A design method of a control chart and a data analysis system

Abstract

The application provides a control chart design method and a data analysis system, including obtaining sample data, generating a sample data set, and generating an EWMA statistic based on an EWMA control chart; calculating the mean of the sample data; dividing the sample data into a first part and a second part according to the mean of the sample data, respectively performing symmetric processing on the first part and the second part to construct corresponding first normal distribution and second normal distribution, and respectively calculating the first normal distribution variance and the second normal distribution variance; calculating the distribution probability of the sample data being less than the mathematical expectation of the sample data set; determining the control limit according to the first normal distribution variance, the second normal distribution variance and the distribution probability; drawing the control limit of the control chart according to the control limit, determining the position of the EWMA statistic in the control chart, and generating the control chart. The control chart proposed in the application does not require the data to meet the normal distribution requirement, and can be widely applied to quality control of intelligent manufacturing processes.

Description

Technical Field

[0001] This invention relates to the technical field of control charts, and more particularly to a control chart design method and data analysis system. Background Technology

[0002] In intelligent manufacturing environments, data is characterized by its large volume, multiple sources, and heterogeneity, resulting in widespread non-normality and rendering traditional control charts inapplicable. Currently, mainstream research on how to use control charts in non-normal data environments is divided into two schools of thought.

[0003] One approach is to transform the data itself into normally distributed data using formulas. For example, the paper "A Bayesian Dynamic Quality Control Method for Multi-variety Small-batch Production" uses the Johnson distribution system to transform non-normal data, making it applicable to conventional control charts. However, this type of method cannot guarantee whether the transformation of the data itself has changed the inherent quality characteristics of the data, thus risking that the data itself loses its meaning.

[0004] Secondly, new control charts applicable to non-normal data are constructed based on control chart principles. For example, the paper "A Variable Sampling Interval EWMA Distribution-Free Control Chart for Monitoring Services Quality" proposes a novel arcsine Shewhart sign and variable sampling interval EWMA (exponentially weighted moving average) distribution-free control chart, which can ignore the data distribution. These methods, starting from the perspective of control charts, use new tools for analysis, ensuring the inherent quality characteristics of the data. However, these methods do not consider the large volume, multiple sources, and small fluctuations of data in the context of intelligent manufacturing. Furthermore, these methods are relatively complex, making them difficult for enterprises to implement quickly, resulting in poor research implementation outcomes. Summary of the Invention

[0005] In view of this, the present invention provides a control chart design method and a data analysis system, which solves the problem that conventional control charts are not applicable to non-normal data, provides a new approach for product process quality control, and also improves the detection efficiency of control charts.

[0006] To achieve the above objectives, the present invention provides a method for designing control charts, the method comprising the following steps:

[0007] S1. Obtain sample data, generate sample dataset, and generate EWMA statistics based on EWMA control charts;

[0008] S2. Constructing control limits based on the probability-weighted variance method;

[0009] S3. Draw the control limits of the control chart according to the control limits, determine the position of the EWMA statistic in the control chart, and generate the control chart;

[0010] Step S2 includes:

[0011] S201. Calculate the mean of the sample data;

[0012] S202. Based on the mean of the sample data, the sample data is divided into a first part that is greater than the mean of the sample data and a second part that is less than the mean of the sample data. The first part is symmetrically processed to construct a first normal distribution, and the second part is symmetrically processed to construct a second normal distribution. The variance of the first normal distribution relative to the mean of the sample data is calculated to obtain the variance of the first normal distribution, and the variance of the second normal distribution relative to the mean of the sample data is calculated to obtain the variance of the second normal distribution.

[0013] S203. Calculate the probability distribution of sample data being less than the expected value of the sample dataset;

[0014] S204. Determine the control limit based on the variance of the first normal distribution, the variance of the second normal distribution, and the distribution probability.

[0015] Furthermore, the population variance of the sample data is expressed as: σ x 2 =σ L 2 +σ R 2

[0016] The variance of the first normal distribution is expressed as: 2σ L 2

[0017] Based on the aforementioned probability distribution, the variance of the first portion of the sample data is expressed as:

[0018] σ 上 2 =2P X σ L 2

[0019] The variance of the second normal distribution is expressed as: 2σ R 2

[0020] Based on the aforementioned probability distribution, the variance of the second part of the sample data is expressed as:

[0021] σ 下 2 =2(1-P) X )σ R2 ;

[0022] In the formula, P X This represents the probability distribution of the sample data being less than the mathematical expectation of the sample dataset.

[0023] Furthermore, the control limit is expressed by the following formula:

[0024]

[0025] In the formula, UCL represents the upper control limit, LCL represents the lower control limit, CL represents the average of the upper and lower control limits, μ represents the average of the sample data, and P x λ represents the probability that the sample data is less than the mathematical expectation of the sample dataset, λ represents the smoothing parameter, n represents the number of samples in a single sampling, and k represents the quantile, which is determined by the significance level of the control limit.

[0026] Furthermore, the significance level is greater than or equal to 0.95.

[0027] Furthermore, the smoothing parameter is greater than or equal to 0.1 and less than or equal to 0.5.

[0028] Furthermore, the method also includes the following steps for correcting the control limit:

[0029] S401. Calculate the average running chain length of the control chart under different smoothing coefficients based on the Monte Carlo simulation method;

[0030] S402. Determine the optimal smoothing parameters based on the average running chain length of the control chart under different smoothing coefficients;

[0031] S403. Correct the control limit according to the optimal smoothing parameter.

[0032] Furthermore, the Monte Carlo simulation method includes:

[0033] S501. Generate N random numbers that approximate the distribution of the sample data;

[0034] S502. Based on the N random numbers and according to the probability-weighted variance method, construct control limits;

[0035] S503. Based on the N random numbers and the EWMA control chart, generate EWMA statistics;

[0036] S504. Compare the EWMA statistic with the control limit and record the number of times the EWMA statistic is out of control.

[0037] S505. Repeat steps S501 to S504 to calculate the average running chain length, which is calculated using the following formula:

[0038]

[0039] In the formula, ARL represents the average running chain length, β represents the number of times the system went out of control, m represents the number of repetitions, and N represents the number of random numbers.

[0040] Furthermore, in step S402, the smoothing parameter corresponding to the average running chain length at the center is selected as the optimal smoothing parameter.

[0041] Furthermore, the EWMA statistic is expressed as follows:

[0042]

[0043] In the formula, Z i Let represent the i-th EWMA statistic, and λ represent the smoothing parameter. This represents the mathematical expectation of the sample dataset.

[0044] The present invention also provides a data analysis system, the analysis system comprising:

[0045] The sample acquisition module is used to collect sample data during the product manufacturing process and generate a sample dataset.

[0046] The data analysis module, based on the control chart design method according to any one of claims 1 to 9, and in conjunction with the sample data, calculates and plots the control limits of the control chart, and determines the position of the EWMA statistic of the sample data in the control chart;

[0047] The data analysis module determines the positional relationship between the EWMA statistic on the control chart and the control limits, and analyzes the sample data based on the positional relationship.

[0048] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0049] This application provides a control chart design method and data analysis system, combining the probability weighted variance method with EWMA control charts to offer a new approach to quality control in intelligent manufacturing. It addresses the issue of conventional EWMA control charts being inapplicable when data is non-normal, allowing for the neglect of non-normal data distribution and direct quality monitoring of the current data, thereby improving the efficiency of data monitoring. Attached Figure Description

[0050] Figure 1This is a schematic diagram of the design process of a control chart provided in the embodiments of this application;

[0051] Figure 2 This is a schematic diagram of the design process of a control chart provided in the embodiments of this application;

[0052] Figure 3 This is a schematic diagram illustrating the principle of the probability-weighted variance method provided in the embodiments of this application;

[0053] Figure 4 This is a schematic diagram of the design process of a control chart provided in the embodiments of this application;

[0054] Figure 5 This is a schematic diagram illustrating the probability weighted variance EWMA control chart capability under different λ values ​​provided in the embodiments of this application;

[0055] Figure 6 This is a schematic diagram of the design process of a control chart provided in the embodiments of this application;

[0056] Figure 7 This is a schematic diagram of a data analysis system provided in an embodiment of this application;

[0057] Figure 8 This is a data analysis diagram of a specific embodiment provided in this application.

[0058] Figure 9 This is an Xbar-R control chart of a specific embodiment provided in this application.

[0059] Figure 10 This is a conventional EWMA control diagram of a specific embodiment provided in this application.

[0060] Figure 11 This is a probability weighted variance EWMA control chart of a specific embodiment provided in this application. Detailed Implementation

[0061] The present application will be described in detail below with reference to the specific embodiments shown in the accompanying drawings. However, these embodiments do not limit the present application. Any structural, methodological, or functional modifications made by those skilled in the art based on these embodiments are included within the protection scope of the present application.

[0062] like Figure 1 As shown in one embodiment of the present invention, the present invention provides a method for designing control charts, the method comprising:

[0063] S1. Obtain sample data, generate sample dataset, and generate EWMA statistics based on EWMA control charts;

[0064] S2. Constructing control limits based on the probability-weighted variance method;

[0065] S3. Draw the control limits of the control chart based on the control limits, determine the position of the EWMA statistic on the control chart, and generate the control chart.

[0066] In step S1, a random variable X can be used as sample data to generate a sample dataset with a probability distribution function of f(X), a process mean of μ, and a variance of σ. 2 The EWMA statistic is:

[0067]

[0068] Where λ is the smoothing parameter, 0 < λ < 1, Z0 = μ. n is the number of subgroups, generally n>25, and m is the size of the subgroup.

[0069]

[0070] Using the above formula, Z i By performing a transformation, it can be determined The smoothing parameter is λ, and the ij-th... The smoothing parameter is λ(1-λ). j j = 1, 2, ... i, confirm Z i Mathematical expectation:

[0071]

[0072] Z i The variance is expressed as follows.

[0073]

[0074] When i is large, (1-λ) 2i It will gradually approach 0, at which point The initial value of EWMA, Z0, is taken as E(X) = μ, Z i This represents the weighted average of all data, and the weight λ(1-λ) can be demonstrated through reasoning. j As the index j in data ij increases, the weight decreases exponentially, meaning that the farther away a data point is from the current data, the smaller its weight becomes.

[0075] Based on the above analysis, it can be seen that EWMA control charts can be constructed with specific attributes by changing the weights used and the number of standard deviations of the control limits, which is more in line with the large volume, multiple sources, and heterogeneous nature of data in the context of intelligent manufacturing.

[0076] For a traditional EWMA control chart, the control limits can be expressed as:

[0077]

[0078] As can be seen from the control limit expression of the traditional EWMA control chart, the control limits of the traditional EWMA control chart require normal data as input. If non-normal data is directly applied for analysis, certain errors will occur.

[0079] This application embodiment constructs statistics using the EWMA method to amplify data fluctuations and address the issue of small data fluctuations in intelligent manufacturing environments; it constructs non-normal sample data into two normally distributed data sets using the probability weighted variance method and calculates control limits; and it generates control charts based on the control limits and the position of the EWMA statistics on the control chart.

[0080] like Figure 2 As shown, step S2 includes:

[0081] S201. Calculate the mean of the sample data;

[0082] S202. Based on the mean of the sample data, divide the sample data into a first part that is greater than the mean of the sample data and a second part that is less than the mean of the sample data. Perform symmetrical processing on the first part to construct a first normal distribution, and perform symmetrical processing on the second part to construct a second normal distribution. Calculate the variance of the first normal distribution relative to the mean of the sample data to obtain the variance of the first normal distribution, and calculate the variance of the second normal distribution relative to the mean of the sample data to obtain the variance of the second normal distribution.

[0083] S203. Calculate the probability distribution of sample data being less than the expected value of the sample dataset;

[0084] S204. Determine the control limits based on the variances of the first and second normal distributions, and in conjunction with the distribution probability.

[0085] As an optional implementation method, the probabilistic weighted variance method is primarily based on the characteristics of biased distributions in the data. For example... Figure 3 As shown, in this embodiment of the application, the sample data A is right-skewed. First, the mean of the sample data A is obtained by calculation, which is μ. Then, according to the probability weighted variance method, the non-normal data A is divided into two parts from the mean μ, which are the first part greater than the sample mean μ and the second part less than the sample mean μ.

[0086] The first part is symmetrically processed by filling in the other side of the symmetrical section at μ, resulting in data C belonging to a normal distribution. The second part is then symmetrically processed by filling in the other side of the symmetrical section at μ, resulting in data B belonging to a normal distribution. At this point, the non-normal sample data A has become two normally distributed data points, C and B. The mean of the normal distribution C and the normal distribution B are the same, both being the mean μ of the original sample data A.

[0087] The variance of the first normal distribution is obtained by calculating the variance of the first normal distribution relative to the sample data mean μ, and the variance of the second normal distribution is obtained by calculating the variance of the second normal distribution relative to the sample data mean μ.

[0088] Dividing the sample data into two different normal distributions is primarily for constructing the upper and lower control limits of the control chart respectively. According to the method provided in this application, in step S203, the probability distribution P(X<μ) = P0 of the sample data being less than the mathematical expectation of the sample dataset is calculated. X .

[0089] In step S204, based on the variance of the first normal distribution, the variance of the second normal distribution, and combined with the probability distribution P... X Determining the control limits of the control chart can solve the problem of overall non-normality, making the setting of control chart parameters more reasonable.

[0090] To further illustrate the specific process of the probability weighted variance method in step S2, the following explanation will be provided in conjunction with specific calculations:

[0091] The skewed distribution has a proportional problem between the left and right sides. Therefore, this application transforms the proportion into a probability factor by assigning probability weights to the two reconstructed normal distributions.

[0092] Assume the probability distribution function of the normal distribution is φ(X), and the probability density function is... The sample data comes from another distribution, with the random variable X. Let the probability distribution function of this distribution be F(X), the probability density function be f(X), and the expected value and variance of X be E(X) = μ and D(X) = σ, respectively. 2 The probability that a random variable X is less than its expected value is P(X<μ) = P X .

[0093] When using the probability-weighted variance method, the probability density function f(X) of the sample data first needs to be divided into two parts at the mean. These two parts are then treated as components of two normal distributions and completed, denoted as f0, f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f2, f3, f4, f5, f6, f7, f8, f9, f10, f2 L (X) and f R (X). Two normal distributions, both with mean μ and variances 2σ. L 2 and 2σ R 2 After determining the basic parameters, the two normal distributions are standardized using the following formulas:

[0094]

[0095]

[0096] The control limits for a standard Shewhart control chart are constructed using the sample mean plus or minus three standard deviations. The probability-weighted variance method (PWMA) uses a similar approach to construct control limits. However, because the PWMA divides the data into two normal distributions based on left and right probabilities, the PWMA control chart constructed using this method requires multiplying by a semi-variance probability factor when calculating the control limits.

[0097] That is, assume σ x 2 It is the entire region of the original sample data relative to μ under f(x). x Let σ be the variance. L 2 For μ x The above region (i.e., the first part) is relative to μ x Let σ be the variance. R 2 For μ x The following region (i.e., the second part) is relative to μ x The variance.

[0098] Then σ x 2 =σ L 2 +σ R 2 .

[0099] If the original sample data is symmetrically distributed, then σ L 2 =σ R 2 =σ x 2 / 2.

[0100] However, since the current non-normal distribution has a certain skew, the left side of the distribution can be simply approximated as P. X σ L 2 The right side of the distribution can be simply approximated as (1-P) X )σ R 2 By multiplying by a semivariance probability factor, these approximations can be very robust even for highly skewed distributions and are accurate when f(x) is symmetric.

[0101] Based on the above explanation, the variance of the normal distribution reconstructed in the upper region (i.e., the first part) can be expressed as:

[0102] σ 上 2 =2P X σ L 2 .

[0103] The variance of the normal distribution reconstructed in the lower half of the region (i.e., the second part) can be expressed as:

[0104] σ 下 2 =2(1-P) X )σ R 2 .

[0105] As an optional implementation, the control limit is expressed by the following formula:

[0106]

[0107] In the formula, UCL represents the upper control limit, LCL represents the lower control limit, CL represents the mean of the upper and lower control limits, μ represents the mean of the sample data, and P x This represents the probability distribution of sample data being less than the expected value of the sample dataset, where λ is the smoothing parameter, n is the number of samples per run, and k is the quantile, determined by the significance level of the control limit. Furthermore, this control limit effectively accounts for skewed and non-normal data, thus expanding the applicability of the control chart.

[0108] As an optional implementation, the significance level can be set according to actual needs; for example, the significance level can be greater than or equal to 0.95.

[0109] As an optional implementation, the smoothing parameter can be estimated empirically; for example, the smoothing parameter can be greater than or equal to 0.1 and less than or equal to 0.5.

[0110] like Figure 4 As shown, as an optional implementation, the control chart design method provided in this application further includes the following steps for correcting the control limits:

[0111] S401. Calculate the average running chain length of the control chart under different smoothing coefficients based on the Monte Carlo simulation method;

[0112] S402. Determine the optimal smoothing parameters based on the average running chain length of the control chart under different smoothing coefficients;

[0113] S403. Adjust the control limits according to the optimal smoothing parameters.

[0114] Monte Carlo simulation is a statistical simulation method that uses computers to generate random numbers to simulate various scenarios. According to the definition of probability, the probability of an event occurring can be obtained through a large number of experiments, such as a coin toss experiment. Furthermore, with a sufficient number of trials, the probability of heads and tails will approach 1:1. Therefore, Monte Carlo simulation can also be used to calculate the Average Running Chain Length (ARL), generating random numbers for step size calculation. With the widespread availability of computers and significantly increased processing speed, Monte Carlo simulation can perform tens of thousands of simulations. Compared to Markov chain methods, this is more convenient, faster, and avoids computational errors and other human mistakes.

[0115] This application focuses on calculating the average run length (ARL) of EWMA control charts, employing the Monte Carlo method and utilizing Matlab software for computer simulation. After calculating the average run length (ARL), the optimal smoothing parameters are determined based on the average run length (ARL) under different smoothing parameters, and the control limits are then adjusted according to the optimal smoothing parameters.

[0116] like Figure 5 As shown, as an optional implementation method, the Monte Carlo simulation method includes:

[0117] S501. Generate N random numbers that approximate the distribution of the sample data;

[0118] S502. Construct control limits based on N random numbers and according to the probability-weighted variance method;

[0119] S503. Generate EWMA statistics based on N random numbers and the EWMA control chart;

[0120] S504. Compare the EWMA statistic with the control limits and record the number of times the EWMA statistic is out of control.

[0121] S505. Repeat steps S501 to S504 to calculate the average running chain length. The average running chain length is calculated using the following formula:

[0122]

[0123] In the formula, ARL represents the average running chain length, β represents the number of times the system went out of control, m represents the number of repetitions, and N represents the number of random numbers.

[0124] To determine the optimal smoothing parameter λ for the control chart and thus improve its ability to detect defective products using the probability-weighted variance (EWMA) control chart, this application employs Monte Carlo simulation to simulate the parameters of the EWMA control chart. This method can directly simulate data generation during the production process, and its simulation results are highly valuable and easy to implement. Matlab is used to simulate and plot the ARL (average chain length) under different λ values ​​to obtain the changes in average chain length under different λ values, thereby determining the optimal smoothing coefficient to improve monitoring effectiveness and reduce the probability of false alarms.

[0125] For example, this application uses production data from a smart manufacturing bottle cap company to obtain ARL results for different smoothing parameters as shown in Table 1, and plots them accordingly. Figure 6 The curves showing the variation of the average running chain length (ARL) under different smoothing parameters λ are shown.

[0126] Table 1. Variation of average chain length under the same λ.

[0127]

[0128] like Figure 6 The curves showing the variation of the average running chain length (ARL) under different smoothing parameters λ are illustrated. Observing the curves, it can be found that the larger the value of λ, the less effective the average running chain length (ARL) is at monitoring small offsets; conversely, the smaller the value of λ, the more effective the average running chain length (ARL) is at monitoring small offsets, and it can quickly detect changes in the mean. However, the probability of false alarms in the control chart will increase accordingly. Therefore, in order to improve the monitoring effect of the average running chain length (ARL) on small offsets and reduce the probability of false alarms in the control chart, in step S402, the smoothing parameter corresponding to the middle average running chain length is selected as the optimal smoothing parameter. Figure 5 As shown, in this embodiment, the smoothing parameter λ used in the probability weighted variance EWMA control chart is recommended to be 0.3 or 0.4.

[0129] like Figure 7 As shown, this application also provides a data analysis system 100, including: a sample acquisition module 11 and a data analysis module 12.

[0130] The sample acquisition module 11 is used to collect sample data during the product manufacturing process and generate a sample dataset.

[0131] Data analysis module 12, based on the control chart design method provided in this application and combined with sample data, calculates and plots the control limits of the control chart, and determines the position of the EWMA statistic of the sample data in the control chart.

[0132] The data analysis module 12 determines the positional relationship between the EWMA statistic on the control chart and the control limits, and analyzes the sample data based on the positional relationship.

[0133] To further illustrate the control chart design method provided in the embodiments of this application, the following will be explained with reference to specific examples:

[0134] This application uses production data from a smart manufacturing bottle cap company as an example to collect data on the bottle caps of the research product. The sampling plan is shown in Table 2. A total of 125 data points were collected over a period of 25 days. Five data points on the inner and outer diameters of the bottle cap were collected each day to ensure that the number of subgroups was greater than or equal to 25, and the subgroup size was 4-5. The collected data are shown in Table 2.

[0135] Table 2

[0136]

[0137] like Figure 8 The data analysis results for the molded caps shown have a P-value < 0.005, indicating that the collected product data is non-normally distributed and therefore unsuitable for conventional control charts. Figure 8 We know that the sample mean of this product is 22.491, the standard deviation is 0.017, and out of 140 data points, 67 data points are below the mean, and 73 data points are above or equal to the mean. Therefore, P can be calculated. X The value of .

[0138]

[0139] σ L =0.010

[0140] σ R =0.013

[0141] The control chart statistics are:

[0142]

[0143] Where Z0 = μ = 22.491, and the significance level of the control limit is taken as 95%, therefore, based on the 95% quantile of the standard normal distribution, k is determined to be 1.65, and λ = 0.3 is set, obtaining the control limit based on the probability-weighted variance method as follows:

[0144]

[0145] Based on the above data, the method provided in this application can be used to obtain the following: Figure 9 The EWMA control chart shown is based on probability-weighted variance.

[0146] Based on the above data, this application also draws the following diagrams according to traditional control chart design methods: Figure 10 The Xbar-R (normal mean-range) control chart shown, and as follows Figure 11The traditional EWMA control chart is shown.

[0147] Combination Figures 9 to 11 As can be seen, when using the Xbar-R control chart, no outliers were found through the mean and range plots, indicating overall stability. When using the traditional EWMA control chart, the statistical transformation made the overall data changes significantly, but the traditional EWMA control chart still did not find any outliers, indicating that the current process is under stable control. When using the probability-weighted variance EWMA control chart, one outlier exceeding the control limit was clearly detected, along with three other potentially dangerous points, and the overall data showed a large fluctuation range. Therefore, this control chart clearly indicates that the current production process is unstable and has certain quality defects. The comparison of these three control charts demonstrates that, in a smart manufacturing environment, the probability-weighted variance-based EWMA control chart improves the detection capability for non-normally distributed data.

[0148] In summary, this application provides a control chart design method and data analysis system. First, sample data is collected, and statistics are generated based on the EWMA control chart. The mean of the sample data is calculated, and the sample data is divided into two parts from the mean, constructing two normal distributions, denoted as the first normal distribution and the second normal distribution. The variances of the first and second normal distributions are calculated, and the distribution probability of the sample data is calculated. The average running chain length of the control chart is calculated using the Monte Carlo simulation method, and the optimal smoothing coefficient is determined based on the average running chain length of the control chart under different smoothing coefficients. The optimal smoothing coefficient is substituted into the formula for calculating the control limits, and combined with the distribution probability of the sample data, the control limits are calculated. Finally, an EWMA control chart based on probability-weighted variance is obtained, solving the problem that conventional EWMA control charts are not applicable when the data is non-normal.

[0149] The above-disclosed embodiments are merely preferred embodiments of this application, but are not intended to limit the scope of this application. Those skilled in the art will understand that any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and scope of this application and the appended claims are equivalent substitutions and still fall within the scope of this application.

Claims

1. A method of designing a control chart, characterized by, The design method comprises the following steps: S1, obtaining production sample data, generating a production sample data set, and generating an EWMA statistic based on an EWMA control chart; S2, constructing a control limit based on a probability-weighted variance method; S3, drawing a control limit of the control chart according to the control limit, determining a position of the EWMA statistic in the control chart, and generating the control chart; In step S2, the following steps are included: S201, calculating a mean value of the production sample data; S202, dividing the production sample data into a first part greater than the mean value of the production sample data and a second part less than the mean value of the production sample data according to the mean value of the production sample data, constructing a first normal distribution by symmetrically processing the first part, constructing a second normal distribution by symmetrically processing the second part, calculating a variance of the first normal distribution relative to the mean value of the production sample data to obtain a first normal distribution variance, and calculating a variance of the second normal distribution relative to the mean value of the production sample data to obtain a second normal distribution variance; S203, calculating a distribution probability of the production sample data being less than a mathematical expectation of the production sample data set; S204, determining the control limit according to the first normal distribution variance, the second normal distribution variance, and in combination with the distribution probability; The overall variance of the production sample data is expressed as: ; The first normal distribution variance is represented as: ; In combination with the distribution probability, the variance of the first part of the production sample data is represented as: The second normal distribution variance is represented as: ; In combination with the distribution probability, the variance of the second part of the production sample data is expressed as: ; wherein P X denotes the probability of the production sample data being less than the mathematical expectation of the production sample data set; The control limit is represented by the following formula: wherein UCL represents the upper control limit, LCL represents the lower control limit, CL represents the mean of the upper control limit and the lower control limit, μ represents the sample data mean, P x represents the probability that the production sample data is less than the mathematical expectation of the production sample data set, λ represents a smoothing parameter, n represents the number of single sampling, k represents the quantile, which is determined by the significance level of the control limit.

2. The design method of the control chart according to claim 1, wherein The significance level is greater than or equal to 0.

95.

3. The design method of the control chart according to claim 1, wherein The smoothing parameter is greater than or equal to 0.1 and less than or equal to 0.

5.

4. The design method of a control chart according to Claim 1, characterized by, The method further comprises the following step of correcting the control limit: S401, calculating an average run length of the control chart under different smoothing coefficients based on a Monte Carlo simulation method; S402, determining an optimal smoothing parameter based on the average run length of the control chart under different smoothing coefficients; S403, correcting the control limit according to the optimal smoothing parameter.

5. The design method of a control chart according to claim 4, characterized by, The Monte Carlo simulation method comprises: S501, generating N random numbers subject to a distribution approximating the production sample data; S502, constructing a control limit according to the N random numbers and based on the probability-weighted variance method; S503, generating an EWMA statistic based on an EWMA control chart according to the N random numbers; S504, comparing the EWMA statistic with the control limit and recording a number of out-of-control times in the EWMA statistic; S505, repeating steps S501-S504 to calculate the average run length, which is calculated by the following formula: In the formula, ARL represents the average running chain length, β represents the number of out-of-control times, m represents the number of repetitions, N represents the number of random numbers.

6. The design method of a control chart according to claim 4, wherein In step S402, the smoothing parameter corresponding to the average run length in the middle is selected as the optimal smoothing parameter.

7. The design method of the control chart according to claim 1, wherein The EWMA statistic is represented as: wherein Z i denotes the i EWMA statistic, λ denotes the smoothing parameter, denotes the mathematical expectation of the production sample data set.

8. A data analysis system, characterized by The analysis system comprises: A sample collection module for collecting production sample data in a product production process to generate a production sample data set; a data analysis module, based on the design method of the control chart according to any one of claims 1 to 7 and in combination with the production sample data, calculates and draws control limits of the control chart, and determines a position of an EWMA statistic of the production sample data in the control chart; the data analysis module judges a positional relationship between the position of the EWMA statistic in the control chart and the control limits, and analyzes the production sample data according to the positional relationship.

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