Self-starting control chart sequence rebound parameter updating method based on warning limit triggering

Abstract

The invention provides a self-starting control chart sequence rebound parameter updating method based on warning limit triggering, and relates to the field of statistical process control. Different from a traditional product quality characteristic distribution model based on normal distribution, the method mainly takes product quality monitoring in a high-quality manufacturing process as a target, modeling is performed on an event occurrence interval variable Xt in the process by using gamma distribution, a pivot vector # imgabs0 # is constructed based on the modeling, and mapping from the Xt to self-starting event occurrence interval data St is completed. Further constructing a monitoring statistic Qt of the self-starting control chart by using an exponential weighted moving average method, dynamically switching a parameter updating process based on a time sequence and a sequence bounce according to position information of the Qt in a safety domain, a warning domain and an out-of-control domain of the control chart, delaying the progress that an out-of-control sample flows into parameter estimation, and calculating the out-of-control sample according to the parameter updating process. Data pollution caused by out-of-control samples to parameter estimation is reduced, and the monitoring efficiency of the self-starting control chart is improved.

Description

Technical Field

[0001] The present invention relates to the field of statistical process control, and in particular to a method for updating jump parameters of a self-starting control chart sequence based on warning limit triggering. Background Art

[0002] The optimization and upgrading of traditional manufacturing has led to a growing number of product manufacturing processes transitioning to high-quality manufacturing. Given that high-quality manufacturing processes require extremely low product rejection rates, collecting event interval samples typically requires a long wait time or a large number of product inspections. This increases the cost and frequency of acquiring these samples, significantly hindering the acquisition of sufficient, controlled event interval samples (hereinafter referred to as baseline data) for accurate parameter estimation in the first phase. Consequently, control charts designed based on the traditional "first-phase parameter estimation, second-phase online monitoring" model are unsuitable for practical applications in high-quality manufacturing processes.

[0003] The self-starting control chart operates based on the "parameter estimation and online monitoring" model, which can help users start production process monitoring immediately after obtaining limited baseline data, effectively eliminating the significant difference between the first and second stages in the traditional model.

[0004] However, in the study of self-starting control charts, it was found that if a parameter shift occurs during the monitoring process of the manufacturing process, the out-of-control samples will gradually contaminate the parameter estimation model's estimation of the controlled parameters as data is collected. At this time, if the self-starting control chart cannot identify the parameter shift within the effective monitoring window, the parameter shift will be gradually masked as the out-of-control samples are collected, thereby affecting the self-starting control chart's ability to monitor the out-of-control process. Summary of the Invention

[0005] Purpose of the invention: To propose a method for updating the parameters of a self-starting control chart sequence back-jump based on warning limit triggering, aiming to reduce the negative impact caused by the parameter masking phenomenon, reduce the degree of contamination of out-of-control samples on the estimated parameters, expand the monitoring window period, and help the self-starting control chart effectively identify parameter deviations in the manufacturing process.

[0006] The present invention proposes a method for updating the jump parameters of a self-starting control diagram sequence based on a warning limit trigger, comprising the following steps:

[0007] Set control limits and warning limits, and divide the self-starting control chart into safe area, warning area, and out-of-control area;

[0008] In a manufacturing process based on the gamma distribution, event interval data X is collected in time series (t = 1, 2, 3, ...) t , based on the event occurrence interval data X t Construct the pivot volume At , through the pivot volume A t Mapping to obtain the self-start event interval data S t ;

[0009] Constructing the monitoring statistic Q of the self-starting control chart t ;

[0010] Observe and obtain monitoring statistics Q t Position information in the self-starting control diagram:

[0011] If the monitoring statistic Q t If it falls into the out-of-control region, the self-starting control diagram will send out an alarm signal;

[0012] Otherwise, if the monitoring statistic Q t Falling into the safe domain, the pivot quantity A is updated online based on the time series t Parameters in If the monitoring statistic Q t Falling into the warning domain, the pivot quantity A is updated online based on sequence backjump t Parameters in

[0013] In a further embodiment, setting control limits and warning limits specifically includes:

[0014] Assuming that the process mean in the manufacturing process is μ0 and the process standard deviation is σ0, let the center limit CL = μ0; let the upper control limit UCL = μ0 + L1σ0, the lower control limit LCL = μ0 - L2σ0, L1 and L2 are control limit coefficients; the upper warning limit UWL = μ0 + c1L1σ0, the lower warning limit LWL = μ0 - c1L2σ0, c1 and c1 are warning limit coefficients;

[0015] Given the ideal controlled average running chain length value ARL0;

[0016] Perform a Monte Carlo simulation of the control chart based on the system's controlled state. Adjust the control limit coefficients L1 and L2, as well as the warning limit coefficients c1 and c2, to ensure that the chart satisfies the constraint of ARL0 = w, where w is a constant given by the user. On this basis, obtain the values of the upper control limit UCL, lower control limit LCL, center limit CL, upper warning limit UWL, and lower warning limit LWL.

[0017] In a further embodiment, for the gamma distribution, its normalized form is expressed as follows:

[0018] U t =X t / β

[0019] Where, X t Gamma distribution X with shape parameter α and scale parameter βt ~Γ(α,β);U t Obey the standard gamma distribution X with shape parameter α and scale parameter 1 t ~Γ(α,1);

[0020] When the shape parameter α is known, the maximum likelihood estimator of the scale parameter β of the gamma distribution is It is defined as follows:

[0021]

[0022] Where, t=1, 2, 3… is the time of data collection; X i is the event interval data at the i-th data collection moment; Represents the sample mean at the time t when the data is collected.

[0023] In a further embodiment, based on the event occurrence interval data X t Construct the pivot volume A t :

[0024]

[0025] Pivot Amount A t Obey the generalized beta prime distribution GBP(α,αt,1,t).

[0026] In a further embodiment, by designing a transformation model MT(A t ) Mapping to obtain the self-start event interval data S t :

[0027]

[0028] Where, T -1 is the inverse cumulative distribution function of the standard gamma distribution; β ′ Represents the cumulative distribution function of the generalized beta prime distribution GBP(α,αt,1,t).

[0029] In a further embodiment, a monitoring statistic of a self-starting control chart is constructed, and the expression is as follows:

[0030] Q t =λS t +(1-λ)Q t-1

[0031] Where λ is the smoothness coefficient of the self-starting control chart; Q t is the monitoring statistic at time t; Q t-1 is the monitoring statistic at time t-1.

[0032] In a further embodiment, the monitoring statistic Q is obtained by observingt Position information in the self-starting control diagram, if t = i-1, the monitoring statistic Q i-1 Located in the warning zone, i.e. Q i-1 ∈(LCL,LWL] or Q i-1 ∈[UWL,UCL), the self-starting control chart triggers the sequence jump parameter update process based on the warning line, which is specifically manifested as follows:

[0033] At the next moment t=i, the self-starting event occurs at the interval data S i During the mapping process, all parameters The estimation operations are no longer performed based on the time series update method, but the baseline data at time t = i is used to jump back to time v to estimate the pivot quantity A. i Parameters in to update.

[0034] In a further embodiment, after completing the self-starting event occurrence interval data S at time t=i i After the mapping, further calculate the monitoring statistic Q at that moment i , and according to the monitoring statistic Q i The location information determines which parameter to use in the next moment to update the process, which is specifically as follows:

[0035] If the monitoring statistic Q t Still in the warning zone, that is, Q i ∈(LCL,LWL] or Q i ∈[UWL,UCL), then the self-starting control chart at time t=i+1 continues to execute the parameter update process based on sequence back-jump; on the contrary, if the monitoring statistic Q t Falling in the controlled domain, that is, Q i ∈(LWL,UWL), then the self-starting control chart executes the parameter update process based on the time series;

[0036] Repeat the above steps until the monitoring statistic Q t Falling into the out-of-control region, that is, Q t ∈[LCL,-∞) or Q t ∈[UCL,+∞), the manufacturing process is judged to be out of control, and an alarm signal is issued by the self-starting control chart.

[0037] In addition, the present invention also discloses an electronic device, which includes: a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements the above-mentioned self-starting control diagram sequence jump parameter update method based on warning limit triggering.

[0038] In addition, the present invention also discloses a computer-readable storage medium, which stores at least one executable instruction. When the executable instruction is run on an electronic device, the electronic device executes the above-mentioned self-starting control diagram sequence jump back parameter update method based on warning limit triggering.

[0039] Compared with the prior art, the present invention has at least the following beneficial effects:

[0040] The present invention introduces a warning limit trigger mechanism, which enables the self-starting control chart to dynamically switch between the parameter update process based on time series and the parameter update process based on sequence rebound according to the position information of the monitoring statistic, delaying the progress of the out-of-control samples flowing into the parameter estimation, reducing the data pollution caused by the out-of-control samples to the parameter estimation, and achieving the purpose of slowing down the rate of offset masking (i.e., increasing the monitoring window period) and eliminating the negative impact of offset masking.

[0041] The present invention has a low demand for baseline data when implementing high-quality manufacturing process monitoring, and is applicable to applications where sample data is difficult to obtain and where sample data is easy to obtain but the production cycle is short. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A simulation diagram of the offset masking problem.

[0043] Figure 2 The flowchart of the method for updating the jump parameters of the self-starting control chart sequence based on the warning limit trigger is shown in FIG.

[0044] Figure 3 This is a schematic diagram of event interval variables. DETAILED DESCRIPTION

[0045] In the following description, numerous specific details are provided to provide a more thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced without one or more of these details. In other instances, certain technical features well known in the art have not been described to avoid confusion with the present invention.

[0046] Figure 1 A simulation of the offset masking problem is given. During the simulation, it is assumed that the controlled mean in the original distribution model of the process is μ0 = 0. When the process does not have parameter offset (t < 30), the baseline data in the "parameter estimation and online monitoring" mode can estimate the controlled mean in the process, that is, At this time, if the process has a parameter shift (μ0=0→μ1=1) at time t=30, as the process monitoring progresses, the estimated out-of-control mean value in the process Will change gradually over time, and parameter deviation will be gradually masked. Figure 1It can be seen that when the process undergoes a greater degree of parameter deviation (μ0=0→μ1=2), the rate at which the deviation is masked will further accelerate.

[0047] In this regard, this patent application proposes a method for updating the jump parameters of a self-starting control diagram sequence based on a warning limit trigger. t The position information of the warning limit and the control limit at the previous moment (i.e., t = i-1) is compared to determine the estimated parameter update process of the self-starting control chart at the next moment (i.e., t = i-1). Specifically, if t = i-1, the monitoring statistic Q i-1 ∈(LCL,LWL] or Q i-1 ∈[UWL,UCL), the self-start control diagram triggers the sequence jump parameter update process based on the warning line. At the next moment (i.e., t=i), the interval data S i In the mapping process, all operations related to parameter estimation are no longer updated according to the process based on time series, but use the baseline data (i.e. {X1, X2, ..., X i-v}) Update the parameters. Based on the estimated parameters, further calculate the monitoring statistic Q at this moment i , and according to the monitoring statistic Q i The location information determines which parameter update process to use at the next moment (t=i+1). Specifically, if the monitoring statistic Q t Still in the warning zone (ie Q i ∈(LCL,LWL] or Q i ∈[UWL,UCL)), then at time t=i+1, the self-starting control chart continues to execute the parameter update process based on sequence back-jump. On the contrary, if the monitoring statistic Q t Falling in the controlled domain (i.e. Q i ∈(LWL,UWL)), the self-starting control chart executes a time-series-based parameter update process. This approach can effectively mitigate the negative impact of parameter masking, reduce the degree of contamination of estimated parameters by out-of-control samples, expand the monitoring window, and help the self-starting control chart effectively identify parameter drift in the manufacturing process.

[0048] The following is combined with Figure 2 The present invention is described in further detail.

[0049] The present invention provides a method for updating sequence back-jump parameters based on a warning line, comprising the following steps:

[0050] (1) The upper control limit UCL, the lower control limit LCL, the center limit CL, the upper warning limit UWL, and the lower warning limit LWL are selected. Based on the above control limits and warning limits, the self-starting control chart for high-quality manufacturing processes is divided into a safe region, a warning region, and an out-of-control region.

[0051] (2) In the high-quality manufacturing process based on the gamma distribution, the event interval data X is collected at time t = 1, 2, 3 t , from time t = 3, construct the pivot quantity The transformed model MT(A t ) Mapping to obtain the self-start event interval data S t Furthermore, the exponentially weighted moving average (EWMA) method is used to construct the monitoring statistic Q of the self-starting control chart. t .

[0052] (3) Observe and obtain monitoring statistics Q t The position information in the self-starting control chart is based on the monitoring statistic Q t Position information in the self-starting control diagram, dynamically switch the parameter update method based on time series or the parameter update method based on sequence back jump to adjust the parameters If t = i-1, the monitoring statistic is in the warning region, that is, Q i-1 ∈(LCL,LWL] or Q i-1 ∈[UWL,UCL), the self-start control diagram triggers the sequence jump parameter update process based on the warning line, which is specifically manifested as follows: at the next moment (i.e., t = i), in the interval data S of the self-start event i During the mapping process, all parameters The estimation-related operations are no longer performed according to the time series update method, but the baseline data at time t = i and time v (i.e., t = iv) (i.e., {X1, X2, ..., X i-v}) For the pivot quantity A i Parameters in to update.

[0053] (4) The interval data S of the self-starting event at the completion time t=i i After the mapping, further calculate the monitoring statistic Q at that moment i , and according to the monitoring statistic Q i The location information determines which parameter update process to use at the next moment (t=i+1). Specifically, if the monitoring statistic Q t Still in the warning zone (ie Q i ∈(LCL,LWL] or Q i∈[UWL,UCL), then at time t=i+1 the self-starting control chart continues to execute the parameter update process based on sequence back-jump. On the contrary, if the monitoring statistic Q t Falling in the controlled domain (i.e. Q i ∈(LWL,UWL)) then the self-starting control chart executes the parameter update process based on the time series.

[0054] (5) Repeat the above steps until the monitoring statistic Q t Falling into the out-of-control region (i.e. Q t ∈[LCL,-∞) or Q t ∈[UCL,+∞)), the manufacturing process is judged to be out of control, and an alarm signal is issued from the self-starting control chart.

[0055] Step (1) is as follows:

[0056] (1-1) Assuming the process mean of the monitored high-quality manufacturing process is μ0 and the process standard deviation is σ0, let the center limit CL = μ0. Also, let the upper control limit UCL = μ0 + L1σ0 and the lower control limit LCL = μ0 - L2σ0, where L1 and L2 are control limit coefficients. Furthermore, let the upper warning limit UWL = μ0 + c1L1σ0 and the lower warning limit LWL = μ0 - c2L2σ0, where c1 and c2 are warning limit coefficients, which can be freely selected according to actual needs, such as c1 = c2 = 0.5.

[0057] (1-2) Given an ideal controlled average run length (ARL0) value, for example, ARL0 = w, where w is a constant given according to requirements, such as w = 370.

[0058] (1-3) Carry out Monte Carlo simulation of the control chart according to the situation that the system is controlled (μ1=μ0), adjust the control limit coefficients L1 and L2 and the warning limit coefficients c1 and c2, so that the control chart meets the restriction condition ARL0=w, and then obtain the values of the upper control limit UCL, lower control limit LCL, center limit CL, upper warning limit UWL, and lower warning limit LWL.

[0059] The specific mapping model construction process of step (2) is as follows:

[0060] (2-1) In a high-quality manufacturing process based on the gamma distribution, event interval data X is collected at time t = 1, 2, 3. t , where the event interval data refers to the time interval between two consecutive defective products in the manufacturing process. Figure 3 As shown in the figure, when the gamma distribution is used to mathematically describe the high-quality manufacturing process, its shape parameter α is the cumulative number of event interval data. When α = 1, the gamma distribution degenerates into an exponential distribution, and the event interval data X t=T1, T2, T3, ...; when α = 2, the event interval data X t =T1+T2, T3+T4, ...; When α=3, the event interval data X t =T1+T2+T3,T4+T5+T6,…, and so on.

[0061] (2-2) For the gamma distribution, its standardized form can be expressed as follows:

[0062] U t =X t / β

[0063] Among them, X t Obey the gamma distribution with shape parameter α and scale parameter β, that is, X t ~Γ(α,β);U t It obeys the standard gamma distribution with shape parameter α and scale parameter 1, that is, X t ~Γ(α,1). Furthermore, when the shape parameter α is known, the maximum likelihood estimator of the scale parameter β of the gamma distribution is It can be defined as follows:

[0064]

[0065] Based on the above form, construct the pivot quantity:

[0066]

[0067] Through mathematical derivation, we know that the pivot quantity A t Obey the generalized beta prime distribution GBP(α,αt,1,t), that is, A t ~GBP(α,αt,1,t).

[0068] (2-3) Constructing the transformation model MT(A t ), so that it can store event interval data X t , through the constructed pivot quantity A t , mapping to obtain the self-start event interval data S t ,Right now:

[0069]

[0070] Among them, T -1 is the inverse cumulative distribution function of the standard gamma distribution, β ′ is the cumulative distribution function of the generalized beta prime distribution GBP(α,αt,1,t). So far, the event interval data X is completed. t To the self-starting event interval data S that follows the standard gamma distribution t The mapping transformation between .

[0071] (2-4) Based on the monitoring statistic Q of the self-starting control chart constructed using the exponentially weighted moving average (EWMA) method t ,Right now:

[0072] Q t =λS t +(1-λ)Q t-1

[0073] Where λ is the smoothness coefficient of the self-starting control chart.

[0074] In step (3), the specific sequence jump parameter update process is as follows:

[0075] (3-1) According to the monitoring statistic Q t The position information in the self-starting control diagram dynamically selects which parameter update process to use at the next moment;

[0076] (3-2) If t = i-1, the monitoring statistic Q i-1 ∈(LCL,LWL] or Q i-1 ∈[UWL,UCL), the self-start control diagram triggers the sequence jump parameter update process based on the warning line, which is specifically manifested as follows: at the next moment (i.e., t = i), in the interval data S of the self-start event i During the mapping process, all parameters The estimation-related operations are no longer performed according to the time series update method, but the baseline data at time t = i and time v (i.e., t = iv) (i.e., {X1, X2, ..., X i-v}), for the pivot quantity A i Parameters in To update, that is:

[0077]

[0078] Corresponding self-start event occurrence interval data At this time, β ′ is the cumulative distribution function of the generalized beta prime distribution GBP(α,α(iv),1,iv), and the monitoring statistic Q of the self-starting control chart i =λS i +(1-λ)Q i-1 . Further, the rebound time v in parameter estimation is clearly defined as in This is a round-up operation.

[0079] (3-3) In order to use more accurate estimated parameters in the sequence back-jump process, the present invention provides the following preferred solution for selecting the back-jump time v, which is specifically expressed as follows: when the monitoring statistic is in the warning domain at time t=i-1, that is, Q i-1 ∈(LCL,LWL] or Q i-1 ∈[UWL,UCL), the self-starting control chart triggers the sequence jump back parameter update process, extracts the time when the monitoring statistic was last in the safe domain, recorded as t=j. At the same time, the estimated parameters at time t=j are recorded as And set the acceptable estimation parameter interval Ω = [98% × B, 102% × B]. Further, calculate Estimated parameters at time like The sequence jumps back to And if The sequence then jumps back to the time when the last monitored statistic was in the safe domain, that is, t=j.

[0080] (3-4) If t = i-1, the monitoring statistic Q i-1 ∈(LWL,UWL), the self-starting control diagram triggers the parameter update process based on the time series, which is specifically manifested as follows: at the next moment (i.e., t = i), in the interval data S of the self-starting event i During the mapping process, all parameters All estimation-related operations are still performed according to the time series-based update method. The baseline data used for parameter estimation is {X1, X2, …, X i},Right now:

[0081]

[0082] Corresponding self-start event occurrence interval data At this time, β ′ is the cumulative distribution function of the generalized beta prime distribution GBP(α,αi,1,i), and the monitoring statistic Q of the self-starting control chart i =λS i +(1-λ)Q i-1 .

[0083] In step (4), the specific parameter update process based on the monitoring statistic location information is dynamically selected and includes the following steps:

[0084] (4-1) At time t, when the monitoring statistic Q t When ∈(LWL,UWL), the monitoring statistic is determined to be in the controlled domain, indicating that the system parameters in the manufacturing process are stable and production is proceeding normally. At this time, the time series-based parameter update method should be triggered to update the estimated parameters in sequence according to the time series, realizing real-time online monitoring of the manufacturing process.

[0085] (4-2) At time t, when the monitoring statistic Q t ∈(LCL,LWL] or Q t ∈[UWL,UCL), the monitoring statistic is judged to be in the warning domain. This indicates that the parameters in the manufacturing process may have shifted, and sample data in an out-of-control state may have participated in parameter estimation and parameter update. This will cause shift masking, resulting in a decrease in the efficiency of the self-starting control chart for parameter shift monitoring. At this time, the parameter update method based on sequence rebound should be triggered to delay the progress of the out-of-control samples in the parameter estimation, thereby slowing the rate of shift masking (i.e., increasing the monitoring window period) and eliminating the negative impact of shift masking.

[0086] In step (5), at time t, when the monitoring statistic Q t Falling into the out-of-control region (i.e., Q t ∈[LCL,-∞) or Q t ∈[UCL,+∞)), there is sufficient probability to show that parameter deviation has occurred in the manufacturing system, and then it can be determined that the manufacturing process is out of control, and the self-starting control chart sends an alarm signal.

[0087] The technical process of the method for updating the self-starting control diagram sequence jump back parameters based on warning limit triggering disclosed in the above embodiment can be implemented in whole or in part through software, hardware, firmware or any other combination.

[0088] When implemented in hardware, the above embodiments can be run on an electronic device by compiling all or part of the operating logic and computational processes into software. The electronic device includes a processor, a memory, a communication interface, and a communication bus. The processor, memory, and communication interface communicate with each other via the communication bus. The memory is used to store at least one executable instruction that causes the processor to execute the technical process of the warning limit-triggered self-starting control diagram sequence back-jump parameter update method disclosed in the above embodiments.

[0089] When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. If the above method is implemented in the form of a software function module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present application can be embodied in the form of a software product in essence or in other words, the part that contributes to the relevant technology. The software product is stored in a storage medium and includes several instructions to enable an electronic device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in each embodiment of the present application. The aforementioned storage medium includes various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM), a magnetic disk or an optical disk. In this way, the embodiment of the present application is not limited to any specific hardware, software or firmware, or any combination of hardware, software and firmware.

[0090] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A method for updating the jump parameters of a self-starting control chart sequence based on a warning limit trigger, characterized in that: include: Set control limits and warning limits, and divide the self-starting control chart into safe area, warning area, and out-of-control area; In a manufacturing process based on gamma distribution, event occurrence interval data X is collected in a preset time series. t , based on the event occurrence interval data X t Construct the pivot volume A t , mapping to obtain the self-start event interval data S t ; Constructing the monitoring statistic Q of the self-starting control chart t ; Observe and obtain monitoring statistics Q t Position information in the self-starting control diagram: If the monitoring statistic Q t If it falls into the out-of-control region, the self-starting control diagram will send out an alarm signal; Otherwise, if the monitoring statistic Q t Falling into the safe domain, the pivot quantity A is updated online based on the time series t Parameters in If the monitoring statistic Q t Falling into the warning domain, the pivot quantity A is updated online based on sequence backjump t Parameters in 2. The method for updating parameters of a self-starting control diagram sequence back-jump based on a warning limit trigger according to claim 1, characterized in that: Set control limits and warning limits, including: Assuming that the process mean in the manufacturing process is μ0 and the process standard deviation is σ0, let the center limit CL = μ0; let the upper control limit UCL = μ0 + L1σ0, the lower control limit LCL = μ0 - L2σ0, L1 and L2 are control limit coefficients; the upper warning limit UWL = μ0 + c1L1σ0, the lower warning limit LWL = μ0 - c2L2σ0, c1 and c2 are warning limit coefficients; Given the ideal controlled average running chain length value ARL0; Carry out Monte Carlo simulation of the control chart according to the controlled situation of the system, adjust the control limit coefficients L1 and L2 and the warning limit coefficients c1 and c2, so that the control chart meets the restriction condition ARL0=w, where w is a constant given according to the requirements; on this basis, obtain the values of the upper control limit UCL, lower control limit LCL, center limit CL, upper warning limit UWL, and lower warning limit LWL.

3. The method for updating parameters of a self-starting control diagram sequence back-jump based on a warning limit trigger according to claim 1, characterized in that: For the gamma distribution, its standardized form is expressed as follows: U t =X t / b Where, X t Gamma distribution X with shape parameter α and scale parameter β t ~Γ(α,β);U t Obey the standard gamma distribution X with shape parameter α and scale parameter 1 t ~Γ(α,1); When the shape parameter α is known, the maximum likelihood estimator of the scale parameter β of the gamma distribution is It is defined as follows: Where, t=1, 2, 3… is the time of data collection; X i is the event interval data at the i-th data collection moment; Represents the sample mean at the time t when the data is collected.

4. The method for updating parameters of a self-starting control diagram sequence back-jump based on a warning limit trigger according to claim 3 is characterized in that: Based on the event occurrence interval data X t Construct the pivot volume A t : Pivot Amount A t Obey the generalized beta prime distribution GBP(α,αt,1,t).

5. The method for updating parameters of a self-starting control diagram sequence back-jump based on a warning limit trigger according to claim 4, characterized in that: Based on the event occurrence interval data X t Construct the pivot volume A t , mapping to obtain the self-start event interval data S t : Where, T -1 is the inverse cumulative distribution function of the standard gamma distribution; β ′ Represents the cumulative distribution function of the generalized beta prime distribution GBP(α,αt,1,t).

6. A method for updating parameters of a self-starting control diagram sequence back-jump based on a warning limit trigger according to claim 1 or 5, characterized in that: Construct the monitoring statistics of the self-start control chart, the expression is as follows: Q t =λS t +(1-λ)Q t-1 Where λ is the smoothness coefficient of the self-starting control chart; Q t is the monitoring statistic at time t; Q t-1 is the monitoring statistic at time t-1.

7. The method for updating parameters of a self-starting control diagram sequence back-jump based on a warning limit trigger according to claim 1, characterized in that: Observe and obtain monitoring statistics Q t Position information in the self-starting control diagram, if t = i-1, the monitoring statistic Q i-1 Located in the warning zone, i.e. Q i-1 ∈(LCL,LWL] or Q i-1 ∈[UWL,UCL), the self-starting control chart triggers the sequence jump parameter update process based on the warning line, which is specifically manifested as follows: At the next moment t=i, the self-starting event occurs at the interval data S i During the mapping process, all parameters The estimation operations are no longer performed based on the time series update method, but the baseline data at time t = i is used to jump back to time v to estimate the pivot quantity A. i Parameters in to update.

8. The method for updating parameters of a self-starting control diagram sequence back-jump based on a warning limit trigger according to claim 7, characterized in that: The interval data S of the self-starting event at the completion time t=i i After the mapping, further calculate the monitoring statistic Q at that moment i , and according to the monitoring statistic Q i The location information determines which parameter to use in the next moment to update the process, which is specifically as follows: If the monitoring statistic Q t Still in the warning zone, that is, Q i ∈(LCL,LWL] or Q i ∈[UWL,UCL), then the self-starting control chart at time t=i+1 continues to execute the parameter update process based on sequence back-jump; on the contrary, if the monitoring statistic Q t Falling in the controlled domain, that is, Q i ∈(LWL,UWL), then the self-starting control chart executes the parameter update process based on the time series; Repeat the above steps until the monitoring statistic Q t Falling into the out-of-control region, that is, Q t ∈[LCL,-∞) or Q t ∈[UCL,+∞), the manufacturing process is judged to be out of control, and an alarm signal is issued by the self-starting control chart.

9. An electronic device, characterized in that: The device includes: a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements the self-starting control diagram sequence jump back parameter updating method based on warning limit triggering according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that The storage medium stores at least one executable instruction, and when the executable instruction is executed on the electronic device, the electronic device executes the self-starting control diagram sequence jump back parameter updating method based on warning limit triggering according to any one of claims 1 to 8.

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