A method and system for dynamic analysis of production line stability based on fault tree

Abstract

The present invention discloses a method for evaluating production line stability based on a fault tree, comprising the following steps: obtaining multiple parameters of each device on the production line collected by sensors over a period of time, calculating the process capability index corresponding to each parameter, inputting the obtained process capability index corresponding to each parameter of each device into a pre-trained multiple linear regression model to obtain a stability index for the device, and inputting the stability index of each device into a pre-built fault tree-based stability analysis model to obtain a final stability judgment result for the device. The present invention can solve the technical problem that existing machine learning methods are complex for production lines, require long training times, and are unable to adapt to the real-time requirements of production environments in actual deployment and operation.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial equipment stability analysis, and more specifically, relates to a method and system for dynamic analysis of production line stability based on a fault tree. Background Art

[0002] In recent years, with the rapid development of internet technology, data volumes have exploded, ushering in the era of big data. Many industrial manufacturing companies have adopted automated assembly line production. A production line producing high-precision finished products often consists of highly complex production processes, involving numerous devices and thousands of interdependent process parameters. Any one of these parameters can potentially impact final yield and production capacity. Therefore, implementing automated production technology requires evaluating the reliability and stability of existing production lines.

[0003] Most existing stability assessment methods still rely on manual inspection, observing abnormalities in equipment parameters and indicators. However, manual inspections are prone to errors and omissions, and error correction takes a long time. To address the time-consuming nature of manual inspections, developers are experimenting with building a stability assessment model using deep neural networks. This model uses the data from various sensors as input and the final success rate as output. Through model training and optimization, a stability assessment model for the production line is developed.

[0004] However, the above-mentioned stability assessment model based on deep neural networks still has some defects that cannot be ignored: First, when there are many devices and too many process parameters in the production line, the model training time takes a long time, the model scale is large, and it takes too long to run the model to get the results, making it difficult to achieve real-time indicators; Second, most neural network construction models are based on a static environment and have poor adaptability to dynamic environments (such as real-time changes in various sensor parameters, equipment replacement in the assembly line, etc.); Third, the model has poor scalability. When there are changes to the production line, such as adding a new process, all models have to be retrained, which is costly; Fourth, the model ignores the environmental characteristics of industrial production, resulting in poor interpretability, which in turn leads to the technical problem of being unable to customize different assembly lines. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a method and system for dynamic analysis of production line stability based on a fault tree, which aims to solve the technical problems that the existing machine learning methods are complex for production lines and have long training time, resulting in the inability of actual deployment and operation to adapt to the real-time requirements of the production environment, as well as the poor adaptability to dynamic environments and the inability to adapt to relevant dynamic changes in the production line process (such as real-time changes in various sensor parameters, equipment replacement in the assembly line, etc.), and the high cost of retraining all models when changes occur in the production line, as well as the technical problem that the model is not easy to interpret and cannot be customized for different assembly lines.

[0006] To achieve the above object, according to one aspect of the present invention, a method for evaluating production line stability based on a fault tree is provided, which is characterized by comprising the following steps:

[0007] (1) Obtain multiple parameters of each device on the production line collected by the sensor of the device over a period of time, and calculate the process capability index corresponding to each parameter.

[0008] (2) Inputting the process capability index corresponding to each parameter of each device obtained in step (1) into a pre-trained multiple linear regression model to obtain the stability index of the device.

[0009] (3) The stability index of each device obtained in step (2) is input into a pre-built stability analysis model based on a fault tree to obtain the final stability judgment result of the device.

[0010] Preferably, for each parameter in step (1), the corresponding process capability index is calculated according to the following formula:

[0011]

[0012] Where: C is the process capability index corresponding to the parameter, T is the specification value and USL is the upper limit of the parameter specified by the equipment manufacturer, LSL is the lower limit of the parameter specified by the equipment manufacturer, d is the specification width, and d = USL-LSL, t represents the time to obtain the parameter, a total of t sampling cycles, the intermediate parameter μ is the mean value, and σ is the standard deviation, and v i It represents the parameter value of the parameter obtained in the i-th sampling period, and i∈[1, the total number of sampling periods].

[0013] Preferably, the multivariate linear regression model is trained by the following steps:

[0014] (2-1) Obtain a wafer production dataset and divide the dataset into a training set and a test set;

[0015] (2-2) Initializing the parameters of the multiple linear regression model to obtain an initialized multiple linear regression model;

[0016] (2-3) Inputting the training set obtained in step (2-1) into the multiple linear regression model initialized in step (2-2) to obtain the loss function value of the multiple linear regression model, and calculating the gradient of each feature weight of the multiple linear regression model based on the loss function value.

[0017] (2-4) processing each feature weight using the gradient descent method based on the bias term of the multiple linear regression model and the gradient of each feature weight obtained in step (2-3) to obtain the processed bias term and each feature weight;

[0018] (2-5) Repeat steps (2-3) and (2-4) until the loss function converges to obtain a trained multivariate linear regression model.

[0019] Preferably, step (2-1) is specifically as follows: for each parameter of each device in the wafer production data set, the process capability index corresponding to the time series of the parameter is calculated using the method of the above step (1), and the process capability index corresponding to all parameters in all devices (which serve as the characteristic value of the linear regression model) and the qualified rate of semi-finished products produced by each device (which serves as the predicted value of the linear regression model) are divided into a training set and a test set in a 1:1 ratio, that is, 50% is randomly divided as a training set and the remaining 50% is used as a test set, and the division is repeated 10 times to reduce random errors.

[0020] Preferably, the initial value of the weight parameter in step (2-2) is a random value output by a truncated normal distribution with a standard deviation of 0.1, the initial value of the bias parameter is set to 0, the initial learning rate of the model is 0.01, and a step-by-step learning strategy is adopted with a step size of stepsize = 200, that is, the learning rate is multiplied by 0.1 every 200 rounds;

[0021] The multiple linear regression model is y=w1x1+w2x2+…+w n x n +b. Among them, y is the predicted value of the qualified rate of semi-finished products produced by the equipment, that is, the predicted stability of the equipment; n is the number of parameters of the equipment; {x1, x2, ..., x n} is the process capability index of each parameter of the equipment; the bias term b and all feature weights {w1,w2,…,w n} is learned through model training.

[0022] Preferably, the multiple linear regression model in step (2-3) uses mean square error as the loss function, which is specifically expressed as:

[0023]

[0024] Where MSE is the mean square error, y k is the predicted value of the multiple linear regression model for the kth training sample, is the actual value of the kth training sample, that is, the qualified rate of the semi-finished products produced by this equipment, and n is the number of samples in the training set;

[0025] The gradient calculation of the feature weight is to first calculate the partial derivative of the bias term and each feature weight according to the MSE expression to obtain the partial derivative calculation formula of the bias term and each feature weight; then, traverse each training sample in the training set, and import the partial derivative calculation formula of the bias term and each feature weight calculated in the previous step in turn to obtain the partial derivative value of the bias term and each feature weight for each training sample; finally, accumulate the partial derivative values ​​of the bias term and each feature weight for each training sample, divide the sum by the number of training samples, and calculate the average value of the partial derivative values ​​of the bias term and each feature weight, and use the average value as the gradient of the bias term and each feature weight.

[0026] Preferably, the construction process of the fault tree-based stability analysis model is completed through the following steps:

[0027] (3-1) Construct the root node of the fault tree and mark it as the node to be processed N (pre) ;

[0028] (3-2) Set a counter a = m to represent the ath production link on the production line, and m represents the total number of production links on the production line;

[0029] (3-3) Determine whether a is equal to 0. If so, proceed to step (3-15), otherwise proceed to step (3-4);

[0030] (3-4) Determine whether there is only one device involved in the a-th production link. If so, proceed to step (3-5); otherwise, proceed to step (3-6);

[0031] (3-5) Identify the fault event of the equipment involved in the a-th production link as the fault tree node C, and set C as the node N in the fault tree (pre) The child node of node N (pre) The connection relationship with node C is set as the AND gate relationship in the fault tree, and then go to step (3-12);

[0032] (3-6) Grouping multiple devices involved in the a-th production link by type, and grouping devices of the same type into the same group, thereby obtaining M groups of devices, and proceeding to step (3-7);

[0033] (3-7) Set counter b = 1, and then go to step (3-8);

[0034] (3-8) Determine whether b is less than or equal to M. If so, proceed to step (3-9), otherwise proceed to step (3-12);

[0035] (3-9) Add an intermediate node B to the fault tree for the entire group b equipment, indicating that a part of the group b equipment has a problem, and set the intermediate node B as node N in the fault tree. (pre) The child node of node N (pre) The connection relationship with node B is set as the AND gate relationship in the fault tree, and proceed to step (3-10).

[0036] (3-10) Create a new leaf node in the fault tree for each device in group b. Each leaf node represents a problem with a part of the corresponding device. Set all newly created leaf nodes as child nodes of node B. Set the connection relationship between the leaf nodes and node B as an OR gate relationship in the fault tree, and go to step (3-11).

[0037] (3-11) Set counter b=b+1 and return to step (3-8);

[0038] (3-12) Add an intermediate node F to the fault tree, indicating that a failure event occurred in the previous a-1 production links, and set node F to N (pre) A child node of node N (pre) The connection relationship with node F is set as the AND gate relationship in the fault tree.

[0039] (3-13) The node to be processed N (pre) Set to node F;

[0040] (3-14) Set counter a=a-1 and return to step (3-3);

[0041] (3-15) Delete node N in the fault tree (unvisited) , then go to step (3-16);

[0042] (3-16) Based on the constructed fault tree diagram, the probability of occurrence of the top event is calculated, and the probability of occurrence of the top event is converted into the stability probability of the production line, that is, the final stability analysis model based on the fault tree is obtained.

[0043] Preferably, step (3-16) is specifically as follows: first, obtain the occurrence probability expression of each leaf node: P(L s )=1-rR s , where L s represents the sth leaf node, P(L s ) represents the probability of occurrence of the sth leaf node, R s is the stable value of the device represented by the sth leaf node, and r is obtained by subsequent model training. Then, based on the occurrence probability of each leaf node and the gate probability transfer formula in the fault tree, the occurrence probability of the top event, that is, the failure probability of the production line, is calculated. Among them, the probability transfer formula of the AND gate is The probability transfer formula of the OR gate is P is the probability of occurrence of the parent node event, l means that the AND gate has l child nodes, N s represents the sth child node, and P(N s ) is the probability of occurrence of the sth child node event.

[0044] Preferably, the training process of the fault tree-based stability analysis model is completed through the following steps:

[0045] (a) Obtain a wafer production dataset and divide it into a training set and a test set.

[0046] (b) Initializing the parameters of the fault tree-based stability analysis model to obtain the initialized fault tree-based stability analysis model.

[0047] (c) inputting the training set obtained in step (a) into the fault tree-based stability analysis model initialized in step (b) to obtain a loss function value at this time, and calculating the gradient of each feature weight of the fault tree-based stability analysis model based on the loss function value;

[0048] Among them, the stability analysis model based on the fault tree uses the mean square error as the loss function, which is specifically expressed as:

[0049]

[0050] Where MSE is the mean square error, y k is the predicted value of the k-th training sample based on the stability analysis model of the fault tree, is the actual value of the kth training sample, that is, the qualified rate of the finished wafers in the kth training sample, and n is the number of samples in the training set. The gradient calculation method for the feature weights of the fault tree-based stability analysis model is to first calculate the partial derivative of each feature weight of the fault tree-based stability analysis model based on the MSE expression, obtaining the partial derivative calculation formula for each feature weight of the fault tree-based stability analysis model. Then, each training sample in the training set is traversed and sequentially imported into the partial derivative calculation formula for each feature weight calculated in the previous step, thereby obtaining the partial derivative value of each feature weight for each training sample. Finally, each feature weight is processed, and the partial derivative values ​​of the feature weight for each training sample are accumulated. The sum is divided by the number of training samples to calculate the average of the partial derivative values ​​of each feature weight, and the average value is used as the gradient of the feature weight.

[0051] (d) processing each feature weight using a gradient descent method according to the gradient of each feature weight of the fault tree-based stability analysis model obtained in step (2-3) to obtain a processed feature weight;

[0052] (e) Repeat steps (b) and (e) until the loss function converges, and obtain a trained fault tree-based stability analysis model.

[0053] According to another aspect of the present invention, a system for evaluating production line stability based on a fault tree is provided, characterized in that it includes:

[0054] The first module is used to obtain multiple parameters of each device on the production line collected by the sensor of the device over a period of time, and calculate the process capability index corresponding to each parameter.

[0055] The second module is used to input the process capability index corresponding to each parameter of each device obtained in the first module into a pre-trained multiple linear regression model to obtain the stability index of the device;

[0056] The third module is used to input the stability index of each device obtained in the second module into a pre-built stability analysis model based on a fault tree to obtain the final stability judgment result of the device.

[0057] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0058] (1) Since the present invention adopts steps (1) and (2-1), the parameters on each device are processed using the process capability index calculation method for multi-dimensional time series, which greatly reduces the amount of data for training samples, reduces the complexity of the model, reduces the training time, and solves the problem of traditional deep neural networks being time-consuming and large-scale;

[0059] (2) Since the present invention adopts steps (1) and (3-16), the dynamics of the time series of parameters is first converted into a static failure probability by means of the process capability index, and step (3-16) combines the static failure probability of the equipment with the fault tree to obtain the final stability analysis model based on the fault tree, so that the adaptation range of the final model is changed from a static probability model to a dynamic time series, which can solve the problem that the relevant machine learning methods have poor adaptability to dynamic environments;

[0060] (3) Because the present invention employs steps (2) and (3), when a small-scale change occurs to the production line, the stability calculation model for a single device, i.e., the training results of the multiple linear regression model from steps (2-1) to (2-5), can be reused, and the weight parameters remain unchanged. Therefore, only the relevant positions of the fault tree-based stability analysis model in step (3) need to be changed. This greatly improves the applicability and scalability of the model, solving the problem of the difficulty in scalability of existing large-scale neural networks.

[0061] (4) Since the present invention adopts steps (1) and (3), on the one hand, the process capability index is a recognized indicator in the industry for identifying changes in the operating status of equipment. Secondly, the construction of the fault tree also depends on the actual production process. The higher the level of the event in the fault tree, the more important it is to stability. All of the above greatly increases the interpretability of the model and solves the problem of poor interpretability of the existing neural network model. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flow chart of the production line stability analysis method based on the fault tree of the present invention;

[0063] Figure 2 It is a detailed flow chart of the production line stability analysis method based on the fault tree of the present invention;

[0064] Figure 3 is a fault tree diagram of a specific embodiment of the present invention;

[0065] Figure 4 It is a comparison curve between the predicted value and the actual value of the production line stability after using the method of the present invention. DETAILED DESCRIPTION

[0066] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0067] The basic concept of this invention is to use process capability indices to process data samples and then analyze production line stability using a fault tree model. First, a data set is collected, including the time series of each sensor parameter on each device, as well as the pass rate of semi-finished and finished products produced by each device. This data set is then used to train a multivariate linear regression model for stability analysis of each device and a fault tree-based stability analysis model for the entire production line. In actual use, after obtaining the time series of parameters on the production line over a period of time, the two stability analysis models are input into the stability analysis model to obtain the stability value of the current production line.

[0068] like Figure 1 and Figure 2 As shown, the present invention provides a method for evaluating production line stability based on a fault tree, comprising the following steps:

[0069] (1) Obtain multiple parameters of each device on the production line collected by the sensor of the device over a period of time, and calculate the process capability index corresponding to each parameter.

[0070] Specifically, the equipment parameters collected in this step include, but are not limited to, environmental parameters, process parameters, process parameters, raw material properties, etc. The time for acquiring parameters in this step is more than 20 sampling cycles, preferably 25 sampling cycles, and the duration of the sampling cycle is 1 to 3 seconds, preferably 1 second.

[0071] For each parameter, the corresponding process capability index is calculated according to the following formula:

[0072]

[0073] Where: C is the process capability index corresponding to the parameter, T is the specification value and USL is the upper limit of the parameter specified by the equipment manufacturer, LSL is the lower limit of the parameter specified by the equipment manufacturer, d is the specification width, and d = USL-LSL, t represents the time to obtain the parameter, a total of t sampling cycles, the intermediate parameter μ is the mean value, and σ is the standard deviation, and v i It represents the parameter value of the parameter obtained in the i-th sampling period, and i∈[1, the total number of sampling periods].

[0074] The advantage of this step is that it converts the dynamic time series into a static process capability index, allowing the model to adapt to dynamically changing environments and resolving the problem of poor adaptability to dynamic environments of related machine learning methods. In addition, the process capability index is a recognized indicator in the industry for identifying changes in equipment operating status and can improve the interpretability of the model. The most important point is that it greatly reduces the input size of the model and reduces the training time of the model.

[0075] (2) Inputting the process capability index corresponding to each parameter of each device obtained in step (1) into a pre-trained multiple linear regression model to obtain the stability index of the device.

[0076] Specifically, the multivariate linear regression model is trained through the following steps:

[0077] (2-1) Obtain a wafer production dataset and divide the dataset into a training set and a test set;

[0078] Specifically, the data set used in this step is the wafer production data set provided by Hunan Chuwei Semiconductor Technology Co., Ltd. The data of each device in the wafer production data set includes the time series of each parameter of the device and the pass rate of the semi-finished products produced by the device.

[0079] Specifically, for each parameter of each device in the wafer production data set, the process capability index corresponding to the time series of the parameter is calculated using the method of the above step (1), and the process capability index corresponding to all parameters in all devices (which serve as the characteristic value of the linear regression model) and the qualified rate of semi-finished products produced by each device (which serves as the predicted value of the linear regression model) are divided into training set and test set in a 1:1 ratio, that is, 50% is randomly divided as the training set and the remaining 50% is used as the test set, and the division is repeated 10 times to reduce random errors.

[0080] (2-2) Initializing the parameters of the multiple linear regression model to obtain an initialized multiple linear regression model;

[0081] Specifically, the initial value of the weight parameter is a random value output by a truncated normal distribution with a standard deviation of 0.1. The initial value of the bias parameter is set to 0. The initial learning rate of the model is 0.01. A step-by-step learning strategy is adopted with a step size of 200, that is, the learning rate is multiplied by 0.1 every 200 epochs.

[0082] Specifically, the multiple linear regression model is y=w1x1+w2x2+…+w n x n+b. Among them, y is the predicted value of the qualified rate of semi-finished products produced by the equipment, that is, the predicted stability of the equipment; n is the number of parameters of the equipment; {x1, x2, ..., x n} is the process capability index of each parameter of the equipment; the bias term b and all feature weights {w1,w2,…,w n} is learned through model training.

[0083] The advantage of this sub-step is that it allows model training to converge faster through a step-by-step learning strategy.

[0084] (2-3) Inputting the training set obtained in step (2-1) into the multiple linear regression model initialized in step (2-2) to obtain the loss function value of the multiple linear regression model, and calculating the gradient of each feature weight of the multiple linear regression model based on the loss function value.

[0085] Among them, the multiple linear regression model uses the mean square error as the loss function, which is specifically expressed as:

[0086]

[0087] Where MSE is the mean square error, y k is the predicted value of the multiple linear regression model for the kth training sample, is the actual value of the kth training sample, that is, the qualified rate of the semi-finished products produced by this equipment, and n is the number of samples in the training set.

[0088] For the gradient calculation method of feature weights, first, the partial derivative of the bias term and each feature weight is calculated according to the MSE expression to obtain the partial derivative calculation formula of the bias term and each feature weight; then, each training sample in the training set is traversed, and the partial derivative calculation formula of the bias term and each feature weight calculated in the previous step is imported in turn to obtain the partial derivative value of the bias term and each feature weight for each training sample; finally, the partial derivative values ​​of the bias term and each feature weight for each training sample are accumulated, and the sum is divided by the number of training samples to calculate the average value of the partial derivative values ​​of the bias term and each feature weight, and the average value is used as the gradient of the bias term and each feature weight.

[0089] (2-4) processing each feature weight using the gradient descent method based on the bias term of the multiple linear regression model and the gradient of each feature weight obtained in step (2-3) to obtain the processed bias term and each feature weight;

[0090] Specifically, for the processing process of the gradient descent method: first, the bias term obtained in (2-3) and the gradient of each feature weight are multiplied by the learning rate set in step (2-2), and the product is saved; then, the old bias term and each feature weight are subtracted from the product to obtain a new bias term and each feature weight.

[0091] (2-5) Repeat steps (2-3) and (2-4) until the loss function converges to obtain a trained multivariate linear regression model.

[0092] The advantage of this step is that the stability analysis of the equipment is also presented separately. When small-scale changes occur in the production line, the calculation model for the stability of a single device can be reused, increasing the scalability of the entire stability model.

[0093] (3) The stability index of each device obtained in step (2) is input into a pre-built stability analysis model based on a fault tree to obtain the final stability judgment result of the device.

[0094] In this invention, a stability analysis model based on a fault tree is used. First, a fault is selected as a top event (TE), where the top event is a production line failure, and the cause of the TE is deduced and analyzed. Subsequently, the fault is gradually decomposed into multiple levels of intermediate events (ME), where the intermediate events are failures in various production links of the production line, until it is decomposed into indecomposable basic events (BE), where the basic event is the failure of a single device, thereby obtaining a tree-like logic diagram, namely a fault tree (FT) diagram.

[0095] Specifically, the construction process of the stability analysis model based on the fault tree is completed through the following steps:

[0096] (3-1) Construct the root node of the fault tree (which represents the fault event of the entire production line) and mark the node as the node to be processed N (pre) ;

[0097] (3-2) Set a counter a = m to represent the ath production link on the production line, and m represents the total number of production links on the production line;

[0098] (3-3) Determine whether a is equal to 0. If so, proceed to step (3-15), otherwise proceed to step (3-4);

[0099] (3-4) Determine whether there is only one device involved in the a-th production link. If so, proceed to step (3-5); otherwise, proceed to step (3-6);

[0100] (3-5) Identify the fault event of the equipment involved in the a-th production link as the fault tree node C, and set C as the node N in the fault tree (pre) The child node of node N (pre) The connection relationship with node C is set as the AND gate relationship in the fault tree, and then go to step (3-12);

[0101] (3-6) Grouping the multiple devices involved in the a-th production link by type, and grouping the same type of devices (i.e., devices that perform the same work in the production line) into the same group, thereby obtaining M groups of devices, and proceeding to step (3-7);

[0102] (3-7) Set counter b = 1, and then go to step (3-8);

[0103] (3-8) Determine whether b is less than or equal to M. If so, proceed to step (3-9), otherwise proceed to step (3-12);

[0104] (3-9) Add an intermediate node B to the fault tree for the entire group b of equipment, indicating that a part of the group b of equipment (one or more equipment) has a problem, and set the intermediate node B as node N in the fault tree. (pre) The child node of node N (pre) The connection relationship with node B is set as the AND gate relationship in the fault tree, and proceed to step (3-10).

[0105] (3-10) Create a new leaf node in the fault tree for each device in group b. Each leaf node represents a problem with a part of the corresponding device. Set all newly created leaf nodes as child nodes of node B. Set the connection relationship between the leaf nodes and node B as an OR gate relationship in the fault tree, and go to step (3-11).

[0106] (3-11) Set counter b=b+1 and return to step (3-8);

[0107] (3-12) Add an intermediate node F to the fault tree, indicating that a failure event occurred in the previous a-1 production links, and set node F to N (pre) A child node of node N (pre) The connection relationship with node F is set as the AND gate relationship in the fault tree.

[0108] (3-13) The node to be processed N (pre) Set to node F;

[0109] (3-14) Set counter a=a-1 and return to step (3-3);

[0110] (3-15) Delete node N in the fault tree(unvisited) , then go to step (3-16);

[0111] (3-16) Based on the constructed fault tree diagram, the probability of occurrence of the top event is calculated, and the probability of occurrence of the top event is converted into the stability probability of the production line, that is, the final stability analysis model based on the fault tree is obtained.

[0112] Specifically, this step is to first obtain the occurrence probability expression of each leaf node: P(L s )=1-rR s , where L s represents the sth leaf node, P(L s ) represents the probability of occurrence of the sth leaf node, R s is the stable value of the device represented by the sth leaf node, and r is obtained by subsequent model training. Then, based on the occurrence probability of each leaf node and the gate probability transfer formula in the fault tree, the occurrence probability of the top event, that is, the failure probability of the production line, is calculated. Among them, the probability transfer formula of the AND gate is The probability transfer formula of the OR gate is P is the probability of occurrence of the parent node event, l means that the AND gate has l child nodes, N s represents the sth child node, and P(N s ) is the probability of occurrence of the sth child node event.

[0113] It should be pointed out that the sum of the production line stability probability and the production line failure probability is 1. The production line stability probability is converted from the top event occurrence probability, which is the final fault tree-based stability analysis model.

[0114] like Figure 3 This is a fault diagram of one of the specific embodiments, and the corresponding probability distribution expression of the fault is as follows:

[0115] P(TE)=P(BE1)×P(ME1)

[0116] =P(BE1)×P(ME2)×P(ME3)

[0117] =P(BE1)×(1-(1-P(BE2))×(1-P(BE3)))×(1-(1-P(BE4))×(1-P(BE5)))

[0118] =(1-r1R1)(1-r2R2r3R3)(1-r4R4r5R5)

[0119] According to the relationship between the production line stability probability and the production line failure probability, the final stability analysis model based on the fault tree is converted as follows:

[0120] S=1-P(TE)=1-(1-r1R1)(1-r2R2r3R3)(1-r4R4r5R5)

[0121] Among them, S is the probability of production line stability, P(TE) is the probability of top event occurrence; and R1, R2, ..., R n is the characteristic value of the stability analysis model based on the fault tree, that is, the stability value of each device; r1, r2, ..., r n It is the characteristic weight of the stability analysis model based on the fault tree and is the goal to be achieved in subsequent training.

[0122] Specifically, the training process of the fault tree-based stability analysis model is completed through the following steps:

[0123] (a) Obtain a wafer production dataset and divide it into a training set and a test set.

[0124] Specifically, the data set used in this step is still the wafer production data set provided by Hunan Chuwei Semiconductor Technology Co., Ltd., which provides the pass rate of semi-finished products produced by each device and the pass rate of the final wafer finished product. The pass rate of semi-finished products produced by each device (which serves as the characteristic value of the stability analysis model based on the fault tree) and the pass rate of the final wafer finished product (as the predicted value of the stability analysis model based on the fault tree) are divided into training sets and test sets in a 1:1 ratio, that is, 50% is randomly divided as the training set and the remaining 50% is used as the test set. The division is repeated 10 times to reduce random errors.

[0125] (b) Initializing the parameters of the fault tree-based stability analysis model to obtain the initialized fault tree-based stability analysis model.

[0126] Specifically, the initial values ​​of all feature weights of the fault tree-based stability analysis model are set to 1, the initial learning rate of the model is 0.01, and a step-by-step learning strategy is adopted, multiplying the learning rate by 0.1 every 200 epochs.

[0127] (c) Inputting the training set obtained in step (a) into the fault tree-based stability analysis model initialized in step (b) to obtain the loss function value at this time, and calculating the gradient of each feature weight of the fault tree-based stability analysis model based on the loss function value.

[0128] Among them, the stability analysis model based on the fault tree uses the mean square error as the loss function, which is specifically expressed as:

[0129]

[0130] Where MSE is the mean square error, y k is the predicted value of the k-th training sample based on the stability analysis model of the fault tree, is the actual value of the kth training sample, that is, the qualified rate of the finished wafers in the kth training sample, and n is the number of samples in the training set. The gradient calculation method for the feature weights of the fault tree-based stability analysis model is to first calculate the partial derivative of each feature weight of the fault tree-based stability analysis model based on the MSE expression, obtaining the partial derivative calculation formula for each feature weight of the fault tree-based stability analysis model. Then, each training sample in the training set is traversed and sequentially imported into the partial derivative calculation formula for each feature weight calculated in the previous step, thereby obtaining the partial derivative value of each feature weight for each training sample. Finally, each feature weight is processed, and the partial derivative values ​​of the feature weight for each training sample are accumulated. The sum is divided by the number of training samples to calculate the average of the partial derivative values ​​of each feature weight, and the average value is used as the gradient of the feature weight.

[0131] (d) processing each feature weight using a gradient descent method according to the gradient of each feature weight of the fault tree-based stability analysis model obtained in step (2-3) to obtain a processed feature weight;

[0132] Specifically, the processing process of the gradient descent method is as follows: first, the gradient of each feature weight of the fault tree-based stability analysis model obtained in (c) is multiplied by the learning rate set in step (b), and the product is saved; then, each feature weight of the old fault tree-based stability analysis model is subtracted from the product to obtain a new feature weight.

[0133] (e) Repeat steps (b) and (e) until the loss function converges, and obtain a trained fault tree-based stability analysis model.

[0134] The advantage of this step is that it proposes a method to construct a fault tree diagram based on the production line, and on this basis proposes a stability analysis model based on the fault tree, rather than the previous method of manually constructing the fault tree diagram through experience, which reduces the human cost investment and increases the usability of the model.

[0135] Experimental results

[0136] This section illustrates the practical effect of this method through the test results on the wafer production data set provided by Hunan Chuwei Semiconductor Technology Co., Ltd. We selected one of the actual production lines to intuitively verify the accuracy of the model. The evaluation production line has a total of 17 devices with sensor recordings, and each device has 20 to 45 sensor parameters. The historical data of the sensor within a certain period of time is selected as input to predict the stability of the production line and compare it with the stability of the actual production line (with the qualified rate of finished wafers as a reference indicator). The results are as follows Figure 4 As shown:

[0137] It can be seen from the line graph that this stability model can accurately predict the stability of the production line at this time with high precision.

[0138] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for evaluating production line stability based on a fault tree, characterized in that: The following steps are involved: (1) Obtain multiple parameters of each device on the production line collected by the sensor of the device over a period of time, and calculate the process capability index corresponding to each parameter; (2) inputting the process capability index corresponding to each parameter of each device obtained in step (1) into a pre-trained multiple linear regression model to obtain the stability index of the device; (3) Input the stability index of each device obtained in step (2) into the pre-built stability analysis model based on the fault tree to obtain the final stability judgment result of the device; the construction process of the stability analysis model based on the fault tree is completed through the following steps: (3-1) Construct the root node of the fault tree and mark it as the node to be processed N (pre) ; (3-2) Set a counter a = m to represent the ath production link on the production line, and m represents the total number of production links on the production line; (3-3) Determine whether a is equal to 0. If so, proceed to step (3-15), otherwise proceed to step (3-4); (3-4) Determine whether there is only one device involved in the a-th production link. If so, proceed to step (3-5); otherwise, proceed to step (3-6); (3-5) Identify the fault event of the equipment involved in the a-th production link as the fault tree node C, and set C as the node N in the fault tree (pre) The child node of node N (pre) The connection relationship with node C is set as the AND gate relationship in the fault tree, and then go to step (3-12); (3-6) Grouping multiple devices involved in the a-th production link by type, and grouping devices of the same type into the same group, thereby obtaining M groups of devices, and proceeding to step (3-7); (3-7) Set counter b = 1, and then go to step (3-8); (3-8) Determine whether b is less than or equal to M. If so, proceed to step (3-9), otherwise proceed to step (3-12); (3-9) Add an intermediate node B to the fault tree for the entire group b equipment, indicating that a part of the group b equipment has a problem, and set the intermediate node B as node N in the fault tree. (pre) The child node of node N (pre) The connection relationship with node B is set as the AND gate relationship in the fault tree, and go to step (3-10); (3-10) Create a new leaf node in the fault tree for each device in group b. Each leaf node represents a problem with a part of the corresponding device. Set all newly created leaf nodes as child nodes of node B. Set the connection relationship between the leaf nodes and node B as an OR gate relationship in the fault tree, and go to step (3-11). (3-11) Set counter b=b+1 and return to step (3-8); (3-12) Add an intermediate node F to the fault tree, indicating that a failure event occurred in the previous a-1 production links, and set node F to N (pre) A child node of node N (pre) The connection relationship with node F is set as the AND gate relationship in the fault tree; (3-13) The node to be processed N (pre) Set to node F; (3-14) Set counter a=a-1 and return to step (3-3); (3-15) Delete node N in the fault tree (unvisited) , then go to step (3-16); (3-16) Based on the constructed fault tree diagram, the probability of occurrence of the top event is calculated, and the probability of occurrence of the top event is converted into the stability probability of the production line, that is, the final stability analysis model based on the fault tree is obtained.

2. The method for evaluating production line stability based on a fault tree according to claim 1, characterized in that: For each parameter in step (1), the corresponding process capability index is calculated according to the following formula: Where: C is the process capability index corresponding to the parameter, T is the specification value and USL is the upper limit of the parameter specified by the equipment manufacturer, LSL is the lower limit of the parameter specified by the equipment manufacturer, d is the specification width, and d = USL-LSL, t represents the time to obtain the parameter, a total of t sampling cycles, the intermediate parameter μ is the mean value, and σ is the standard deviation, and v i It represents the parameter value of the parameter obtained in the i-th sampling period, and i∈[1, the total number of sampling periods].

3. The method for evaluating production line stability based on a fault tree according to claim 1 or 2, characterized in that: The multiple linear regression model is trained through the following steps: (2-1) Obtain a wafer production dataset and divide the dataset into a training set and a test set; (2-2) Initializing the parameters of the multiple linear regression model to obtain an initialized multiple linear regression model; (2-3) inputting the training set obtained in step (2-1) into the multiple linear regression model initialized in step (2-2) to obtain the loss function value of the multiple linear regression model, and calculating the gradient of each feature weight of the multiple linear regression model based on the loss function value; (2-4) processing each feature weight using the gradient descent method based on the bias term of the multiple linear regression model and the gradient of each feature weight obtained in step (2-3) to obtain the processed bias term and each feature weight; (2-5) Repeat steps (2-3) and (2-4) until the loss function converges to obtain a trained multivariate linear regression model.

4. The method for evaluating production line stability based on a fault tree according to claim 3, characterized in that: Specifically, step (2-1) is to calculate the process capability index corresponding to the time series of each parameter of each device in the wafer production data set using the method of step (1) above, and divide the process capability indexes corresponding to all parameters in all devices and the qualified rate of semi-finished products produced by each device into training set and test set in a 1:1 ratio, that is, randomly divide 50% as the training set and the remaining 50% as the test set, and repeat the division 10 times to reduce random errors.

5. The method for evaluating production line stability based on a fault tree according to claim 3, characterized in that: The initial value of the weight parameter in step (2-2) is a random value output by a truncated normal distribution with a standard deviation of 0.

1. The initial value of the bias parameter is set to 0. The initial learning rate of the model is 0.

01. A step-by-step learning strategy is adopted with a step size of 200, that is, the learning rate is multiplied by 0.1 every 200 rounds. The multiple linear regression model is y=w1x1+w2x2+…+w n x n +b; where y is the predicted value of the qualified rate of semi-finished products produced by the equipment, that is, the stability of the equipment is predicted; n is the number of parameters of the equipment; {x1, x2, ..., x n } is the process capability index of each parameter of the equipment; the bias term b and all feature weights {w1,w2,…,w n } is learned through model training.

6. The method for evaluating production line stability based on a fault tree according to claim 3, characterized in that: The multiple linear regression model in step (2-3) uses the mean square error as the loss function, which is specifically expressed as: Among them, MSE is the mean square error, y k is the predicted value of the multiple linear regression model for the kth training sample, is the actual value of the kth training sample, that is, the qualified rate of the semi-finished products produced by this equipment, and n is the number of samples in the training set; The gradient calculation of the feature weight is to first calculate the partial derivative of the bias term and each feature weight according to the MSE expression to obtain the partial derivative calculation formula of the bias term and each feature weight; then, traverse each training sample in the training set, and import the partial derivative calculation formula of the bias term and each feature weight calculated in the previous step in turn to obtain the partial derivative value of the bias term and each feature weight for each training sample; finally, accumulate the partial derivative values ​​of the bias term and each feature weight for each training sample, divide the sum by the number of training samples, and calculate the average value of the partial derivative values ​​of the bias term and each feature weight, and use the average value as the gradient of the bias term and each feature weight.

7. The method for evaluating production line stability based on a fault tree according to claim 1, characterized in that: Step (3-16) is specifically to first obtain the occurrence probability expression of each leaf node: P(L s )=1-rR s , where L s represents the sth leaf node, P(L s ) represents the probability of occurrence of the sth leaf node, R s is the stable value of the device represented by the sth leaf node, and r is obtained by subsequent model training. Then, based on the occurrence probability of each leaf node and the gate probability transfer formula in the fault tree, the occurrence probability of the top event, that is, the failure probability of the production line, is calculated. Among them, the probability transfer formula of the AND gate is The probability transfer formula of the OR gate is P is the probability of occurrence of the parent node event, l means that the AND gate has l child nodes, N s represents the sth child node, and P(N s ) is the probability of occurrence of the sth child node event.

8. The method for evaluating production line stability based on a fault tree according to claim 1, characterized in that: The training process of the fault tree-based stability analysis model is completed through the following steps: (a) Obtain a wafer production dataset and divide it into a training set and a test set; (b) initializing parameters of the fault tree-based stability analysis model to obtain an initialized fault tree-based stability analysis model; (c) inputting the training set obtained in step (a) into the fault tree-based stability analysis model initialized in step (b) to obtain a loss function value at this time, and calculating the gradient of each feature weight of the fault tree-based stability analysis model based on the loss function value; Among them, the stability analysis model based on the fault tree uses the mean square error as the loss function, which is specifically expressed as: Among them, MSE is the mean square error, y k is the predicted value of the k-th training sample based on the stability analysis model of the fault tree, is the actual value of the kth training sample, that is, the qualified rate of the finished wafers in the kth training sample, and n is the number of samples in the training set; for the gradient calculation method of the feature weight of the fault tree-based stability analysis model, first, the partial derivative of each feature weight of the fault tree-based stability analysis model is calculated according to the MSE expression to obtain the partial derivative calculation formula of each feature weight of the fault tree-based stability analysis model; then, each training sample in the training set is traversed and sequentially imported into the partial derivative calculation formula of each feature weight calculated in the previous step, so as to obtain the partial derivative value of each feature weight for each training sample; finally, each feature weight is processed, the partial derivative value of the feature weight for each training sample is accumulated, the sum is divided by the number of training samples, and the average value of the partial derivative value of each feature weight is calculated, and the average value is used as the gradient of the feature weight; (d) processing each feature weight using a gradient descent method according to the gradient of each feature weight of the fault tree-based stability analysis model obtained in step (2-3) to obtain a processed feature weight; (e) Repeat steps (b) and (e) until the loss function converges, and obtain a trained fault tree-based stability analysis model.

9. A system for evaluating production line stability based on a fault tree, characterized in that: include: The first module is used to obtain multiple parameters of each device on the production line collected by the sensor of the device over a period of time, and calculate the process capability index corresponding to each parameter; The second module is used to input the process capability index corresponding to each parameter of each device obtained in the first module into a pre-trained multiple linear regression model to obtain the stability index of the device; The third module is used to input the stability index of each device obtained in the second module into the pre-built fault tree-based stability analysis model to obtain the final stability judgment result of the device. The construction process of the fault tree-based stability analysis model is completed through the following steps: (3-1) Construct the root node of the fault tree and mark it as the node to be processed N (pre) ; (3-2) Set a counter a = m to represent the ath production link on the production line, and m represents the total number of production links on the production line; (3-3) Determine whether a is equal to 0. If so, proceed to step (3-15), otherwise proceed to step (3-4); (3-4) Determine whether there is only one device involved in the a-th production link. If so, proceed to step (3-5); otherwise, proceed to step (3-6); (3-5) Identify the fault event of the equipment involved in the a-th production link as the fault tree node C, and set C as the node N in the fault tree (pre) The child node of node N (pre) The connection relationship with node C is set as the AND gate relationship in the fault tree, and then go to step (3-12); (3-6) Grouping multiple devices involved in the a-th production link by type, and grouping devices of the same type into the same group, thereby obtaining M groups of devices, and proceeding to step (3-7); (3-7) Set counter b = 1, and then go to step (3-8); (3-8) Determine whether b is less than or equal to M. If so, proceed to step (3-9), otherwise proceed to step (3-12); (3-9) Add an intermediate node B to the fault tree for the entire group b equipment, indicating that a part of the group b equipment has a problem, and set the intermediate node B as node N in the fault tree. (pre) The child node of node N (pre) The connection relationship with node B is set as the AND gate relationship in the fault tree, and go to step (3-10); (3-10) Create a new leaf node in the fault tree for each device in group b. Each leaf node represents a problem with a part of the corresponding device. Set all newly created leaf nodes as child nodes of node B. Set the connection relationship between the leaf nodes and node B as an OR gate relationship in the fault tree, and go to step (3-11). (3-11) Set counter b=b+1 and return to step (3-8); (3-12) Add an intermediate node F to the fault tree, indicating that a failure event occurred in the previous a-1 production links, and set node F to N (pre) A child node of node N (pre) The connection relationship with node F is set as the AND gate relationship in the fault tree; (3-13) The node to be processed N (pre) Set to node F; (3-14) Set counter a=a-1 and return to step (3-3); (3-15) Delete node N in the fault tree (unvisited) , then go to step (3-16); (3-16) Based on the constructed fault tree diagram, the probability of occurrence of the top event is calculated, and the probability of occurrence of the top event is converted into the stability probability of the production line, that is, the final stability analysis model based on the fault tree is obtained.

Images