Fuel assembly manufacturing process reliability evaluation method considering workpiece size deviation

Abstract

The invention belongs to the technical field of reliability, and particularly relates to a fuel assembly manufacturing process reliability evaluation method considering workpiece size deviation. Comprising the following steps: step 1, modeling dimensional deviation of a workpiece in process and key reliability characteristics of a fuel assembly; 2, fuel assembly manufacturing process reliability characteristic relevance mining considering workpiece size deviation is carried out; and step 3, fuel assembly manufacturing process reliability characteristic risk grading evaluation based on the extended RPN value. The method has the beneficial effects that the limitation of disjunction of traditional design and manufacturing is broken through, and accurate identification and scientific grading of key reliability characteristics (KRC) are realized.

Description

Technical Field

[0001] This invention belongs to the field of reliability technology, and specifically relates to a reliability evaluation method for the fuel assembly manufacturing process that takes into account workpiece dimensional deviations. Background Technology

[0002] Quality characteristics can be divided into specific quality characteristics and general quality characteristics. Integrating the design of performance parameters for specific quality characteristics with reliability design is an inevitable trend that fundamentally guarantees and improves product reliability. Among specific quality characteristics, those that affect reliability are called reliability characteristics, while critical reliability characteristics are those that require more resources and focused attention. For a clearer explanation of the connotations of critical reliability characteristics, please refer to... Figure 1 The diagram shown is shown in the image.

[0003] Reliability characteristics describe the reliability performance of a product at various stages of its life cycle from multiple dimensions. They are numerous and often interfere with each other, with redundant and complex data. Deviations in reliability characteristics throughout the life cycle affect the overall performance of the final product. Therefore, control of reliability characteristics is necessary. Under the principle of "critical few," the identification and control technology of the few key reliability characteristics that determine and influence product reliability has become a key focus for enterprises. Referring to current academic definitions of critical quality characteristics, these are considered to directly affect product safety, main functions, and customer satisfaction when they deviate from specified ranges. Therefore, in a narrow sense, reliability is an indicator of the degree to which product functions are achieved. To comprehensively assess the criticality of reliability characteristics, the concept of a key reliability characteristic (KRC) is defined as a reliability characteristic whose deviation, when it occurs, will lead to the failure of the product's main functions or a reduction in its lifespan, directly determining the product's reliability level. Among them, the key connotation of critical reliability characteristics is "risk consequences" and "functional failure or reduced lifespan". On the one hand, the risk value is an important basis for judging whether a reliability characteristic is critical. On the other hand, compared with the broad range of critical quality characteristics, KRC is directly related to product reliability and places more emphasis on its impact on product function.

[0004] It is important to note that during the design process, designers achieve the product's functional goals through the physical structure design. Therefore, by mapping between product function and physical structure, the key reliability characteristics (KRCs) of the design process are determined. At this stage, the KRCs are primarily based on the product's physical structure, emphasizing the impact of parameter tolerance design on product reliability, without considering the processing difficulties in actual production. However, during the fuel assembly manufacturing process, some characteristics, which were considered in the design phase to cause product failure if their tolerances were exceeded, are actually not difficult to manufacture and are easily met under current process conditions. Therefore, the probability of such deviations is very small and will not induce reliability degradation in the manufactured product. Conversely, due to designers' lack of actual understanding of the process, some characteristics with low tolerance impact on product reliability but high processing difficulty often exhibit large process deviations with a high probability of occurrence during the manufacturing stage. Process deviations in work-in-process are a direct cause of reliability degradation in the manufactured product. Therefore, during fuel assembly manufacturing, the KRCs of the manufacturing process are determined by comprehensively evaluating the "risk consequences" of process parameters through three risk factors: "probability of deviation occurrence," "importance," and "undetectability." Summary of the Invention

[0005] The purpose of this invention is to provide a key reliability characteristic model and identification method for the manufacturing process that takes into account workpiece size deviations, which can effectively solve the problem of identifying key reliability characteristics of the manufacturing process with workpiece size deviations.

[0006] The technical solution of the present invention is as follows: A reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations, comprising the following steps: Step 1: Modeling the dimensional deviations of the in-process workpiece and the key reliability characteristics of the fuel assembly; Step 2: Mining the correlation between reliability characteristics of fuel assembly manufacturing process considering workpiece dimensional deviations; Step 3: Risk classification and evaluation of reliability characteristics of fuel assembly manufacturing process based on extended RPN value.

[0007] Step 1, as described above, includes a framework for analyzing and identifying key reliability characteristics of fuel assembly manufacturing processes within the modeling of workpiece dimensional deviations and key reliability characteristics of fuel assemblies. This framework includes: Step 11: Collect process parameters for fuel assembly manufacturing Collect process specification documents and processing guidance documents during the fuel assembly manufacturing process. Based on the axiomatic domain mapping and the evolution mechanism of KRC, determine the process parameter names of the work-in-process inputs and outputs of each process. At the same time, collect process deviation data in the actual production of this batch. Step 12: Analyze the correlation between process parameters and product reliability By using the collected data on the processing, assembly, and finished product quality of the fuel assembly manufacturing process, a transaction database was constructed based on the record data of this batch of products through association rule mining, and association rules were mined to identify the initial set of KRC for the fuel assembly manufacturing process. Step 13: Assess the reliability risks of the fuel assembly manufacturing process By collecting process quality data and processing flow data during the fuel assembly manufacturing process, three risk factors—probability of deviation occurrence, significance, and undetectability—we modeled the risk values ​​and calculated the risk values.

[0008] In step 2, regarding the correlation mining of reliability characteristics in the fuel assembly manufacturing process, considering workpiece dimensional deviations, the evolution process of reliability characteristics with different manifestations during the product life cycle is expressed from top to bottom in the form of a correlation tree. The specific construction steps are as follows: Step 21: Design - Functional Decomposition Based on the principle of functional independence, user requirements are decomposed into corresponding functional nodes and auxiliary functional nodes layer by layer, forming a multi-level functional decomposition association tree structure. Step 22: Design - Structural Decomposition The physical structure is decomposed from top to bottom according to the product's functional requirements; Step 23: Manufacturing - Process Breakdown The part-level reliability characteristics are mapped to the manufacturing reliability characteristics. According to the design document, the part-level RC is converted into a series of process parameters for each process step in the manufacturing process. Step 24: Manufacturing-Structure Mapping Map the machining RC to the assembly RC in the assembly workshop; Step 25: Manufacturing - Function Mapping.

[0009] In step 3, based on LASSO regression, the importance I of KRC to product reliability characteristics is taken as the first risk factor; the probability P of KRC deviation is taken as the second risk factor; and the undetectability D of KRC deviation is taken as the third risk factor. The RPN value is obtained by combining the values ​​of the three risk factors and the degree of preference, thus realizing the classification of KRC in the fuel assembly manufacturing process.

[0010] Step 3 includes: KRC's risk value is expressed as: (1) Calculation of importance based on LASSO regression Regression coefficient Represented as: In the formula, It is a constant. It is the first j Observations of a reliability characteristic These are the observed values ​​of the corresponding finished product reliability characteristics. , It refers to the number of sample data. , The number of critical reliability characteristics and the importance I of each critical reliability characteristic are expressed as: The collected process deviation data are standardized. In the formula, and These represent the mean and standard deviation of the observed values, respectively. (2) Calculation of the probability of occurrence based on the deviation formation mechanism The probability P of deviation occurring in the KRC during the fuel assembly manufacturing process. v It is event P n The reverse time, expressed as: (3) Calculation of undetectability based on average running chain length The undetectability D is represented as: The KRC observations monitored during fuel assembly manufacturing follow a normal distribution. If the sample size is n, then the KRC sample mean follows... ; The ARL is solved using the Markov chain solver, and the ARL is represented as: In the formula, the matrix P It is an m-dimensional transition probability matrix, S i It is the initial probability matrix , E It is the identity matrix transition probability matrix P It consists of a series of states z i Transition to state z j probability elements Composition, then In the formula, It is a statistic of the EWMA control chart that satisfies r is the drift coefficient. At any moment i In state z j The probability is: In the formula, h is the width of the interval between the upper and lower limits, satisfying... T u and T l These are the upper and lower limits of the control chart, respectively, and K is the number of intervals to be divided. In addition, because Convert it to , is represented as: (4) Calculation of risk value of key reliability characteristics based on hesitant fuzzy decision theory Three risk sets It is a set of solutions. It is an attribute set, m n This is a KRC deviation pattern, with expert weights of 100%. Based on the deviation occurrence patterns in different schemes, fuzzy semantic scores are given. The standardized value of the comprehensive evaluation of the three schemes in the scheme set represents the degree of preference for the three risk factors. The fuzzy semantic set is represented as follows: The fuzzy semantic evaluation of the set of alternatives was transformed into a hesitant fuzzy decision matrix. ,in , (c g =1, 2, 3, 4); l Experts on scheme set X n The combined attribute value of all attributes is expressed as: In the formula, i = I , P , D， If it is a rounding function, then , , l The comprehensive attribute values ​​of three risk factors for each proposed solution were evaluated by several experts. right l The comprehensive attribute values ​​provided by several experts were aggregated and processed using a function. Calculate operator weights; operator weights The calculation process is expressed as follows: In the formula, , It is the number of comprehensive attribute values; Incorporating expert weights, the corrected operator weights are: in, It is the j-th largest parameter, and M is a piecewise function, where This allows us to obtain the comprehensive evaluation values ​​from experts for each solution in solution set X. Finally, the comprehensive evaluation value is converted into a constant using the following formula. After standardization, the experts' preference for the three risk factors I, P, and D is calculated. Further processing yields: At this point, based on the assessment of the importance of different attribute values ​​in each option, the final comprehensive evaluation value of each option is obtained, which is the degree of preference for the three risk factors.

[0011] The probability of the device not failing in formula (5) in step 3 is... The calculation is as follows: The operating state of the equipment, from ideal state to complete failure, is divided into the following discrete levels: In the formula, Represents the ideal operating state of the equipment. The probability set represents the complete failure state of the device. The probability of each operating state of the corresponding processing equipment is expressed as: In the formula, This corresponds to the probability of the equipment operating in its ideal state. This corresponds to the probability of a complete equipment failure. It is the proportionality constant of each device, and the operating states of each device are independent of each other, satisfying: The probability of the equipment changing from an ideal state to this defective state is expressed as: Establish the following equation: In the formula, It is the expected number of equipment failures (t) within the production cycle. It refers to the downtime due to equipment failure. and These represent the frequency of planned maintenance and the corresponding downtime, respectively. The probability that the processing equipment will not fail during the production cycle is: In step 3, the probability that environmental factors are at normal levels in formula (5) is... The calculation is as follows: The capacity index of environmental factors is expressed by the following formula. When both upper and lower limits of the design specifications for environmental factors exist: When the design specifications for environmental factors only have an upper limit: When the design specifications for environmental factors only have a lower limit: In the formula, and These represent the upper and lower limits of the range given in the environmental factor design specifications, respectively. and These are the mean and standard deviation of observed values ​​in actual production. It is the nominal value of the standard distribution. Furthermore, Within the production cycle t, the set of capacity indices for environmental factors is: The probability that environmental factors are at normal levels is expressed as: In the formula, The ability index in the representative set satisfies Quantity, This represents the total number of samples taken.

[0012] The beneficial effects of this invention are: overcoming the limitations of traditional design-manufacturing disconnect, and achieving accurate identification and scientific classification of Key Reliability Characteristics (KRCs). This method unfolds through a three-step core process: First, process parameters and deviation data from the manufacturing process are collected, and an initial set of KRCs is constructed using association rule mining, followed by risk factor modeling; second, a link mapping from design to structure and then to function is completed in the form of an association tree, clearly presenting the evolution process of reliability characteristics; finally, the importance of KRCs is quantified based on LASSO regression, the probability of deviation occurrence is calculated by combining equipment and environmental mechanisms, undetectability is solved through Markov chains, and then expert preferences are incorporated through hesitant fuzzy decision theory to derive an extended RPN value to achieve KRC classification. Compared with existing technologies, this method abandons subjective scoring, relying on data and mechanisms to solve the ambiguity and classification problems of traditional risk assessment. It not only aligns with the actual processing difficulty in production but also accurately identifies the core characteristics affecting product reliability, providing a more practical basis for quality control in the fuel assembly manufacturing process. (See attached figures.) Figure 1 A schematic diagram illustrating the key reliability characteristics of a product; Figure 2 A flowchart for mining the correlation of reliability characteristics in the fuel assembly manufacturing process considering workpiece dimensional deviations; Figure 3 A framework for modeling the evolution of product KRC; Figure 4 This is a schematic diagram of process parameter types; Figure 5 A schematic diagram for modeling risk factors. Detailed Implementation

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0014] The present invention provides a reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations, comprising the following steps: Step 1: Modeling In-Process Workpiece Dimensional Deviations and Key Reliability Characteristics of Fuel Assemblies The key reliability characteristics in fuel assembly manufacturing are the embodiment of design reliability characteristics and are closely related to the complexity of the product structure and the difficulty of the manufacturing process. Generally, the more complex the manufacturing process, the more key reliability characteristics (KRCs) are involved in the fuel assembly manufacturing process. In reality, only a few characteristics actually affect the reliability of the manufactured product.

[0015] By analyzing the correlation between dimensional deviations in the manufactured parts and product reliability, and comprehensively assessing the criticality of characteristics from a risk perspective, the KRC (Key Risk Concern) of the fuel assembly manufacturing process is ultimately identified. The specific identification framework is as follows: Figure 2 As shown.

[0016] like Figure 2 As shown, the framework for identifying key reliability characteristics of fuel assembly manufacturing processes consists of three steps. Blue circles represent the technologies and models involved in each step, while orange circles represent the information and data required for each step. The specific tasks are as follows: Step 11: Collect process parameters for fuel assembly manufacturing; Critical reliability characteristics originate from user requirements. As the design process progresses, their granularity decreases while their number increases. The granularity reaches its minimum during the manufacturing stage, and then gradually increases again while the number decreases during the assembly stage. During product design, designers decompose key reliability characteristics at the product, component, and part levels. Guided by the Key Reliability Control (KRC) process, process specifications and manufacturing guidance documents for fuel assembly manufacturing are collected. Based on axiomatic domain mapping and the evolution mechanism of KRC, the process parameter names of the work-in-process inputs and outputs for each process are determined. Simultaneously, process deviation data from the actual production of this batch are collected, providing a solid data foundation for the identification of critical reliability characteristics.

[0017] Step 12: Explore the correlation between process parameters and product reliability The process parameters of work-in-process are characteristics that affect the reliability of the manufactured products. Therefore, by mining the correlation between the process parameters collected in the previous step and product reliability, we can identify a few key fuel assembly manufacturing process KRCs that can provide focused references for preventive control of product reliability. In this step, using the collected processing, assembly, and finished product process quality data of the fuel assembly manufacturing process, we construct a transaction database based on the record data of this batch of products through association rule mining and mine association rules, thus identifying the initial set of fuel assembly manufacturing process KRCs.

[0018] Association rules are constraints used in data mining to discover potential relationships between component variables. By analyzing production data (such as process parameters of manufacturing process, quality inspection results, etc.), they identify "the probability of B occurring when A occurs".

[0019] Step 13: Assess the reliability risks of the fuel assembly manufacturing process Based on the connotations of key reliability characteristics of the product, and building upon the initial set of identified key reliability characteristics (KRCs) for the fuel assembly manufacturing process, redundant characteristics are eliminated from the initial set, and their risk values ​​are assessed to obtain their risk values. A comprehensive and quantitative evaluation of the risk consequences determines the final set of fuel assembly manufacturing process KRCs and classifies their criticality. This step primarily involves collecting process quality data and processing flow data within the fuel assembly manufacturing process to model three risk factors: the probability of deviation occurrence, the degree of importance, and the undetectability. Based on this, the risk values ​​are calculated. This process identifies the final set of fuel assembly manufacturing process KRCs, which serves as the primary tool for subsequent quality control of the fuel assembly manufacturing process.

[0020] Step 2: Correlation mining of reliability characteristics in fuel assembly manufacturing process considering workpiece dimensional deviations Considering workpiece dimensional deviations, the evolution of reliability characteristics exhibiting different behaviors throughout the product's lifecycle is expressed from top to bottom in the form of an association tree. Furthermore, the association tree for product reliability characteristics was constructed under the guidance of axiomatic domain mapping theory. For example... Figure 3 As shown.

[0021] Figure 3 The evolutionary modeling framework shown, through layer-by-layer decomposition and mapping, corresponds to the connotation and evolution mechanism of the product's key reliability characteristics. It completes the reliability characteristics at each level of the entire process from user functional requirements to the formation of the manufactured product during the fuel assembly manufacturing process. At this point, the names of the reliability characteristics at each level are determined, which is the candidate set of the product's RC. The specific construction steps are explained as follows: Step 21: Design - Functional Decomposition User needs regarding product features, as revealed by research, are often disorganized and complex. In such cases, the design team should, following the principle of functional independence, decompose user needs layer by layer into corresponding functional nodes and auxiliary functional nodes, forming a multi-level functional decomposition tree structure. Figure 3 The nodes in the association tree are represented as FD1~FD1.3, where FD represents the structural support function of the fuel assembly, FD1.1 is the fuel rod positioning function, FD1.2 is the assembly shell sealing function, and FD1.3 is the seismic buffering function.

[0022] Step 22: Design - Structural Decomposition Accurately and maximally mapping user requirements for product functionality to actual product design metrics is a key focus of product development and a prerequisite for ensuring product reliability meets user needs. The main task of this step is to decompose the physical structure from top to bottom based on product functional requirements. Since product reliability is perceived by users based on the degree of functional completion, through domain mapping between functionality and physical structure, product functions are mapped to product-level reliability characteristics. Subsequently, based on product design drawings and 3D models, component-level reliability characteristics and part-level reliability characteristics are sequentially decomposed, forming a multi-level product structure decomposition tree structure. Figure 3 The nodes in the association tree are represented as product-level RC, component-level RC, and part-level RC.

[0023] Step 23: Manufacturing - Process Breakdown Based on the process plan and design drawings, in this process, production engineers complete the production environment layout, processing equipment parameter adjustments, and production schedule for this batch of products. The main task of this step is to map the part-level reliability characteristics to the processing reliability characteristics. According to the design documents, the part-level RC (Reliability and Reliability) is converted into a series of process parameters for each step of the manufacturing process. For example... Figure 4 As shown, process parameters include verification parameters, constraint parameters, and control parameters before the start of the process, and validation parameters at the end of the process. Constraint and control parameters mainly refer to equipment operating parameters and production environment conditions during processing. In this patent, machining RC refers to two types of process parameters directly related to the work-in-process: verification parameters and validation parameters. These include parameters such as the incoming dimensions of the material flowing to this process and the dimensional deviations of the work-in-process output by the process. Examples include dimensional errors, positional errors, and surface quality parameters. These are represented as nodes in the machining RC node in the association tree.

[0024] Step 24: Manufacturing-Structure Mapping Assembly is the final step in the formation of a manufactured product. Similar to machining RC (Role-Specific Assembly), based on the machining sequence, assembly drawings, and design documents, the machined parts are assembled through specific processes to form components and ultimately the finished product. The main task of this step is to map the machined RC to the assembly RC in the assembly workshop. Assembly RC is used to characterize the mating parameters between components during the assembly process. For example, reliability characteristics include mating accuracy, parallelism between planes, and relative motion accuracy. Furthermore, welding is an important process in assembly. The characteristic parameters related to the welding process are also considered as assembly RC. Figure 3 In the association tree, it is represented as the assembly RC node.

[0025] Step 25: Manufacturing-Function Mapping Each component undergoes assembly, bringing the designed product to life. The manufactured product enters the usage phase, and its functionality is perceived by the user. Based on the evolution of product reliability over its lifespan, and considering the transmission of deviations in processing and assembly RC (Reliability Control) during fuel assembly manufacturing, the reliability of the manufactured product is significantly lower than the reliability targets set in the design process. This phenomenon is reflected in the early stages of user use, where environmental stress triggers premature product failures or performance degradation. Therefore, the key reliability characteristics at the manufactured product level often differ from the product-level RC at the design stage; in other words, the dimensional data of the manufactured product often cannot meet the nominal dimensional specifications of the product at the design stage.

[0026] In summary, the constructed evolutionary model framework for reliability characteristics defines the RC set. However, determining specific key reliability characteristics requires the support of large amounts of data throughout the product lifecycle. Therefore, a product lifecycle database is constructed by collecting relevant data such as product design structural parameters, manufacturing process parameters, test data, assembly process data, and failure data.

[0027] Based on the aforementioned KRC evolution framework and the association tree node weight mining algorithm, the processing and assembly KRC in the fuel assembly manufacturing process was identified. First, using the KRC evolution framework, data within the product lifecycle was preprocessed, transformed, and stored in a transaction database. Next, association rules were used to mine association rules from the database based on minimum support and minimum confidence, calculating the nodes in the fuel assembly manufacturing process on the association tree, thus obtaining the initial set of manufacturing RCs.

[0028] Step 3: Risk grading assessment of reliability characteristics in fuel assembly manufacturing process based on extended RPN values A comprehensive risk assessment of key reliability characteristics is crucial for integrating risk management into the quality control of fuel assembly manufacturing. Traditional process failure mode and consequence analysis (FEMA) methods, when applied to fuel assembly manufacturing, can identify potential failure modes and consequences in process units by assessing the risk value of failure modes, thereby proposing corresponding prevention and control measures to ensure product quality. Therefore, using risk values ​​to classify key reliability characteristics is a reasonable choice. However, in traditional risk assessment, severity, incidence, and detectability are the three risk factors constituting the risk priority number (RPN). These factors are typically assigned values ​​through highly subjective expert scoring, and the risk value is calculated by multiplying the three factors. This often results in the same risk value corresponding to different combinations of risk factor parameters, leading to deviations in the final classification results. This paper models the three risk factors based on the initial set of KRCs (Key Reliability Components) in the fuel assembly manufacturing process to determine the risk values ​​of processing and assembling KRCs during fuel assembly manufacturing. The risk factor modeling process is as follows: Figure 5 As shown.

[0029] like Figure 5 As shown, firstly, based on LASSO regression, the importance (I) of KRC to product reliability characteristics is taken as the first risk factor; secondly, the mechanism of KRC deviation in the fuel assembly manufacturing process is analyzed, and the probability (P) of KRC deviation is taken as the second risk factor; subsequently, based on the manufacturer's current process control control chart's ability to detect deviations, the undetectability (D) of KRC deviation is taken as the third risk factor; then, hesitant fuzzy decision theory is applied to calculate the experts' preference for the three risk factors. Finally, the RPN value is derived by combining the values ​​of the three risk factors and the preference levels, thus achieving the classification of KRC in the fuel assembly manufacturing process. Therefore, the risk value of KRC can be expressed as: in, It is a risk factor synthesis function used to integrate three risk factors (importance I, probability of deviation P, and undetectability D) and the degree of expert preference. It is the expert preference weight calculated using the hesitant fuzzy decision theory.

[0030] (1) Calculation of importance based on LASSO regression Deviations in key reliability characteristics during fuel assembly manufacturing are causally related to the reliability of the finished product. In this patent, importance is considered the degree of influence of deviations in the processing and assembly KRC (Kind Reliability Components) during fuel assembly manufacturing on the deviations in the finished product KRC; the greater the influence, the more important the KRC. Interaction relationships between characteristics are mined from association rules, and rules with strong positive correlations are found. Correlation analysis is the foundation and prerequisite for regression analysis, which constructs the causal relationship between independent and dependent variables. Correlation analysis indicates a correlation between two characteristics, but this is far from sufficient; further quantitative analysis of the relationships between characteristics is needed through regression analysis to infer the change in the dependent variable caused by changes in the independent variable.

[0031] In this embodiment, based on LASSO (Least Absolute Shrinkage and Selection Operator) regression, a regression equation is constructed between the processed and assembled KRC and the finished KRC. This equation compares the influence of different KRCs on a specific related KRC within the same dimension to achieve a hierarchical ranking of the importance of risk factors. LASSO regression introduces a penalty value to progressively compress the coefficients in the regression equation to zero, selecting high-dimensional data from the fuel assembly manufacturing process, eliminating redundant independent variables, and choosing variables with a significant impact on the dependent variable. Since regression coefficients can measure the influence between independent and dependent variables, the regression coefficients from LASSO regression are used as the importance of key reliability characteristics. It can be represented as: In the formula, It is a constant. It is the first j The observed values ​​of each reliability characteristic (independent variable), These are the observed values ​​of the corresponding finished product reliability characteristics. This represents the baseline observation value of the finished product KRC when all machining / assembly KRC observations are 0. Indicates the first The regression coefficients of key reliability characteristics reflect the intensity and direction of the influence of the deviation of this KRC on the deviation of the finished KRC. , It refers to the number of sample data. , This refers to the number of key reliability characteristics (KRCs). Furthermore, the absolute value of the regression coefficients can be directly used to measure and compare the importance of different KRCs to the final product KRC. Therefore, processing the regression coefficients yields the degree of influence of the independent variable on the dependent variable, which is the importance I of the key reliability characteristics, expressed as: Indicates the first The importance index of a key reliability characteristic is used to quantify the impact of the KRC deviation on the reliability of the finished product.

[0032] Standardizing the collected process deviation data is a prerequisite for establishing the regression equation; therefore, In the formula, and These represent the mean and standard deviation of the observed values, respectively.

[0033] In summary, by establishing the LASSO regression equation, the impact of the fuel assembly process (KRC) on the finished KRC was calculated, thus obtaining the first risk factor for risk modeling. It is important to note that after constructing the regression equation, the sign and magnitude of the regression coefficients should be checked to ensure they match actual production conditions.

[0034] Furthermore, through the LASSO regression process, redundant characteristics in the KRC set of the fuel assembly manufacturing process are eliminated. In the process of calculating other risk factors, it is only necessary to model the KRC involved in the regression equation.

[0035] (2) Calculation of the probability of occurrence based on the deviation formation mechanism Traditional methods for measuring the probability of characteristic deviations involve directly counting the number of defective products generated within a certain time period to determine the frequency of non-conforming products. However, in today's high-reliability manufacturing systems, the number of non-conforming products exceeding a threshold is very small, and the time interval between two non-conforming products is uncertain. In the fuel assembly manufacturing process, KRC (Knock-down Rectifier) ​​is typically processed on designated equipment according to specific process flows and environmental conditions. It is known that noise factors such as equipment operating condition degradation and abnormal fluctuations in environmental factors are the direct causes of deviations in the process parameters of the workpiece during fuel assembly manufacturing. This is the mechanism of KRC deviations in the fuel assembly manufacturing process. The probability of KRC deviations in the fuel assembly manufacturing process depends on the above-mentioned deviation mechanism and the quality data within the manufacturing system.

[0036] The sensors currently ubiquitous on production lines and in the production environment make noise factors easier to acquire; therefore, the probability P of no deviation occurring in the KRC during the fuel assembly manufacturing process is... n This can be considered as the probability that the corresponding processing equipment will not malfunction and environmental factors will remain within normal ranges during the production cycle. Then, the probability P of a deviation occurring during the fuel assembly manufacturing process (KRC) is... v It is event P n The inverse time can be expressed as: (a) The probability that the equipment will not fail Due to the diversity of production environments, the variability of production tasks, and the wear and tear of processing equipment, different failure modes may occur, such as loosening, component damage, and downtime. The impact of each failure mode on the equipment varies. During operation, equipment undergoes a series of discrete degradation states, from ideal state to defective operation to complete failure. Therefore, the operating state of equipment from ideal state to complete failure can be divided into the following discrete levels: In the formula, Represents the ideal operating state of the equipment. It is the intermediate degradation state of the equipment between its ideal state and its complete failure state. This represents the complete failure state of the device. Furthermore, the probability set... The probability of each operating state of the corresponding processing equipment can be expressed as: In the formula, This corresponds to the probability of the equipment operating in its ideal state, and the probability of the equipment being in the corresponding intermediate degradation state (e2, e3...e...). m The probability of occurrence of ). This corresponds to the probability of a complete equipment failure. It is the proportionality constant of each device, and the operating states of each device are independent of each other, satisfying: Furthermore, assume that the operating state of a certain device is as follows: At this point, the equipment is not completely faulty and has stopped, but it is no longer able to meet the production task on time and needs to be shut down for maintenance. Therefore, the probability of the equipment changing from its ideal state to this defective state can be expressed as: Different failure modes will cause varying downtime and maintenance periods for equipment, rendering it unusable. On one hand, equipment unavailability can be considered as the ratio of production losses incurred during the production cycle to the equipment's ideal processing capacity. On the other hand, equipment unavailability can be considered as the ratio of downtime to ideal operating time. Therefore, the following equation can be established: In the formula, It is the expected number of equipment failures within the production cycle t. It refers to the downtime due to equipment failure. and These represent the frequency of planned maintenance and the corresponding downtime, respectively.

[0037] Therefore, combining formulas (9) and (10), the probability that the equipment will change from an ideal operating state to an undesirable state during the production cycle, which is also the probability that the processing equipment will not fail during the production cycle, is: (b) Probability that environmental factors are at normal levels During product manufacturing, fluctuations in environmental factors exceeding specified ranges can lead to deviations in the process parameters of the workpiece. The process capability index, calculated as the ratio of the tolerance range of a characteristic to the fluctuation range of its value, reflects the degree to which the processing capability meets process specifications and measures the overall processing capability. Inspired by this, production data, including factors such as temperature and noise, are collected within the manufacturing system during product processing. Assuming that environmental factors follow a normal distribution within specified ranges, the basic capability index is... a When the capacity index of environmental factors in actual production is lower than a When this occurs, it indicates that the manufacturer should make improvements to environmental factors. The capability index for environmental factors is expressed by the following formula.

[0038] When both upper and lower limits of the design specifications for environmental factors exist: When the design specifications for environmental factors only have an upper limit: When the design specifications for environmental factors only have a lower limit: In the formula, and These represent the upper and lower limits of the range given in the environmental factor design specifications, respectively. and These are the mean and standard deviation of observed values ​​in actual production. It is the nominal value of the standard distribution. Furthermore, During the actual production process of the product, environmental factors occur every [period]. Sampling and capacity indices are performed. Therefore, the set of capacity indices for environmental factors within production cycle t is: . This is the environmental factor capability index calculated during the first sampling within the production cycle. Therefore, the probability that the environmental factor is at a normal level can be expressed as: In the formula, The ability index in the representative set satisfies Quantity, This represents the total number of samples taken.

[0039] (3) Calculation of undetectability based on average running chain length The undetectability of a critical reliability characteristic (KRC) refers to the ability to detect deviations in the KRC in a timely manner under the existing control conditions of the current manufacturing system. In the production process, control charts are common process control tools in fuel assembly manufacturing, and they are typically used to monitor the fluctuations in process parameters of work-in-process within the manufacturing system.

[0040] Average running chain length (ARL) is a crucial metric for evaluating control chart performance. When the production process is under control, if a point accidentally goes out of bounds, it is considered an anomaly, resulting in a Type I error in the control chart, where normal operations are misclassified as abnormal. When the production process is out of control, if some sampled points remain within the bounds, they are considered normal, resulting in a Type II error in the control chart, where anomalies are misclassified as normal. In the case of an out-of-control production process, we expect the control chart to detect anomalies as early as possible. The ARL in an out-of-control state is the number of samples between two false alarms. Obviously, a shorter ARL is better, meaning that deviations in the fuel assembly manufacturing process's KRC can be detected quickly, the undetectability of deviations is lower, and the resulting risks are smaller.

[0041] In this patent, the undetectability of deviations in the KRC (Kindness Control Regulator) of the fuel assembly manufacturing process can be expressed as the ratio of the ARL (Advanced Range Limit) under current control conditions in a runaway state to the longest acceptable ARL0 for the enterprise. It is important to note that ideally, ARL0 should be as short as possible, close to 0. However, this needs to be balanced with the production costs incurred by control chart sampling. Therefore, when the ARL meets... This is acceptable for businesses. When This means that the detection capability of KRC deviation under the current control conditions is very poor, and the current control chart parameters need to be improved. Therefore, the undetectability D is expressed as: Here, we take the EWMA control chart, suitable for monitoring small fluctuations, as an example. We assume that a manufacturer has deployed an EWMA control chart during the production and processing of a batch of products to achieve quality control in the fuel assembly manufacturing process. We also assume that the KRC observations monitored during fuel assembly manufacturing follow a normal distribution. If the sample size is n, then the KRC sample mean follows... .

[0042] There are several methods for solving ARL, including Monte Carlo simulation, integration, and Markov chain methods. Here we introduce the Markov chain method, which has strong applicability. ARL can be represented as: In the formula, the matrix P It is an m-dimensional transition probability matrix, S i It is the initial probability matrix , E It is the identity matrix Transition probability matrix P It consists of a series of states z i Transition to state z j probability elements Composition. Then In the formula, It is a statistic of the EWMA control chart that satisfies , where r is the drift coefficient. At any moment i In state z j The probability is: In the formula, h is the width of the interval between the upper and lower limits, satisfying... T u and T l These are the upper and lower limits of the control chart, respectively, and K is the number of intervals to be divided. Therefore, combining formulas (19) and (20)... In addition, because Convert it to Then formula (21) can be converted into the standard normal probability distribution obtained by looking up a table. , can be represented as: In summary, by combining formulas (17), (18), (19), and (22), the undetectability of deviations in key reliability characteristics was calculated, and the third risk factor was thus calculated.

[0043] (4) Calculation of risk value of key reliability characteristics based on hesitant fuzzy decision theory The risk tolerance assessment (KRC) of the fuel assembly manufacturing process is evaluated using three risk factors: importance (I), probability of deviation (P), and undetectability of deviation (D). In actual production, decision-makers have varying degrees of preference for these three risk factors. When conducting a graded evaluation of the KRC of the fuel assembly manufacturing process, it is necessary to consider not only the levels of the three risk factors but also their importance, and adjust the risk value of the KRC accordingly.

[0044] Assume three risk sets It is a set of solutions. It is an attribute set, mn This refers to deviation patterns in KRC, such as dimensional errors, perpendicularity errors, etc., with expert weights being... Experts assign fuzzy semantic scores, such as {c1,0}, based on the deviation patterns in different options. The standardized value of the comprehensive evaluation of the three options in the option set represents the experts' preference for the three risk factors. The fuzzy semantic set is represented as: in, This represents three risk assessment schemes in hesitant and fuzzy decision-making, corresponding to three risk factors: importance, probability of deviation, and undetectability, respectively. This indicates the specific types of deviations that may occur in the critical reliability characteristic (KRC). The first person to participate in the risk assessment The weighting coefficients of each expert.

[0045] Subsequently, the experts' fuzzy semantic evaluation of the solution set was transformed into a fuzzy decision matrix due to hesitation. ,in , (c g =1, 2, 3, 4), It represents a set of fuzzy semantics. l Experts on scheme set X n The combined attribute value of all attributes is expressed as: In the formula, i =I, P, D. If it is a rounding function, then , .at this time, l The comprehensive attribute values ​​of three risk factors for each proposed solution were evaluated by several experts.

[0046] Subsequently, it is necessary to... l The comprehensive attribute values ​​provided by several experts were compiled. Under the principle of maximizing the number of parameters, the results were analyzed using functions. Calculate the operator weights. operator weights The calculation process is represented as follows: In the formula, . It represents the number of comprehensive attribute values.

[0047] Furthermore, incorporating expert weights, the corrected operator weights are: in, It is the j-th largest parameter, and M is a piecewise function, where Subsequently, the comprehensive evaluation values ​​of each scheme in scheme set X by experts were obtained. . Finally, the comprehensive evaluation value is converted into a constant using the following formula. After standardization, the experts' preference for the three risk factors I, P, and D is calculated. Further processing yields: At this point, based on the experts' assessment of the importance of different attribute values ​​in each option, the final comprehensive evaluation value of each option is obtained, which is the degree of preference for the three risk factors.

[0048] Similarly, we consider the set of KRCs as a set of solutions. The calculated risk factor levels are considered as three sets of comprehensive attribute values. The preference level of each risk factor is its own weight value. This allows us to calculate the comprehensive evaluation value of each KRC in the solution set, which represents the risk consequence of each KRC. Thus, the risk value of each KRC is calculated. .

[0049] After obtaining the risk values ​​of the key reliability characteristics (KRCs) in the fuel assembly manufacturing process, the initial set of KRCs is prioritized. Therefore, based on this initial set, a final set of KRCs for the fuel assembly manufacturing process is obtained through redundant characteristic elimination and risk assessment. This aligns with the definition of a critical reliability characteristic: "a deviation in a reliability characteristic can lead to the failure of major product functions or a reduction in product lifespan due to risk consequences." Determining the KRCs in the fuel assembly manufacturing process allows manufacturers to prioritize critical reliability characteristics with higher risk consequences, facilitating targeted and differentiated control of process quality.

Claims

1. A reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations, characterized in that, Includes the following steps: Step 1: Modeling the dimensional deviations of the in-process workpiece and the key reliability characteristics of the fuel assembly; Step 2: Mining the correlation between reliability characteristics of fuel assembly manufacturing process considering workpiece dimensional deviations; Step 3: Risk classification and evaluation of reliability characteristics of fuel assembly manufacturing process based on extended RPN value.

2. The reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations as described in claim 1, characterized in that, Step 1, as described above, includes a framework for analyzing and identifying key reliability characteristics of fuel assembly manufacturing processes within the modeling of workpiece dimensional deviations and key reliability characteristics of fuel assemblies. This framework includes: Step 11: Collect process parameters for fuel assembly manufacturing Collect process specification documents and processing guidance documents during the fuel assembly manufacturing process. Based on the axiomatic domain mapping and the evolution mechanism of KRC, determine the process parameter names of the work-in-process inputs and outputs of each process. At the same time, collect process deviation data in the actual production of this batch. Step 12: Analyze the correlation between process parameters and product reliability By using the collected data on the processing, assembly, and finished product quality of the fuel assembly manufacturing process, a transaction database was constructed based on the record data of this batch of products through association rule mining, and association rules were mined to identify the initial set of KRC for the fuel assembly manufacturing process. Step 13: Assess the reliability risks of the fuel assembly manufacturing process By collecting process quality data and processing flow data during the fuel assembly manufacturing process, three risk factors—probability of deviation occurrence, significance, and undetectability—we modeled the risk values ​​and calculated the risk values.

3. The reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations as described in claim 1, characterized in that, In step 2, regarding the correlation mining of reliability characteristics in the fuel assembly manufacturing process, considering workpiece dimensional deviations, the evolution process of reliability characteristics with different manifestations during the product life cycle is expressed from top to bottom in the form of a correlation tree. The specific construction steps are as follows: Step 21: Design - Functional Decomposition Based on the principle of functional independence, user requirements are decomposed into corresponding functional nodes and auxiliary functional nodes layer by layer, forming a multi-level functional decomposition association tree structure. Step 22: Design - Structural Decomposition The physical structure is decomposed from top to bottom according to the product's functional requirements; Step 23: Manufacturing - Process Breakdown The part-level reliability characteristics are mapped to the manufacturing reliability characteristics. According to the design document, the part-level RC is converted into a series of process parameters for each process step in the manufacturing process. Step 24: Manufacturing-Structure Mapping Map the machining RC to the assembly RC in the assembly workshop; Step 25: Manufacturing - Function Mapping.

4. The reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations as described in claim 1, characterized in that, In step 3, based on LASSO regression, the importance I of KRC to product reliability characteristics is taken as the first risk factor; and the probability P of KRC deviation is taken as the second risk factor. The undetectability D of the KRC bias is used as the third risk factor; The RPN value is derived by combining the values ​​of three risk factors and the degree of preference, thus realizing the classification of KRC in the fuel assembly manufacturing process.

5. The reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations as described in claim 4, characterized in that, Step 3 includes: KRC's risk value is expressed as: (1) Calculation of importance based on LASSO regression Regression coefficient Represented as: In the formula, It is a constant. It is the first j Observations of a reliability characteristic These are the observed values ​​of the corresponding finished product reliability characteristics. , It refers to the number of sample data. , The number of critical reliability characteristics and the importance I of each critical reliability characteristic are expressed as: The collected process deviation data are standardized. In the formula, and These represent the mean and standard deviation of the observed values, respectively. (2) Calculation of the probability of occurrence based on the deviation formation mechanism The probability P of deviation occurring in the KRC during the fuel assembly manufacturing process. v It is event P n The reverse time, expressed as: (3) Calculation of undetectability based on average running chain length The undetectability D is represented as: The KRC observations monitored during fuel assembly manufacturing follow a normal distribution. If the sample size is n, then the KRC sample mean follows... ; The ARL is solved using the Markov chain solver, and the ARL is represented as: In the formula, the matrix P It is an m-dimensional transition probability matrix, S i It is the initial probability matrix , E It is the identity matrix transition probability matrix P It consists of a series of states z i Transition to state z j probability elements Composition, then In the formula, It is a statistic of the EWMA control chart that satisfies r is the drift coefficient. At any moment i In state z j The probability is: In the formula, h is the width of the interval between the upper and lower limits, satisfying... T u and T l These are the upper and lower limits of the control chart, respectively, and K is the number of intervals to be divided. In addition, because Convert it to , represented as: (4) Calculation of risk value of key reliability characteristics based on hesitant fuzzy decision theory Three risk sets It is a set of solutions. It is an attribute set, m n This is a KRC deviation pattern, with expert weights of 100%. Based on the deviation occurrence patterns in different schemes, fuzzy semantic scores are given. The standardized value of the comprehensive evaluation of the three schemes in the scheme set represents the degree of preference for the three risk factors. The fuzzy semantic set is represented as follows: The fuzzy semantic evaluation of the set of alternatives was transformed into a hesitant fuzzy decision matrix. ,in , (c g =1, 2, 3, 4); l Experts on scheme set X n The combined attribute value of all attributes is expressed as: In the formula, i = I , P , D， If it is a rounding function, then , , l The comprehensive attribute values ​​of three risk factors for each proposed solution were evaluated by several experts. right l The comprehensive attribute values ​​provided by several experts were aggregated and processed using a function. Calculate operator weights; operator weights The calculation process is expressed as follows: In the formula, , It is the number of comprehensive attribute values; Incorporating expert weights, the corrected operator weights are: in, It is the j-th largest parameter, and M is a piecewise function, where This allows us to obtain the comprehensive evaluation values ​​from experts for each solution in solution set X. Finally, the comprehensive evaluation value is converted into a constant using the following formula. After standardization, the experts' preference for the three risk factors I, P, and D is calculated. Further processing yields: At this point, based on the assessment of the importance of different attribute values ​​in each option, the final comprehensive evaluation value of each option is obtained, which is the degree of preference for the three risk factors.

6. The reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations as described in claim 5, characterized in that, The probability of the device not failing in formula (5) in step 3 is... The calculation is as follows: The operating state of the equipment, from ideal state to complete failure, is divided into the following discrete levels: In the formula, Represents the ideal operating state of the equipment. The probability set represents the complete failure state of the device. The probability of each operating state of the corresponding processing equipment is expressed as: In the formula, This corresponds to the probability of the equipment operating in its ideal state. This corresponds to the probability of a complete equipment failure. It is the proportionality constant of each device, and the operating states of each device are independent of each other, satisfying: The probability of the equipment changing from an ideal state to this defective state is expressed as: Establish the following equation: In the formula, It is the expected number of equipment failures (t) within the production cycle. It refers to the downtime due to equipment failure. and These represent the frequency of planned maintenance and the corresponding downtime, respectively. The probability that the processing equipment will not fail during the production cycle is:

7. The reliability evaluation method for fuel assembly manufacturing process considering workpiece dimensional deviations as described in claim 5, characterized in that, In step 3, the probability that environmental factors are at normal levels in formula (5) is... The calculation is as follows: The capacity index of environmental factors is expressed by the following formula. When both upper and lower limits of the design specifications for environmental factors exist: When the design specifications for environmental factors only have an upper limit: When the design specifications for environmental factors only have a lower limit: In the formula, and These represent the upper and lower limits of the range given in the environmental factor design specifications, respectively. and These are the mean and standard deviation of observed values ​​in actual production. It is the nominal value of the standard distribution. Furthermore, Within the production cycle t, the set of capacity indices for environmental factors is: The probability that environmental factors are at normal levels is expressed as: In the formula, The ability index in the representative set satisfies Quantity, This represents the total number of samples taken.

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