CN104700200A - Multivariate product quality monitoring method oriented to digital workshop - Google Patents

Abstract

A multivariate product quality monitoring method for digital workshops. First, a set of quality information collection schemes suitable for digital workshops is constructed; Multivariate process capability analysis based on the improved principal component analysis method was carried out for multi-quality characteristics; for the problem that the multivariate statistical control control chart is difficult to diagnose and locate process abnormalities, it is proposed to use principal component analysis technology to realize multivariate quality control and diagnosis; the invention can make the workshop Quantitatively evaluate the quality assurance capabilities of key processes of key products, and locate the source of quality problems in a timely manner when quality problems occur, thereby avoiding further cost losses.

Description

A multivariate product quality monitoring method for digital workshop

technical field

The invention belongs to the technical field of quality control in the processing and manufacturing process of mechanical products, and in particular relates to a product multivariate quality monitoring method for digital workshops, which is a process capability analysis and quality problem diagnosis for the manufacturing quality of machine-added products based on the principal component analysis method Technology.

Background technique

Statistical process control (SPC) refers to the method of applying mathematical statistical analysis theory to monitor and control product quality in the production process. It is an important technology in quality control and an effective guarantee tool for obtaining qualified product quality. It is also a process performance monitoring and The basis for process anomaly diagnosis. Traditional SPC technology utilizes the standard Shewhart control chart, which can monitor whether the process is in a stable state, and give early warning of process abnormalities. This quality control method has been widely used and has achieved good economic benefits. SPC technology is quite mature, but there are still some problems in the practical application of traditional SPC technology:

First of all, the level of my country's manufacturing industry has been continuously improved, a large number of advanced production equipment has been continuously put into use, and the production efficiency has been amazingly improved. The traditional working method of relying on manual collection and recording of quality characteristic data has been unable to meet the needs of enterprises. At present, manufacturing enterprises adopt a large number of advanced CNC processing equipment, which improves the productivity of the workshop. The amount of quality data that needs to be measured in the workshop has shown explosive growth. The efficiency of workshop quality inspection has become a bottleneck restricting the improvement of production efficiency. In addition, in order to reduce unnecessary transfers between processes, the workshop adopts the assembly line working method. This working method puts forward higher requirements for the collection of quality data, and requires that the quality data can be obtained and processed in time to prevent the previous process from being lost. Quality problems enter the next process, resulting in unnecessary waste of resources. Finally, there is a trend of flexibility in enterprise workshop production, and there are various types of products in the workshop, which also puts forward new requirements for the collection of quality data, requiring timely collection and analysis of different types of quality data. Based on the latest characteristics of the digital workshop, the traditional data acquisition methods can no longer meet the requirements of statistical process control for data acquisition in the digital workshop.

Secondly, traditional statistical process control can only complete single-variable statistical process control due to the limitations of measurement technology and analysis technology. In practical applications, the key quality characteristics of key processes are individually monitored. This method has been widely used in the past few decades and has greatly improved the level of workshop processing quality to a certain extent. However, with the continuous improvement of the manufacturing level and the continuous improvement of people's quality requirements, this method of independent control of single variables has exposed some problems. In the actual workshop manufacturing process, the various processes and quality characteristics are not all independent of each other, they are often related, and simply monitoring them separately will definitely bring certain errors to the quality control of the workshop . In the digital processing workshop, these errors will bring greater economic losses to the enterprise. In order to take into account the correlation between variables, K.S.Chen, W.L.Pearn and P.C.Lin proposed to use the correlation diagram between variables for further monitoring. The disadvantage of this method is that when there are many variables to be monitored, the correlation The number of graphs increases too fast, the workload is heavy and the maneuverability is not great. In this context, we urgently need to apply multivariate statistical process control (Multivariate Statistical Process Control, MSPC) and diagnostic technology to workshop statistical process quality control. Using MSPC technology to manage the quality of the workshop manufacturing process can effectively monitor all variables in the manufacturing process in a unified manner, timely discover hidden dangers in the entire manufacturing process and deal with them in time, and improve the production quality level of the workshop.

In view of the problems existing in the quality control of the traditional workshop, it is of urgent and practical significance to construct a workshop quality information collection scheme for the digital workshop and conduct in-depth research on the multivariate quality control problems of the workshop.

Contents of the invention

Aiming at the problems existing in the prior art, the purpose of the present invention is to provide a multivariate product quality monitoring method for digital workshops, through which the workshop can conduct quantitative assessments on the quality assurance capabilities of the key processes of key products, and in the event of In case of quality problems, locate the source of quality problems in a timely manner, thereby avoiding further cost losses.

In order to achieve the above object, the present invention adopts the following technical means.

A digital workshop-oriented product multivariate quality monitoring method, comprising the following steps:

Step 1: Build a digital workshop quality data collection scheme through the internal LAN of the machining workshop;

Step 2: Obtain quality data by collecting key quality characteristics of key processes, and perform multivariate process capability analysis on the multivariate quality characteristics of key processes. When the results of multivariate process capability analysis meet customer requirements or quality management system requirements, transfer to the basis The key quality characteristics are used to determine the sampling plan and the type of control chart; when the multivariate process capability analysis results do not meet the requirements of the customer or the requirements of the quality management system, it is necessary to analyze the quality problems, find out the measures to solve the problems and correct them , until the quality level is reached;

Step 3: The general principle of control chart selection is that the measurement value control chart is given priority. If no suitable measurement value control chart is found, consider the piece counting or point counting control chart; process the sample data according to the collected quality data, and calculate Corresponding specification limits, and draw the corresponding initial control chart to judge the stability of the process;

Step 4: When the control chart is not in a controlled state, look for the system variation. If no system variation is found, supplement sampling and draw the control chart; Draw the control chart; when the control chart is in the controlled state, monitor the production status;

Step 5: When there is an abnormality in the monitoring process, find the cause of the abnormality; if the abnormal cause is found, check whether the control chart needs to be modified; if the control chart needs to be modified, the sampling rules should be re-determined, and the control chart should be drawn. On the contrary, use the previous control chart to monitor the production status; if there is no abnormality in the monitoring process, the processing will end and the process control of the next sample will be transferred.

The present invention has the following advantages:

The digital workshop quality data collection scheme proposed by the invention has the characteristics of reliability, timeliness, completeness and continuity. These data are the basis for ensuring the accuracy and reliability of quality data analysis results.

The invention improves the traditional problem of dimensionality reduction for multivariate process capability analysis, and proposes an improved principal component specification interval calculation method and a set of multivariate process capability index calculation methods to make the analysis results more accurate.

Aiming at the multivariate quality control chart, the present invention can only monitor the multivariate statistics, and proposes a multivariate quality diagnosis method based on principal component analysis to help quickly locate the abnormal location, reducing the resulting loss of workshop costs.

Description of drawings

Fig. 1 is the data acquisition scheme of the digitized workshop of the present invention.

Fig. 2 is a multivariate quality control and improvement model diagram of the present invention.

Fig. 3 is a flow chart of control map selection in the present invention.

Fig. 4 is a flow chart of multivariate quality control diagnosis based on principal component analysis in the present invention.

Fig. 5 is a part diagram of an example.

Fig. 6 is a control diagram of the hole milling process T2.

Fig. 7 is a MEWMA control diagram of the milling process.

Fig. 8 is the first principal component control diagram.

Fig. 9 is the second principal component control diagram.

Figure 10 The third principal component control chart.

Figure 11 is a mean control chart for the diameter variable.

Figure 12 is a mean control chart for the depth variable.

Figure 13 is a mean control chart for the distance 1 variable.

Figure 14 is a distance 2-variable mean control chart.

Table 1 is the quality characteristic requirements of parts.

Table 2 is the actual measurement data.

Table 3 is the results of principal component analysis of the sample data of the milling process.

Detailed ways

The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.

Step 1: Build a digital workshop quality data collection scheme through the internal LAN of the machining workshop, as shown in Figure 1. The manual data collection method is mainly aimed at some data that can only be obtained through special gauges and visual measuring tools and some counting data. RFID is mainly used for the preparation of quality plans. The RFID tag corresponds to each model of the product in the workshop. The inspection item corresponding to the product can be displayed in the statistical process control system by scanning the RFID tag with a scanning gun at the production site. The digital intelligent measuring instrument is mainly connected to the computer through wired/wireless means. When the quality inspector measures the characteristics of the parts, the measurement data can be automatically transmitted to the statistical quality control system for data analysis.

Step 2: Through the collected quality data, perform multivariate process capability analysis on the multivariate quality characteristics of key processes, using a multivariate process capability analysis method based on principal component analysis.

The variable X represents the key quality characteristics of the key process, let F ₁ represent the principal component formed by the first linear combination of the original variables, that is, F ₁ =a ₁₁ X ₁ +a ₂₁ X ₂ +...+a _p1 X _p ,a _i ＝(a _1i ,a _2i ,...,a _pi ) ^T is the eigenvector of the i-th characteristic root λ _i of the covariance matrix Σ of the variable X, assuming that the variable X obeys p-dimensional normality The distribution is in line with the actual situation of workshop data collection. Under the p-dimensional normal distribution, the calculation formulas of covariance matrix Σ, covariance matrix Σ eigenroots and eigenvectors will be explained below. The size of the original variable information contained in the first principal component It can be measured by its variance. The larger the variance value Var(F ₁ ), it indicates that the first principal component contains more information about the original variable. It is required that the first principal component F ₁ contains the largest amount of original variable information, so The selected F ₁ should have the largest variance among all linear combinations of the original variables X ₁ , X ₂ ,...,X _p , so that the second, third,...,pth ones with decreasing variance values can be constructed Principal components, as shown in the following formula:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; pp</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\end{array}\right.$

The principal component F _i is a linear combination with the eigenvector a _i =(a _1i ,a _2i ,...,a _pi ) ^T of the i-th characteristic root λ _i of the covariance matrix Σ of the data matrix X as the coefficient, And Var(F _i )=λ _i .

It represents the contribution rate of the i-th principal component, and Var(F _i ) represents the variance of the principal component F _i . Indicates the sum of variances of the first P principal components;

In practical applications, for p original variable information, it is not necessary to construct p principal components for analysis. When m≤p, m principal components can reflect most of the information in the original variables, and it is not necessary to continue to construct principal components. Component component, the accumulation and contribution rate of the current m principal component components When it is greater than 90%, we can think that the m principal components reflect most of the information contained in the p original variables.

Suppose the variable X obeys p-dimensional normal distribution, that is, X～N _p (μ,Σ), where μ is the overall mean vector, and Σ is the covariance matrix.

Since Σ _p×p is a positive definite symmetric matrix, there is a positive definite matrix U such that

${\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; \&Sigma;U</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; o</span>}& \mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}$

Among them, λ ₁ , λ ₂ ,...,λ _p are the eigenvalues of Σ, and satisfy λ ₁ ≥λ ₂ ≥...≥λ _p >0, U=(U ₁ ,U ₂ ,..., U _p ) is a unit orthogonal matrix,

Denote Y=(Y ₁ ,Y ₂ ,...,Y _p )=U ^T X, then Y ₁ ,Y ₂ ,...,Y _p are respectively called the 1st,2nd,...,p principals of X Element,

Because X obeys multivariate normal distribution, according to the linear combination of normal distribution still obeys normal distribution, then Y obeys multivariate normal distribution.

again

EY＝E(U ^T X)＝U ^T EX＝U ^T μ

Cov(Z,Y ^T )＝Cov(U ^T X,X ^T U)＝U ^T Cov(X,X ^T )U＝U ^T ΣU＝Λ

After transformation, the proportions of the original variable information of each principal component component are different. When using the process capability index of the principal component component to construct the multivariate process capability, it is necessary to assign different weight coefficients to each principal component. From the principle of principal component analysis, it can be known that the use of principal components It is reasonable to use the component contribution rate as a weight coefficient, so the multivariate process capability index can be defined as:

${\mathrm{<span\; class="notranslate">\; MC</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

${\mathrm{<span\; class="notranslate">\; MC</span>}}_{\mathrm{<span\; class="notranslate">\; pk</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; pk</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

${\mathrm{<span\; class="notranslate">\; MC</span>}}_{\mathrm{<span\; class="notranslate">\; pm</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; pm</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

where r _i =r _i /tr(Λ), tr(Λ)=λ ₁ +λ ₂ +...+λ _p , is the single variable process capability index of the i-th principal component,

If MC _P ≥ 0.9973, then the potential capability of the process is satisfactory. If the processing process satisfies MC _P ≥ 0.9973, turn to step 3 as shown in Figure 2, otherwise, carry out quality improvement until the process capability index meets the requirements.

Step 3: Select the control chart according to the overall principles of economy and accuracy. Since the piece count or point value data control chart often requires a large sample size, the sampling cost is high and the inspection time is long. Therefore, the control chart is selected The general principle is that the measurement value control chart is given priority. If no suitable measurement value control chart is found, the piece counting or point counting control chart should be considered. The control chart selection process is shown in Figure 3. Process the sample data according to the collected quality data, calculate the corresponding specification limits, and draw the corresponding initial control chart to judge the stability of the process. The reason why it is necessary to judge and stabilize first is that if the process is in a non-statistical process controlled state, using the control chart established by the sample point to control the subsequent production process will not only fail to achieve a good control effect, but will bring errors to the enterprise. Forecast, causing losses to the enterprise.

Step 4: As shown in Figure 2, if the result of the system judgment in step 3 is in a controlled state, the statistical process control chart can be used to monitor the production process, and timely give early warning of abnormal changes in production. Processing, if there is no abnormality, the next sample will be controlled until the processing process ends or an abnormality occurs.

If the process is in a state of non-statistical process control, the workshop should organize personnel to find the cause and eliminate it. After eliminating the cause of the system, it should re-sample according to the sampling plan and draw a control chart to see if the system is in control. This step should be repeated until the process is under control.

Step 5: In the previous step, it was determined that the abnormality of the control chart in the controlled state would not be caused by external factors, but could only be caused by internal factors. If there is no abnormality in the monitoring process, the processing ends and the process control of the next sample is transferred. When there is an abnormality in the monitoring process, the principal component analysis technology is used to realize multivariate quality control and diagnosis. Its process is shown in Figure 4. The main steps are as follows:

(1) When an abnormality occurs, the principal component analysis calculation is performed on the multivariate quality data sample data.

(2) After principal component analysis, the first k principal components that account for about 90% of the variance are obtained.

(3) Draw the control chart (mean control chart or EWMA control chart) of the first k principal component variables.

(4) Once the principal component PC _i is found to be abnormal, determine the original variable X _i that has the greatest impact on the principal component PC _i , and preliminarily diagnose that the abnormality of the principal component control chart and the abnormality of the multivariate quality control chart are caused by the abnormality of the original variable _Xi of.

(5) Draw the corresponding single-value control chart of the original variable _Xi , monitor the original variable _Xi , and judge whether the abnormality of the multivariate quality control chart is caused by the abnormality of the original variable _Xi .

(6) According to the abnormality of the original variable _Xi , take corrective and improvement measures for the process, and carry out cycle control improvement for the process, so as to realize the continuous improvement of quality.

Example

As shown in Figure 5, a switch company needs to mill a blind hole on the surface of a switch part during the process of processing a switch part. This process has four specific parameter requirements, as shown in Table 1. Multivariate quality control and diagnosis research was carried out for the four quality characteristics in Table 1, and the measurement data of the four quality characteristics are shown in Table 2. The ^T2 control chart and MEWMA control chart of 50 sets of sample data collected based on the four quality characteristics of diameter, depth, distance 1 and distance 2 at the workshop site are shown in Figure 6 and Figure 7.

Comparing and observing the T ² control chart and the MEWMA control chart of the milling process, we can easily find that in the T ² control chart, sample 37 is about to exceed the T ² upper control limit, but not exceeded; in the MEWMA control chart, sample 37 The upper control limit of the control chart is obviously exceeded, and an abnormality occurs.

While using the multivariate quality control chart to detect abnormalities in the processing process in time, for multivariate quality control, we also need to promptly determine which variable (diameter, depth, distance 1, distance 2) is caused by the abnormality, so as to timely correct the abnormality to process. Use principal component analysis technology to conduct principal component analysis on the process, and further find the error source according to the results of principal component analysis.

Table 3 shows the calculation results of the principal component analysis on the sample data of the milling process.

From the above principal component analysis results, we can see that the cumulative contribution rate of the first three principal components is about 85%, which can basically reflect the abnormal situation of the sample, so we take the first three principal components for analysis, thus achieving Dimensionality reduction processing of multivariate quality data (dimensions are reduced from four dimensions to three dimensions), which reduces the difficulty of analysis. The single-value control charts of the three principal components were made respectively, as shown in Figure 8, Figure 9, and Figure 10.

From the single-value control charts of the above three principal components, it can be seen that the 37th sample has an abnormality at the second principal component, and the calculation formula of the second principal component is: PC ₂ =0.992x ₁ +0.01x ₂ +0.074x ₃ -0.1x ₄ , where x ₁ , x ₂ , x ₃ , and x ₄ represent the four variable values of hole diameter, depth, distance 1, and distance 2 respectively. From the expression of the second principal component, it can be seen that the diameter of the hole accounts for the largest proportion in the second principal component, which is the main factor for the variation of this principal component, followed by the influence of distance 2. When diagnosing the source of error in the milling process, the diameter of the hole should be considered first. It is preliminarily judged that the abnormality of this process is caused by the abnormality of the hole diameter variable at the sample point 37. As shown in Figure 11, Figure 12, Figure 13, and Figure 14 for the single-value control charts of the four variables, the control chart for the diameter variable is abnormal at sample point 37, which exceeds the upper control limit. It is consistent with the diagnostic results obtained by our principal component analysis.

The method of the present invention can be used for abnormal alarm of quality problems of machining products in digital workshops and diagnosis of process abnormalities, which can detect quality problems in the workshop in time, prevent the quality problems of the previous process in the workshop from flowing into the next process, and eliminate the potential cost of the workshop Loss has a broad application prospect in the actual production of the workshop.

Table 1 Quality characteristic requirements

Table 2 Actual measurement data

Table 3 Principal component analysis results of sample data in milling process

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the applicant has described the present invention in detail with reference to the preferred embodiments, those skilled in the art should understand that those who understand the present invention Any modification or equivalent replacement of the technical solution without departing from the spirit and scope of the technical solution of the present invention shall be covered by the scope of the claims of the present invention.

Claims (4)

1. the product multivariate quality method for supervising in Facing Digital workshop, is characterized in that, comprise the following steps:

Step 1: add the acquisition scheme that workshop internal lan builds digitizing workshop qualitative data by machine;

Step 2: obtain qualitative data by the Critical to quality gathering critical process, complex process capability analysis is carried out to the Multivariate Quality Characteristics of critical process, when complex process capability analysis result meets the requirement of client's requirement or quality management system, proceed to the process of the type determining sampling plan and control chart according to Critical to quality; When complex process capability analysis result does not meet the requirement of client's requirement or quality management system, need analyze quality problems, find the measure of dealing with problems also to be corrected, until reach quality level;

Step 3: it is that variable control chart is preferential that control chart chooses rule, when really not finding suitable variable control chart, then considers to reckon by the piece or enumeration control chart; Qualitative data according to collecting processes sample data, calculates corresponding specification limit, and the corresponding initial control chart of drafting is sentenced surely to process;

Step 4: when control chart is not in controlled state, searching system different because of, if do not find system different because of, then supplement and sample and carry out the drafting of control chart; If find system different because of, eliminate different because of after, repaint control chart according to sampling plan; When control chart is in controlled state, carry out the monitoring of production status.

Step 5: when monitor procedure occurs abnormal, find abnormal Producing reason, if find abnormal different because of, see the need of change control figure, if desired control chart modified, sampling prescription should be redefined, and carry out the drafting of control chart, otherwise the control chart before using carries out the monitoring of production status, if exception does not appear in monitor procedure, then process finishing, proceeds to the process control to next sample.

2. the product multivariate quality method for supervising in a kind of Facing Digital workshop according to claim 1, it is characterized in that, the acquisition scheme of the structure digitizing workshop qualitative data described in step one specifically: manual data acquisition mode mainly for be that some only have the data by dedicated gauge and range estimation formula weight tool just obtainable data and some attributes; When RFID is mainly used for quality planning establishment, the product one_to_one corresponding of RFID label tag and each model of workshop, just can be presented at inspection item corresponding for this product in statistical process control system by scanner scanning RFID label tag in production scene.Digital intelligent instrument is connected with computing machine mainly through wire/wireless mode, when quality inspection personnel is measured parts characteristic just can by measurement data automatic transmission to Statistical Quality Control System to carry out the analysis of data.

3. the product multivariate quality method for supervising in a kind of Facing Digital workshop according to claim 1, is characterized in that, the complex process capability analysis method described in step 2 is specially:

Variable X represents the Critical to quality of critical process, if F ₁represent the major component component that first linear combination of original variable is formed, i.e. F ₁=a ₁₁x ₁+ a ₂₁x ₂+ ...+a _p1x _p, a _i=(a _1i, a _2i..., a _pi) ^ti-th characteristic root λ of the covariance matrix Σ of variable X _iproper vector, what suppose that variable X obeys is that p ties up normal distribution, and meet the actual conditions that workshop data gathers, first principal component comprises original variable information size and can measure by its variance size, its variance yields Var (F ₁) larger, show first principal component component to comprise the information of original variable more, require first principal component component F ₁comprise original variable quantity of information maximum, the F therefore chosen ₁should be original variable X ₁, X ₂..., X _pall linear combinations in variance maximum, the can construct that variance yields reduces successively like this second, three ..., p major component, as shown by the following formula:

$\left\{\begin{array}{c}{F}_1=a_{11}{X}_1+a_{12}{X}_2+...+a_{1p}{X}_p\\ F_2=a_{21}{X}_1+a_{22}{X}_2+...+a_{2p}{X}_p\\ M\\ F_p=a_{p1}{X}_1+a_{p2}{X}_2+...+a_{\mathrm{pp}}{X}_p\end{array}\right.$

Wherein major component F _ibe exactly i-th characteristic root λ with the covariance matrix Σ of data matrix X _iproper vector a _i=(a _1i, a _2i..., a _pi) ^tfor the linear combination of coefficient, and there is Var (F _i)=λ _i;

what represent is the contribution rate of i-th major component, Var (F _i) represent major component F _ivariance size, the variance size sum of P major component before representing;

In actual applications, for p original variable information, do not need to build p major component component and analyze, as m≤p, when m major component component can reflect most information in original variable, can no longer continue to build major component component, the Cumulate Sum contribution rate of current m major component component when being greater than 90%, we can think most information that this m major component component reflects p original variable and comprise;

Suppose that variable X is obeyed p and tieed up normal distribution, i.e. X ~ N _p(μ, Σ), wherein μ is population mean vector, and Σ is covariance matrix;

Due to Σ _{p × p}for positive definite symmetric matrices, therefore there is positive definite matrix U, make

$U^T\mathrm{\&Sigma;U}=\left[\begin{array}{cccc}{\mathrm{\&lambda;}}_1& 0& ...& 0\\ 0& {\mathrm{\&lambda;}}_2& ...& 0\\ M& M& O& M\\ 0& 0& ...& {\mathrm{\&lambda;}}_p\end{array}\right]=\mathrm{\&Lambda;}$

Wherein, λ ₁, λ ₂..., λ _pbe the eigenwert of Σ, and meet λ ₁>=λ ₂>=...>=λ _p>0, U=(U ₁, U ₂..., U _p) be unit orthogonal matrix,

Note Y=(Y ₁, Y ₂..., Y _p)=U ^tx is Y then ₁, Y ₂..., Y _pbe called the 1st of X the, 2 ..., p major component,

Because X obeys multivariate normal distribution, according to the linear combination still Normal Distribution of normal distribution, then Y obeys multivariate normal distribution;

Again

EY＝E(U ^TX)＝U ^TEX＝U ^Tμ

Cov(Z,Y ^T)＝Cov(U ^TX,X ^TU)＝U ^TCov(X,X ^T)U＝U ^TΣU＝Λ

The proportion of the comprehensive original variable information of each major component component after conversion is different, need to give different weight coefficients to each major component when utilizing major component component processes Capability index to construct complex process ability, be rational by the known major component component contribution rate that utilizes of the principle of principal component analysis (PCA) as weight coefficient, therefore multivariable process Capability index may be defined as:

${\mathrm{MC}}_p=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{r}_i{C}_{p,{\mathrm{pc}}_i}$

${\mathrm{MC}}_{\mathrm{pk}}=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{r}_i{C}_{\mathrm{pk},{\mathrm{pc}}_i}$

${\mathrm{MC}}_{\mathrm{pm}}=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{r}_i{C}_{\mathrm{pm},{\mathrm{pc}}_i}$

Wherein r _i=r _i/ tr (Λ), tr (Λ)=λ ₁+ λ ₂+ ...+λ _p, be the single multivariable process Capability index of the i-th major component,

If MC _p>=0.9973, so the potential ability of process meets the demands.If process meets MC _p>=0.9973, proceed to step 3, otherwise carry out quality improvement, until reaching is that process capability index meets the demands.

4. the product multivariate quality method for supervising in a kind of Facing Digital workshop according to claim 1, is characterized in that, the monitor procedure of working as described in step 5 occurs abnormal, finds abnormal Producing reason key step as follows:

(1) when after abnormal generation, principal component analysis (PCA) calculating is carried out to multivariate quality data sample data;

(2) by k major component component before obtaining accounting for about 90% to variation influence after principal component analysis (PCA);

(3) control chart of front k main variables, mean chart or EWMA control chart is drawn;

(4) once find major component PC _ioccur abnormal, determine major component PC _ithe original variable X had the greatest impact _i, the exception of tentative diagnosis major component control chart and the exception of multivariate process quality control figure are due to original variable X _iexception to cause;

(5) original variable X is drawn _icorresponding monodrome control chart, to original variable X _imonitor, judge whether it is due to original variable X _ithe multivariate process quality control figure that causes of exception abnormal;

(6) according to original variable X _iabnormal take to correct innovative approach to operation, cycle control improvement is carried out to operation, to realize the Continual Improvement of quality.