Electronic part production sampling decision-making system based on dynamic programming

Abstract

The invention relates to the technical field of electronic part production, and discloses an electronic part production sampling decision-making system based on dynamic programming, which comprises a data acquisition module for collecting raw material information, production equipment parameters, production environment data and product quality detection data through a sensor, a data interface and the like, and sending the data to a data processing module; the real-time performance, accuracy and integrity of the data are ensured, and the data are transmitted to the data processing module. According to the electronic part production sampling decision-making system based on dynamic programming, the dynamic programming model module takes minimization of quality cost as a target, multiple cost factors are comprehensively considered, a constructed sampling decision-making model is more comprehensive, the production state of the next stage is flexibly determined according to whether sampling is carried out or not through a state transition equation, and the production efficiency is improved. The optimal decision sequence can be deduced from the perspective of the overall production cycle by adopting an inverted order solving method, so that the sampling strategy is adjusted in time according to the dynamic change of the production process, and the scientificity and adaptability of the sampling decision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic component production, and particularly to a sampling decision-making system for electronic component production based on dynamic programming. Background Technique

[0002] With the rapid development of electronic technology, the electronic component production industry shows the characteristics of continuous expansion in scale and increasing richness in product variety. From smart phones, tablets to automotive electronics, industrial control and many other fields, the demand for electronic components continues to grow, and at the same time, the requirements for their quality and performance are getting higher and higher. The defective rate of components will have an important impact on the quality of electronic products. Electronic products often detect components, semi-finished products and finished products to reduce the risk of product unqualified, thereby increasing their profits. Therefore, electronic products need to continuously optimize the production process, improve product quality and production efficiency, so as to promote the high-quality development of China's electronic product industry and improve international competitiveness.

[0003] Traditional sampling methods are mostly based on fixed rules. When determining key parameters such as sampling quantity and sampling frequency, they usually rely on experience or industry standards for annual inspection only. Traditional sampling methods are difficult to adapt to the dynamic changes such as raw material batch differences and equipment performance fluctuations during component production, resulting in too many or too few sampling quantities and unreasonable sampling frequencies, which not only increases the inspection cost but also cannot effectively control the quality.

[0004] In view of the above problems, there is an urgent need to innovate and design on the basis of the original electronic component production sampling. Summary of the Invention

[0005] The purpose of the present invention is to provide a sampling decision-making system for electronic component production based on dynamic programming, so as to solve the problem in the above background technique that traditional sampling methods are mostly based on fixed rules and are difficult to adapt to the dynamic changes during component production, resulting in unreasonable traditional sampling frequencies and increasing inspection costs.

[0006] To achieve the above purpose, the present invention provides the following technical solution: A sampling decision-making system for electronic component production based on dynamic programming, including a data acquisition module: collecting raw material information, production equipment parameters, production environment data and product quality detection data through sensors, data interfaces, etc., ensuring the real-time, accurate and complete nature of the data, and transmitting it to the data processing module;

[0007] A data processing module: cleaning the data collected by the data acquisition module, removing outliers and error data, and performing standardization processing on the data to make the data from different sources and formats comparable;

[0008] Dynamic programming model module: constructs a sampling decision model based on dynamic programming. The dynamic programming module inputs the production data processed by the data processing module, and uses the dynamic programming algorithm to solve the optimal sampling strategy based on the set state variables, decision state variables and state transfer direction in the production process, with minimizing quality cost as the objective function;

[0009] Decision output module: The sampling decision results calculated by the dynamic programming model are displayed to production management personnel and quality control personnel. The sampling decision results include specific sampling plans, sampling time points, inspection standards, etc., to guide the sampling inspection work in actual production.

[0010] By adopting the above technical solution, dynamic programming is used to provide a better sampling effect for electronic parts production sampling at the minimum quality cost.

[0011] Preferably, the data acquisition module collects data through sensors and data interfaces, obtains raw material information by connecting with the information system of the raw material supplier, and collects product quality data by setting quality inspection points on the production line.

[0012] By adopting the above technical solution, corresponding data is added to the spare parts production equipment, which facilitates the rapid acquisition of spare parts data.

[0013] Preferably, the data acquisition module continuously collects new data during spare parts production, and the data processing module merges and updates the new data with historical data.

[0014] The above technical solutions are used to continuously provide more accurate and appropriate data for the dynamic programming model.

[0015] Preferably, the data processing module stores the standardized data in categories and establishes an associated database for quick query and call.

[0016] By adopting the above technical solution and increasing the database, it is convenient to quickly investigate the data when using the model training.

[0017] Preferably, when the data processing module cleans the collected data, abnormal values ​​are eliminated by setting reasonable thresholds, and the raw material information is organized and stored in a unified format.

[0018] The above technical solution is adopted to facilitate unified processing of data in different formats and to facilitate information processing.

[0019] Preferably, the state transfer equation in the dynamic programming model module is divided into two cases according to whether sampling is performed:

[0020] When no sampling is done, the production status of the next stage is predicted through the production process model;

[0021] When sampling, the production status of the next stage is jointly determined based on the sampling results and the natural variations in the production process.

[0022] By adopting the above technical solution, a stable calculation effect is provided for the finished product status through the state transition equation.

[0023] Preferably, the objective function of the dynamic programming model module is to minimize the total cost including sampling cost and loss cost caused by unqualified products during the entire production cycle.

[0024] By adopting the above technical solution, the cost calculation of the dynamic programming model module is used as the guiding target.

[0025] Preferably, the dynamic programming model module adopts the reverse order solution method. Starting from the last stage of the production cycle, it gradually derives forward. Under different states of each stage, by comparing the costs when taking different decisions, the decision with the minimum cost is selected to obtain the optimal decision sequence.

[0026] By adopting the above technical solution, the sampling decision of spare parts can adjust the sampling strategy in a timely manner according to the dynamic changes in the production process.

[0027] Preferably, the minimized quality cost includes sampling cost, unqualified product handling cost, rework cost, and customer complaint cost.

[0028] By adopting the above technical solution, by determining the range of minimized quality cost, it is convenient for the dynamic programming model to provide a better choice for sampling selection.

[0029] Preferably, the dynamic programming model module accepts the latest data to recalculate the optimal sampling strategy, and the system regularly evaluates and optimizes the model. By comparing the quality cost in actual production with the quality cost predicted by the model, the parameters of the model are adjusted.

[0030] By adopting the above technical solution, by continuously inputting the latest data, it is convenient for the dynamic programming model to provide the optimal sampling strategy for electronic spare parts.

[0031] Compared with the prior art, the beneficial effects of the present invention are: The electronic spare parts production sampling decision system based on dynamic programming:

[0032] 1. The dynamic programming model module aims to minimize the quality cost. By comprehensively considering various cost factors, the constructed sampling decision model is more comprehensive. Through the state transition equation, it can flexibly determine the production status of the next stage based on whether to sample. Using the reverse order solution method, it can deduce the optimal decision sequence from the perspective of the overall production cycle, enabling the sampling strategy to be adjusted in a timely manner according to the dynamic changes in the production process, better coping with situations such as equipment aging and raw material fluctuations, improving the scientificity and adaptability of sampling decisions. The data acquisition module collects data comprehensively through various methods. While ensuring the real-time, accurate, and complete data, it continuously collects new data during production, providing a rich and dynamic information basis for the system. As the data processing module cleans, standardizes, and classifies and stores the data, it can effectively remove interference information, making different data comparable and facilitating quick query and call, thus improving the data quality and utilization efficiency, enabling the data to more accurately reflect the actual production situation and providing a reliable basis for subsequent decisions;

[0033] 3. The decision output module outputs the detailed sampling decision results, directly guiding actual production through the decision results and reducing human decision-making errors. At the same time, the system can recalculate the optimal sampling strategy based on the latest data, regularly evaluate and optimize the model, continuously adjust parameters to fit the actual production, and continuously improve the accuracy and effectiveness of the system, helping to minimize the quality cost to the greatest extent while ensuring product quality and enhancing competitiveness. Description of the Drawings

[0034] Figure 1 It is a schematic diagram of the genetic algorithm process of the present invention;

[0035] Figure 2 It is a schematic diagram of the production process of the present invention;

[0036] Figure 3 It is a schematic diagram of the maximum benefit idea process of the present invention;

[0037] Figure 4 It is a schematic diagram of the stage decision idea of the present invention;

[0038] Figure 5 It is a relationship diagram of the sample size n and the allowable error E of the present invention;

[0039] Figure 6 It is a schematic diagram of the result testing of the present invention;

[0040] Figure 7 It is a schematic diagram of the average profit and standard deviation of 6 cases of the traversal algorithm of the present invention;

[0041] Figure 8 It is a schematic diagram of the finished product production process of the present invention;

[0042] Figure 9This is the average profit graph of all combinations in the dynamic programming of the present invention;

[0043] Figure 10 This is the comparison graph of the number of detections in the implementation method of Embodiment 4 of the present invention;

[0044] Figure 11 This is the comparison graph of the defective rate estimation in the implementation method of Embodiment 4 of the present invention. Detailed implementation manners

[0045] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0046] Please refer to Figures 1 - 11 As shown, the present invention provides a technical solution: an electronic spare parts production sampling decision-making system based on dynamic programming; among them, the data acquisition module: in the electronic spare parts production workshop, various sensors such as temperature sensors and pressure sensors are installed at key parts of the production equipment to collect the operating parameters of the equipment in real time, and are connected to the workshop automation control system through a data interface to obtain data such as production progress. Negotiate with raw material suppliers to establish an information docking channel so that they can transmit information such as the model, batch, and quality inspection report of raw materials to the system in a timely manner. At the same time, quality inspection points are set at different process nodes on the production line, and corresponding inspection equipment is equipped to collect quality data of the products during production;

[0047] The data processing module: selects MySQL as the database management system to build a data storage platform, realizes data cleaning and standardization processing programs, automatically eliminates the collected data when it exceeds the set reasonable outlier threshold range, sorts out and stores the raw material information according to a unified format template, classifies and stores the cleaned and standardized data according to categories such as equipment data and product quality data, and establishes an associated database for convenient subsequent query and call;

[0048] The dynamic programming model module: constructs a sampling decision-making model based on the principle of dynamic programming and in combination with the actual characteristics of electronic spare parts production;

[0049] Embodiment 1:

[0050] At one's own expense, a sampling inspection method is used to decide whether to accept a batch of spare parts. When sampling the spare parts and not knowing the actual defective rate, the claimed defective rate of the supplier is used to estimate the required sample size. The sample size estimation formula is:

[0051]

[0052] Among them, n is the sample size, Z a is the quantile of the normal distribution, corresponding to the two-sided tail probabilities of the selected confidence level, p0 is the defective rate claimed by the supplier, E is the allowable error, and then the critical value is determined. The critical value is the threshold for deciding whether to accept or reject this batch of spare parts. In the normal distribution, the Z-score is used to determine this value. Among them, "Z" as the test statistic can be expressed as the difference between the sample mean and the population mean:

[0053]

[0054] When it is necessary to judge whether to accept a large number of batches of parts, two critical values are selected for calculation. When z > Z 0.05 , this batch of spare parts should be rejected, and its corresponding critical value is:

[0055]

[0056] The solution for the total sample size is:

[0057]

[0058] When z < Z 0.1 , this batch of spare parts should be accepted, and its corresponding critical value is

[0059]

[0060] The solution for the total sample size is:

[0061]

[0062] At a 95% confidence level, the solution for the minimum number of samples to be tested is n = 139, and the critical number of defective products is 20. If the number of defective products exceeds the critical number, this batch of spare parts will be rejected. At a 90% confidence level, the solution for the minimum number of samples to be tested is n = 98, and the acceptable number of defective products is 5. If the number of defective products is less than the acceptable number, this batch of spare parts will be accepted. By selecting different allowable errors and calculating their sample sizes, the results are shown in Table 1;

[0063] Table 1 Sample Sizes under Different Allowable Errors

[0064] Tolerance error 95% confidence level 90% confidence level 10.00％ 35 25 5.00％ 139 98 3.00％ 385 271 1.00％ 3458 2435 0.50％ 13830 9740

[0065] Then, by analyzing the results, a relationship graph between the sample size n and the allowable error E can be obtained, as Figure 5 shown. Whether at a 95% confidence level or a 90% confidence level, the sample size n decreases as the allowable error E increases. Further analyzing the relationships among the sample size n, the actual defective rate p, the number of defective products x, and the z value, as Figure 6 andFigure 6 As shown, a schematic diagram showing the variation of the sample size n with the actual defective rate p and the relationship between the number of defective products x and the z value is given. Combining with the Figure 6 shown in the attached drawings of the specification, after establishing a dynamic programming model, according to the various stages of electronic component production, that is, for the four stages of component inspection, finished product inspection, disassembly of unqualified finished products, and return and replacement, as Figure 2 shown, specific decisions are given according to the size relationship between the inspection cost and the non-inspection loss cost. After the dynamic programming model is established, taking the minimum cost as the decision-making basis, the optimal strategies for 16 situations are obtained respectively by using the traversal algorithm iteration. The overall analysis idea flowchart is as Figure 3 shown;

[0066] Example 2: When receiving a batch of spare parts, given the defective rates of two types of spare parts and finished products, make decisions for the four stages of the production process, and according to the decisions at each stage, give specific decision-making plans for the situations in Table 1, and give relevant bases and corresponding index results. By comparing the cost of inspecting spare parts and the losses caused by not inspecting, a reasonable decision on spare part inspection is designed. Inspecting all spare parts in this batch will consume a certain cost, that is

[0067] C 零检 = d1×x1×n + d2×x2×n

[0068] Among them, C 零检 is the cost required to inspect spare parts. Considering the possible losses when spare parts are not inspected as

[0069] E 损失 = n×p m ×C 装配损失 + n×p m ×p a ×C 调换损失

[0070] Among them, E 损失 is the possible loss caused by not inspecting this batch of spare parts. When both spare parts are unqualified spare parts, the assembled finished product is unqualified. At this time, C 装配损失 is the loss caused by unqualified products, pa is the defective rate of the finished product in the assembly stage, and C 调换损失 is the cost loss incurred when the product purchased by the user is unqualified and needs to be replaced;

[0071] To sum up, the spare part inspection criterion is: when C 零检 < E 损失If the cost of inspecting this batch of spare parts is less than the loss caused by not inspecting, then this batch of spare parts should be inspected; otherwise, they should not be inspected. When the cost of inspecting the finished product is less than the loss caused by not inspecting the finished product, the assembled finished product needs to be inspected, so as to minimize the input and maximize the benefit. The cost of finished product inspection is

[0072] C 成检 = C b × x m × N C

[0073] Similarly, the possible loss caused by not inspecting the finished product is

[0074] E 损失 = n × p m × C 调换损失

[0075] To sum up, the finished product inspection criterion is: when C 成检 < E 损失 then the cost of inspecting the finished product is less than the loss caused by not inspecting, and the assembled finished product should be inspected; otherwise, it should not be inspected. For the unqualified finished products detected in the previous stage, it is necessary to judge whether they need to be disassembled. On the one hand, disassembly will generate corresponding costs, and the obtained spare parts 1 and spare parts 2 will repeat the spare parts inspection and finished product inspection stages. On the other hand, if the unqualified products are not disassembled and the unqualified finished products are directly discarded, it will cause economic losses. The cost of disassembling unqualified finished products is

[0076]

[0077] Among them, C s is the cost generated by disassembling each unqualified finished product. Since both types of spare parts obtained after disassembling the finished product can be reused, by disassembling unqualified finished products and reusing the still usable spare parts, it is possible to avoid these spare parts being treated as waste, thereby saving the use of raw materials. Reusing effectively replaces high-cost links such as the production of new spare parts, so as to significantly reduce the replacement cost. Then the profit generated is

[0078]

[0079] Among them, p 合格 represents the probability of the spare parts obtained after disassembling unqualified finished products, and C recovery represents the value of each recycled spare part. To sum up, the disassembly criterion for unqualified finished products is: when C 拆解 < E 利润If the cost of disassembling the unqualified finished products is less than the profit obtained without disassembling, then the unqualified finished products should be disassembled; otherwise, they should not be disassembled.

[0080] If the spare parts or finished products are not inspected in the above stage, some unqualified finished products will flow into the market. When users buy unqualified products, they will be unconditionally replaced, and there will also be certain cost losses. Disassembling the returned unqualified products requires a certain amount of labor. Although the disassembling process will not damage the spare parts, it also increases the cost input. At this time, the above stage decision needs to be repeated. The decision variables are:

[0081] x1: Whether to inspect spare part 1;

[0082] x2: Whether to inspect spare part 2;

[0083] x m : Whether to inspect the finished product;

[0084] x n : Whether to disassemble the unqualified finished products;

[0085] The cost of inspecting spare parts is

[0086] C 零检 = d1×x1×n + d2×x2×n

[0087] After the spare parts go through the first stage to the assembly stage, the assembly cost is

[0088] C 装配 = L1×N C

[0089] After assembly, the finished product is obtained. As long as one of the spare part 1 and spare part 2 is unqualified, the assembled finished product is also unqualified. Even if both spare parts are qualified, the assembled finished product may still be unqualified. Then it is necessary to inspect the finished product, and its inspection cost is:

[0090] C 成检 = C b ×x m ×N C

[0091] For unqualified finished products, directly discarding them will directly cause cost losses. Therefore, to save costs and make reasonable use of resources, the unqualified products are disassembled, and the corresponding disassembly cost is generated:

[0092] C 调换 = (1 - x n )×C n ×N C ×p m

[0093] The total cost is then

[0094] C 总 = C 零检 + C 装配 + C 成品 + C 拆解 + C 调换

[0095] The total revenue is

[0096]

[0097] where L is the total revenue, is the number of qualified finished products, and q is the market selling price;

[0098] The objective function is

[0099] maxM = L - C 总

[0100] The constraints are: x1, x2, x m , x n

[0101] where x1 represents whether to inspect spare part 1, x2 represents whether to inspect spare part 2, x m represents whether to inspect the finished product, and x n represents whether to disassemble the unqualified finished product. They are equal to 0 for "no" and 1 for "yes";

[0102] In summary, the dynamic programming model for comprehensive decision-making is:

[0103]

[0104] s, t, x i = 0 or 1, (i = 1, 2, m, n)

[0105] For spare part 1 and spare part 2, there are two choices at each stage. In the first stage, each spare part can choose to be inspected or not. In the second stage, the spare parts are assembled into a finished product, and the finished product can also choose to be inspected or not. In this way, there are 16 different strategy combinations. For each combination, based on the dynamic programming model, a traversal algorithm is used to traverse each combination in 6 cases. With the maximum profit as the goal, an optimal decision-making plan is given. The specific steps are as follows:

[0106] Step 1: According to the four stages of the production process, simulate the distribution of spare parts in the production process. Whether to inspect or disassemble at each stage is controlled by decision variables. In this paper, the process functions of each stage are constructed separately and finally pieced together into a total integrated function. The production process of the finished product is simulated by taking the dot product of the vector formed by the values of the decision variables;

[0107] Step 2: Conduct self-inspection of spare parts, semi-finished products and finished products, as well as self-decomposition, and integrate these three steps into a complete production process;

[0108] Step 3: Further simulate using the Monte Carlo algorithm, which is essentially a random simulation method, also known as the statistical simulation method and random sampling technique, to handle the uncertainties in the production process and improve the stability and practicality of the model;

[0109] Step 4: Adopt a traversal algorithm to traverse the 16 strategies corresponding to each case, select the combination with the maximum profit as the decision-making plan, and give a schematic diagram of the average profit and standard deviation of 6 cases, combined with the Figures 7 - 7 as shown in;

[0110] With the optimal decision-making calculations for 6 cases using different combined strategy algorithms, the results are shown in Table 2, which successively lists the corresponding decision-making plans, decision-making bases, and corresponding indicators for 6 cases;

[0111] Table 2 Index Results of Optimal Decision-Making

[0112] Situation Optimal strategy Maximum profit / yuan Number of finished products / piece 1 (1，1，0，0) 12180.97 805.14 2 (1，1，0，0) 2779.31 633.74 3 (1，1，0，0) 10036.99 805.03 4 (1，1，0，0) 2055.91 635.08 5 (0，1，0，0) 6939.89 647.56 6 (0，0，0，0) 18602.85 857.62

[0113] In the first case, based on the maximum profit as the decision-making basis, the corresponding optimal strategy is to inspect both spare part 1 and spare part 2, not to inspect the finished products, and not to disassemble the unqualified finished products, but to directly discard them;

[0114] In the second case, based on the maximum profit as the decision-making basis, the corresponding optimal strategy is to inspect both spare part 1 and spare part 2, not to inspect the finished products, and not to disassemble the unqualified finished products, but to directly discard them. Compared with case 1, the profit is greatly reduced;

[0115] In the third case, based on the maximum profit as the decision-making basis, the corresponding optimal strategy is to inspect both spare part 1 and spare part 2, not to inspect the finished products, and not to disassemble the unqualified finished products, but to directly discard them. The difference in the maximum profit from case 1 is relatively small;

[0116] In the fourth case, based on the maximum profit as the decision-making basis, the corresponding optimal strategy is to inspect both spare part 1 and spare part 2, not to inspect the finished products, and not to disassemble the unqualified finished products, but to directly discard them. Compared with the maximum profit in case 3, there is a significant decrease;

[0117] In the fifth case, based on the maximum profit as the decision-making criterion, the corresponding optimal strategy is that parts 1 and 2 need to be inspected, the finished product does not need to be inspected, and the unqualified finished product is not disassembled and is directly discarded. Compared with the maximum profits in cases 2 and 4, it is relatively stable. Compared with the maximum profits in cases 1 and 3, it decreases significantly;

[0118] In the sixth case, based on the maximum profit as the decision-making criterion, the corresponding optimal strategy is that parts 1 and 2 need to be inspected, the finished product does not need to be inspected, and the unqualified finished product is not disassembled and is directly discarded. Compared with the maximum profits in the previous 5 cases, it is the maximum profit;

[0119] To sum up, when all costs and losses remain the same, as the defective rate increases, the profit will decrease. Among them, the profit in case 1 is the smallest, and the profit in case 6 is the largest. When semi-finished products appear among the parts, following the idea of maximum benefit, that is, the Figure 3 in the attached drawings of the specification. Further thinking about the decision-making idea of obtaining stage benefits, that is, the Figure 4 in the attached drawings of the specification. At this time, case 3 appears, that is, knowing the defective rates of parts, semi-finished products and finished products;

[0120] Example 3: On the basis of Example 2, that is, adding a semi-finished product process in the assembly and disassembly links. First, directly establish a general dynamic programming model for m processes and n parts, and apply it to the case of 2 processes and 8 parts. Although the number of combinations is large, it can still be solved by the traversal algorithm. Finally, use the genetic algorithm to optimize and find the optimal strategy. As Figure 4 shown, before making an optimization decision, define the decision variables:

[0121] x i : Whether to inspect the parts. Among them, i = 1, 2,..., n, xi = 0 or 1. When i takes 0, it means not to inspect the parts. When i takes 1, it means to inspect the parts;

[0122] y j : Whether to inspect the semi-finished product of process j. Among them, j = 1, 2,..., n, yj = 0 or 1. When j takes 0, it means not to inspect the semi-finished product of process j. When j takes 1, it means to inspect the semi-finished product;

[0123] a: Whether to inspect the final finished product. Among them, a = 0 or 1. When a takes 0, it means not to inspect the final finished product. When a takes 1, it means to inspect the final finished product;

[0124] b: Whether to disassemble the unqualified finished product. Among them, b = 0 or 1. When b takes 0, it means not to disassemble the unqualified finished product and directly discard it. When b takes 1, it means to disassemble the unqualified finished product;

[0125] c: Whether to disassemble unqualified semi-finished products, where c = 0 or 1. When c takes 0, it means not to disassemble unqualified semi-finished products and directly discard them. When c takes 1, it means to disassemble unqualified semi-finished products;

[0126] Assume that each spare part has its fixed defective rate represented by p i If the spare parts are not inspected, they will directly enter the next stage and be assembled into finished products. At this time, the number of qualified spare parts is

[0127]

[0128] Calculate the defective rate of semi-finished products. By analyzing the assembly of multiple processes and multiple parts, it is not difficult to find that the defective rate of semi-finished products is directly determined by the defective rate of its spare parts. Then the defective rate of semi-finished products is:

[0129]

[0130] This means that the defective rate of semi-finished products in the jth process is equal to 1 minus the product of the qualification rates of all spare parts in the jth process. Calculate the defective rate of finished products. The defective rate of finished products is affected by the defective rate p j of semi-finished products in each process, that is, the defective rate of semi-finished products is

[0131]

[0132] Then the number of qualified pieces of the final finished product is

[0133]

[0134] The number of final qualified finished products is equal to the product of the total number of the last finished products and the qualification rate of finished products

[0135] After that, start to calculate the total cost. The cost of purchasing spare parts is equal to the sum of the products of the quantity of each type of spare part and its corresponding purchase unit price

[0136]

[0137] Total inspection cost: C 总 = C 零检 + C 半检 + C 成检

[0138]

[0139]

[0140] C 成检 = N c × a × C f

[0141] The assembly cost includes the expenses incurred in assembling various spare parts into semi-finished products and assembling semi-finished products into finished products.

[0142]

[0143] The disassembly cost consists of two parts. One part is the cost generated by disassembling unqualified semi-finished products, and the other part is the cost generated by disassembling finished products, that is

[0144]

[0145] For unqualified finished products, if they are not disassembled, then only scrapping can be chosen, and the scrapping cost is

[0146] C 报废 =(1 - c)×N j ×p j +(1 - b)×p

[0147] To sum up, the total cost to be borne is

[0148] C 总成本 =C 购买 +C 零检 +C 半检 +C 成检 +C 装配 +C 拆解 +C 丢弃 The income is equal to the product of the quantity and the selling price, and the total income L can be obtained as

[0149]

[0150] After that, the dynamic programming model is further optimized with the goal of minimizing cost or maximizing profit. Since the profit is equal to the income minus the cost, the profit M = L - C total cost can be obtained, and then the total income is

[0151]

[0152] So the objective function is

[0153]

[0154] When further optimizing the dynamic programming model through the constraint conditions, combined with the Figure 1 shown in the accompanying drawings of the specification, the optimal decision-making combination under the corresponding conditions can be obtained. In actual production and life, there is a certain sequence for the inspection of semi-finished products and the inspection of finished products. Here are several constraints:

[0155] 1. Only after all the spare parts of semi-finished product j have been inspected can semi-finished product j be inspected, that is

[0156]

[0157] 2. The inspection of the finished product can only be carried out after all the semi-finished products that make up the finished product have been inspected, that is

[0158]

[0159] In summary, the optimized model of dynamic programming for Case 3 is

[0160]

[0161]

[0162] Give the strategies in turn for the four stages of the production process in Case 3;

[0163] 1) Spare part inspection decision

[0164] If the defective rate of the spare parts in the j-th process is relatively high and the inspection cost is relatively low, in order to prevent defective products from flowing into the next process and increasing the defective rate, it is necessary to choose to inspect the spare parts. The inspection cost for each spare part i is

[0165]

[0166] The possible loss caused by not inspecting is

[0167] E 损失 =p i ×n i ×r i

[0168] where r i is the possible loss caused by unqualified finished products after the spare parts are assembled into finished products;

[0169] In summary, the inspection criterion is

[0170]

[0171] 2) Semi-finished product inspection decision

[0172] The quality of semi-finished products will directly affect the quality of finished products. Therefore, a decision is made on whether to inspect semi-finished products to ensure the quality of the finished products assembled in the next process. The inspection cost involved is

[0173]

[0174] On the contrary, the possible loss caused by not inspecting is the possible loss caused by not inspecting is

[0175] E 损失 =p j ×nj ×r j

[0176] where r j is the assembly cost of the next process;

[0177] In summary, the inspection criteria are:

[0178]

[0179] 3) Final product inspection decision

[0180] When the semi-finished product is assembled into the final product, a decision still needs to be made on whether to inspect the final product. If no inspection is carried out and unqualified products flow into the market, then users will surely return the unqualified products for replacement, causing some unnecessary losses, such as logistics costs, and seriously, it may lead to the loss of credibility. The final product inspection cost is

[0181] C 成检 = N c ×a×C f

[0182] The possible loss is

[0183] E 损失 = p m ×N c ×r 退还

[0184] where r 退还 is the loss caused by the return of each unqualified product;

[0185] In summary, the inspection criteria are

[0186]

[0187] 4) Decision on whether to disassemble unqualified products

[0188] For the unqualified products detected in the final product or semi-finished products, choose to disassemble or directly discard. If disassembled, the required cost is

[0189]

[0190] Since parts can be obtained after disassembling the final product or semi-finished product, and some of the parts are qualified products themselves and can be reused to synthesize new semi-finished products or final products;

[0191] So assume that R is the total value brought by the parts after disassembly, that is, the disassembly income. The disassembly criteria are:

[0192]

[0193] The above dynamic programming models are all established based on general m processes and n spare parts. When m = 2 and n = 8, that is, for 2 processes and 8 spare parts, specific solution steps are given;

[0194] To further ensure the accuracy of the results and optimize the solution steps, next, a genetic algorithm is used to optimize the entire decision-making process. The solution process of the genetic algorithm is as Figure 1 shown;

[0195] Its algorithm pseudocode is

[0196] The optimal decision is

[0197] (1,1,1,1,0,1,1,0,0,1,1,1)

[0198] That is, spare parts 1, 2, 3, 4, 6, and 7 are inspected, spare parts 5 and 8 are not inspected, semi-finished product 1 is not inspected, semi-finished products 2 and 3 are inspected. If defective products are detected, they are directly disassembled into spare parts, and the finished products are not inspected;

[0199] As Figure 9 shown, it is not difficult to see that taking the combination of 500 - 600 as a cycle, the average profit as a whole shows an upward trend in each cycle;

[0200] Example 4: On the basis of Examples 2 and 3, assume that spare parts, semi-finished products, and finished products all pass the sampling inspection method. Considering that there are six situations in Example 2 and the defective rates in each situation are not the same, using only the expectation may be one-sided. Therefore, consider using the Monte Carlo algorithm to simulate the production process and then calculate the corresponding defective rates. The specific steps are as follows:

[0201] Step 1: Assume that there are 10,000 finished products now, given an error of 0.1, and randomly generate defective products at a probability of 0.1;

[0202] Step 2: Use common sampling inspection methods such as stratified sampling, systematic sampling, simple random sampling, sequential sampling, and Poisson sampling to sample and inspect the above products. The given tolerance error and significance level are both 0.05;

[0203] Step 3: Use Monte Carlo simulation 1000 times, compare the average number of inspections and the defective rate, and select the optimal inspection method, which is of great significance for protecting the interests of both the producer and the user;

[0204] As Figures 10 - 11 , a comparison box plot of the number of inspections and the estimated defective rate of five sampling methods, namely simple random sampling, sequential sampling, Poisson sampling, stratified sampling, and systematic sampling, is given;

[0205] In terms of the number of inspections, the average number of inspections in sequential sampling is too small, while that in systematic sampling and stratified sampling is too large, being at two extremes.

[0206] In terms of the estimation of the defective rate, the estimation errors of stratified sampling and systematic sampling are relatively large, while those of sequential sampling, simple random sampling, and Poisson sampling are relatively small. In comparison, the defective rate estimated by Poisson sampling is closer to the true defective rate, that is, the previously given probability is 0.1.

[0207] Step 4: Through comparison, the detection method of Poisson sampling is superior, so Poisson sampling is selected.

[0208] For the situation in Example 2, Poisson tests are conducted on each spare part and the finished product, and the actual defective rates in six cases are obtained again. Then, the optimal strategy, decision basis, and corresponding results are calculated by applying the dynamic programming model in Example 2. Since only the actual defective rate has changed and other factors such as the purchase unit price and detection cost have not changed, the decisions at each stage given in Example 2 are still applicable, so they will not be elaborated here. The following mainly presents the optimal decisions in various cases. In this example, the Monte Carlo algorithm is used to simulate data, and the defective rates of spare parts and finished products in the actual production process in six cases are obtained again, as shown in Table 3.

[0209] Table 3: Defective Rates of Spare Parts and Finished Products

[0210]

[0211] At this time, based on the dynamic programming model established in Example 2, the genetic algorithm is used to solve it again. The results of the optimal decision finally obtained are shown in Table 4. The decision basis for all cases is to ensure the minimum cost and thus obtain the maximum profit, which is the index result.

[0212] Table 4: Results Table of Optimal Decisions

[0213] Situation Optimal decision Maximum profit / yuan Number of finished products / piece 1 (1,1,0,0) 12067.47 802.83 2 (1,1,0,0) 2769.40 633.37 3 (1,1,0,0) 9945.29 803.17 4 (1,1,0,0) 1947.95 632.68 5 (0,1,0,0) 6959.84 648.05 6 (0,0,0,0) 18601.93 857.61

[0214] In the first case, the optimal decision is to inspect spare part 1, inspect spare part 2, not inspect the finished product, and do not disassemble the non-conforming products, but directly scrap them. The corresponding decision basis is to ensure the maximum profit.

[0215] In the second case, the optimal decision is to inspect both spare part 1 and spare part 2, not inspect the finished product, and do not disassemble the non-conforming products, but directly scrap them.

[0216] In the third case, the optimal decision is to inspect both spare part 1 and spare part 2, not inspect the finished product, and do not disassemble the non-conforming products, but directly scrap them.

[0217] In the fourth case, the optimal decision is to inspect both spare parts 1 and 2, not to inspect the finished product, and not to disassemble the defective products, but directly scrap them.

[0218] In the fifth case, the optimal decision is not to inspect spare part 1, to inspect spare part 2, not to inspect the finished product, and not to disassemble the defective products.

[0219] In the sixth case, the optimal decision is not to inspect either spare part 1 or 2, not to inspect the finished product, and not to disassemble the defective products.

[0220] For the decisions made in the same cases as in Example 3, the principle is the same as that in Example 2. The decisions at each stage of the production process will not change due to the individual defective rate, but only relate to the relationship between the inspection cost, disassembly cost, and the losses caused by not performing inspections or disassembly. Moreover, in Example 3, there are multiple processes and procedures, and different procedures will have different degrees of impact on all aspects of the finished product quality. Therefore, each procedure needs to be optimized, and the entire process also needs to be comprehensively optimized.

[0221] In this embodiment, Poisson tests are performed on the products generated from the defective rates of each spare part and each semi-finished product in Example 3 to re-obtain the actual defective rates of the spare parts and semi-finished products, and then apply them to the dynamic model established in Example 3 to calculate the optimal strategy, decision basis, and corresponding results. Based on this, the defective rates of each spare part, semi-finished product, and finished product are re-obtained respectively, as shown in Table 5:

[0222] Table 5 Spare Part Cost Analysis Table

[0223]

[0224] Further substituting into the multi-process dynamic programming model established in Example 3, first use the traversal algorithm to solve for all combinations, and then use the genetic algorithm for optimization to find the optimal decision combination. The result of the optimal decision finally obtained is (1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0)

[0225] That is, the decision plan is to inspect spare parts 1, 3, 4, 5, 6, and 7, not to inspect spare part 2, not to inspect semi-finished product 1, to inspect semi-finished products 2 and 3, and choose to disassemble if defective, and not to disassemble the finished product. The decision basis is to maximize the profit in the production process, and the corresponding indicators are profit and product quantity.

[0226] In the entire dynamic programming model module, the model can be optimized and improved into a probability decision model of dynamic programming. The ratio of the number of inspected spare parts or finished products to the total number that should be inspected can be used, and this ratio is defined as the probability of whether this material or finished product makes a decision at this step. At this time, the decision variable takes values in the interval [0, 1], and the objective function is defined as the maximum profit.

[0227] Decision output module: It adopts a simple and intuitive user interface. Through this interface, the sampling decision results calculated by the dynamic programming model, including data such as specific sampling plans, sampling time points, and inspection criteria, are presented to production managers and quality control personnel in the form of tables, charts, etc. At the same time, a data export function is developed to facilitate relevant personnel to print or save the decision results;

[0228] The dynamic programming model module continuously accepts the latest data during subsequent use and recalculates the optimal sampling strategy according to the new data. At the same time, the system sets a fixed period to evaluate the model, compares the quality cost in actual production with the quality cost predicted by the model, analyzes the reasons for the differences, and adjusts the relevant parameters of the model accordingly to improve the accuracy and adaptability of the model;

[0229] Furthermore, a system monitoring mechanism is established in the system to monitor the running status of each module in real time. Once problems such as abnormal data collection and model calculation errors are found, an alarm is issued in a timely manner, and professional technicians are arranged to conduct fault troubleshooting and repair to ensure the stable operation of the system. Compared with the traditional fixed sampling plan, this sampling decision system can adjust the sampling strategy in a timely manner according to the dynamic changes in the production process, better cope with situations such as equipment aging and raw material fluctuations, and improve the scientificity and adaptability of sampling decisions.

[0230] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention.

Claims

1. An electronic parts production sampling decision system based on dynamic programming, characterized in that: include: Data acquisition module: collects raw material information, production equipment parameters, production environment data and product quality inspection data through sensors and data interfaces, ensures the real-time, accuracy and integrity of the data, and transmits it to the data processing module; Data processing module: cleans the data collected by the data collection module, removes abnormal values ​​and erroneous data, and standardizes the data to make data from different sources and formats comparable; Dynamic programming model module: constructs a sampling decision model based on dynamic programming. The dynamic programming module inputs the production data processed by the data processing module, and uses the dynamic programming algorithm to solve the optimal sampling strategy based on the set state variables, decision state variables and state transfer direction in the production process, with minimizing quality cost as the objective function; Decision output module: The sampling decision results calculated by the dynamic programming model are displayed to production management personnel and quality control personnel. The sampling decision results include specific sampling plans, sampling time points, and inspection standards to guide the sampling inspection work in actual production.

2. The electronic parts production sampling decision system based on dynamic programming according to claim 1 is characterized by: The data acquisition module collects data through sensors and data interfaces, obtains raw material information by connecting with the information system of the raw material supplier, and collects product quality data by setting quality inspection points on the production line.

3. The electronic parts production sampling decision system based on dynamic programming according to claim 1 is characterized by: The data acquisition module continuously collects new data during the production of spare parts, and the data processing module merges and updates the new data with historical data.

4. The electronic parts production sampling decision system based on dynamic programming according to claim 1 is characterized by: The data processing module classifies and stores the standardized data and establishes an associated database for quick query and call.

5. The electronic parts production sampling decision system based on dynamic programming according to claim 1 is characterized by: When the data processing module cleans the collected data, it removes abnormal values ​​by setting reasonable thresholds and organizes and stores the raw material information in a unified format.

6. The electronic parts production sampling decision system based on dynamic programming according to claim 1 is characterized by: The state transfer equation in the dynamic programming model module is divided into two cases according to whether sampling is performed: When no sampling is done, the production status of the next stage is predicted through the production process model; When sampling, the production status of the next stage is determined based on the sampling results and the natural changes in the production process.

7. The electronic parts production sampling decision system based on dynamic programming according to claim 1 is characterized by: The objective function of the dynamic programming model module is to minimize the total cost including sampling cost and loss cost caused by defective products in the entire production cycle.

8. The electronic parts production sampling decision system based on dynamic programming according to claim 1 is characterized by: The dynamic programming model module adopts a reverse solution method, starting from the last stage of the production cycle and gradually deducing forward. Under different conditions in each stage, by comparing the costs of taking different decisions, the decision with the lowest cost is selected to obtain the optimal decision sequence.

9. The electronic parts production sampling decision system based on dynamic programming according to claim 1, characterized in that: The minimized quality costs include sampling costs, non-conforming product handling costs, rework costs, and customer complaint costs.

10. The electronic parts production sampling decision system based on dynamic programming according to claim 1, characterized in that: The dynamic programming model module accepts the latest data to recalculate the optimal sampling strategy, and the system regularly evaluates and optimizes the model, and adjusts the parameters of the model by comparing the quality cost in actual production with the quality cost predicted by the model.

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