CN113807014A - Non-parametric self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy - Google Patents

Non-parametric self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy Download PDF

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CN113807014A
CN113807014A CN202111094421.1A CN202111094421A CN113807014A CN 113807014 A CN113807014 A CN 113807014A CN 202111094421 A CN202111094421 A CN 202111094421A CN 113807014 A CN113807014 A CN 113807014A
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陈克强
姜兴宇
刘伟军
田志强
徐思迪
孙豪杰
王润林
谭清泽
李世磊
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Abstract

The invention relates to a non-parameter self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy, and belongs to the field of statistical process control. The method comprises the following steps: constructing a non-parameter self-adaptive dynamic EWMA control chart for key procedures in a multi-variety small-batch manufacturing process; determining a statistical index and an economic index calculation method based on the Markov chain; establishing a control chart multi-objective optimization design model, and performing linear weighting processing on a target function by adopting a cloud clear comprehensive evaluation method; solving the model based on an improved artificial fish swarm algorithm; taking the production and manufacturing process flow of a certain aerospace complex component manufacturing enterprise as an example, the optimized control chart is adopted to control the chart, and the effectiveness and feasibility of the proposed model and method are verified. The invention ensures the control effect, reduces the control cost and realizes the quality control of the multi-variety small-batch manufacturing process. The method provides reference for the control chart research in a multi-variety small-batch production mode and provides support for the quality control of the control chart.

Description

Non-parametric self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy
Technical Field
The invention relates to a non-parametric adaptive dynamic EWMA (exponential weighted moving average) control chart multi-objective optimization design method considering statistics and economy, in particular to a non-parametric adaptive dynamic EWMA control chart multi-objective optimization design method for a multi-variety small-batch manufacturing process, and belongs to the field of statistical process control.
Background
Due to the increasing diversity of individual requirements of customers, a multi-variety small-batch production mode becomes a leading production mode of global enterprises, but the quality control problems of insufficient sample data, uncertain distribution, repeated and variable process drift and the like caused by multiple batches, less process quality data and variable product parameters are solved. The traditional SPC control chart is based on a statistical control method which has enough sample data and is assumed to be normally distributed, and the problem of dynamically variable quality control such as less sample data, uncertain distribution and the like in a multi-variety small-batch production mode is difficult to solve. Although there are improved methods based on grouping technology, Bayes, etc., the quality control effect is far from reaching the expected effect.
Disclosure of Invention
Therefore, the research on small-sample and non-normal quality control charts is the key to realize the quality control of the multi-variety small-batch manufacturing process. Based on the fact that the performance of the quality control chart is determined by statistics and economy, the invention designs a non-parameter self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy, solves the problem of quality control in the multi-variety small-batch manufacturing process, effectively improves the efficiency of quality control, and reduces the control cost.
Aiming at the problems, the invention provides a dynamic EWMA control chart facing unknown distribution, self-adaptive detection drift and solving the problem of insufficient quality control effect in the process of manufacturing multiple varieties in small batches. Meanwhile, in order to take account of statistics and economy, more accurate average product length and average product cost are introduced as calculation bases, an EWMA control chart parameter multi-objective optimization design model is constructed, and an improved artificial fish swarm algorithm is adopted for solving. On the basis, the optimal solution is selected as a parameter to construct a control chart, so that quality monitoring of key processes in the multi-variety small-batch manufacturing process is realized, and the product quality is improved.
The invention provides a non-parameter self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy, which comprises the following steps of:
s1, constructing a non-parameter self-adaptive dynamic EWMA control chart facing the key process of the multi-variety small-batch manufacturing process.
S2, determining a statistical index and an economic index calculation method based on the Markov chain.
And S3, establishing a control chart multi-objective optimization design model, and performing linear weighting processing on the objective function by adopting a cloud clear comprehensive evaluation method.
And S4, solving the model based on the improved artificial fish swarm algorithm.
And S5, taking the production and manufacturing process flow of a certain aerospace complex component manufacturing enterprise as an example, controlling a diagram by using the optimized control diagram, and verifying the effectiveness and feasibility of the proposed model and method.
Preferably, the step S1 includes the following sub-steps:
specifically, in the sub-step S11 of the step S1, a non-parametric adaptive EWMA control chart is constructed based on the U statistics, and the process is as follows:
let the distribution of quality characteristic data in the process of manufacturing multiple varieties in small batches be unknown, let the mean value be mu and the variance be sigma2. When the process is controlled, the target value of the process mean is recorded as μ0And the standard deviation is recorded as σ0Then when the process is controlled, mu-mu0，σ＝σ0(ii) a When the process is out of control, σ is not changed, but μ ═ μ0+ δ σ, where δ is the fluctuation of the process mean. Based on this, the statistics of the non-parametric EWMA control chart constructed based on the U statistics are:
Zt＝ω(et)Ut+(1-ω(et))Zt-1
wherein, UtFor the sample mean estimated based on the U statistic, λ ∈ (0.1), ω (e)t) Is an equivalent smoothing function, and
Figure BDA0003268595790000021
therefore, the following steps are carried out:
Figure BDA0003268595790000022
specifically, the substep S12 in the step S1 designs a dynamic sampling method with variable sampling ratio and sample capacity, which comprises the following substeps:
s121, selecting a reference key process, and determining the required sample capacity N;
s122, obtaining a historical data sample volume N of the reference key process0If N is present0If the number is more than N, no sample data of the clustering key process is extracted; otherwise, acquiring the clustering distance of each clustering key process, and determining the sample proportion of the clustering processes.
Let N1，N2，…，NnRespectively the number of samples of each clustering key process, d1，d2，…，dnFor referring to the clustering distance between the key process and each clustering key process, the sample proportion of the clustering process is N1：…：Ni：…：Nn＝d1：…：di：…：dn；
S123, calculating the number N of theoretically extracted samples of each clustering key processiThe specific calculation formula is as follows:
Figure BDA0003268595790000031
and S124, adjusting the extracted sample size of each clustering key process according to the actual historical data size.
And S125, normalizing the extracted data by adopting a relative tolerance conversion method.
Specifically, in the sub-step S13 of the step S1, a control limit, an early warning limit, and a stability limit are determined, and a specific formula is as follows:
UCL＝μ0+k1σz LCL＝μ0-k1σZ
UWL＝μ0+k2σz LWL＝μ0-k2σz
USL＝μ0+k3σz LSL＝μ0-k3σz
wherein k is1、k2、k3Respectively is a control limit coefficient, an early warning limit coefficient, a stable limit coefficient, and 0 < | k3|＜|k2|＜|k1Taking k2＝2/3 k1，k3＝1/3 k1，
Figure BDA0003268595790000032
Preferably, the step S2 includes the following sub-steps:
specifically, in the sub-step S21 in the step S2, a non-parametric adaptive dynamic EWMA control chart markov chain model based on U statistics is constructed, and the control process of the non-parametric adaptive dynamic EWMA control chart is regarded as a markov chain with an absorption wall, and a state transition matrix P thereof can be represented as:
Figure BDA0003268595790000033
wherein, U is a 2m +1 dimensional column vector with elements of 1; r is a real-valued matrix of (2m +1) × (2m +1) dimensions, since Zi＝ωUi+(1-ω)Zi-1And Z isj-1＝ZiElement r in matrixijFor the probability of transitioning state i to state j, then:
Figure BDA0003268595790000041
where ω is the equivalent smoothing function value, d is the width of each equal-width sub-interval after dividing the control chart UCL and LCL into 2m +1 equal-width sub-intervals, and
Figure BDA0003268595790000042
specifically, in the sub-step S22 in the step S2, a statistical indicator is calculated, and an average run length ARL of the non-parametric adaptive dynamic EWMA control chart is calculated according to the markov chain model in S21, where ARL is Pm·(I-R)-1U, and then the statistical indicator average product length APL, the specific formula is as follows:
Figure BDA0003268595790000043
wherein N is the sample volume; h represents the number of products spaced among the samples, namely the number of key processes in the sample set; the ARL is the average run length calculated by the markov chain method.
Specifically, the sub-step S23 in the step S2 calculates the economic indicator, and the specific steps are as follows:
(1) the quality loss cost can be divided into a controlled quality loss C1 cost and an out-of-control quality cost C2 according to a Tageuchi secondary quality loss function, and the specific formula is as follows:
Figure BDA0003268595790000044
where K is a fixed constant, often K1, process drift
Figure BDA0003268595790000045
(2) Calculating the average product cost APC in a quality period, which is specifically represented by the following formula:
Figure BDA0003268595790000046
wherein the content of the first and second substances,
Figure BDA0003268595790000047
for time-averaged production process control states, APL1 is the average product length at run-away, and W is the average cost per search and exception.
Preferably, the step S3 includes the following sub-steps:
specifically, the substep S31 of the step S3 is used for constructing a multi-objective optimization design model for control chart, f1Is a statistical objective function and f2For an economic objective function, B is a threshold value for a controlled average product length, NmaxIs the total number of samples, NrFor reference (quality control) key process, alpha and beta are respectively f1And f2And α + β ═ 1, specifically as follows:
min f＝α·f1+β·f2
Figure BDA0003268595790000051
specifically, the substep S32 of the step S3 adopts a cloud-clear comprehensive evaluation method to evaluate α and β, and specifically includes the substeps of:
s321, based on a clear comprehensive evaluation method, selecting a plurality of expert groups to evaluate the importance of n indexes to obtain a clear evaluation vector W ═ omega1，ω1，…，ωn}；
S322, the importance degree is divided into 5 evaluation levels, and each expert agrees to grade the index evaluation result and determines the characteristic value of the corresponding forward cloud model;
s323, according to the characteristic value of the forward cloud model, an x-condition cloud generator is utilized to generate a plurality of quantitative values of the rating values, the average value of the quantitative values is taken as the quantitative value corresponding to the final evaluation level of each index, a cloud matrix is formed, the final quantitative value is selected according to the maximum membership principle, and the cloud value vector mu is obtained, wherein mu is { mu1，μ2，…，μn}。；
S324, multiplying the clear evaluation vector by the cloud value vector corresponding term to obtain a weight vector r ═ r { (r)1，r1，…，rn}。
Preferably, the step S4 is mainly characterized by the following substeps:
specifically, in the step S4, the sub-step S41 determines variables.
Specifically, the sub-step S42 in the step S4 improves the field of view of the artificial fish, specifically as follows:
Figure BDA0003268595790000061
wherein N isiterFor the total number of iterations, i is the artificial fish number, the initial field of view
Figure BDA0003268595790000062
dj、dkRespectively the distance between the current artificial fish and the j and k fish.
Specifically, the step length of the artificial fish is improved in the sub-step S43 in the step S4, which is specifically as follows:
Figure BDA0003268595790000063
specifically, in the sub-step S44 of the step S4, initial parameters, the initial number of artificial fish 30, the number of attempts 50, the maximum number of iterations 900, and the crowdedness 0.1 are set.
Specifically, the sub-steps S45, S46, S47 and S48 in the step S4 complete the solution of the model based on the initial settings of the sub-steps S41, S42, S43 and S44.
Preferably, the step S5 is mainly characterized in that the method is applied to a production and manufacturing process flow of an aerospace complex component manufacturing enterprise, an optimized control chart is used for controlling a manufacturing process, and validity and feasibility of the proposed model and method are verified.
Aiming at the problems of insufficient quality control effect caused by small sample data amount and difficult distribution determination in the multi-variety small-batch manufacturing process, the invention constructs a non-parameter self-adaptive dynamic EWMA control chart and performs multi-objective optimization design on the control chart, thereby reducing the control cost while ensuring the control effect and realizing the quality control of the multi-variety small-batch manufacturing process. The accuracy, effectiveness and feasibility of the method are verified through program simulation and example analysis, reference can be provided for control chart research under a multi-variety small-batch production mode, and support is provided for multi-variety small-batch quality control.
Drawings
FIG. 1 is a diagram of a quality control method for a key process of a multi-variety small-lot manufacturing process according to the present invention.
Fig. 2 is a basic flow chart of the dynamic sampling method of the present invention.
Fig. 3 is a flow chart of the improved artificial fish school algorithm of the invention.
Fig. 4(1) and 4(2) are comparison graphs before and after the algorithm of the present invention is improved, wherein fig. 4(1) is a graph before the algorithm of the present invention is improved, and fig. 4(2) is a graph after the algorithm of the present invention is improved.
FIG. 5 is a diagram of an optimized non-parametric adaptive dynamic EWMA control chart according to the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The invention provides a dynamic EWMA control chart facing distribution unknown and self-adaptive detection drift. Meanwhile, in order to take account of statistics and economy, more accurate average product length and average product cost are introduced as calculation bases, an EWMA control chart parameter multi-objective optimization design model is constructed, and an improved artificial fish swarm algorithm is adopted for solving. On the basis, the optimal solution is selected as a parameter to construct a control chart, so that the quality monitoring of key processes in the multi-variety small-batch manufacturing process is realized, and the product quality is further improved, as shown in fig. 1.
The invention provides a non-parameter self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy, which comprises the following steps of:
s1, constructing a non-parameter self-adaptive dynamic EWMA control chart facing the key process of the multi-variety small-batch manufacturing process.
S2, determining a statistical index and an economic index calculation method based on the Markov chain.
And S3, establishing a control chart multi-objective optimization design model, and performing linear weighting processing on the objective function by adopting a cloud clear comprehensive evaluation method.
And S4, solving the model based on the improved artificial fish swarm algorithm.
And S5, taking the production and manufacturing process flow of a certain aerospace complex component manufacturing enterprise as an example, controlling a diagram by using the optimized control diagram, and verifying the effectiveness and feasibility of the proposed model and method.
The step S1 includes the following sub-steps:
in the sub-step S11 of the step S1, a non-parametric adaptive EWMA control chart is constructed based on U statistics, and the process is as follows:
let the distribution of quality characteristic data in the process of manufacturing multiple varieties in small batches be unknown, let the mean value be mu and the variance be sigma2. When the process is controlled, the target value of the process mean is recorded as μ0And the standard deviation is recorded as σ0Then when the process is controlled, mu-mu0，σ＝σ0(ii) a When the process is out of control, σ is not changed, but μ ═ μ0+ δ σ, where δ is the fluctuation of the process mean. Based on this, the statistics of the non-parametric EWMA control chart constructed based on the U statistics are:
Zt＝ω(et)Ut+(1-ω(et))Zt-1
wherein, UtFor the sample mean estimated based on the U statistic, λ ∈ (0.1), ω (e)t) Is an equivalent smoothing function, and
Figure BDA0003268595790000081
therefore, the following steps are carried out:
Figure BDA0003268595790000082
the sub-step S12 in the step S1 designs a dynamic sampling method with variable sampling proportion and sample capacity, which comprises the following sub-steps:
s121, selecting a reference key process, and determining the required sample capacity N;
s122, obtaining a historical data sample volume N of the reference key process0If N is present0If the number is more than N, no sample data of the clustering key process is extracted; otherwise, acquiring the clustering distance of each clustering key process, and determining the sample proportion of the clustering processes.
Let N1，N2，…，NnRespectively the number of samples of each clustering key process, d1，d2，…，dnFor referring to the clustering distance between the key process and each clustering key process, the sample proportion of the clustering process is N1：…：Ni：…：Nn＝d1：…：di：…：dn；
S123, calculating the number N of theoretically extracted samples of each clustering key processiThe specific calculation formula is as follows:
Figure BDA0003268595790000083
and S124, adjusting the extracted sample size of each clustering key process according to the actual historical data size, as shown in FIG. 2.
And S125, normalizing the extracted data by adopting a relative tolerance conversion method.
In the step S1, a sub-step S13 determines a control limit, an early warning limit and a stability limit, and the specific formula is as follows:
UCL＝μ0+k1σZ LCL＝μ0-k1σZ
UWL＝μ0+k2σZ LWL＝μ0-k2σZ
USL＝μ0+k3σZ LSL＝μ0-k3σz
wherein k is1、k2、k3Respectively is a control limit coefficient, an early warning limit coefficient, a stable limit coefficient, and 0 < | k3|＜|k2|＜|k1Taking k2＝2/3 k1，k3＝1/3 k1，
Figure BDA0003268595790000084
The step S2 includes the following sub-steps:
in the sub-step S21 in the step S2, a non-parametric adaptive dynamic EWMA control chart markov chain model based on U statistics is constructed, and the control process of the non-parametric adaptive dynamic EWMA control chart is regarded as a markov chain with an absorption wall, and a state transition matrix P thereof can be represented as:
Figure BDA0003268595790000091
wherein, U is a 2m +1 dimensional column vector with elements of 1; r is a real-valued matrix of (2m +1) × (2m +1) dimensions, since Zi＝ωUi+(1-ω)Zi-1And Z isj-1＝ZiElement r in matrixijFor the probability of transitioning state i to state j, then:
Figure BDA0003268595790000092
in the formula of omegaD is the width of each equal-width sub-interval after dividing the control chart between the UCL and the LCL into 2m +1 equal-width sub-intervals, and
Figure BDA0003268595790000093
in the step S2, the sub-step S22 calculates a statistical index, and calculates an average run length ARL of the non-parametric adaptive dynamic EWMA control chart according to the markov chain model in S21, where ARL is Pm·(I-R)-1U, and then the statistical indicator average product length APL, the specific formula is as follows:
Figure BDA0003268595790000094
wherein N is the sample volume; h represents the number of products spaced among the samples, namely the number of key processes in the sample set; the ARL is the average run length calculated by the markov chain method.
Specifically, the sub-step S23 in the step S2 calculates the economic indicator, and the specific steps are as follows:
(1) the quality loss cost can be divided into a controlled quality loss C1 cost and an out-of-control quality cost C2 according to a Tageuchi secondary quality loss function, and the specific formula is as follows:
Figure BDA0003268595790000095
where K is a fixed constant, often K1, process drift
Figure BDA0003268595790000101
(2) Calculating the average product cost APC in a quality period, which is specifically represented by the following formula:
Figure BDA0003268595790000102
wherein the content of the first and second substances,
Figure BDA0003268595790000103
for time-averaged production process control states, APL1 is the average product length at run-away, and W is the average cost per search and exception.
The step S3 includes the following sub-steps:
substep S31 of the step S3 is used for constructing a multi-objective optimization design model for control chart, f1Is a statistical objective function and f2For an economic objective function, B is a threshold value for a controlled average product length, NmaxIs the total number of samples, NrFor reference (quality control) key process, alpha and beta are respectively f1And f2And α + β ═ 1, specifically as follows:
min f＝α·f1+β·f2
Figure BDA0003268595790000104
in the substep S32 of the step S3, evaluation and assignment are performed on α and β by using a cloud-clear comprehensive evaluation method, which specifically includes the following substeps:
s321, based on a clear comprehensive evaluation method, selecting a plurality of expert groups to evaluate the importance of n indexes to obtain a clear evaluation vector W ═ omega1，ω1，…，ωn}；
S322, the importance degree is divided into 5 evaluation levels, and each expert agrees to grade the index evaluation result and determines the characteristic value of the corresponding forward cloud model;
s323, according to the characteristic value of the forward cloud model, an X-condition cloud generator is utilized to generate a plurality of quantitative values of the rating values, the average value of the quantitative values is taken as the quantitative value corresponding to the final evaluation level of each index, a cloud matrix is formed, the final quantitative value is selected according to the maximum membership principle, and the cloud value vector mu is obtained, wherein mu is { mu1，μ2，…，μn}。；
S324, multiplying the clear evaluation vector with the cloud value vector corresponding item to obtain the weightWeight vector r ═ r1，r1，…，rn}。
The step S4 is mainly characterized by the following substeps:
sub-step S41 of the step S4 determines variables.
The sub-step S42 of the step S4 improves the field of vision of the artificial fish, and the method specifically comprises the following steps:
Figure BDA0003268595790000111
wherein N isiterFor the total number of iterations, i is the artificial fish number, the initial field of view
Figure BDA0003268595790000112
dj、dkRespectively the distance between the current artificial fish and the j and k fish.
The step length of the artificial fish is improved in the sub-step S43 of the step S4, and the steps are as follows:
Figure BDA0003268595790000113
in the sub-step S44 of the step S4, initial parameters, an initial artificial fish number of 30, an attempt number of 50 times, a maximum iteration number of 900 times, and a crowding degree of 0.1 are set.
And in the step S4, sub-steps S45, S46, S47 and S48 complete the solution of the model based on the initial setting of the sub-steps S41, S42, S43 and S44.
The step S5 is mainly characterized in that the method is applied to the production and manufacturing process flow of a certain aerospace complex component manufacturing enterprise, the optimized control chart is adopted to control the manufacturing process continuously, and the effectiveness and the feasibility of the proposed model and method are verified.
The overall technical scheme of the nonparametric self-adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy comprises the following steps: s1, constructing a non-parameter self-adaptive dynamic EWMA control chart for key processes of a multi-variety small-batch manufacturing process; s2, determining a statistical index and an economic index calculation method based on the Markov chain; s3, establishing a control chart multi-objective optimization design model, and performing linear weighting processing on the objective function by adopting a cloud clear comprehensive evaluation method; s4, solving the model based on an improved artificial fish swarm algorithm; and S5, taking the production and manufacturing process flow of a certain aerospace complex component manufacturing enterprise as an example, controlling a diagram by using the optimized control diagram, and verifying the effectiveness and feasibility of the proposed model and method.
The step S1 includes the following sub-steps: s11, constructing a non-parametric adaptive EWMA control chart based on the U statistic; s12, designing a dynamic sampling method with variable sampling proportion and sample capacity to complete data sampling, wherein the method is specifically shown in tables 1 and 2; and S13, determining a control limit, an early warning limit and a stable limit.
TABLE 1 clustering distance, technical requirement and sampling result of each key process
Figure BDA0003268595790000121
TABLE 2 relative tolerance converted sample data set
Figure BDA0003268595790000122
The step S2 includes the following sub-steps: s21, constructing a Markov chain model of the non-parameter self-adaptive dynamic EWMA control chart; s22, calculating a statistical index APL; and S23, calculating the economic index APC.
The step S3 includes the following substeps: s31, constructing a control chart multi-objective optimization design model; s32 assigns weights by cloud-based comprehensive evaluation, and obtains a clear evaluation vector W {2.8229,2.9553}, a cloud value vector μ {0.8342, 0.9956}, and a weight vector r {0.4447,0.5553}, as shown in table 3 and table 4.
TABLE 3 clear comprehensive evaluation results of expert groups
Figure BDA0003268595790000123
TABLE 4 results of grade scoring for each index agreed with experts
Figure BDA0003268595790000124
Figure BDA0003268595790000131
As shown in fig. 3, the step S4 is to solve the model by using an improved artificial fish swarm algorithm, including the following substeps: s41, determining variables; s42, improving the visual field of the artificial fish; s43, improving the step length of the artificial fish; s44, setting initial parameters; s45, the artificial fish executes the rear-end collision behavior; s46, the artificial fish executes the clustering behavior; s47, the artificial fish executes foraging behavior; and S48, outputting the optimal solution. The algorithm has obvious improvement effect, effectively improves iteration speed and iteration precision, is specifically shown in figures 4(1) and 4(2), and obtains a better solution shown in table 5.
As shown in fig. 5, the step S5 uses the optimized control chart to control the manufacturing process, and the statistical and economic comparison results with other control charts are shown in table 6.
Table 5 optimal solution and corresponding index value updated by algorithm in each iteration
Figure BDA0003268595790000132
TABLE 5 continuation
Figure BDA0003268595790000133
Figure BDA0003268595790000141
TABLE 6 statistical, economic comparison of different control charts
Figure BDA0003268595790000142
The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and the scope of the present invention should not be limited thereby, and all equivalent changes or modifications made according to the spirit of the present invention are included in the scope of the present invention.

Claims (10)

1. A non-parametric adaptive dynamic EWMA control chart multi-objective optimization design method considering statistics and economy is characterized by comprising the following steps:
s1, constructing a non-parameter self-adaptive dynamic EWMA control chart for key processes of a multi-variety small-batch manufacturing process;
s2, determining a statistical index and an economic index calculation method based on the Markov chain;
s3, establishing a control chart multi-objective optimization design model, and performing linear weighting processing on the objective function by adopting a cloud clear comprehensive evaluation method;
s4, solving the model based on an improved artificial fish swarm algorithm;
and S5, taking the production and manufacturing process flow of a certain aerospace complex component manufacturing enterprise as an example, controlling a diagram by using the optimized control diagram, and verifying the effectiveness and feasibility of the proposed model and method.
2. The statistical and economic non-parametric adaptive dynamic EWMA control map multi-objective optimization design method as claimed in claim 1, wherein the step S1 includes the following sub-steps:
s11, constructing a non-parametric adaptive EWMA control chart based on U statistics, wherein the statistics are as follows:
Zt＝ω(et)Ut+(1-ω(et))Zt-1
wherein, UtFor the sample mean based on the U statistic estimation, the estimated term of the process error is et＝Ut-Zt-1，ω(et) Is an equivalent smoothing function, and
Figure FDA0003268595780000011
gamma is a threshold value of the error estimation term;
s12, designing a dynamic sampling method with variable sampling proportion and sample capacity, which comprises the following steps:
(1) selecting a reference key process, and determining the required sample capacity N;
(2) obtaining a historical data sample size N of a reference key process0If N is present0>N, not extracting sample data of a clustering key process; otherwise, acquiring the clustering distance of each clustering key process, and determining the sample proportion of the clustering processes;
(3) calculating the number N of theoretically extracted samples of each clustering key procedurei；
(4) Adjusting the sample size extracted by each clustering key process according to the actual historical data size;
(5) normalizing the extracted data by adopting a relative tolerance conversion method;
and S13, determining a control limit, an early warning limit and a stable limit.
3. The statistical and economic non-parametric adaptive dynamic EWMA control map multi-objective optimization design method as claimed in claim 1, wherein the step S2 includes the following sub-steps:
s21, constructing a non-parametric self-adaptive dynamic EWMA control chart Markov chain model based on U statistics;
s22, calculating the average product length APL of the statistical indexes;
and S23, calculating the average product length APC of the statistical indexes.
4. The statistical and economic non-parametric adaptive dynamic EWMA control map multi-objective optimization design method as claimed in claim 1, wherein the step S3 includes the following sub-steps:
s31, constructing a control chart multi-objective optimization design model, which is concretely as follows:
min f＝α·f1+β·f2
Figure FDA0003268595780000021
wherein f is1Is a statistical objective function and f2For an economic objective function, B is a threshold value for a controlled average product length, NmaxIs the total number of samples, NrFor reference (quality control) key process, alpha and beta are respectively f1And f2And α + β is 1;
s32, evaluating and assigning the alpha and the beta by adopting a cloud clear comprehensive evaluation method, and specifically comprising the following steps:
(1) based on a clear comprehensive evaluation method, selecting a plurality of expert groups to evaluate the importance of n indexes to obtain clear evaluation vectors;
(2) the importance degree is divided into 5 evaluation levels, and each expert agrees to grade and grade the index evaluation result and determines the characteristic value of the corresponding forward cloud model;
(3) generating a plurality of quantitative values of the rating values by using an X-condition cloud generator according to the characteristic values of the forward cloud model, taking the average value of the quantitative values as the quantitative value corresponding to each final index rating, and forming a cloud matrix;
(4) and multiplying the clear evaluation vector by the corresponding item of the cloud value vector to obtain the weight value.
5. The statistical and economic non-parametric adaptive dynamic EWMA control map multi-objective optimization design method as claimed in claim 1, wherein the step S4 comprises the following sub-steps:
s41, determining variables;
s42, improving Visual field of artificial fishi；
S43, improving Step length of artificial fishi；
S44, setting the initial artificial fish number to be 30, the trial times to be 50, the maximum iteration times to be 900 and the crowding degree to be 0.1;
s45, the artificial fish executes the rear-end collision behavior;
s46, the artificial fish executes the clustering behavior;
s47, the artificial fish executes foraging behavior
And S48, outputting the optimal solution.
6. The statistically and economically feasible multiparameter-based adaptive dynamic EWMA control chart multi-objective optimization design method as claimed in claim 1, wherein the step S5 applies the control chart optimized and designed in S4 to a multi-variety small-lot manufacturing process, verifies the effectiveness and feasibility of the control chart, and continuously controls the manufacturing process.
7. The multi-objective optimization design method for the non-parametric adaptive dynamic EWMA control chart considering statistics and economy as claimed in claim 2, wherein the sub-step S13 determines a control limit, an early warning limit and a stability limit, and the specific formula is as follows:
UCL＝μ0+k1σZ LCL＝μ0-k1σZ
UWL＝μ0+k2σZ LWL＝μ0-k2σZ
USL＝μ0+k3σZ LSL＝μ0-k3σZ
wherein k is1、k2、k3Respectively is a control limit coefficient, an early warning limit coefficient, a stable limit coefficient, and 0<|k3|<|k2|<|k1Taking k2＝2/3k1，k3＝1/3k1，
Figure FDA0003268595780000031
8. The statistical and economic non-parametric adaptive dynamic EWMA control chart multi-objective optimization design method as claimed in claim 3, wherein the sub-step S21 in the step S2 constructs a non-parametric adaptive dynamic EWMA control chart Markov chain model based on U statistics, and considers the control process of the non-parametric adaptive dynamic EWMA control chart as a Markov chain with absorption walls, and the state transition matrix P can be expressed as:
Figure FDA0003268595780000041
wherein, U is a 2m +1 dimensional column vector with elements of 1; r is a real-valued matrix of (2m +1) × (2m +1) dimensions, since Zi＝ωUi+(1-ω)Zi-1And Z isj-1＝ZiElement r in matrixijFor the probability of transitioning state i to state j, then:
Figure FDA0003268595780000042
where ω is the equivalent smoothing function value, d is the width of each equal-width sub-interval after dividing the control chart UCL and LCL into 2m +1 equal-width sub-intervals, and
Figure FDA0003268595780000043
in the step S2, the sub-step S22 calculates a statistical index, and calculates an average run length ARL of the non-parametric adaptive dynamic EWMA control chart according to the markov chain model in S21, where ARL is Pm·(I-R)-1U, and then the statistical indicator average product length APL, the specific formula is as follows:
Figure FDA0003268595780000044
wherein N is the sample volume; h represents the number of products spaced among the samples, namely the number of key processes in the sample set; ARL is the average running length calculated by the Markov chain method;
in the sub-step S23 of the step S2, the economic indicator is calculated, and the specific steps are as follows:
(1) the quality loss cost can be divided into a controlled quality loss C1 cost and an out-of-control quality cost C2 according to a Tageuchi secondary quality loss function, and the specific formula is as follows:
Figure FDA0003268595780000045
where K is a fixed constant, often K1, process drift
Figure FDA0003268595780000046
(2) Calculating the average product cost APC in a quality period, which is specifically represented by the following formula:
Figure FDA0003268595780000051
wherein the content of the first and second substances,
Figure FDA0003268595780000052
for time-averaged production process control states, APL1 is the average product length at run-away, and W is the average cost per search and exception.
9. The statistical and economic non-parametric adaptive dynamic EWMA control map multi-objective optimization design method as claimed in claim 5, wherein the sub-step S42 in the step S4 improves the view of artificial fish as follows:
Figure FDA0003268595780000053
wherein N isiterFor the total number of iterations, i is the artificial fish number, the initial field of view
Figure FDA0003268595780000054
dj、dkRespectively the distance between the current artificial fish and the j and k fish.
10. The statistical and economic non-parametric adaptive dynamic EWMA control map multi-objective optimization design method as claimed in claim 5, wherein the sub-step S43 in the step S4 improves the step size of the artificial fish as follows:
Figure FDA0003268595780000055
specifically, in the sub-step S44 of the step S4, initial parameters, the initial number of artificial fish 30, the number of attempts 50, the maximum number of iterations 900, and the crowdedness 0.1 are set.
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CN112465377A (en) * 2020-12-09 2021-03-09 沈阳工业大学 Key process identification and cluster analysis method for multi-variety small-batch manufacturing process
CN113379140A (en) * 2021-06-22 2021-09-10 郑州航空工业管理学院 Economic design method for EWMA control chart with variable sampling interval and sample volume under non-normal distribution

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* Cited by examiner, † Cited by third party
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CN112465377A (en) * 2020-12-09 2021-03-09 沈阳工业大学 Key process identification and cluster analysis method for multi-variety small-batch manufacturing process
CN113379140A (en) * 2021-06-22 2021-09-10 郑州航空工业管理学院 Economic design method for EWMA control chart with variable sampling interval and sample volume under non-normal distribution

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