An optimal multi-level continuous sampling inspection and process capability index integration method

Abstract

The present invention discloses an optimal multi-level continuous sampling inspection and process capability index integration method, comprising the following steps: setting the current average detection quality limit and the long-term average inspection number limit; calculating the normal fit, when the normal fit is greater than or equal to the preset value, calculating the process qualified product rate estimate and its lower confidence limit, otherwise stopping production for repair; calculating the continuous qualified product number and inspection score of the optimal multi-level continuous sampling inspection, determining the risk control sample size and the key value of the process capability index; executing the optimal multi-level inspection scheme; comparing the key value of the process capability index with the process capability index estimate, the process qualified product rate estimate and the lower confidence limit of the process qualified product rate estimate at the same time, and making a decision to continue the inspection, return to the normal fit or terminate production. The present invention meets the quality and risk constraints at the lowest cost, realizes the simultaneous control and quantitative control of two types of risks, and is suitable for production process control without inspection capability restrictions.

Description

Technical Field

[0001] The invention relates to the technical field of product manufacturing process control, in particular to an optimal multi-level continuous sampling inspection and process capability index integration method. Background Art

[0002] Process control in a production workshop is a complex system engineering that requires taking into account multiple constraints such as quality, cost and risk. Among them, customer requirements for product quality constitute quality constraints, while the costs involved in production operations constitute cost constraints. In order to avoid the risks caused by misjudgment of process status while meeting quality and cost constraints, risk constraints are generated. These constraints jointly require that the process control solution must have multiple functions, including timely collection of process data, accurate monitoring of process status, in-depth data analysis and real-time feedback. In modern industrial production, there are many process control methods, such as continuous sampling plan (CSP), process yield index, process capability index, process qualified product rate, equipment maintenance and control charts. These methods have their own applications in process control, but they also have obvious limitations. Among them, continuous sampling plan (CSP) is one of the important methods of process control. It is widely used in the control link of factory production process. Its main goal is to improve product quality and reasonably reduce production costs.

[0003] Traditional continuous sampling inspection (CSP) has certain defects. When formulating the inspection plan, it fails to fully consider the key factor of the capability level of the controlled process. This leads to a disconnect between the inspection plan and the actual situation of the production process in practical applications, which in turn affects the precise control of product quality and the effective management of costs. Summary of the invention

[0004] In view of the deficiencies of the prior art, the present invention provides an optimal multi-level continuous sampling inspection and process capability index integration method, which aims to solve the problems mentioned in the background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: an optimal multi-level continuous sampling inspection and process capability index integration method, comprising the following steps:

[0006] Step S1: Set the current average detection quality limit and the long-term average test number limit ;

[0007] Step S2: Use the current Perform normality test on production data; calculate normality fit , when the normal fit is Greater than or equal to the preset value, calculate the estimated process yield and the lower confidence limit of the process yield estimate , otherwise stop production for repair;

[0008] Step S3: Estimation of process qualified product rate and and Compared with the process yield estimate , exemption from inspection; when , execute step S4; when , stop production for repair;

[0009] Step S4: Test the number limit by long-term average Calculate the limit process failure rate , by the limit process failure rate Calculate the limit process capability index , the average detection mass limit Calculate the process capability index of the quality requirement limit ;

[0010] Step S5: Calculate the optimal multi-level continuous sampling test The number of continuous qualified products and test scores , determine the risk control sample size and process capability index key values ;

[0011] Step S6: Execution parameters are of Inspection plan;

[0012] Step S7: Keep records while executing the inspection plan The latest data, recorded The process capability index estimate is calculated based on the latest data and process yield estimate ;

[0013] Step S8: Estimation of process qualified product rate and the lower confidence limit of the process yield estimate and process capability index estimator Process Capability Index Key Value For comparison, and , execute step S6, when and , execute step S2; otherwise, stop production for repair.

[0014] Furthermore, the process yield estimate It is expressed as:

[0015] (1);

[0016] In the formula, Indicates the upper tolerance limit; Indicates the lower limit of tolerance; Cumulative distribution function representing the normal distribution; represents the sample standard deviation, For the sample observations, It is the number of the collected inspection data, which is a positive integer; represents the sample mean; is the sample size.

[0017] Furthermore, the lower confidence limit of the process conformity rate estimate is It is expressed as:

[0018] (2);

[0019] In the formula, represents the quantile of the chi-square distribution; express Chi-square distribution with degrees of freedom The sample observation value under the quantile.

[0020] Furthermore, the limit process failure rate It is expressed as:

[0021] (3).

[0022] Furthermore, the limit process capability index It is expressed as:

[0023] (4);

[0024] In the formula, Represents the inverse of the normal cumulative distribution function.

[0025] Furthermore, the quality requirement limit process capability index It is expressed as:

[0026] (5).

[0027] Furthermore, the number of continuous qualified products and test scores are the solutions of equation (6) and equation (7) respectively;

[0028] (6);

[0029] (7);

[0030] In the formula, express of Power; express of 2 Power; express of 3 Power; express of 4 Power; express of Power; express of Power.

[0031] Furthermore, the sample size of risk control and process capability index key values are the solutions of equation (8) and equation (9) respectively;

[0032] (8);

[0033] (9);

[0034] In the formula, , , and The simplified symbols representing the first and second constant strings respectively; The degrees of freedom are Chi-square distribution with degrees of freedom The cumulative distribution function of represents the probability density function of the standard normal distribution; represents the integral variable; represents the integral symbol; Indicates the first type of risk value set; Indicates the second type of risk value set.

[0035] Furthermore, the execution parameters are of The specific process of the inspection plan is: first, start continuous inspection of the processed parts. When all parts are qualified, the score test is carried out, that is, One part is randomly selected from the parts processed continuously for inspection; when continuous inspection is performed, When a defective product appears in a part, the count is reset to zero and the continuous inspection is restarted; when performing fractional inspection, when a defective product appears, it immediately returns to the continuous inspection.

[0036] Furthermore, the process capability index estimator It is expressed as:

[0037] (10);

[0038] In the formula, Indicates the target value of the quality indicator during the processing.

[0039] Compared with the existing technology, the present invention has the following beneficial effects:

[0040] (1) The present invention introduces the optimal multi-level continuous sampling inspection scheme and the process capability index by integrating the two control methods. As a core quality control indicator, it realizes real-time monitoring and precise regulation of the production process quality, ensures the stability and consistency of product quality, meets cost constraints, and quantitatively controls the first and second risks.

[0041] (2) The present invention integrates dynamic sampling inspection and process capability assessment, dynamically adjusts the sampling frequency and position according to real-time production data, quantitatively expresses the process status, and realizes real-time monitoring of product quality during the production process without increasing the inspection workload, quickly discovers and corrects potential quality problems, and meets multiple functional requirements such as status monitoring, four constraints and feedback control. It helps to improve the processing and production capacity of enterprises, reduce costs, and enhance market competitiveness.

[0042] (3) The present invention integrates the optimal multi-level continuous sampling inspection with the process capability index to conduct uninterrupted real-time monitoring of the production process quality, thereby reducing unnecessary inspection costs and making production quality changes transparent. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0044] like Figure 1 As shown, the present invention provides a technical solution: an optimal multi-level continuous sampling inspection and process capability index integration method, comprising the following steps:

[0045] Step S1: Set the current average detection quality limit and the long-term average test number limit .

[0046] Step S2: Use the current Perform normality test on production data; calculate normality fit , if the normal fit is Greater than or equal to 0.05, calculate the process yield estimate and the lower confidence limit of the process yield estimate , otherwise the production will be stopped for repair.

[0047] Among them, the process qualified product rate estimate It is expressed as:

[0048] (1);

[0049] In the formula, Indicates the upper tolerance limit; Indicates the lower limit of tolerance; Cumulative distribution function representing the normal distribution; It represents the standard deviation of the sample (inspection data of process qualified product rate), For the sample observations, It is the number of the collected inspection data, which is a positive integer; represents the sample mean; is the sample size.

[0050] Among them, the lower confidence limit of the process conforming rate estimate is It is expressed as:

[0051] (2);

[0052] In the formula, represents the quantile of the chi-square distribution; express Chi-square distribution with degrees of freedom The sample observation value under the quantile.

[0053] Step S3: Estimation of process qualified product rate and and Compared with the process yield estimate , exemption from inspection; when , execute step S4; when , stopped production for repairs.

[0054] Step S4: Test the number limit by long-term average Calculate the limit process failure rate , by the limit process failure rate Calculate the limit process capability index , the average detection mass limit Calculate the process capability index of the quality requirement limit .

[0055] Among them, the limit process failure rate It is expressed as:

[0056] (3).

[0057] Among them, the limit process capability index It is expressed as:

[0058] (4);

[0059] In the formula, Represents the inverse of the normal cumulative distribution function.

[0060] Among them, the quality requirement limit process capability index It is expressed as:

[0061] (5).

[0062] Step S5: Calculate the optimal multi-level continuous sampling test The number of continuous qualified products and test scores , determine the risk control sample size and process capability index key values .

[0063] Among them, the number of continuous qualified products and test scores are the solutions of equation (6) and equation (7) respectively;

[0064] (6);

[0065] (7);

[0066] In the formula, express of Power; express of 2 Power; express of 3 Power; express of 4 Power; express of Power; express of Power.

[0067] Among them, the risk control sample size and process capability index key values are the solutions of equation (8) and equation (9) respectively;

[0068] (8);

[0069] (9);

[0070] In the formula, , , and The simplified symbols representing the first and second constant strings respectively; The degrees of freedom are Chi-square distribution with degrees of freedom The cumulative distribution function of represents the probability density function of the standard normal distribution; represents the integral variable; represents the integral symbol; Indicates the first type of risk value set; Indicates the second type of risk value set.

[0071] Step S6: Execution parameters are of Inspection plan, first of all, start with continuous inspection of processed parts. When all parts are qualified, the score test is carried out, that is, One part is randomly selected from the parts processed continuously for inspection; when continuous inspection is performed, If a defective product appears in each part, the count is reset to zero and continuous inspection is restarted. When performing fractional inspection, if a defective product appears, the continuous inspection is immediately resumed.

[0072] Step S7: Keep records while executing the inspection plan The latest data, recorded The process capability index estimate is calculated based on the latest data and process yield estimate .

[0073] Among them, the process capability index estimator It is expressed as:

[0074] (10);

[0075] In the formula, Indicates the target value of the quality indicator during the processing.

[0076] Step S8: Estimation of process qualified product rate and the lower confidence limit of the process yield estimate and process capability index estimator Process Capability Index Key Value For comparison, and , execute step S6, when and , execute step S2; otherwise, stop production for repair.

[0077] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An optimal multi-level continuous sampling inspection and process capability index integration method, characterized in that: The steps include: Step S1: Set the current average detection quality limit and the long-term average test number limit ; Step S2: Use the current Perform normality test on production data; calculate normality fit , when the normal fit is Greater than or equal to the preset value, calculate the estimated process yield and the lower confidence limit of the process yield estimate , otherwise stop production for repair; Step S3: Estimation of process qualified product rate and and Compared with the process yield estimate , exempt from inspection; when , execute step S4; when , stop production for repair; Step S4: Test the number limit by long-term average Calculate the limit process failure rate , by the limit process failure rate Calculate the limit process capability index , the average detection mass limit Calculate the process capability index of the quality requirement limit ; Step S5: Calculate the optimal multi-level continuous sampling test The number of continuous qualified products and test scores , determine the risk control sample size and process capability index key values ; Step S6: Execution parameters are of Inspection plan; Step S7: Keep records while executing the inspection plan The latest data, recorded The process capability index estimate is calculated based on the latest data and process yield estimate ; Step S8: Estimation of process qualified product rate and the lower confidence limit of the process yield estimate and process capability index estimator Process Capability Index Key Value For comparison, and , execute step S6, when and , execute step S2; otherwise, stop production for repair; Risk Control Sample Size and process capability index key values are the solutions of equation (8) and equation (9) respectively; （8）； （9）； In the formula, , , and The simplified symbols representing the first and second constant strings respectively; The degrees of freedom are Chi-square distribution with degrees of freedom The cumulative distribution function of represents the probability density function of the standard normal distribution; represents the integral variable; represents the integral symbol; Indicates the first type of risk value set; Indicates the second type of risk value set; The execution parameters are of The specific process of the inspection plan is: first, start continuous inspection of the processed parts. When all parts are qualified, the score test is carried out, that is, One part is randomly selected from the parts processed continuously for inspection; when continuous inspection is performed, When a defective product appears in a part, the count is reset to zero and the continuous inspection is restarted; when performing fractional inspection, when a defective product appears, it immediately returns to the continuous inspection.

2. The optimal multi-level continuous sampling inspection and process capability index integration method according to claim 1, characterized in that: Process yield estimator It is expressed as: （1）； In the formula, Indicates the upper tolerance limit; Indicates the lower limit of tolerance; Cumulative distribution function representing the normal distribution; represents the sample standard deviation, For the sample observations, is the number of the collected inspection data, which is a positive integer; represents the sample mean; is the sample size.

3. The optimal multi-level continuous sampling inspection and process capability index integration method according to claim 2, characterized in that: Lower confidence limit for process yield estimate It is expressed as: （2）； In the formula, represents the quantile of the chi-square distribution; express Chi-square distribution with degrees of freedom The sample observation value under the quantile.

4. The optimal multi-level continuous sampling inspection and process capability index integration method according to claim 3, characterized in that: Limit process failure rate It is expressed as: （3）。 5. The optimal multi-level continuous sampling inspection and process capability index integration method according to claim 4, characterized in that: Limit process capability index It is expressed as: （4）； In the formula, Represents the inverse of the normal cumulative distribution function.

6. The optimal multi-level continuous sampling inspection and process capability index integration method according to claim 5, characterized in that: Quality requirement limit process capability index It is expressed as: （5）。 7. The optimal multi-level continuous sampling inspection and process capability index integration method according to claim 6, characterized in that: Continuous qualified products and test scores are the solutions of equation (6) and equation (7) respectively; （6）； （7）； In the formula, express of Power; express of 2 Power; express of 3 Power; express of 4 Power; express of Power; express of Power.

8. The optimal multi-level continuous sampling inspection and process capability index integration method according to claim 7, characterized in that: Process capability index estimator It is expressed as: （10）； In the formula, Indicates the target value of the quality indicator during the processing.

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