Quality online monitoring method for multivariate nonlinear process data

Abstract

The invention discloses an online quality monitoring method for multivariate nonlinear process data, and belongs to the technical field of quality control. The method aims at solving the problem that a traditional quality monitoring method is based on linear hypothesis and single variable analysis, and multivariate nonlinear process data cannot be effectively processed. The method comprises two stages: a first stage, collecting historical controlled data, calculating a local statistical feature of each sample by using a k-nearest neighbor method, further calculating a local mahalanobis distance and a sample depth, constructing a monitoring statistical magnitude through a depth rank, and determining a quality control limit by using Monte Carlo simulation; in the second stage, new samples are collected in real time, and the statistical magnitude of the new samples is calculated and compared with the quality control limit. And if the statistic exceeds the control limit, determining that the process is out of control and giving an alarm. The method has a non-parametric characteristic, does not depend on data distribution hypothesis, can accurately capture a complex non-linear relationship between variables, and realizes efficient and accurate online quality monitoring of a multivariate process.

Description

Technical Field

[0001] This invention belongs to the field of quality control and monitoring technology, and relates to a production quality management method based on statistical process control. Specifically, it relates to an online quality monitoring method for multivariate nonlinear process data, which is particularly applicable to quality monitoring in industries such as industry, medicine, and services where multivariate nonlinear observations coexist. Background Technology

[0002] In modern industry, healthcare, and service sectors, the importance of quality monitoring is increasingly prominent as production processes and service quality become more complex. Traditional quality monitoring methods are mostly based on linear assumptions and single-variable analysis, typically only able to handle limited linear relationships. With advancements in data acquisition technology, enterprises can collect vast amounts of multidimensional data, encompassing not only product physical characteristics but also production environment, operating conditions, and human-machine interaction. Existing quality monitoring methods often cannot handle the complex relationships between multiple variables and struggle to meet the analytical needs of multivariate nonlinear process data. Especially in multivariate nonparametric scenarios, the relationships between various quality characteristics often exhibit complex nonlinear features, making it difficult for traditional statistical process control methods to effectively identify and control quality fluctuations. This leads to potential quality problems being difficult to detect and resolve in a timely manner, mainly manifested in the following aspects:

[0003] 1. Limitations of the linear assumption: Traditional quality control methods are usually based on linear models, which cannot adapt to the analysis needs of multivariate nonlinear data. This limitation makes the monitoring results often inaccurate and unable to effectively reflect the actual quality status when complex relationships exist.

[0004] 2. Single-variable analysis: Many existing methods focus on monitoring a single variable, neglecting the interactions between multiple quality characteristics. This approach is prone to missing important quality information in multivariate nonlinear environments, creating blind spots in quality control.

[0005] 3. Lack of real-time capability: Existing technologies struggle to achieve real-time online monitoring when processing large-scale data, making it difficult to provide timely feedback on anomalies in the production process and reducing the response speed to quality issues.

[0006] 4. Insufficient nonparametric analysis: Although some methods can handle nonlinear relationships, there is still a lack of effective tools and methods for nonparametric data analysis, making it difficult to fully capture the information in the data.

[0007] 5. Complexity and operability: Although some advanced statistical methods can handle nonlinear relationships, their complexity and high skill requirements for users make them difficult to operate in practice, which limits their widespread adoption in production.

[0008] In this context, effectively monitoring and analyzing multivariate nonlinear process data in real time has become a major challenge in quality management. Summary of the Invention

[0009] To address the shortcomings of existing technologies in quality monitoring of multivariate nonlinear process data, which limit the effectiveness and flexibility of enterprise quality management, this invention provides an online quality monitoring method for multivariate nonlinear process data. By introducing a highly adaptable nonlinear model, it can simultaneously process multiple quality characteristics, accurately capture and analyze the complex relationships between various quality characteristics in multivariate nonlinear process data, comprehensively reflect the quality status in the production process, and ensure the accuracy and reliability of monitoring results.

[0010] The objective of this invention is achieved through the following technical solution:

[0011] A method for online quality monitoring of multivariate nonlinear process data includes the following steps:

[0012] Phase 1: Calculate the quality control limit (UCL) using controlled data.

[0013] S1. Sample preparation: Collect a large amount of controlled data as a sample, and collect corresponding quality characteristic data according to the different monitoring objects of the controlled data;

[0014] S2. Determine the nearest neighbors of the sample: For each sample collected in step S1, find K nearest neighbors;

[0015] S3. Calculate the local metrics of the samples, including the local mean vector, local covariance matrix, local Mahalanobis distance, depth, and depth rank for each sample;

[0016] S4. Construct statistics by converting the depth rank of the sample calculated in step S3 into statistics;

[0017] S5. Simulate the quality control limit (UCL) using controlled data;

[0018] Phase Two: Real-time collection of product data, and monitoring of product quality through the aforementioned quality control limits (UCLs):

[0019] S6. Collect real-time sample data, and repeat step S2 to determine the K nearest neighbors of the real-time sample;

[0020] S7. Repeat step S3 to calculate the local index of the real-time sample and compare the depth value of the real-time sample with the depth value of each of the controlled samples.

[0021] S8. Repeat step S4 to calculate the statistics for the real-time sample;

[0022] S9. Based on the statistics obtained in step S8, draw a control chart to monitor product quality in real time.

[0023] Furthermore, in step S1, the collected controlled data is Y = Y 1i ,Y 2i ,…,Y pi , i = 1, 2, ..., n, where n represents the number of samples, and p is the quality feature collected for each sample.

[0024] Furthermore, step S3 specifically includes:

[0025] Calculate the local mean vector Y for each sample. K :

[0026]

[0027] Among them, Y l It is the i-th sample Y i The l-th sample among K nearest neighbors;

[0028] Calculate the i-th sample Y i The local covariance matrix S K (Y i ):

[0029]

[0030] Calculate the i-th sample Y i Local Mahalanobis distance d K (Y i ):

[0031]

[0032] Calculate the i-th sample Y i AMD (Y) depth i ):

[0033] AMD(Y i )=1 / (1+d K (Y i ));

[0034] Calculate the i-th sample Y i Depth Rank r-AMD(Y i ):

[0035]

[0036] in, This is an indicator function, representing the condition that if the depth value of the sample is r - AMD(Y) i ) is greater than or equal to the depth value of other samples AMD(Y) jIf the value is 1, then the indicator function is 1; otherwise, the indicator function is 0.

[0037] Furthermore, in step S4, the statistic Z of the controlled data is calculated. n :

[0038] Z n =(1-λ)Z n-1 +λR n

[0039] Among them, Z n-1 R is the statistic of the (n-1)th sample. n =1-(r-AMD(Y) i )), R n λ is the observation value of the nth sample, and λ is the smoothing parameter.

[0040] Further, step S5 includes:

[0041] S51. Set the median running length (ICMRL) of the product under controlled conditions;

[0042] S52. The quality control limit (UCL) is simulated for the controlled data using the Monte Carlo simulation method.

[0043] Further, step S52 includes:

[0044] Define the required parameter as the median of the run length;

[0045] Calculate the corresponding statistics based on the controlled data;

[0046] Set initial control limits and repeat this process through multiple simulations, recording the length of time the operation exceeds the control limits in each simulation;

[0047] Calculate the median length of operation that exceeds the control limits, and use this information to adjust and determine the final control limits.

[0048] Furthermore, in step S9, the quality of real-time production of the product is monitored based on the statistics of the real-time sample and the control limit UCL calculated in step one. If the statistics are greater than or equal to the control limit, the control chart issues an alarm.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] Effective handling of nonlinear relationships and high monitoring accuracy: This invention abandons the traditional global linear assumption by introducing a k-nearest neighbor local modeling method. By calculating the mean, covariance, and Mahalanobis distance of each sample in its local nearest neighbor space, it can accurately capture and describe the complex nonlinear correlations between multiple quality characteristics, thereby greatly improving the accuracy and reliability of quality monitoring and avoiding false alarms and missed alarms caused by inappropriate model assumptions.

[0051] True multi-dimensional monitoring, avoiding information blind spots: The method of this invention simultaneously performs a holistic analysis of multiple quality characteristics, comprehensively evaluating the interactions between multiple variables through local Mahalanobis distance and data depth. This overcomes the shortcomings of traditional single-variable analysis methods that neglect the mutual influence between variables, comprehensively reflecting the quality status of the production process and completely eliminating quality control blind spots in a multi-dimensional environment.

[0052] Achieving online real-time monitoring with rapid response: The method's structural design is suitable for online real-time applications. Once the control limits are calculated based on historical controlled data, monitoring subsequent new samples only requires simple distance calculations and comparisons, resulting in high computational efficiency. It can instantly issue alerts for abnormal fluctuations in the production process, significantly improving the response speed and timeliness of handling quality issues.

[0053] Powerful nonparametric analysis capabilities and wide applicability: The core of this invention is based on nonparametric statistics such as data depth and depth rank, requiring no prior assumptions about the distribution of process data (such as normal distribution). This method works effectively for data with normal, skewed, or other complex distributions, exhibiting strong robustness and wide applicability, thus overcoming the shortcomings of traditional parametric methods in nonparametric data analysis.

[0054] The concept is intuitive, highly operable, and easy to promote: Although the algorithm itself is advanced, its core idea (finding nearest neighbors and comparing the degree of "alternativeness") is very intuitive. The control limits are determined through Monte Carlo simulation, and the objective is clear (controlling ARL0). The entire scheme has clear steps and is easy to implement in common software such as R and Python, reducing the technical threshold for deployment and application in actual production environments, and has good operability and promotion value. Attached Figure Description

[0055] Figure 1 This is a flowchart of an online quality monitoring method for multivariate nonlinear process data as described in this invention.

[0056] Figure 2 This is a cigarette quality control chart and control limit statistics chart in an embodiment of the present invention. Detailed Implementation

[0057] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments:

[0058] A method for online quality monitoring of multivariate nonlinear process data, such as Figure 1 As shown, it includes the following steps:

[0059] Phase 1: Calculate the quality control limit (UCL) using controlled data.

[0060] S1. Sample Preparation

[0061] Relevant staff collected a large amount of controlled data (data on qualified products) as a sample, and collected corresponding quality characteristic data according to different monitoring objects of the controlled data. The collected controlled data is Y = Y 1i ,Y 2i ,…,Y pi , i = 1, 2, ..., n, where n represents the number of samples, and p is the quality feature collected for each sample.

[0062] S2. Determine the nearest neighbors of the sample

[0063] Because there is usually a non-linear correlation between various quality characteristics, the K-nearest neighbor method is introduced to narrow the sample range and reduce the impact of the non-linear correlation between various quality characteristics on product quality.

[0064] For the n samples collected in step S1, the number of nearest neighbors for each sample is: Find the K nearest neighbors of each sample, calculate the Euclidean distance between each pair of samples, and find the K nearest neighbors of each sample from the distances to other samples.

[0065] S3. Calculate local indices of the sample.

[0066] Calculate the local mean vector for each sample.

[0067]

[0068] Among them, Y l It is the i-th sample Y i The l-th sample among K nearest neighbors;

[0069] Calculate the i-th sample Y i The local covariance matrix S K (Y i ):

[0070]

[0071] Calculate the i-th sample Y i Local Mahalanobis distance d K (Y i ):

[0072]

[0073] Calculate the i-th sample Y i AMD (Y) depth i ):

[0074] AMD(Y i )=1 / (1+d K (Y i ));

[0075] Calculate the i-th sample Y i Depth Rank r-AMD(Y i ):

[0076]

[0077] in, This is an indicator function, representing the condition that if the depth value of the sample is r - AMD(Y) i ) is greater than or equal to the depth value of other samples AMD(Y) j If the value is 1, then the indicator function is 1; otherwise, the indicator function is 0.

[0078] S4. Construct statistics: Convert the depth rank calculated in step S3 into statistics.

[0079] Calculate the statistic Z of the controlled data n :

[0080] Z n =(1-λ)Z n-1 +λR n

[0081] Among them, Z n-1 R is the statistic of the (n-1)th sample. n =1-(r-AMD(Y) i )), R n λ is the observation value of the nth sample, and λ is the smoothing parameter of the control chart. In this embodiment, λ is 0.03.

[0082] S5. Determine the quality control limits (UCLs) through simulation of controlled data.

[0083] S51. Based on experience, set the median running length (ICMRL) of the product under controlled conditions. This means that we want to obtain a control limit (UCL) such that the statistics of our controlled product exceed the median running length of the control limit.

[0084] S52. Simulate the quality control limit (UCL) of the controlled data using the Monte Carlo simulation method, including the following steps:

[0085] Define the required parameters, such as the median of the run length;

[0086] Calculate the corresponding statistics based on the controlled data;

[0087] Set initial control limits and repeat this process through multiple simulations (e.g., 20,000 times), recording the length of time the operation exceeds the control limits in each simulation;

[0088] The median of these run lengths is calculated to adjust and determine the final control limits, thereby effectively identifying controlled and uncontrolled states. This process can be implemented in the R programming language.

[0089] Phase Two: Collect product data in real time and monitor product quality.

[0090] S6. Collect real-time sample data

[0091] Relevant staff collect product quality characteristic data in real time as real-time samples, calculate the Euclidean distance between samples, and find the K nearest neighbors for each sample.

[0092] S7. Calculate local indices for real-time samples

[0093] Repeat step S3 to calculate the local mean vector, local covariance matrix, local Mahalanobis distance, depth, and depth rank of the real-time sample, respectively.

[0094] The depth value of the real-time sample is compared with the depth value of each of the controlled samples;

[0095] In this step, the depth rank indicator function indicates that if the depth value of the real-time sample is greater than or equal to the depth value of the controlled sample, the indicator function is 1; otherwise, it is 0.

[0096] S8. Repeat step S4 to calculate the statistics for the real-time sample.

[0097] S9. Based on the statistics obtained in step S8, draw a control chart to monitor product quality in real time.

[0098] Based on the statistics of real-time samples and the control limits (UCLs) calculated in step one, the quality of real-time product production is monitored. If the statistics are greater than or equal to the control limits, the control chart will issue an alarm, reminding relevant personnel to check in a timely manner and take relevant quality improvement measures.

[0099] The following are examples of implementations of the present invention:

[0100] Taking the tobacco quality data of a tobacco manufacturing company as an example, 60 controlled data points were collected as sample data for Phase 1, as shown in Table 1. Following the method provided in this invention, 60 monitoring data points were obtained for Phase 2. The control limits (UCLs) and control chart statistics for monitoring cigarette quality were calculated, as shown in Table 2. Figure 2 As shown.

[0101] Table 1. Tobacco quality data of a tobacco manufacturing company in Phase 1.

[0102]

[0103]

[0104] Table 2. Phase II Tobacco Quality Data of a Tobacco Manufacturing Company

[0105]

[0106]

[0107] from Figure 2 As can be seen, the method provided by this invention can detect statistical quantities exceeding control limits in a timely manner at the initial stage of the process, identify quality problems in cigarette products, and issue timely alarms, so that relevant personnel can take corresponding quality measures.

Claims

1. A method for online quality monitoring of multivariate nonlinear process data, characterized in that, Includes the following steps: Phase 1: Calculate the quality control limit (UCL) using controlled data. S1. Sample preparation: Collect a large amount of controlled data as a sample, and collect corresponding quality characteristic data according to the different monitoring objects of the controlled data; S2. Determine the nearest neighbors of the sample: For each sample collected in step S1, find K nearest neighbors; S3. Calculate the local metrics of the samples, including the local mean vector, local covariance matrix, local Mahalanobis distance, depth, and depth rank for each sample; S4. Construct statistics by converting the depth rank of the sample calculated in step S3 into statistics; S5. Simulate the quality control limit (UCL) using controlled data; Phase Two: Real-time collection of product data, and monitoring of product quality through the aforementioned quality control limits (UCLs): S6. Collect real-time sample data, and repeat step S2 to determine the K nearest neighbors of the real-time sample; S7. Repeat step S3 to calculate the local index of the real-time sample and compare the depth value of the real-time sample with the depth value of each of the controlled samples. S8. Repeat step S4 to calculate the statistics for the real-time sample; S9. Based on the statistics obtained in step S8, draw a control chart to monitor product quality in real time.

2. The online quality monitoring method for multivariate nonlinear process data as described in claim 1, characterized in that, In step S1, the collected controlled data is Y = Y 1i ,Y 2i ,…,Y pi , i = 1, 2, ..., n, where n represents the number of samples, and p is the quality feature collected for each sample.

3. The online quality monitoring method for multivariate nonlinear process data as described in claim 1, characterized in that, Step S3 specifically includes: Calculate the local mean vector for each sample. Among them, Y l It is the i-th sample Y i The l-th sample among K nearest neighbors; Calculate the i-th sample Y i The local covariance matrix S K (Y i ): Calculate the i-th sample Y i Local Mahalanobis distance d K (Y i ): Calculate the i-th sample Y i AMD (Y) depth i ): AMD(Y i )=1 / (1+d K (Y i )); Calculate the i-th sample Y i Depth Rank r-AMD(Y i ): in, This is an indicator function, representing the condition that if the depth value of the sample is r - AMD(Y) i ) is greater than or equal to the depth value of other samples AMD(Y) j If the value is 1, then the indicator function is 1; otherwise, the indicator function is 0.

4. The online quality monitoring method for multivariate nonlinear process data as described in claim 1, characterized in that, In step S4, the statistic Z of the controlled data is calculated. n : WITH n =(1-λ)Z n-1 +λR n Among them, Z n-1 R is the statistic of the (n-1)th sample. n =1-(r-AMD(Y) i )), R n λ is the observation value of the nth sample, and λ is the smoothing parameter.

5. The online quality monitoring method for multivariate nonlinear process data as described in claim 1, characterized in that, Step S5 includes: S51. Set the median running length (ICMRL) of the product under controlled conditions; S52. The quality control limit (UCL) is simulated for the controlled data using the Monte Carlo simulation method.

6. The online quality monitoring method for multivariate nonlinear process data as described in claim 1, characterized in that, Step S52 includes: Define the required parameter as the median of the run length; Calculate the corresponding statistics based on the controlled data; Set initial control limits and repeat this process through multiple simulations, recording the length of time the operation exceeds the control limits in each simulation; Calculate the median length of operation that exceeds the control limits, and use this information to adjust and determine the final control limits.

7. The online quality monitoring method for multivariate nonlinear process data as described in claim 1, characterized in that, In step S9, the quality of real-time production of the product is monitored based on the statistics of the real-time sample and the control limit UCL calculated in step one. If the statistics are greater than or equal to the control limit, the control chart issues an alarm.

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