the average defective product rate is 11%, the defective product rate of manufacturing device 1 is 10/51 = about 20%, and the defective product rate of manufacturing device 2 is 1/49 = about 2%. It is. There are 12 possible combinations of the observed frequencies when the peripheral frequencies are fixed, that is, when f1, · 2, ·, f · 1, and f · 2 are fixed. FIG. 11 shows the occurrence probabilities that a contingency table can occur for each combination. For example, the occurrence probability of the first row (f11 = 0, f12 = 51, f21 = 11, f21 = 38) is calculated by the following equation.

If f11 is a random variable, this probability distribution is known to be a hypergeometric distribution.

In FIG. 11, -ΔP1 and ΔP2 are parameters indicating that there is a difference in the defective product occurrence rate between the manufacturing apparatuses. ΔPi is the difference from the average defective product occurrence rate of the manufacturing apparatus i, and is expressed by the following equation.
ΔPi = Pi−P

Here, P is an average defective product occurrence rate of all manufacturing apparatuses (in this example, the manufacturing apparatus 1 and the manufacturing apparatus 2), and Pi is a defective product occurrence rate of the manufacturing apparatus i, which is expressed by the following equation.
P = f · 1 / n
Pi = fi1 / fi ·
Therefore, ΔP1 · ΔP2 is obtained by multiplying the difference of the defective product occurrence rate of each manufacturing apparatus from the average defective product occurrence rate. Since ΔP1 and ΔP2 are non-positive values, −ΔP1 and ΔP2 to which a minus sign is added are non-negative values. Therefore, the larger −ΔP1 · ΔP2 is, the larger the difference between the manufacturing apparatuses in the defective product occurrence rate is.

  Now, the observed contingency table shown in FIG. 10 corresponds to the 11th row of FIG. 11, and the occurrence probability is 0.004421. That is, when the null hypothesis is correct, the probability that the observation frequency shown in FIG. 11 is obtained is only about 0.4%. The significance probability is a probability that a rare case including the eleventh row will occur. Therefore, the occurrence probability of the first, second, eleventh and twelfth rows is the sum of the occurrence probabilities of 0.004421 or less among twelve combinations. What is necessary is just to total the probability. Therefore, the significance probability is 0.007921 = about 0.7%. For example, if the significance level α is 1%, the null hypothesis is rejected because the significance probability is smaller than the significance level. That is, it is determined that there is a correlation between the manufacturing apparatus and the defective product occurrence rate. In this way, the exact probability test can determine the test result (whether the null hypothesis is rejected or adopted) and the significance probability.

  FIG. 12 shows an example of a contingency table when an incorrect test result is obtained in the chi-square test. In addition, FIG. 13 shows the probability of occurrence that a contingency table may occur for each combination. The significance probability calculated based on the chi-square test is 0.0006538 = about 0.07%, and the significance probability calculated based on the exact probability test is 0.080000 = 8%. The significant probabilities of both are far apart. For example, if the significance level α is 1%, the chi-square test rejects the null hypothesis, while the exact probability test adopts the null hypothesis. Thus, the chi-square test is an incorrect test result.

  As described above, the chi-square test may give an incorrect test result. Therefore, if an accurate probability test is performed instead of the chi-square test, the test is literally accurate. Therefore, it is desirable to perform an exact probability test instead of the chi-square test.

A condition under which there is a possibility that the chi-square test may result in an incorrect test result has been known. For example, in Non-Patent Document 1, when there is at least one cell with an expected frequency of less than 1 in the contingency table, or when there are 20% or more of cells with an expected frequency of less than 5, the exact probability test It is stated that you should consider using. If this condition is satisfied, an accurate probability test is performed. If not, a chi-square test can be performed to eliminate errors in the chi-square test. As a result, the test result can be made accurate.
JP 2005-142406 A Shigenobu Aoki, “Some Precautions”, [online], May 16, 2002, [Search May 16, 2006], Internet, <URL: http://aoki2.si .gunma-u.ac.jp / lecture / Cross / warning.html ＞

  However, the exact probability test may have an enormous number of combinations. For this reason, the process of calculating the significance probability may take a very long time, and in some cases, the calculation is not completed within the allowable time, and thus the test result may not be obtained. Even if the above-described chi-square test is a condition that may result in an erroneous test result, the number of combinations may become enormous. For this reason, it is difficult to adopt an exact probability test uniformly instead of the chi-square test.

  FIG. 14 is an example of a contingency table that requires a long time for the accuracy test. The total number of manufactured products is n = 425, the number of manufacturing devices is m = 8, and the average defective product occurrence rate is 23/425 = about 5%. The number of combinations is as large as 2035800. Further, out of 80 manufactured products processed by the manufacturing apparatus 1 of FIG. 14, if the number of defective products is increased by 3 and the number of non-defective products is decreased by 1 to 77, the number of combinations is 2629575, which is compared with the original 2035800. It increases by about 30%. Thus, even if the total number n of manufactured products is the same, even if the defective product generation rate of the manufacturing apparatus is slightly different, the number of combinations varies greatly, and it is difficult to predict the processing time in advance. When targeting such a manufacturing process, there is a possibility that the process of calculating the significance probability does not end within the allowable time. For this reason, conventionally, as an actual problem, an exact probability test has not been adopted in place of the chi-square test. On the other hand, when the chi-square test is adopted for the test, there has been a problem that the result of the defective process estimation may be inaccurate as described above.

  Accordingly, an object of the present invention is to provide a defective process estimation method in which estimation is accurate and processing time is within an allowable time.

  Moreover, the subject of this invention is related with the defect process estimation apparatus used for implementing such a defect process estimation method.

  Moreover, the subject of this invention is related with the program for making a computer perform such a defective process estimation method.

  Another object of the present invention is to provide a computer-readable recording medium in which a program for causing a computer to execute such a defective process estimation method is recorded.

In order to solve the above problems, the defective process estimation method of the present invention is:
Inspection of the above inspection process for a manufacturing process including a plurality of manufacturing processes sequentially performed on the manufactured product and at least one inspection process for inspecting whether the manufactured product is a non-defective product or a defective product Based on the results, in the defective process estimation method for estimating the manufacturing process that is a defective product generation factor among the plurality of manufacturing processes,
As a manufacturing process in the manufacturing process, a manufacturing process using a plurality of manufacturing apparatuses capable of performing the manufacturing process in parallel is included.
Non-defective products that represent the frequency of non-defective products and the frequency of defective products that are the results of inspection in the above-mentioned inspection process, while counting the number of process item data representing the frequencies of manufactured products processed by a plurality of manufacturing devices used in a certain manufacturing process / Aggregate the number of defective item data and create a contingency table that categorizes the number of processed item data and non-defective / defective item number data,
When using the contingency table to test whether there is a significant difference in the incidence of defective products in manufactured products processed by each manufacturing equipment used in the manufacturing process, the independence chi-square test and accurate In order to determine which test is suitable between the probability test and the chi-square test of independence, the null hypothesis is rejected as the result of the chi-square test, and the manufacturing process is defective. Under the condition that it is estimated that it is the cause of the occurrence, when the predetermined transition condition is satisfied, it is determined that the above accurate probability test is suitable,
Based on the result of the test determined to be suitable between the chi-square test of independence and the accurate probability test, it is estimated whether or not the manufacturing process is a cause of defective products.

  According to the defective process estimation method of the present invention, based on the result of the test judged to be suitable between the independence chi-square test and the accurate probability test, it is estimated whether or not the manufacturing process is a cause of defective products. Do. Therefore, accurate estimation can be performed and the processing time can be kept within the allowable time.

In addition, the defective process estimation method of the present invention can prevent an error (a first type error) that is estimated as a defective process even though it is not a defective process.

In the defective process estimation method according to an embodiment, the transition condition includes a condition for generating a first type error that rejects the place where the null hypothesis should be adopted .

Bad step estimation method of one embodiment, the transition condition, the expected frequency of the contingency table cells less than a predetermined value, characterized in that it comprises a condition that is at least one.

In general, if the expected frequency of the contingency table is less than the predetermined value, the test results of chi-square test is not known to be accurate. Here, the defective step estimating method of this embodiment, since the expected frequency of the contingency table cell less than the predetermined value to select the exact test if at least one, can be accurately estimated.

Bad step estimation method of one embodiment, the transition condition is characterized by expected frequency of the contingency table contains a condition that the cell is less than the predetermined value account for at least a predetermined percentage of the total number of cells.

In general, if the cell Le as the expected frequency of the contingency table is less than the predetermined value account for at least a predetermined percentage of the total number of cells constituting the contingency table, it is known that chi-square test of assay results is not exact ing. Here, the defective step estimating method of this embodiment, the contingency table of expected frequencies are cell long as the exact test accounts for more than a predetermined percentage of the total number of cells constituting the contingency table less than a predetermined value Since it is selected, accurate estimation can be performed.

In the defective process estimation method of one embodiment,
In the above test, the null hypothesis is that the defective product occurrence rates in the manufactured products processed in each manufacturing apparatus used in a certain manufacturing process are equal to each other, and the alternative hypothesis is that these defective product occurrence rates are not equal to each other. age,
When the result of the above test rejects the above null hypothesis and adopts the above alternative hypothesis, it is estimated that the manufacturing process is a cause of defective products, while the result of the above test adopts the above null hypothesis. Then, when rejecting the alternative hypothesis, it is estimated that the manufacturing process is not a cause of defective products.

The defective process estimation method of one embodiment is as follows:
For each manufacturing process above,
Determine which test is appropriate between the above independence chi-square test and exact probability test,
According to the chi-square test or the accurate probability test determined to be suitable, a significant probability representing the correlation between the manufacturing apparatus used in the manufacturing process and the defective product occurrence rate is calculated.

  In the defective process estimation method of this embodiment, for each of the manufacturing processes, the presence or absence of a correlation between the manufacturing apparatus used in the manufacturing process and the defective product occurrence rate can be known.

  The defective process estimation method of one embodiment arranges the manufacturing processes in ascending order of significance calculated for each of the manufacturing processes, and outputs a candidate list representing manufacturing processes estimated to be defective product occurrence factors. Features.

  In the defective process estimation method according to this embodiment, a person can easily recognize which manufacturing process is a cause of a defective generating a defective product.

  The defective process estimation method according to an embodiment is characterized in that a manufacturing process showing the minimum significance probability among the significance probabilities calculated for each manufacturing process is an estimation result as a defective product occurrence factor.

  In the defective process estimation method of this embodiment, a manufacturing process that is most likely to be a defective product occurrence factor can be estimated.

  In the process of estimating a defective process according to one embodiment, in the process of calculating the significance probability by the exact probability test, when it is found that the significance probability during the calculation exceeds the significance level, the calculation is stopped at the time when the significance is found, The significant probability calculated up to that point is output as a calculation result.

  In the defective process estimation method of this embodiment, waste of processing time can be prevented.

  The defective process estimation method according to one embodiment stops the execution of the accurate probability test and stops the test when the test cannot be completed when a predetermined time-out period elapses after the accurate probability test is started. A significant probability calculated by a square test is output.

  In the defective process estimation method of this embodiment, the defective process estimation can be surely completed within a predetermined timeout time.

  According to one embodiment, a defective process estimation method includes a manufacturing apparatus that shows the highest defective product occurrence rate among defective products generated in a plurality of manufacturing apparatuses used in a certain manufacturing process. It is estimated that it is a defective device that is a cause of defective products.

  In the defective process estimation method of this embodiment, it is possible to estimate a manufacturing apparatus that is most likely to be a defective product generation factor.

  According to one embodiment, a defective process estimation method uses a manufacturing apparatus that indicates the largest number of defective products among the number of defective products processed by a plurality of manufacturing apparatuses used in a certain manufacturing process. It is characterized by estimating as a defective device.

  In the defective process estimation method of this embodiment, it is possible to estimate a manufacturing apparatus that is most likely to be a defective product generation factor.

The defective process estimation device of the present invention is
Inspection of the above inspection process for a manufacturing process including a plurality of manufacturing processes sequentially performed on the manufactured product and at least one inspection process for inspecting whether the manufactured product is a non-defective product or a defective product Based on the results, in the defective process estimation device for estimating the manufacturing process that is a defective product generation factor among the plurality of manufacturing processes,
As a manufacturing process in the manufacturing process, a manufacturing process using a plurality of manufacturing apparatuses capable of performing the manufacturing process in parallel is included.
Non-defective products that represent the frequency of non-defective products and the frequency of defective products that are the results of inspection in the above-mentioned inspection process, while counting the number of process item data representing the frequencies of manufactured products processed by a plurality of manufacturing devices used in a certain manufacturing process / A contingency table creation unit that aggregates the number of defective item data and creates a contingency table that classifies the processing number item data and non-defective / defective item number data,
When using the contingency table to test whether there is a significant difference in the incidence of defective products in manufactured products processed by each manufacturing equipment used in the manufacturing process, the independence chi-square test and accurate In order to determine which test is suitable between the probability test and the chi-square test of independence, the null hypothesis is rejected as the result of the chi-square test, and the manufacturing process is defective. A test selection unit that determines that the exact probability test is suitable when a predetermined transition condition is satisfied under the condition that the generation factor is estimated ;
An estimation unit that estimates whether or not the manufacturing process is a cause of defective products based on the result of the test that the test selection unit determines to be suitable between the independence chi-square test and the exact probability test It is characterized by comprising.

  In the defective process estimation apparatus of the present invention, it is estimated whether or not the manufacturing process is a cause of defective products based on the result of the test determined to be suitable between the chi-square test of independence and the accurate probability test. . Therefore, accurate estimation can be performed and the processing time can be kept within the allowable time.

  The program of this invention is a program for making a computer perform the said defective process estimation method.

  The recording medium of the present invention is a computer-readable recording medium that records a program for causing a computer to execute the defective process estimation method.

  Hereinafter, the present invention will be described in detail with reference to the illustrated embodiments.

  FIG. 3 schematically shows a manufacturing process to which the defective process estimation method according to one embodiment of the present invention is applied. This manufacturing process includes a plurality of manufacturing steps S0, S1, S2, and S3 that are sequentially performed on the manufactured product, and an inspection step T that checks the quality value of the manufactured product.

  The flow of the manufactured product will be described based on FIG. The manufactured product is processed in the order of the manufacturing processes S0, S1, S2, and S3, and passes through the inspection process T. In the manufacturing process S1, two manufacturing apparatuses 1-1 and 1-2 that can execute the manufacturing process S1 independently are used in parallel. Similarly, in the manufacturing process S2, three manufacturing apparatuses 2-1, 2-2, and 2-3 that can independently execute the manufacturing process S2 are used in parallel. The three manufacturing apparatuses 3-1, 3-2, and 3-3 that can independently execute the manufacturing process S 3 are used in parallel. The inspection process T inspects each manufactured product to obtain a quality value, and classifies each manufactured product as either a good product or a defective product based on the magnitude relationship between the obtained quality value and a reference value. .

Now, a detailed description will be given focusing on the manufacturing process S1. Let f1 · be the number of manufactured products processed by the manufacturing apparatus 1-1 used in the manufacturing process S1 during a certain period. The number of manufactured products processed by the manufacturing apparatus 1-1 by examining the manufacturing history in the manufacturing step S1 of the manufactured products inspected in the inspection step T executed after the manufacturing step S3. f1 · can be classified into the number of defective products f11 and the number of non-defective products f12. That is,
f1 ・ = f11 + f12
It becomes. Similarly, the number f2 · of manufactured products processed by the manufacturing apparatus 1-2 used in the manufacturing process S1 can be classified into the number f21 of defective products and the number f22 of non-defective products. That is,
f2 ・ = f21 + f22
It becomes.

In addition, the total number of manufactured products processed in the manufacturing process S1 in a certain period is n. Of the n manufactured products, the number of manufactured products classified as defective products in the inspection process T is f · 1, and the number of manufactured products classified as non-defective products is f · 2. After all,
n = f1 ・ + f2 ・ = f ・ 1 + f ・ 2
It becomes.

  FIG. 4 shows a block configuration of a defective process estimation apparatus 300 for carrying out the defective process estimation method. The defective process estimation apparatus 300 includes an input unit 301 that functions as a contingency table creation unit, a calculation unit 302 that functions as a test selection unit and an estimation unit, and an output unit 303. The input unit 301 inputs inspection result data and manufacturing history data, and creates a contingency table as described later using these data. The arithmetic unit 302 uses the contingency table data from the input unit 301 to select a test and estimate a defective process as described later. The output unit 303 receives the estimation result from the calculation unit 302 and outputs the estimation result.

FIG. 5 shows a contingency table in which the manufactured products processed in the manufacturing process S1 are tabulated. The item on the front side is a processing number item in which the frequencies of manufactured products processed by the manufacturing apparatuses 1-1 and 1-2 are totaled, and the number of items is m = 2. The top item is a non-defective product / defective product number item in which the frequencies of the non-defective product and the defective product, which are inspection results of the inspection process T, are tabulated, and the number of items is two. Thus, the contingency table for the manufacturing process S1 is a 2 × 2 contingency table. The observation frequency of each cell (i, j) constituting this contingency table is represented by fij. Here, i represents an item on the front side, i = 1 represents that the manufactured product has been processed by the manufacturing apparatus 1-1, and i = 2 represents that the manufactured product has been processed by the manufacturing apparatus 1-2. To express. Further, j represents the head item, j = 1 represents that the manufactured product is defective, and j = 2 represents that the manufactured product is non-defective. The peripheral frequency fi · in the i-th row means the sum of fij for j and is expressed by the following equation.

Further, the peripheral frequency f · j in the j-th column means the sum of fij for i, and is expressed by the following equation.

In order to know whether or not the manufacturing process S1 of interest is a defective product occurrence factor, it is verified whether the processed / unprocessed number item and the non-defective product / defective product number item are independent. Here, the test by the chi-square test of independence will be described. The null hypothesis H0 is H0: Pij = Pi · × P · j
And Here, Pij is the occurrence probability of the cell (i, j). Pi · is the marginal probability of the i-th row,
Pi · = fi · / n
It becomes. P · j is the marginal probability of the jth column,
P · j = f · j / n
It becomes.

と計算できる。また、２×２分割表の自由度νは、（表側の項目数−１）×（表頭の項目数−１）＝１×１＝１である。カイ２乗検定では、
有意確率＝１−Ｆ（χ²，ν）≦α
であれば有意水準αで、帰無仮説が棄却されて、製造装置と不良品発生率に相関があると推定される。すなわち、２つの製造装置の間で、不良品発生率に有意な差があることになる。また、有意確率が有意水準αより大きければ、帰無仮説が採択されて、製造装置と不良品発生率に相関があるとはいえない。すなわち、２つの製造装置の間で、不良品発生率に有意な差があるとはいえない。このようにして、著しく不良品を発生させる製造装置を用いている製造工程が存在する可能性を見つけることができる。 Under the null hypothesis H0, the maximum likelihood estimator P′ij of the occurrence probability Pij is
P′ij = (fi · / n) × (f · j / n) = (fi · × f · j) / n ²
It becomes. The theoretical frequency f′ij of the cell (i, j) under the null hypothesis H0 is
f′ij = n × P′ij = fi · × f · j / n
It becomes. After all, the chi-square independence statistic χ ² is

Can be calculated. The degree of freedom ν of the 2 × 2 contingency table is (number of front side items−1) × (number of front head items−1) = 1 × 1 = 1. In the chi-square test,
Significance probability = 1−F (χ ² , ν) ≦ α
If so, the null hypothesis is rejected at the significance level α, and it is estimated that there is a correlation between the manufacturing apparatus and the defective product occurrence rate. That is, there is a significant difference in the defective product occurrence rate between the two manufacturing apparatuses. If the significance probability is greater than the significance level α, the null hypothesis is adopted and it cannot be said that there is a correlation between the manufacturing apparatus and the defective product occurrence rate. That is, it cannot be said that there is a significant difference in the defective product occurrence rate between the two manufacturing apparatuses. In this way, it is possible to find a possibility that there is a manufacturing process using a manufacturing apparatus that significantly generates defective products.

  As described above, the defective process is estimated for the manufacturing process S1. Similarly, defective process estimation is performed for each of the manufacturing process S2 and the manufacturing process S3. That is, it is possible to estimate a defective process for each of the manufacturing processes S1, S2, and S3 and obtain an estimation result as to whether each of the manufacturing processes S1, S2, and S3 is a defective process.

  FIG. 1 is a flowchart showing a procedure of a defective process estimation method 100 according to an embodiment for performing defective process estimation for all manufacturing processes according to the present invention. The inspection result data 101 is data representing a non-defective product or a defective product output from the inspection process T and associated (linked) to each manufactured product. The manufacturing history data 102 is data representing a manufacturing apparatus in each manufacturing process in which the manufactured product is processed for each manufactured product. In processing step 103, the inspection result data 101 and the manufacturing history data 102 are input, and a contingency table is created for each manufacturing process. The next step 112 outlines the estimation procedure executed for each manufacturing process (details will be described later). In step 109 following step 112, if all the manufacturing processes have not been estimated, the process branches to execute step 112 for the unestimated manufacturing process. If it is determined in step 109 that all manufacturing processes have been estimated, the process branches to execute step 110 (details will be described later).

  Step 112 will be described. First, in step 104, a chi-square test is performed based on the contingency table, and a test result as to whether the target manufacturing process is a defective process and a significance probability are calculated. In step 105, it is determined whether or not a predetermined transition condition (details will be described later) including a condition based on the result of the chi-square test is satisfied, and the process is branched based on the determination result. If the above transition condition is satisfied, it is determined that the correct probability test is suitable between the independence chi-square test and the correct probability test, and the process proceeds to step 107 to perform the correct probability test based on the contingency table. When step 107 is completed, the routine proceeds to step 108. In step 108, the accurate probability test is performed as the defective process estimation result, and the process proceeds to step 109. On the other hand, if it is determined in step 105 that the transition condition is not satisfied, it is determined that the chi-square test is suitable, and the process proceeds to step 106. In step 106, the result of the chi-square test is regarded as a defective process estimation result, and the process proceeds to step 109.

  The significance probability is the probability of an error that rejects the null hypothesis when the null hypothesis is correct, and is equal to the probability of the first type error. In other words, the significance probability is a probability that a manufacturing process is not a defective product generation factor, and an erroneous estimation that it is a defective product generation factor. Therefore, the lower the probability of significance, the less likely the first type error is committed, and the higher the possibility that the manufacturing process is a cause of defective products.

  In step 110, only the manufacturing process that is estimated to be a defective process (only the manufacturing process that rejected the null hypothesis) is calculated using the defective process estimation result and the significance probability estimated for each manufacturing process. List in ascending order. That is, the manufacturing process with the lowest significance probability is set to the top of the list. Moreover, the manufacturing process estimated not to be a defective process is not listed. This list is output as the final estimation result 111. Thereby, a person can easily recognize which manufacturing process is the cause of the occurrence of a defective product.

  Incidentally, there are cases where it is important to reduce the first type of error. That is, to reduce errors that reject the place where the null hypothesis should be adopted. In the defective process estimation, it is an error that estimates a defective process even though it is not a defective process. If there are many errors of the first type, the number of defective processes estimated by the defective process estimation becomes larger than the actual number, and there is a problem that the work for the operator to check whether it is correct increases. If there are too many errors of the first type, the worker will not believe any bad process estimation results. Therefore, in order to reduce the first type of error in the chi-square test, an accurate probability test may be performed when the null hypothesis is rejected as a result of the chi-square test. When the null hypothesis is adopted as the result of the chi-square test, the result of the chi-square test is adopted as it is. In this way, it is not necessary to always perform an accurate probability test, and the total processing time for performing the test for each of a plurality of manufacturing processes can be shortened.

  On the other hand, it may be important to reduce the second type of error. In other words, it is to reduce errors that adopt the place where the null hypothesis should be rejected. The defect process estimation is an error that estimates that the process is not a defective process even though it is a defective process. If there are many second type errors, there will be a problem of overlooking a defective process. If there are too many second type errors, it is not possible to identify the defective process and improve the cause of the defect, and there is a problem that the defective product cannot be reduced indefinitely. Therefore, in order to reduce the second type of error in the chi-square test, an accurate probability test may be performed when the null hypothesis is adopted as the result of the chi-square test. When the null hypothesis is rejected as the result of the chi-square test, the result of the chi-square test is adopted as it is. In this way, it is not necessary to always perform an accurate probability test, and the total processing time for performing the test for each of a plurality of manufacturing processes can be shortened.

  Whether to reduce the first type of error or the second type of error is not generally determined, but may be determined according to the circumstances of the manufacturing process.

Next, details of the transition condition used as a determination criterion in step 105 will be described. As described above, when the first type error is reduced, the transition condition is the following condition (a).
Condition (a): The null hypothesis is rejected as a result of the chi-square test.
Further, as described above, when the second type of error is reduced, the transition condition is the following condition (b).
Condition (b): The null hypothesis is adopted as a result of the chi-square test.

The reason for performing an accurate probability test was that it would be an accurate test without an incorrect test result like the chi-square test. Therefore, if the chi-square test can be tested without error, it is not necessary to perform an accurate probability test. In other words, the condition for performing the accurate probability test is when the test result of the chi-square test is not accurate. The chi-square test has the advantage that the processing can be completed in a short time because the processing is extremely small compared to the exact probability test. As the conditions for performing this accurate probability test, the following conditions (c) or (d) are known as described above.
Condition (c): At least one cell having an expected frequency of the contingency table of less than 1.
Condition (d): The number of cells having an expected frequency of less than 5 is 20% or more of the total number of cells.

  The transition condition is preferably a condition in which any one of the condition (a) and the condition (b) is combined with the condition (c) and / or the condition (d). In this case, when the condition (a) is combined with the condition (c) and / or the condition (d), the first type error of the chi-square test can be prevented. Further, when the condition (b) is combined with the condition (c) and / or the condition (d), the second type error of the chi-square test can be prevented. In this way, more accurate estimation can be performed.

Figure 2 is a reference example of the present invention, is a flowchart illustrating the procedure of a line cormorants bad step estimation method 200 bad step estimated for the entire manufacturing process. Step 212 in this flowchart generally shows an estimation procedure executed for each manufacturing process (details will be described later). Processing 203, 204, 206, 207, 208, 209, 210 in FIG. 2 is the same as the processing 103, 104, 106, 107, 108, 109, 110 in FIG. Reference numerals 201, 202, and 211 indicate inspection result data, manufacturing history data, and estimation results, respectively.

Step 212 will be described. In this step 212, first, in step 213, the expected processing time of the accurate probability test is calculated based on the number of manufactured products and the number of manufacturing devices used in the manufacturing process (details will be described later). Subsequently, in step 205, it is determined whether or not a predetermined transition condition (details will be described later) is satisfied, and the process is branched based on the determination result. If the above transition condition is satisfied, the process proceeds to step 207, and an accurate probability test is performed based on the contingency table. On the other hand, if the above transition condition does not hold, the routine proceeds to step 204, where the chi-square test is performed based on the contingency table. In this example, the transition condition is the following condition (e).
Condition (e): Expected processing time does not exceed a predetermined allowable time.
That is, if the expected processing time does not exceed the predetermined allowable time, the process proceeds to step 207, and an accurate probability test is performed. If the predicted processing time exceeds a predetermined allowable time, the process proceeds to step 204 to perform a chi-square test. As described above, when the expected processing time of the accurate probability test exceeds the predetermined time, the processing time can be kept within the allowable time by selecting the chi-square test.

  The transition condition used as the determination criterion in step 205 is preferably a condition in which the condition (e) is combined with the condition (c) and / or the condition (d). For example, condition (e) and condition (c). In another example, the condition (e), the condition (c), and the condition (d). In yet another example, the condition (e) is satisfied, and one or more of the conditions (c) and (d) are satisfied. In this case, more accurate estimation can be performed.

ここで、ｙは、２つのパラメータ製造品総数ｎと製造装置数ｍによって作成できる全分割表の中で最大組み合わせ数を表す。また、ｙ’は、ｙの近似値であり、近似値であることを表すためにダッシュ（’）を付している。また、ｂ_０，ｂ_１，ｂ_２，ｂ_３は係数、ｒｏｕｎｄは四捨五入関数、ｅｘｐは指数関数、ｌｏｇは自然対数関数をそれぞれ表す。 Next, a method for calculating the expected processing time of the accurate probability test will be described. As can be easily understood from the significance probability calculation method described above, the processing time of the accurate probability test is proportional to the number of combinations. However, as described above, the number of combinations in the accurate probability test cannot be calculated in advance. The number of combinations is determined by the peripheral frequency. Therefore, if a table of peripheral frequencies and combinations is prepared in advance, the number of combinations can be known by referring to this table. However, since the number of peripheral frequencies is “the number of manufacturing apparatuses + 2”, it is practically impossible. Therefore, the present inventor has devised a method for calculating an approximate value of the maximum number of combinations based on the total number n of manufactured products and the number m of manufacturing apparatuses. That is, the approximate value of the maximum number of combinations is calculated in all contingency tables that can be created by the total number n of two parameter manufactured products and the number m of manufacturing apparatuses. Since the actual number of combinations in the contingency table is less than or equal to the maximum number of combinations, the maximum processing time of the accurate probability test can be predicted as shown in the following approximate expression.

Here, y represents the maximum number of combinations among all the contingency tables that can be created by the total number n of two parameter manufactured products and the number m of manufacturing apparatuses. Further, y ′ is an approximate value of y, and a dash (′) is added to indicate that it is an approximate value. B ₀ , b ₁ , b ₂ , and b ₃ are coefficients, round is a rounding function, exp is an exponential function, and log is a natural logarithmic function.

  FIG. 6 is a diagram depicting the maximum number of combinations determined by the total number n of manufactured products and the number m of manufacturing apparatuses and approximate values thereof. The solid line is the true maximum number of combinations, and the dotted line is the approximate value of the maximum number of combinations obtained by calculating y ′ of the above approximate expression. It can be seen from FIG. 6 that the approximation is approximately performed by the above approximate expression.

  This approximate expression will be described by taking as an example the case where the number n of manufactured products is 12 and the number of manufacturing devices m = 3. In this case, FIG. 7 shows a contingency table that maximizes the number of combinations. That is, f1 · = f2 · = f3 · = 4, f · 1 = f · 2 = 6. As shown in FIG. 7, the number of combinations of the contingency tables with the peripheral frequency is 19. All combinations are shown in FIG. The number of combinations 19 can be calculated as an approximate value 17 as follows according to the above approximate expression.

  Moreover, a timeout process may be further added to the processing time of the accurate probability test for the above-described defective process estimation methods 100 and 200. That is, after starting the exact test, if the test cannot be completed when a predetermined time-out period elapses, the execution of the exact test is stopped and the significance probability calculated by the chi-square test is calculated. Is output. When the accurate probability test is completed before the timeout time elapses, the result of the accurate probability test is output. If such a timeout process is performed, the processing time for estimating a defective process does not exceed a predetermined timeout time. In other words, the defective process estimation can always be completed within a predetermined timeout time.

  In addition, in the process of calculating the significance probability by the above accurate probability test, when it is found that the significance probability being calculated exceeds the significance level, the calculation is stopped at that time point, and the significance value calculated up to that time point is The probability may be output as a calculation result. Thereby, waste of processing time can be prevented.

  In the embodiment of the present invention, the estimation result is a manufacturing process estimated as a defective product generation factor. That is, even if the manufacturing process is specified, it is necessary to further specify which of the plurality of manufacturing apparatuses used in parallel by the manufacturing process is the cause of defective products.

  Therefore, for each estimated manufacturing process, the manufacturing apparatus with the highest defective product occurrence rate in the manufactured products processed by a plurality of manufacturing apparatuses used in the manufacturing process is estimated as a defective apparatus that is a cause of defective products. It is desirable to output in addition to the estimation result. In such a case, not only the manufacturing process that is the cause of defective product generation, but also the manufacturing apparatus with the highest defective product generation rate is estimated. Therefore, the worker can easily specify the cause of defective products.

  In addition, for each manufacturing process of the estimation result, the output unit sets the manufacturing apparatus having the highest number of defective products among the manufactured products processed by the plurality of manufacturing apparatuses used in the manufacturing process as a defective device that is a cause of defective products. It may be estimated and output in addition to the estimation result. In such a case, not only the manufacturing process that is the cause of defective products, but also the manufacturing device with the highest number of defective products is estimated. Therefore, the worker can easily specify the cause of defective products.

  The non-defective product or defective product, which is the inspection result of the inspection process T, represents the result determined from the measured values measured from each manufactured product in the process of manufacturing the manufactured product. For example, the measured value is a value representing the performance of a manufactured product, an electrical inspection result, an appearance inspection result, a visual inspection result, the number of defects included in the manufactured product, and the like.

  The period to be counted in the contingency table may be appropriately determined as several hours, one day, one week, or one month. As the period is shorter, there is an advantage of shortening from the occurrence of a defective product generation factor until estimation is possible, but there is a disadvantage that the estimation accuracy is deteriorated because the number of manufactured products or substrates to be counted is reduced. The longer the period, the longer the time until the estimation can be made after the occurrence of a defective product occurs. On the other hand, the estimation accuracy is improved because the number of manufactured products or substrates to be counted increases.

  The defective process estimation method of the present invention is not applied only to a manufacturing process for manufacturing a semiconductor or a liquid crystal panel, and can also be applied to other manufacturing processes. For example, it can be applied to flat display panels such as plasma display, organic EL (Electroluminescence) display, SED (Surface-conduction Electron-emitter Display), solid-state imaging device, solar cell, hard disk magnetic head, etc. be able to.

  The defective process estimation method of the present invention is easily realized by causing a computer to execute software (program).

  Further, such software may be recorded on a recording medium such as a CD-ROM. In that case, it is possible to cause the personal computer to execute the defective facility estimation method of the present invention by causing a general personal computer or the like to read the software recorded on the recording medium.

It is a flowchart showing the procedure of performing defective process estimation about all the manufacturing processes with the defective process estimation method of one Embodiment of this invention. It is a flowchart showing the procedure of performing defective process estimation about all the manufacturing processes with the defective process estimation method as a reference example of this invention. It is the figure which showed typically the manufacturing process used as the application object of the defective process estimation method of one Embodiment of this invention. It is a figure which shows the block configuration of the defect process estimation apparatus of one Embodiment of this invention. It is an example of a contingency table in which manufactured products processed in the manufacturing process S1 are tabulated. It is the figure which drawn the maximum number of combinations determined by the total number n of manufactured goods, and the number m of manufacturing apparatuses, and its approximate value. It is a figure which shows the division | segmentation table | surface where the number of combinations becomes the maximum when the number of manufactured articles n = 12 and the number of manufacturing apparatuses m = 3. It is a figure showing all the combinations of the contingency table of FIG. It is a figure which shows the division | segmentation table | surface in case the number of manufacturing apparatuses m = 3. It is a figure which shows the contingency table used in order to demonstrate an exact probability test. It is a figure showing all the combinations at the time of fixing the periphery frequency of the contingency table of FIG. It is a figure which shows an example of the contingency table which becomes an incorrect test result in a chi-square test. It is a figure showing all the combinations at the time of fixing the periphery frequency of the contingency table of FIG. It is an example of a contingency table that requires a long time for processing of an accurate probability test.

300 Defect Process Estimation Device 301 Input Unit 302 Calculation Unit 303 Output Unit

Claims (15)

Inspection of the above inspection process for a manufacturing process including a plurality of manufacturing processes sequentially performed on the manufactured product and at least one inspection process for inspecting whether the manufactured product is a non-defective product or a defective product Based on the results, in the defective process estimation method for estimating the manufacturing process that is a defective product generation factor among the plurality of manufacturing processes,
As a manufacturing process in the manufacturing process, a manufacturing process using a plurality of manufacturing apparatuses capable of performing the manufacturing process in parallel is included.
Non-defective products that represent the frequency of non-defective products and the frequency of defective products that are the results of inspection in the above-mentioned inspection process, while counting the number of process item data representing the frequencies of manufactured products processed by a plurality of manufacturing devices used in a certain manufacturing process / Aggregate the number of defective item data and create a contingency table that categorizes the number of processed item data and non-defective / defective item number data,
When using the contingency table to test whether there is a significant difference in the incidence of defective products in manufactured products processed by each manufacturing equipment used in the manufacturing process, the independence chi-square test and accurate In order to determine which test is suitable between the probability test and the chi-square test of independence, the null hypothesis is rejected as the result of the chi-square test, and the manufacturing process is defective. Under the condition that it is estimated that it is the cause of the occurrence, when the predetermined transition condition is satisfied, it is determined that the above accurate probability test is suitable,
A defective process characterized in that, based on the result of the test determined to be suitable between the chi-square test of independence and the exact probability test, it is estimated whether or not the manufacturing process is a cause of defective products. Estimation method. The defective process estimation method according to claim 1,
The method for estimating a defective process, wherein the transition condition includes a condition for generating a first type error that rejects a place where the null hypothesis should be adopted. The defective process estimation method according to claim 1 ,
The transition conditions are poor step estimation method, wherein the expected frequency of the contingency table cell less than the predetermined value, including a condition that at least 1 fold. The defective process estimation method according to claim 1 ,
The transition conditions are poor step estimating method characterized in that the expected frequency of the contingency table contains a condition that the cell is less than the predetermined value account for at least a predetermined percentage of the total number of cells. The defective process estimation method according to claim 1,
In the above test, the null hypothesis is that the defective product occurrence rates in the manufactured products processed in each manufacturing apparatus used in a certain manufacturing process are equal to each other, and the alternative hypothesis is that these defective product occurrence rates are not equal to each other. age,
When the result of the above test rejects the above null hypothesis and adopts the above alternative hypothesis, it is estimated that the manufacturing process is a cause of defective products, while the result of the above test adopts the above null hypothesis. Then, when rejecting the alternative hypothesis, it is estimated that the manufacturing process is not a defective product generation factor. The defective process estimation method according to claim 1,
For each manufacturing process above,
Determine which test is appropriate between the above independence chi-square test and exact probability test,
A defective process estimation method, wherein a significant probability representing a correlation between a manufacturing apparatus used in the manufacturing process and a defective product occurrence rate is calculated by a chi-square test or an accurate probability test determined to be suitable. In the defective process estimation method according to claim 6 ,
A defective process estimation method, wherein manufacturing processes are arranged in ascending order of significance calculated for each manufacturing process, and a candidate list representing manufacturing processes estimated to be defective products is output. In the defective process estimation method according to claim 6 ,
A defective process estimation method characterized in that a manufacturing process showing a minimum significant probability among the significant probabilities calculated for each manufacturing process is used as an estimation result as a defective product generation factor. In the defective process estimation method according to claim 6 ,
In the process of calculating the significance probability by the above accurate probability test, if it is found that the significance probability being calculated exceeds the significance level, the computation is stopped at that time and the significance probability calculated up to that time is calculated. A defective process estimation method characterized by outputting as a calculation result. In the defective process estimation method according to claim 6 ,
If the test cannot be completed when the predetermined time-out period elapses after starting the exact probability test, the execution of the exact probability test is stopped and the significance probability calculated by the chi-square test is output. A defective process estimation method characterized by: The defective process estimation method according to claim 1,
A defective device that is the cause of defective products in the manufacturing process is a manufacturing device that shows the highest defective product generation rate among defective products generated in a plurality of manufacturing devices used in a certain manufacturing process. A defective process estimation method characterized by estimating as follows. The defective process estimation method according to claim 1,
Estimating a manufacturing device that indicates the largest number of defective products among defective products processed by a plurality of manufacturing devices used in a certain manufacturing process as a defective device that is a cause of defective products in the manufacturing process. A defective process estimation method characterized by: Inspection of the above inspection process for a manufacturing process including a plurality of manufacturing processes sequentially performed on the manufactured product and at least one inspection process for inspecting whether the manufactured product is a non-defective product or a defective product Based on the results, in the defective process estimation device for estimating the manufacturing process that is a defective product generation factor among the plurality of manufacturing processes,
As a manufacturing process in the manufacturing process, a manufacturing process using a plurality of manufacturing apparatuses capable of performing the manufacturing process in parallel is included.
Non-defective products that represent the frequency of non-defective products and the frequency of defective products that are the results of inspection in the above-mentioned inspection process, while counting the number of process item data representing the frequencies of manufactured products processed by a plurality of manufacturing devices used in a certain manufacturing process / A contingency table creation unit that aggregates the number of defective item data and creates a contingency table that classifies the processing number item data and non-defective / defective item number data,
When using the contingency table to test whether there is a significant difference in the incidence of defective products in manufactured products processed by each manufacturing equipment used in the manufacturing process, the independence chi-square test and accurate In order to determine which test is suitable between the probability test and the chi-square test of independence, the null hypothesis is rejected as the result of the chi-square test, and the manufacturing process is defective. A test selection unit that determines that the exact probability test is suitable when a predetermined transition condition is satisfied under the condition that the generation factor is estimated ;
An estimation unit that estimates whether or not the manufacturing process is a cause of defective products based on the result of the test that the test selection unit determines to be suitable between the independence chi-square test and the exact probability test And a defective process estimation apparatus.   A program for causing a computer to execute the defective process estimation method according to claim 1.   A computer-readable recording medium recording a program for causing a computer to execute the defective process estimation method according to claim 1.

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