CN113420916A - Design method of multivariate quality characteristic dynamic monitoring strategy - Google Patents
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Abstract
One embodiment of the invention discloses a design method of a multivariate quality characteristic dynamic monitoring strategy, which comprises the following steps: designing a loose monitoring scheme and a strict monitoring scheme criterion: in the initial stage of the production process, a loose monitoring scheme is adopted to collect data, monitoring statistics is obtained, the state of the production process is judged, if the production process is in a controlled state, the loose monitoring scheme is still adopted when the monitoring statistics is obtained next time, if the production process is in an out-of-control state, an alarm signal is given, and if the production process is in an alert state, the strict monitoring scheme is adopted when the monitoring statistics is obtained next time. Based on the design criteria, an optimization model with the shortest average alarm time is established, and design parameters of the optimal loose monitoring scheme and the optimal strict monitoring scheme are solved.
Description
Technical Field
The present invention relates to the field of production monitoring. And more particularly, to a design method of a multivariate quality characteristic dynamic monitoring strategy.
Background
With the gradual development of the traditional production process towards the direction of integration and diversification, more than one key quality characteristic often exists in the production process, so that the multivariate quality characteristic monitoring method based on the multivariate statistical process inspection theory is widely applied to the field of production process monitoring, can timely discover the quality drift of the multivariate production process, and provides decision information support for production process quality managers.
The design parameters of the traditional multivariate quality characteristic monitoring method comprise sampling sample size, sampling interval and control limit, the design parameters are fixed, and the corresponding scheme can be calculated by giving specific false alarm rate requirements. It is characterized by simple design, but this method often requires a large number of samples. In practical engineering application, sometimes a sample to be detected is very expensive, the detection cost can be obviously increased by the requirement of a large sample, and meanwhile, in order to meet the requirement of practical production management, the detection time often has a specific upper limit requirement. When the limitation of resource conditions such as sample size, time, cost and the like cannot meet the requirement of a large sample of the traditional method, once the quality of a multivariate production process drifts, if the quality characteristic monitoring is carried out by continuously adopting the traditional design method with fixed parameters, the average alarm time is obviously increased, so that a manager cannot quickly find the quality defect of the production process. Under the condition that the quality defect of the production process cannot be found in time, the production process is in a quality drifting state in the last period, the defective rate of products is further improved, the quality loss of the production process is aggravated, and unnecessary operation cost is brought to the production process.
Disclosure of Invention
In view of this, a first embodiment of the present invention provides a method for designing a multivariate quality characteristic dynamic monitoring strategy, including:
designing a loose monitoring scheme and a strict monitoring scheme criterion:
in the initial stage of the production process, a loose monitoring scheme is adopted to collect data, a first monitoring statistic is obtained, the state of the production process is judged, if the production process is in a controlled state, the loose monitoring scheme is still adopted when the monitoring statistic is obtained next time, if the production process is in an out-of-control state, an alarm signal is given, and if the production process is in an alert state, a strict monitoring scheme is adopted when the monitoring statistic is obtained next time.
In one embodiment, the loosely monitored scenario parameters include: first sample size n1First sampling interval t1A first control limit CL1And a first warning limit WL1，
And acquiring monitoring statistics according to the first sampling sample amount, if the monitoring statistics is smaller than a first warning limit, judging that the production process is in a controlled state, otherwise judging whether the monitoring statistics is larger than the first control limit, if so, judging that the production process is in an out-of-control state, giving an alarm signal, otherwise, judging that the production process is in a warning state, and acquiring the monitoring statistics according to the strict scheme when acquiring the monitoring statistics next time.
In one embodiment, the rigorous monitoring regimen data comprises: second sample size n2Second sampling interval t2A second control limit CL2And a second warning limit WL2，
And acquiring monitoring statistics according to the second sampling sample size, if the monitoring statistics is smaller than a second warning limit, judging that the production process is in a controlled state, acquiring the monitoring statistics according to a loose monitoring scheme next time, otherwise, judging whether the monitoring statistics is larger than the second control limit, if so, judging that the production process is in an out-of-control state, and giving an alarm signal, otherwise, judging that the production process is in a warning state, and when the monitoring statistics is acquired next time, continuing to adopt the strict scheme.
In a specific embodiment, the optimal design parameters of the loose monitoring scheme and the strict monitoring scheme are selected, so that the alarm time of the monitoring method is shortest.
In a specific embodiment, the step of solving the optimal design parameters of the loose monitoring scheme and the strict monitoring scheme includes:
the type of distribution of the monitoring statistics is obtained,
a state transition probability matrix is established and,
establishing an average alarm time expression of the dynamic monitoring scheme,
the shortest average alarm time is taken as an optimization criterion to establish the optimumModeling to obtain optimal loose monitoring scheme and strict monitoring scheme
In one embodiment, obtaining the monitoring statistic expression comprises:
obtaining n v-element quality characteristic samples X from production line1,X2,...,Xn，XiI is more than or equal to 1 and less than or equal to n, constructing sample statistics
Establishing expressions for monitoring statistics
Wherein the sample X is samplediSubject to a target value of mu0And a multivariate normal distribution of the covariance matrix sigma,
calculating the size of the drift
When a mass characteristic shift of Δ occurs, calculation is made
When no mass drift occurs, the first monitoring statistic obeys chi-square distribution with the degree of freedom v; when a quality characteristic shift of Δ occurs, the first monitoring statistic obeys a degree of freedom of v and the position parameter is nd2Non-central chi-square distribution of (1) is recorded as
In a specific embodiment, the state transition probability matrix is:
wherein ,R*Indicating that the monitoring statistic is in a controlled state, T*Indicating that the monitored statistic is armed, pR*R*Indicating that the state remains at R between two samples*The probability of (c) is:
pR*T*indicates that the current state is R*The next state is T*The probability of (c) is:
pT*R*indicates that the current state is T*The next state is R*The probability of (c) is:
pT*T*indicates that the current state is T*The next state is T*The probability of (c) is:
In one embodiment, the average alarm time expression of the dynamic monitoring scheme is:
ATS(n1,t1,WL1,CL1；n2,t2,WL2,CL2|Δ)
＝[p0,1-p0]×[I2×2-QΔ]-1×[t1,t2]'
wherein ,
p0＝P(Y<WL1|Y<CL1)＝P(Y<WL2|Y<CL2)。
in one embodiment, an optimization model is established and an optimization scheme is solved
Comprises the following steps:
minATS(n1,t1,WL1,CL1,n2,t2,WL2,CL2|Δ)
s.t.n1p0+n2(1-p0)≤n*
t1p0+t2(1-p0)≤t*
n1≤n2
t2≤t1
p0＝P(Y<WL1|Y<CL1)＝P(Y<WL2|Y<CL2)
in one embodiment, the average alarm time of the optimal monitoring method is calculated as
The invention has the following beneficial effects:
the invention solves the problems that the traditional multivariate quality characteristic monitoring method needs large sample amount and low monitoring efficiency and can not meet the actual requirements of high-efficiency monitoring and quick feedback in the modern production process, can flexibly meet the requirements of actual monitoring constraint conditions and provide a dynamic optimization design scheme with the shortest average alarm time, can find the problem of quality drift in shorter time compared with the traditional multivariate quality characteristic monitoring method, further improves the monitoring efficiency, is convenient for engineering technicians to use, and has good application value.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 shows a flow diagram of a method for dynamic monitoring of quality characteristics according to an embodiment of the invention.
Fig. 2 shows a flowchart of a method for obtaining optimal loose monitoring solution data and strict monitoring solution data according to an embodiment of the invention.
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following will describe embodiments of the present invention in further detail with reference to the accompanying drawings.
As shown in fig. 1, a method for designing a multivariate quality characteristic dynamic monitoring strategy includes:
designing a loose monitoring scheme and a strict monitoring scheme criterion:
in the initial stage of the production process, a loose monitoring scheme is adopted to collect data, monitoring statistics is obtained, the state of the production process is judged, if the production process is in a controlled state, the loose monitoring scheme is still adopted when the monitoring statistics is obtained next time, if the production process is in an out-of-control state, an alarm signal is given, and if the production process is in an alert state, a strict monitoring scheme is adopted when the monitoring statistics is obtained next time.
In a specific embodimentIn an example, the loose monitoring scheme parameters include: first sample size n1First sampling interval t1A first control limit CL1And a first warning limit WL1，
And acquiring a monitoring statistic according to the first sampling sample amount, if the monitoring statistic is smaller than a first warning limit, judging that the production process is in a controlled state, otherwise, judging whether the monitoring statistic is larger than the first control limit, if so, judging that the production process is in an out-of-control state, giving an alarm signal, otherwise, judging that the production process is in a warning state, and adopting the strict scheme when the monitoring statistic is acquired next time.
In one embodiment, the rigorous monitoring regimen data comprises: second sample size n2Second sampling interval t2A second control limit CL2And a second warning limit WL2，
And acquiring monitoring statistics according to the second sampling sample amount, if the monitoring statistics is smaller than a second warning limit, judging that the production process is in a controlled state, acquiring the monitoring statistics according to a loose monitoring scheme when acquiring the monitoring statistics next time, otherwise judging whether the monitoring statistics is larger than the second control limit, if so, judging that the production process is out of control, and giving an alarm signal, otherwise, judging that the production process is in a warning state, and adopting the strict scheme when acquiring the monitoring statistics next time.
More preferably, the design parameters of the optimal loose monitoring scheme and the optimal strict monitoring scheme are selected, so that the alarm time of the monitoring method is shortest.
In another embodiment, as shown in fig. 2, solving the design parameters of the optimal relaxed monitoring scheme and the optimal strict monitoring scheme includes:
obtaining a distribution type of the monitoring statistics, comprising:
obtaining n sampling samples X from production line1,X2,...,Xn，XiI is more than or equal to 1 and less than or equal to n, constructing sample statistics
Establishing expressions for monitoring statistics
Wherein the sample X is samplediSubject to a target value of mu0And a multivariate normal distribution of the covariance matrix sigma,
calculating the size of the drift
When a mass characteristic shift of Δ occurs, calculation is made
When no quality drift occurs, monitoring statistics obeying chi-square distribution with the degree of freedom v; when the quality characteristic drift is delta, the monitoring statistic obeys the degree of freedom v and the position parameter nd2Non-central chi-square distribution of (1) is recorded as
The distribution type of the obtained monitoring statistics can be obtained according to the step of obtaining the distribution type of the monitoring statistics, and will not be described in detail herein.
A state transition probability matrix is established and,
the state transition probability matrix is:
wherein ,R*Indicating that the monitoring statistic is in a controlled state, T*Indicating that the monitored statistic is armed, pR*R*Indicating that the state remains at R between two samples*The probability of (c) is:
pR*T*indicates that the current state is R*The next state is T*The probability of (c) is:
pT*R*indicates that the current state is T*The next state is R*The probability of (c) is:
pT*T*indicates that the current state is T*The next state is T*The probability of (c) is:
Establishing an average alarm time expression of the dynamic monitoring scheme,
ATS(n1,t1,WL1,CL1；n2,t2,WL2,CL2|Δ)
＝[p0,1-p0]×[I2×2-QΔ]-1×[t1,t2]'
wherein ,
p0＝P(Y<WL1|Y<CL1)＝P(Y<WL2|Y<CL2)
establishing an optimization model by taking the shortest average alarm time as an optimization criterion to obtain design parameters of an optimal loose monitoring scheme and a strict monitoring scheme
The optimization model is as follows:
minATS(n1,t1,WL1,CL1,n2,t2,WL2,CL2|Δ)
s.t.n1p0+n2(1-p0)≤n*
t1p0+t2(1-p0)≤t*
n1≤n2
t2≤t1
p0＝P(Y<WL1|Y<CL1)＝P(Y<WL2|Y<CL2)
according to the design parameters of the optimal loose monitoring scheme and the strict monitoring scheme, the average alarm time of the optimal monitoring method is calculated as
In one embodiment, let the target value be μ0＝[0.7,1.2,1.4]The mass characteristic number v is 3, and the covariance matrix is:
the mass characteristic shift vector Δ is [0.04,0.15,0.3 ].
Resource bar according to actual monitoringPiece limitation and statistical property requirement, given an upper limit n of the average sample size*20, average sampling interval upper limit t*2 and an average false alarm rate upper limit p*The value is 0.005, so that,
constructing sample statistics
Establishing expressions for monitoring statistics
Calculating the size of the drift amount:
when the mass characteristic shift Δ ═ 0.04,0.15,0.3 occurred, the magnitude of the shift amount was calculated
When no quality drift occurs in the multi-element production process, monitoring the statistic Y to obey chi-square distribution with the degree of freedom of 3; when the multivariate mass characteristic shift Delta is [0.04,0.15,0.3]]Then, the monitoring statistic Y obeys a non-central chi-square distribution with a degree of freedom of 3 and a position parameter of 0.0991n, and is recorded as
According to the magnitude relation of chi-square statistic and control limit and warning limit to establish the transition probability matrix of self state of dynamic multi-element production process and monitoring scheme judging state,
wherein, the calculation steps of each element in the matrix are as follows:
establishing an average alarm time expression of the dynamic monitoring scheme,
wherein ,
determining the constraint conditions of the design of the monitoring optimization scheme according to the specific conditions of the monitoring resources, wherein the constraint conditions comprise an upper limit n of the average sample size*20, average sampling interval upper limit t*2 and false alarm rate upper bound p*0.005, and then solve the optimum
Finally, the optimal dynamic monitoring scheme is obtained
(n1,t1,WL1,CL1；n2,t2,WL2,CL2)＝(18,2.08,6.37,13.02,40,0.66,6.02,9.84).
Estimating the monitoring efficiency of the calculated optimal dynamic monitoring scheme, and calculating the average alarm time of the optimal monitoring scheme:
ATS(18,2.08,6.37,13.02,40,0.66,6.02,9.84|[0.04,0.15,0.3])＝20.53.
therefore, the monitoring statistic is obtained according to the loose monitoring scheme, the state of the production process is judged, if the monitoring statistic is smaller than the first warning limit of 6.37, the production process is judged to be in a controlled state, if not, whether the monitoring statistic is larger than the first control limit of 13.02 is judged, if yes, the production process is judged to be in an out-of-control state, an alarm signal is given, otherwise, the production process is judged to be in a warning state, and when the monitoring statistic is obtained next time, the monitoring statistic is obtained according to the strict scheme.
And acquiring a second monitoring statistic according to the strict scheme, if the monitoring statistic is less than a second warning limit of 6.02, judging that the production process is in a controlled state, acquiring the monitoring statistic next time according to a loose monitoring scheme, otherwise, judging whether the monitoring statistic is greater than a second control limit of 9.84, if so, judging that the production process is in an out-of-control state, giving an alarm signal, otherwise, judging that the production process is in a warning state, and executing according to the strict scheme when acquiring the monitoring statistic next time.
The alarm time given by the scheme is shortest, limited time and sample resources can be utilized to the maximum extent, resource waste is avoided, when parameter drift occurs in the multivariate quality characteristics, the drift can be found quickly by the provided method, and the quality loss in the production process is reduced.
As can be seen from the following table, at n*＝10，h*At 2, p 0.005, and different amounts of drift, the results of comparing ATS of the conventional method and the proposed method,
therefore, under the condition of different drift amounts, the average alarm time ATS of the optimal dynamic monitoring method provided by the invention is obviously smaller than that of the traditional method. This shows that when parameter drift occurs in the multivariate quality characteristics, the proposed method can quickly find the drift, reducing the quality loss of the production process.
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that other variations or modifications may be made on the basis of the above description, and all embodiments may not be exhaustive, and all obvious variations or modifications may be included within the scope of the present invention.
Claims (10)
1. A multivariate quality characteristic dynamic monitoring strategy design method is characterized by comprising the following steps:
designing a loose monitoring scheme and a strict monitoring scheme criterion:
in the initial stage of the production process, a loose monitoring scheme is adopted to collect data, a first monitoring statistic is obtained, the state of the production process is judged, if the production process is in a controlled state, the loose monitoring scheme is still adopted when the monitoring statistic is obtained next time, if the production process is in an out-of-control state, an alarm signal is given, and if the production process is in an alert state, a strict monitoring scheme is adopted when the monitoring statistic is obtained next time.
2. The method of claim 1, wherein the loosely monitored scheme parameters comprise: first sample size n1First sampling interval t1A first control limit CL1And a first warning limit WL1，
And acquiring monitoring statistics according to the first sampling sample amount, if the monitoring statistics is smaller than a first warning limit, judging that the production process is in a controlled state, otherwise judging whether the monitoring statistics is larger than the first control limit, if so, judging that the production process is in an out-of-control state, giving an alarm signal, otherwise, judging that the production process is in a warning state, and acquiring the monitoring statistics according to the strict scheme when acquiring the monitoring statistics next time.
3. The method of claim 2, wherein the rigorous monitoring scenario data comprises: second sample size n2Second sampling interval t2A second control limit CL2And a second warning limit WL2，
And acquiring monitoring statistics according to the second sampling sample size, if the monitoring statistics is smaller than a second warning limit, judging that the production process is in a controlled state, acquiring the monitoring statistics according to a loose monitoring scheme next time, otherwise, judging whether the monitoring statistics is larger than the second control limit, if so, judging that the production process is in an out-of-control state, and giving an alarm signal, otherwise, judging that the production process is in a warning state, and when the monitoring statistics is acquired next time, continuing to adopt the strict scheme.
4. The method of claim 3, wherein the optimal design parameters for the loose monitoring solution and the strict monitoring solution are selected to minimize the alarm time of the monitoring method.
5. The method of claim 4, wherein the step of solving for optimal loosely and tightly monitored solution design parameters comprises:
the type of distribution of the monitoring statistics is obtained,
a state transition probability matrix is established and,
establishing an average alarm time expression of the dynamic monitoring scheme,
the shortest average alarm time is taken as an optimization criterion to establish the optimumModeling to obtain optimal loose monitoring scheme and strict monitoring scheme
6. The method of claim 5, wherein obtaining a monitoring statistic expression comprises:
obtaining n v-element quality characteristic samples X from production line1,X2,...,Xn，XiI is more than or equal to 1 and less than or equal to n, constructing sample statistics
Establishing expressions for monitoring statistics
Wherein the sample X is samplediSubject to a target value of mu0And a multivariate normal distribution of the covariance matrix sigma,
calculating the size of the drift
When a mass characteristic shift of Δ occurs, calculation is made
When no mass drift occurs, the first monitoring statistic obeys chi-square distribution with the degree of freedom v; when a quality characteristic shift of Δ occurs, the first monitoring statistic obeys a degree of freedom of v and the position parameter is nd2The non-central chi-square distribution of (a), noted as Y:
7. the method of claim 5, wherein the state transition probability matrix is:
wherein ,R*Indicating that the monitoring statistic is in a controlled state, T*Indicating that the monitored statistic is in an alert state,
8. The method of claim 5, wherein the average alarm time of the dynamic monitoring scheme is expressed as:
ATS(n1,t1,WL1,CL1；n2,t2,WL2,CL2|Δ)
＝[p0,1-p0]×[I2×2-QΔ]-1×[t1,t2]'
wherein ,
p0＝P(Y<WL1|Y<CL1)＝P(Y<WL2|Y<CL2)。
9. the method of claim 5, wherein the optimization model is established and the optimization solution is solved
Comprises the following steps:
10. the method of claim 8, wherein the average alarm time of the optimal monitoring method is calculated as follows based on the optimal loose monitoring scheme data and the strict monitoring scheme data
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