Double-component maintenance strategy optimization method and system with fault interactivity

Abstract

The invention relates to the technical field of preventive maintenance strategy optimization of double-component equipment in a basic guarantee period, in particular to a double-component maintenance strategy optimization method and system with fault interactivity. The method comprises the following steps: (1) describing an independent fault rate function and an interactive fault rate function of two parts by using a service age reduction and fault rate increase model and a fault rate correlation model; (2) determining a preventive maintenance and fault maintenance strategy implementation method according to the component fault rate function and the reliability function in combination with preventive maintenance related parameters; (3) establishing a maintenance optimization model by taking minimization of the total maintenance cost of the whole warranty period as a target; and (4) using Monte Carlo simulation and grid search to determine an optimal maintenance scheme. According to the optimization technical scheme, the preventive maintenance strategy of the double-component equipment in the guarantee period is optimized, the component failure rate is reduced to a certain extent, and the total maintenance cost of manufacturers is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of preventive maintenance strategy optimization of dual-component equipment within the basic warranty period, and in particular to a dual-component maintenance strategy optimization method and system with fault interactivity. Background Art

[0002] In the field of modern manufacturing, the reliability of equipment is a key factor in ensuring productivity and competitiveness. The market environment has many special regulations for equipment, such as setting a refund warranty period for some equipment. If there are any quality problems or failures in the equipment, the seller must bear the relevant responsibilities and provide repairs; if the number of failures exceeds the specified number, the seller needs to provide refund and return services, etc. The implementation of these refund systems ensures the reliability of equipment and makes consumers more secure when purchasing equipment. In practice, the system is often composed of multiple interdependent components, and the failure of a component may increase the probability of failure of other components. Different components have different effects on the operation of the overall equipment, and there will be differences in the refund system due to the different importance of the components. The refund system often sets stricter corresponding constraints on key components. The implementation of the refund system increases the cost risk that equipment manufacturers need to bear, which in turn increases the complexity and difficulty of formulating maintenance strategies for equipment, especially complex multi-component equipment.

[0003] As the simplest type of component in a complex system, two-component equipment has two components that play a dominant or key role and are correlated with each other. This type of equipment is widely used in various fields, such as wind turbine gearboxes and transmissions, heavy truck gearboxes and clutches, offshore wind turbine blades and motors, etc. Two-component equipment is the main research object of this invention. The core principles and strategies of its maintenance model can be extended to more complex multi-component systems, such as through Bellman function expansion. Manufacturers need a more realistic, universal and scientific maintenance strategy to improve the current status of equipment maintenance, and make a series of optimization improvements on the existing maintenance strategy, focusing on the two-component maintenance strategy with fault correlation under the refund system.

[0004] Monte Carlo method, also known as random sampling or statistical test method, is a branch of computational mathematics. Traditional empirical methods cannot approximate real physical processes, so it is difficult to get satisfactory results. However, Monte Carlo method can simulate real physical processes, so the solution is very consistent with reality and can get very satisfactory results. This is also a computational method based on probability and statistical theory methods. It is a method that uses random numbers (or more commonly pseudo-random numbers) to solve many computational problems. The basic idea of ​​Monte Carlo method is that when the problem to be solved is the probability of occurrence of a certain event, or the expected value of a certain random variable, they can use some "experimental" method to obtain the frequency of occurrence of such an event, or the average value of this random variable, and use them as the solution to the problem. Monte Carlo problem solving can be summarized into three main steps: constructing or describing the probability process; realizing sampling from a known probability distribution; and establishing various estimators.

[0005] Grid search is a parameter tuning method that can help find the best model parameters. In grid search, you first specify the candidate value range of the parameter, then enumerate all possible parameter combinations, and calculate the performance indicators of each model (such as accuracy, precision, etc.). Finally, select the parameter combination with the best performance indicator as the final model parameter. Summary of the invention

[0006] In order to cope with the above-mentioned situation and solve the difficulties, the present invention provides a dual-component maintenance strategy optimization method and system with fault interactivity. Through the optimization technical scheme of the present invention, the preventive maintenance strategy of the dual-component equipment within the warranty period is optimized, the component failure rate is reduced to a certain extent, and the total maintenance cost of the manufacturer is reduced.

[0007] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical solutions: The optimization method of dual-component maintenance strategy with fault interaction includes the following steps: S1, using the service age reduction and failure rate increase model and the failure rate correlation model to describe the independent failure rate function and the interactive failure rate function of the dual components; S2, determine the implementation method of preventive maintenance and corrective maintenance strategies based on the independent failure rate function, interactive failure rate function and reliability function of the dual components and combined with relevant parameters of preventive maintenance; S3, derive maintenance cost solutions based on preventive maintenance and corrective maintenance strategies, and establish a maintenance optimization model with the goal of minimizing the total maintenance cost throughout the warranty period; S4, using Monte Carlo simulation and grid search to solve the maintenance optimization model and establish the optimal maintenance plan.

[0008] Preferably, step S1 specifically includes the following steps: S11, using the service age reduction and failure rate increase model and the failure rate correlation model to describe the independent failure rate functions of the two components, the specific process is as follows: Assuming that the failure rate correlation between components is not considered, the components In the The independent failure rate within a preventive maintenance cycle is obtained by the following formula: ; ; ; in, is the age reduction factor, is the failure rate increasing factor, ; , Is in progress , After preventive maintenance, parts Independent failure rate; It is a component No. S12, based on the independent failure rates described in step S11, establish an interactive relationship between the two components to obtain their respective interactive failure rates. The specific process is as follows: In the interactive failure rate model of two components, the interaction coefficient It is used to indicate the degree of interaction between two related components. When it is 0, it means there is no correlation between the components, and when it is 1, it means that the components are completely correlated. The expression of the interaction failure rate of component 1 and component 2 under the interaction of faults between two components is as follows: ; in, Indicates component 1 Interactive failure rate function of preventive maintenance cycles; Indicates component 2 Interactive failure rate function of preventive maintenance cycles; Indicates that the After preventive maintenance, parts Independent failure rate; Indicates that the The independent failure rate of component 2 after each preventive maintenance.

[0009] Preferably, step S2 specifically includes the following steps: S21, description of corrective maintenance strategy and refund system, the specific process is as follows: When a system fails during the warranty period, the manufacturer or seller immediately begins to perform minimal repairs on the failed system, i.e. corrective maintenance does not change the failure rate of the components; during the refund warranty period The manufacturer or seller sets the parts The failure threshold is , when the component The number of failures reached When the warranty service is terminated, the device will generate a refund; the manufacturer will return the refund to the customer; S22, preventive maintenance strategy description, the specific process is as follows: According to the theoretical relationship between system reliability and failure rate function, the component No. Reliability of preventive maintenance cycles , , It is a component No. Interactive failure rate function of preventive maintenance cycles; when the component The reliability reaches the predetermined threshold When the components Perform a single preventive maintenance action; based on , reliability threshold is converted to: ; in, For components No. preventive maintenance cycle; part No. Length of preventive maintenance cycles It is derived from the following formula: .

[0010] Preferably, step S3 specifically includes the following steps: S31, setting a basic warranty period for dual-component equipment The cost of preventive maintenance activities at the end of the period is expressed as follows: Get the basic warranty period from the equipment manufacturer's perspective The total maintenance cost of the two-component equipment consisting of component 1 and component 2 is C, which is composed of the preventive maintenance cost , Corrective maintenance costs , Refund amount and penalty costs It consists of four parts, namely: ; set up When a refund occurs for a device, ,Right now ; The actual length of the warranty period is , ; Preventive maintenance costs during the warranty period for: ; in, is the specific preventive maintenance cost of the two components, Fixed costs incurred for component maintenance actions, including spare parts and delivery costs; There are two parts in PM times within ; S32, two-component equipment within a basic warranty period The cost incurred due to corrective maintenance activities at the end is represented by a probability formula such as the non-homogeneous Poisson distribution; According to the refund policy, failures are divided into two types: no refund (normal expiration of the warranty period) and refund (warranty interruption, early expiration). Each preventive maintenance resets the failure rate of a component to a certain extent. , , component failures follow a non-homogeneous Poisson distribution, It is a component No. The moment of failure. There are two parts in The number of corrective maintenance within , define the random variable , is the average value calculated through multiple algorithm simulations.

[0011] part exist Internal The probability of a failure is ; in, is an integer greater than or equal to 0; , , Finally, we get ,in It is a component exist The number of preventive maintenance It is a component exist The last moment of preventive maintenance.

[0012] Although there are interactions between components, their interaction parameters And the failure count threshold , Determine, preventive maintenance thresholds Once determined, the interaction failure rate of the two components is also a certain value. Under this setting, the impact of interaction on the failure rate has been fully considered and quantified. Then the number of failures of component 1 and component 2 within a certain period of time is The probability is: .

[0013] (1) No refund The number of failures of internal components 1 and 2 does not exceed their thresholds , , the device will not generate a refund and the warranty period will expire normally. The probability of this happening is: ; The corrective maintenance cost for this situation is ; ; (2) Refund Refunds are divided into: Refund, because the number of component 2 failures reaches the threshold There are two situations for refunds: (a) Because the number of component 1 failures reaches the threshold For refund, the total number of failures of component 1 , the probability of this happening is: ; The total cost of corrective maintenance in this case is for: ; (b) Similarly, because the number of failures of component 2 reaches the threshold For refund, the total number of failures of component 2 , The probability of this happening is: ; The total cost of corrective maintenance in this case is for: ; In summary, the corrective maintenance cost of a two-component device at the end of the basic warranty period is .

[0014] S33, two-component device within a refund warranty period Refund fees incurred due to the number of corrective maintenance activities for any component exceeding its threshold; When the number of equipment failures reaches the threshold and a refund is generated, the manufacturer pays the customer a refund amount. Generally, the refund amount is related to the working time of the warranty product. Assume the refund amount ( ) is a linear function of the product's operating time.

[0015] ; in, and are two parameters of the refund strategy. , =1, the system is a proportional refund warranty system; if , then the system is a one-time refund warranty system.

[0016] S34, two-component equipment within a basic warranty period At the end of the period, the refund fee incurred due to the number of corrective maintenance activities for any component exceeding the corresponding threshold is calculated as follows; If the total equipment downtime due to maintenance (corrective maintenance and preventive maintenance) during the warranty period exceeds the specified contract threshold , then the seller shall bear the penalty cost. Assume that the corrective maintenance and preventive maintenance actions of component 1 and component 2 have constant average durations respectively , and , During this period, the device is unavailable. The device is under warranty The downtime can be expressed as: 。

[0017] The expected penalty cost during the warranty period is: ; in is the penalty cost per unit time.

[0018] Preferably, step S4 comprises the following steps: S41, Monte Carlo simulation is used to estimate the number of failures of dual components in each preventive maintenance cycle through random sampling estimation, and the accuracy of the numerical value is increased after multiple simulations; Considering that component failures follow a non-homogeneous Poisson distribution, a grid search is performed to traverse the given reliability threshold combinations. , and obtain the total maintenance cost under different combinations, where the total maintenance cost is the lowest. The value is the optimal reliability threshold combination required; S42, set the number of simulations for Monte Carlo simulation , Monte Carlo simulation is used to solve the corresponding average cost rate for each group of decision variables; S43, based on the grid search method, searches within the set search space according to the step size , Search for the best maintenance strategy and obtain the best solution for preventive maintenance strategy, including the best decision variables and optimal preventive maintenance cycles.

[0019] The present invention also discloses a dual-component maintenance strategy optimization system with fault interactivity, which includes the following modules: A failure rate function building module is used to build a dual-component failure rate function model with failure rate interaction based on a mixed imperfect preventive maintenance model; A non-homogeneous Poisson process description module is used to describe the process of component failure within the basic warranty period using a non-homogeneous Poisson process; A maintenance strategy establishment module, used to establish an implementation method of preventive maintenance and corrective maintenance strategies and an action mechanism of the preventive maintenance and corrective maintenance strategies on dual component failures; A module for obtaining a preventive maintenance strategy optimization solution is used to establish a dual-component maintenance strategy optimization model that takes interaction into account under refund conditions based on the dual-component failure rate function and reliability function within the basic warranty period and combined with preventive maintenance related parameters; The optimal preventive maintenance plan determination module is used to determine the optimal preventive maintenance plan.

[0020] The beneficial effects of the present invention are as follows: (1) The present invention studies a model of preventive maintenance and corrective maintenance of two components with a refund system under the constraint of a refund period, using preventive maintenance to reduce product failure rate, reduce the risk of refund, and extend product life cycle; Monte Carlo simulation is used to simulate component failure to determine whether the refund condition is triggered; with the goal of minimizing the total maintenance cost during the entire warranty period, the objective functions corresponding to all feasible solutions are compared through grid search to find the optimal preventive maintenance reliability threshold, and obtain the optimal maintenance strategy design scheme when the equipment manufacturer's maintenance cost is minimized; (2) The present invention selects two-component equipment as the object, and combines Monte Carlo simulation and grid search to design an optimization scheme for the maintenance strategy of two-component equipment under the refund system for equipment manufacturers; considering the failure correlation between components, a two-component maintenance model under the refund system is established, and the warranty maintenance strategy is optimized, so as to better balance the maintenance cost and equipment reliability and improve the overall performance and operational efficiency of the equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1A flow chart of a dual-component maintenance strategy optimization method with fault interactivity provided by an embodiment of the present invention; Figure 2 A schematic diagram of the change in the interactive failure rate of the dual components in the present invention; Figure 3 A schematic diagram of two refund situations for two components in the present invention; Figure 4 A schematic diagram of a reliability-centered imperfect preventive maintenance strategy for components in the present invention; Figure 5 A schematic diagram of an optimal preventive maintenance strategy for dual components in the present invention; Figure 6 A schematic diagram of the minimum total cost corresponding to different values ​​of the dual-component decision variables in the present invention; Figure 7 A principle block diagram of a dual-component maintenance strategy optimization system with fault interactivity provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0023] The present invention is further illustrated below in conjunction with specific embodiments. Those skilled in the art should understand that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention, and modifications to various equivalent forms of the present invention fall within the scope defined by the appended claims of this application.

[0024] Embodiment 1: like Figure 1 As shown, this embodiment provides a dual-component maintenance strategy optimization method with fault interactivity, comprising the following steps: 1. Use the service age reduction and failure rate increase model and the failure rate correlation model to describe the independent failure rate function and interactive failure rate function of the dual components; 2. According to the independent failure rate function, interactive failure rate function and reliability function of the dual components, and combined with the relevant parameters of preventive maintenance, determine the implementation method of preventive maintenance and corrective maintenance strategies; 3. Derive a maintenance cost plan based on preventive maintenance and corrective maintenance strategies, and establish a maintenance optimization model with the goal of minimizing the total maintenance cost throughout the warranty period; 4. Use Monte Carlo simulation and grid search to solve the maintenance optimization model and establish the optimal maintenance plan.

[0025] The following is a detailed description of each step.

[0026] Step 1 specifically includes the following steps: 1-1, using the service age reduction and failure rate increase model and the failure rate correlation model to describe the independent failure rate functions of the two components, The failure rate function after maintenance actions is changed from the original becomes The imperfect preventive maintenance strategy of the dual-component equipment of the present invention does not consider the correlation of failure rates between components. in the The independent failure rate within a preventive maintenance cycle is obtained as follows: ; ; ; in, is the service life reduction factor. After the first preventive maintenance, the service life of the equipment will be Reduce to , it can be understood that every preventive maintenance makes the equipment younger. is the failure rate increase factor, After the first preventive maintenance, the failure rate of the equipment is becomes , For components No. Preventive maintenance moment.

[0027] 1-2, establish the interaction relationship between the two components and obtain their respective interaction failure rates.

[0028] The failure rate correlation of the two components is set to interact. The failure of each component will affect the failure rate of other components, and there is no instantaneous induced failure. In this model, the interaction coefficient It is used to express the degree of interaction between two related components. This means that the interaction between components causes their interaction failure rates to change. The following is the expression for the interaction failure rate of component 1 and component 2 under the interaction of two-component failures: ; in, are the correlation coefficients when component 1 is acted upon by component 2 and when component 2 is acted upon by component 1, , when it is 0, it means there is no correlation between components, and when it is 1, it means there is complete correlation between components. The interaction failure rate of component 1 and component 2 is expanded as: ; Figure 2 is the change curve of the interactive failure rate of two components. , , and The time of preventive maintenance for components 1 and 2; ordinate is the failure rate. Figure 2 Both components take into account the influence of the service life reduction factor and the failure rate increase factor. The solid line in the figure is the general trend of the failure rate when there is no interaction between the two components. Since there is an interactive influence on the failure rate between the two components, when one component is maintained, the failure rate of the other component will also decrease to a certain extent.

[0029] Step 2 specifically includes the following steps: 2-1, Description of corrective maintenance strategy and refund system; When a system fails during the warranty period, the manufacturer or seller immediately begins to perform minimal repairs on the failed system, i.e., corrective maintenance does not change the failure rate of the components, and the failure follows a non-homogeneous Poisson distribution. ), the manufacturer or seller sets the parts The failure threshold is , as the maximum number of repair services to meet customer satisfaction. The number of failures reached When the warranty service is terminated, the device generates a refund. The manufacturer must refund a certain amount to the customer, which is related to the time when the refund is generated. During the warranty period, the costs mentioned in this invention are borne by the device manufacturer.

[0030] The number of times of fault repair is limited by the above terms, and the refund will be for parts The number of failures reaches its threshold ,part The number of failures reaches its threshold Assumptions , Figure 3 Two refund situations are shown, including a situation where a refund is generated because the number of failures of component 1 reaches a threshold and a situation where a refund is generated because the number of failures of component 2 reaches a threshold.

[0031] 2-2, Description of preventive maintenance strategy: According to the theoretical relationship between system reliability and failure rate function, the component No. Reliability of preventive maintenance cycles , . Figure 4 Describes the preventive maintenance strategy when parts The reliability reaches the predetermined threshold When the components Perform a single preventive maintenance action.

[0032] Therefore, based on , reliability threshold is converted to: , For components No. preventive maintenance cycle.

[0033] By taking the logarithm of the functional relationship between reliability and failure rate, we can obtain: ; part No. Length of preventive maintenance cycles It is derived from the following formula: .

[0034] Step 3 specifically includes the following steps: 3-1, dual-component equipment within a basic warranty period Costs incurred for preventive maintenance activities at closing; Get the warranty period from the equipment manufacturer's perspective The total maintenance cost of a two-component device consisting of component 1 and component 2. Total cost Preventive maintenance costs , Corrective maintenance costs , Refund amount , and penalty costs Four parts: ; set up When a refund occurs for a device, ,Right now ; The actual length of the warranty period is , .

[0035] Preventive maintenance costs during the warranty period for: ; is the specific preventive maintenance cost of the two components, Fixed costs incurred for component maintenance activities, including spare parts and delivery costs. There are two parts in The number of preventive maintenance tasks within a period is a function of the failure rate of the component. That is, its related factors, preventive maintenance thresholds , Failure threshold for triggering refund , Warranty period length , Length of refund period And so on.

[0036] By updating the failure rate function and alternately calculating the preventive maintenance cycle, the number of preventive maintenance times for component 1 and component 2 during the warranty period can be accurately calculated under the premise of determining other parameters. , develop the best maintenance plan: .

[0037] 3-2, dual-component equipment within a basic warranty period The cost incurred due to corrective maintenance activities at the end is represented by a probability formula such as the non-homogeneous Poisson distribution; The corrective maintenance cost is obtained by giving the probability of each refund situation according to the non-homogeneous Poisson distribution: .

[0038] 3-3, dual-component equipment within a refund warranty period Refund fees incurred due to the number of corrective maintenance activities for any component exceeding its threshold; When a device generates a refund, the manufacturer pays the customer a refund amount. Generally, the refund amount is related to the working time of the warranty product. Assume the refund amount ( ) is a linear function of the product's operating time: ; in and are two parameters of the refund warranty policy. , =1, the system is a proportional refund warranty system; if , then the system is a one-time refund warranty system.

[0039] 3-4, dual-component equipment within a basic warranty period Refund fees incurred when the number of corrective maintenance activities for any part exceeds its threshold at the end of the period.

[0040] During the warranty period, the equipment maintenance adopts the strategy of immediate minimum maintenance. Even if the duration of corrective maintenance and preventive maintenance is ignored in the process, the single maintenance time is very short for the entire warranty period, but frequent maintenance activities will lead to an increase in cumulative downtime. When signing a warranty contract, the buyer has strict requirements on the downtime caused by maintenance actions. Excessively long maintenance activities will lead to additional costs, which will not only affect the seller's profits, but may also affect its market competitiveness. Therefore, in order to ensure the stability of the equipment and prevent such situations that affect the interests of both parties to the warranty, the duration of the maintenance action is considered when calculating the cost. By setting the penalty cost, the seller is forced to consider the overall downtime in the maintenance strategy and optimize the maintenance process.

[0041] If the total downtime of the equipment due to maintenance (corrective maintenance and preventive maintenance) during the warranty period exceeds the specified contract threshold , then the seller shall bear the penalty cost. Assume that the corrective maintenance and preventive maintenance actions of component 1 and component 2 have constant average durations respectively , and , During this period, the device is unavailable. The device is under warranty The downtime can be expressed as: 。

[0042] The expected penalty cost during the warranty period is: ; in is the penalty cost per unit time.

[0043] Step 4 specifically includes the following steps: 4-1, description of maintenance strategy optimization algorithm implementation; The optimization method uses Monte Carlo simulation to estimate the number of failures of dual components in each preventive maintenance cycle through random sampling estimation, and the accuracy of the numerical value is increased through multiple simulations. Component failures follow a non-homogeneous Poisson distribution.

[0044] The following is a specific implementation case of the optimization scheme of the preventive maintenance strategy of dual-component equipment under the refund system using the optimization method of the present invention. Consider a dual-component repairable equipment with fault correlation and a basic warranty period of Months, refund warranty period Month. Assuming that the independent failure rates of the two components in the first cycle follow a Weibull distribution, the failure rate function is: , ; , is the scale parameter, , ; , is the shape parameter, , .

[0045] Table 1 below shows the specific parameters input into the maintenance strategy optimization algorithm: Table 1 Algorithm parameter setting data table

[0046] 4-2, Set the number of simulations for Monte Carlo simulation , Monte Carlo simulation is used to solve the corresponding maintenance cost for each group of decision variables. The specific Monte Carlo simulation process is as follows; The preventive maintenance threshold has upper and lower limit constraints: ; 4-3, based on the grid search method, the step size is set within the set search space. , Search for the best maintenance strategy and obtain the best solution for preventive maintenance strategy, including the best decision variables and optimal preventive maintenance cycles.

[0047] The total cost model was solved by grid search to find the optimal solution. The optimal reliability threshold was found =0.36, =0.44, the corresponding optimal preventive maintenance period is [7.9, 7.89, 6.78, 5.52, 4.44], [7.25, 7.23, 6.28, 5.17, 4.18, 3.39] (warranty period During this period, 5 maintenance operations are to be performed on component 1 and 6 maintenance operations are to be performed on component 2), such as Figure 5 and Figure 6 shown.

[0048] Embodiment 2: like Figure 7 As shown, this embodiment discloses a dual-component maintenance strategy optimization system with fault interactivity, based on the method of embodiment 1, including the following modules: A failure rate function building module is used to build a dual-component failure rate function model with failure rate interaction based on a mixed imperfect preventive maintenance model; A non-homogeneous Poisson process description module is used to describe the process of component failure within the basic warranty period using a non-homogeneous Poisson process; A maintenance strategy establishment module, used to establish an implementation method of preventive maintenance and corrective maintenance strategies and an action mechanism of the preventive maintenance and corrective maintenance strategies on dual component failures; A module for obtaining a preventive maintenance strategy optimization solution is used to establish a dual-component maintenance strategy optimization model that takes interaction into account under refund conditions based on the dual-component failure rate function and reliability function within the basic warranty period and combined with preventive maintenance related parameters; The optimal preventive maintenance plan determination module is used to determine the optimal preventive maintenance plan.

[0049] For other contents of this embodiment, please refer to Embodiment 1.

[0050] The present invention selects dual-component equipment as the object, and combines Monte Carlo simulation and grid search to design an optimization solution for the dual-component equipment maintenance strategy under the refund system for equipment manufacturers; considering the fault correlation between components, a dual-component maintenance model under the refund system is established, and the warranty maintenance strategy is optimized, so as to better balance the maintenance cost and equipment reliability, and improve the overall performance and operational efficiency of the equipment.

[0051] The above description is only a detailed description of the preferred embodiments and principles of the present invention. For ordinary technicians in this field, according to the ideas provided by the present invention, there will be changes in the specific implementation methods, and these changes should also be regarded as the protection scope of the present invention.

Claims

1. Optimization method of dual-component maintenance strategy with fault interaction, It is characterized in that The steps include: S1, using the service age reduction and failure rate increase model and the failure rate correlation model to describe the independent failure rate function and the interactive failure rate function of the dual components; S2, determine the implementation method of preventive maintenance and corrective maintenance strategies based on the independent failure rate function, interactive failure rate function and reliability function of the dual components and combined with relevant parameters of preventive maintenance; S3, derive maintenance cost solutions based on preventive maintenance and corrective maintenance strategies, and establish a maintenance optimization model with the goal of minimizing the total maintenance cost throughout the warranty period; S4, using Monte Carlo simulation and grid search to solve the maintenance optimization model and establish the optimal maintenance plan.

2. The dual-component maintenance strategy optimization method with fault interactivity according to claim 1, It is characterized in that Step S1 includes the following steps: S11, using the service age reduction and failure rate increase model and the failure rate correlation model to describe the independent failure rate functions of the two components, the specific process is as follows: Assuming that the failure rate correlation between components is not considered, the components In the The independent failure rate within a preventive maintenance cycle is obtained by the following formula: ； ； ； in, is the age reduction factor, is the failure rate increasing factor, ; , Is in progress , After preventive maintenance, parts Independent failure rate; It is a component No. S12, based on the independent failure rates described in step S11, establish an interactive relationship between the two components to obtain their respective interactive failure rates. The specific process is as follows: In the interactive failure rate model of two components, the interaction coefficient It is used to indicate the degree of interaction between two related components. When it is 0, it means there is no correlation between the components, and when it is 1, it means that the components are completely correlated. The expression of the interaction failure rate of component 1 and component 2 under the interaction of faults between two components is as follows: ； in, Indicates component 1 Interactive failure rate function of preventive maintenance cycles; Indicates component 2 Interactive failure rate function of preventive maintenance cycles; Indicates that the After preventive maintenance, parts Independent failure rate; Indicates that the The independent failure rate of component 2 after each preventive maintenance.

3. The dual-component maintenance strategy optimization method with fault interactivity according to claim 2, It is characterized in that Step S2 includes the following steps: S21, description of corrective maintenance strategy and refund system, the specific process is as follows: When a system fails during the warranty period, the manufacturer or seller immediately begins to perform minimal repairs on the failed system, i.e. corrective maintenance does not change the failure rate of the components; during the refund warranty period The manufacturer or seller sets the parts The failure threshold is , when the component The number of failures reached When the warranty service is terminated, the device will generate a refund; the manufacturer will return the refund to the customer; S22, preventive maintenance strategy description, the specific process is as follows: According to the theoretical relationship between system reliability and failure rate function, the component No. Reliability of preventive maintenance cycles , , It is a component No. Interactive failure rate function of preventive maintenance cycles; when the component The reliability reaches the predetermined threshold When the components Perform a single preventive maintenance action; based on , reliability threshold is converted to: ； in, For components No. preventive maintenance cycle; part No. Length of preventive maintenance cycles It is derived from the following formula: 。 4. The dual-component maintenance strategy optimization method with fault interactivity according to claim 3, It is characterized in that Step S3 includes the following steps: S31, setting a basic warranty period for dual-component equipment The cost of preventive maintenance activities at the end of the period is expressed as follows: Get the basic warranty period from the equipment manufacturer's perspective The total maintenance cost of the two-component equipment consisting of component 1 and component 2 is C, which is composed of the preventive maintenance cost , Corrective maintenance costs , Refund amount and penalty costs It consists of four parts, namely: ； set up When a refund occurs for a device, ,Right now ; The actual length of the warranty period is ， ; Preventive maintenance costs during the warranty period for: ； in, is the specific preventive maintenance cost of the two components, Fixed costs incurred for component maintenance actions, including spare parts and delivery costs; There are two parts in PM times within ; S32, two-component equipment within a basic warranty period The cost incurred due to corrective maintenance activities at the end is represented by a probability formula such as the non-homogeneous Poisson distribution; The intensity function used is Nonhomogeneous Poisson process Analog components During the refund warranty period The randomness of failures within the Indicates the time interval Upper part The total number of failures, is a non-negative random variable with the intensity function The non-homogeneous Poisson distribution of has a probability distribution function of: ； in, is an integer greater than or equal to 0; , , Finally, we get ,in It is a component exist The number of preventive maintenance It is a component exist The moment of last preventive maintenance within 1 hour; Finally, the calculation formula for corrective maintenance cost is as follows: ； in, , , is the cost corresponding to the three refund situations; is the number of failures of component 1 and component 2 within a certain period of time; represent the single failure repair operation cost of component 1 and component 2 respectively; represents the failure count threshold of component 2; represents the failure count threshold of component 2; S33, two-component device within a refund warranty period The refund fee for any component corrective maintenance activities exceeding the corresponding threshold within the period is calculated as follows: When a device generates a refund, the manufacturer pays the customer a refund amount, which is related to the working time of the warranty product; set the refund amount is a linear function of the product's operating time: ； in, and are the two parameters of the refund strategy; S34, two-component equipment within a basic warranty period At the end of the term, the refund fee for any component corrective maintenance activities exceeding the corresponding threshold is calculated as follows: If the total equipment downtime due to maintenance during the warranty period exceeds the specified contract threshold , then the seller shall bear the penalty cost; assuming that the corrective maintenance and preventive maintenance actions of component 1 and component 2 have constant average durations, respectively , and , , and the equipment is unavailable during the average duration; then the equipment is out of warranty during the basic warranty period The downtime duration is expressed as: ; The expected penalty cost during the warranty period is: ； in is the penalty cost per unit time.

5. The dual-component maintenance strategy optimization method with fault interactivity according to claim 4, It is characterized in that Step S4 includes the following steps: S41, Monte Carlo simulation is used to estimate the number of failures of dual components in each preventive maintenance cycle through random sampling estimation, and the accuracy of the numerical value is increased after multiple simulations; Considering that component failures follow a non-homogeneous Poisson distribution, a grid search is performed to traverse the given reliability threshold combinations. , and obtain the total maintenance cost under different combinations, where the total maintenance cost is the lowest. The value is the optimal reliability threshold combination required; S42, set the number of simulations for Monte Carlo simulation , Monte Carlo simulation is used to solve the corresponding average cost rate for each group of decision variables; S43, based on the grid search method, searches within the set search space according to the step size , Search for the best maintenance strategy and obtain the best solution for preventive maintenance strategy, including the best decision variables and optimal preventive maintenance cycles.

6. A dual-component maintenance strategy optimization system with fault interactivity, based on the method described in any one of claims 1 to 5, It is characterized in that Includes the following modules: A failure rate function building module is used to build a dual-component failure rate function model with failure rate interaction based on a mixed imperfect preventive maintenance model; A non-homogeneous Poisson process description module is used to describe the process of component failure within the basic warranty period using a non-homogeneous Poisson process; A maintenance strategy establishment module, used to establish an implementation method of preventive maintenance and corrective maintenance strategies and an action mechanism of the preventive maintenance and corrective maintenance strategies on dual component failures; A module for obtaining a preventive maintenance strategy optimization solution is used to establish a dual-component maintenance strategy optimization model that takes interaction into account under refund conditions based on the dual-component failure rate function and reliability function within the basic warranty period and combined with preventive maintenance related parameters; The optimal preventive maintenance plan determination module is used to determine the optimal preventive maintenance plan.

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