Optimization Method and System for Dual-Component Maintenance Strategy with Fault Interaction

Abstract

The present invention relates to the technical field of optimizing preventive maintenance strategies for dual-component devices during the basic warranty period, and specifically relates to a method and system for optimizing dual-component maintenance strategies with fault interactivity. The method includes the following steps: (1) Using the 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; (2) According to the component failure rate function and the reliability function, and combining with the relevant parameters of preventive maintenance, determining the implementation methods of preventive maintenance and fault repair strategies; (3) Establishing a maintenance optimization model with the goal of minimizing the total maintenance cost throughout the warranty period; (4) Using Monte Carlo simulation and grid search to determine the optimal maintenance plan. The optimized technical solution of the present invention optimizes the preventive maintenance strategy for dual-component devices during the warranty period, reduces the component failure rate to a certain extent, and reduces the total maintenance cost of the manufacturer.

Description

Technical Field

[0001] The present invention relates to the technical field of optimizing preventive maintenance strategies for dual-component devices during the basic warranty period, and specifically relates to a method and system for optimizing dual-component maintenance strategies 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. For example, some equipment has a refund warranty period set. If any quality problem or fault occurs in the equipment, the seller needs to bear the relevant responsibilities and provide repairs; if the number of faults exceeds the specified number, the seller needs to provide a refund and return service, etc. The implementation of these refund systems ensures the reliability of the equipment, making consumers more secure when purchasing equipment. In practice, a system often consists of multiple interdependent components, and the failure of one component may increase the failure probability of other components. Different components play different roles in the overall operation of the equipment, and there are also differences in the refund system due to the different importance of the components. The refund system often sets more stringent corresponding constraints on key components. The implementation of the refund system increases the cost risk that equipment manufacturers need to bear, and further increases the complexity and difficulty of formulating maintenance strategies for equipment, especially complex multi-component equipment.

[0003] As the simplest type of component composition in a complex system, a dual-component device has two components that play a leading or key role and are correlated with each other. Such devices are widely present in various fields, such as the gearbox and transmission of a wind turbine, the gearbox and clutch of a heavy truck, the blades and motors of an offshore wind turbine, etc. Dual-component devices are the main research objects of the present invention, and the core principles and strategies of their maintenance models can be extended and applied to more complex multi-component systems, such as through Bellman function expansion, etc. Manufacturers need a more realistic, universal, and scientific maintenance strategy to improve the current equipment maintenance situation, and carry out a series of optimization improvements on the existing maintenance strategy, focusing on the dual-component maintenance strategy with fault correlation under the refund system.

[0004] The Monte Carlo method, also known as random sampling or statistical test method, is a branch of computational mathematics. Since traditional empirical methods cannot approximate the real physical process, it is difficult to obtain satisfactory results. However, the Monte Carlo method can truly simulate the actual physical process, so the solutions to problems are very consistent with reality and can obtain very satisfactory results. This is also a computational method based on probability and statistical theory, which uses random numbers (or more commonly, pseudo-random numbers) to solve many computational problems. The basic idea of the Monte Carlo method is that when the problem to be solved is the probability of a certain event occurring or the expected value of a certain random variable, they can be obtained through a certain "test" method, the frequency of this event occurring, or the average value of this random variable, and use them as the solution to the problem. Solving problems with the Monte Carlo method boils down to three main steps: constructing or describing the probability process; implementing sampling from the known probability distribution; and establishing various estimators.

[0005] Grid search is a method for parameter tuning, which can help find the optimal model parameters. In grid search, first specify the range of candidate values for the parameters, then enumerate all possible parameter combinations, and calculate the performance metrics (such as accuracy, precision, etc.) of each model. Finally, select the parameter combination with the optimal performance metric as the final model parameters. Summary of the Invention

[0006] In order to address the above current situation and solve the difficulties, the present invention provides an optimization method and system for a dual-component maintenance strategy with fault interactivity. Through the optimization technical solution of the present invention, the preventive maintenance strategy of dual-component equipment within the warranty period is optimized, which can reduce the component failure rate to a certain extent and reduce the total maintenance cost of the manufacturer.

[0007] In order to achieve the above invention purpose, the present invention adopts the following technical solutions:

[0008] An optimization method for a dual-component maintenance strategy with fault interactivity includes the following steps:

[0009] S1, using the 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;

[0010] S2, according to the independent failure rate function, the interactive failure rate function and the reliability function of the dual components, and combining with the relevant parameters of preventive maintenance, determine the implementation methods of preventive maintenance and corrective maintenance strategies;

[0011] S3, obtain the maintenance cost plan based on the 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;

[0012] S4. Use Monte Carlo simulation and grid search to solve the maintenance optimization model and establish the optimal maintenance plan.

[0013] Preferably, step S1 specifically includes the following steps:

[0014] S11. Use the 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:

[0015] Assume that without considering the failure rate correlation between components, the independent failure rate of component in the th preventive maintenance cycle is obtained through the following formula:

[0016] ;

[0017] ;

[0018] ;

[0019] where is the age reduction factor, is the failure rate increase factor, ; , is the independent failure rate of component , after the th preventive maintenance; is the independent failure rate of component in the th preventive maintenance cycle; S12. Based on the independent failure rates described in step S11, establish the interaction relationship between the two components to obtain their respective interaction failure rates. The specific process is as follows:

[0020] In the interaction failure rate model of the two components, the interaction coefficient is used to represent the interaction degree between two related components. When it takes 0, it means there is no correlation between components; when it takes 1, it means there is a complete correlation between components. The interaction failure rate expressions of component 1 and component 2 under the fault interaction of the two components are as follows:

[0021] ;

[0022] where represents the interaction failure rate function of component 1 in the th preventive maintenance cycle; represents the interaction failure rate function of component 2 in the th preventive maintenance cycle; represents after the After the first preventive maintenance, the component has an independent failure rate; represents the independent failure rate of component 2 after the th preventive maintenance.

[0023] Preferably, step S2 specifically includes the following steps:

[0024] S21, description of corrective maintenance strategy and refund system, the specific process is as follows:

[0025] When the system fails during the warranty period, the manufacturer or seller immediately starts the minimum repair of the faulty system, that is, corrective maintenance does not change the failure rate of the component; within the refund warranty period the manufacturer or seller sets the failure times threshold of the component to be when the number of failures of the component reaches the warranty service stops and the equipment generates a refund; the manufacturer returns the generated refund to the customer;

[0026] S22, description of preventive maintenance strategy, the specific process is as follows:

[0027] According to the theoretical relationship between system reliability and failure rate function, the reliability of the component in the th preventive maintenance cycle is obtained , , is the interactive failure rate function of the component in the th preventive maintenance cycle; when the reliability of the component reaches the predetermined threshold a preventive maintenance action is carried out on the component alone;

[0028] Based on the reliability threshold is transformed into:

[0029] ;

[0030] wherein, is the th preventive maintenance cycle of the component ;

[0031] the length of the th preventive maintenance cycle of the component is obtained from the following formula:

[0032] ​.

[0033] Preferably, step S3 specifically includes the following steps:

[0034] 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:

[0035] 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:

[0036] ;

[0037] set up When a refund occurs for a device, ,Right now ;

[0038] The actual length of the warranty period is , ;

[0039] Preventive maintenance costs during the warranty period for:

[0040] ;

[0041] 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 ;

[0042] 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;

[0043] 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 time of the secondary failure. is the number of corrective maintenance for two components within, and defines the random variable , which is the average value obtained through multiple algorithm simulations.

[0044] Component within has secondary failures with a probability of

[0045] ;

[0046] wherein, is an integer greater than or equal to 0; , , ; finally, we get where is the number of preventive maintenance for component within , is the time of the last preventive maintenance for component within The time of the last preventive maintenance.

[0047] Although there is an interaction between components, its interaction parameter and the failure times threshold , are determined. Once the preventive maintenance threshold is determined, the interaction failure rate of the dual-component is also a determined value. Under this setting, the influence of the interaction on the failure rate has been fully considered and quantified. Then, the probability that the failure times of component 1 and component 2 within a certain time are is:

[0048] .

[0049] (1) No refund

[0050] The failure times of both component 1 and component 2 do not exceed their thresholds , , and the device does not generate a refund, and the quality guarantee period expires normally. The probability of this situation occurring is:

[0051] ;

[0052] The corrective maintenance cost of this situation is ;

[0053] ;

[0054] (2) Refund

[0055] The refund is divided into two cases: refund due to the failure times of Component 1 reaching the threshold and refund due to the failure times of Component 2 reaching the threshold ;

[0056] (a). Refund due to the failure times of Component 1 reaching the threshold The total failure times of Component 1 , and the probability of this situation occurring is:

[0057] ;

[0058] The total cost of corrective maintenance in this case is:

[0059] ;

[0060] (b). Similarly, refund due to the failure times of Component 2 reaching the threshold The total failure times of Component 2 , The probability of this situation occurring is:

[0061] ;

[0062] The total cost of corrective maintenance in this case is:

[0063] ;

[0064] In summary, the corrective maintenance cost at the end of the basic quality assurance period of the dual-component device is .

[0065] S33, the refund cost of the dual-component device due to the number of corrective maintenance activities of any component exceeding its threshold within a refund quality assurance period ;

[0066] When the number of device 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 product during the warranty period. Assume that the refund amount ( ) is a linear function of the product working time.

[0067] ;

[0068] Among them, and are two parameters of the refund policy. If , = 1, then this system is a proportional refund warranty system; if , then this system is a one-time refund warranty system.

[0069] S34, for a dual-component device during a basic warranty period At the end, the refund cost due to the number of corrective maintenance activities of any component exceeding the corresponding threshold is calculated as follows;

[0070] If during the warranty period, the total downtime of the device due to maintenance (corrective maintenance and preventive maintenance) 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 , and , , during which the device is unavailable. The downtime duration of the device during the warranty period can be expressed as: 。

[0071] The expected penalty cost during the warranty period is:

[0072] ;

[0073] where is the penalty cost per unit time.

[0074] Preferably, step S4 includes the following steps:

[0075] S41, Using Monte Carlo simulation, estimate the number of failures of the dual-component within each preventive maintenance cycle through random sampling estimation, and increase the accuracy of the value through multiple simulations;

[0076] Considering that component failures follow a non-homogeneous Poisson distribution, traverse the given combination of reliability thresholds through grid search , obtain the total maintenance cost under different combinations, and the value when the total maintenance cost is the lowest is the optimal combination of reliability thresholds sought;

[0077] S42, Set the number of simulation times of Monte Carlo simulation , and use the Monte Carlo simulation method to solve the corresponding average cost rate for each group of decision variables;

[0078] S43, Based on the grid search method, within the set search space, step by step 、 search for the optimal maintenance strategy, and obtain the optimal solution of the preventive maintenance strategy, including the optimal decision variable and the optimal preventive maintenance cycle.

[0079] The present invention also discloses a dual-component maintenance strategy optimization system with fault interactivity, which includes the following modules:

[0080] A failure rate function construction module, which is used to establish a dual-component failure rate function model with failure rate interaction according to the hybrid imperfect preventive maintenance model;

[0081] A non-homogeneous Poisson process description module, which is used to describe the process of component failure during the basic warranty period using the non-homogeneous Poisson process;

[0082] A maintenance strategy establishment module, which is used to establish the implementation methods of preventive maintenance and corrective maintenance strategies and the action mechanisms of the preventive maintenance and corrective maintenance strategies on dual-component failures;

[0083] A preventive maintenance strategy optimization plan obtaining module, which is used to establish an optimization model of the dual-component maintenance strategy considering interaction under the refund condition according to the dual-component failure rate function and reliability function during the basic warranty period and in combination with preventive maintenance related parameters;

[0084] An optimal preventive maintenance plan determination module, which is used to determine the optimal preventive maintenance plan.

[0085] The beneficial effects of the present invention are as follows: (1) The present invention studies the models of preventive maintenance and corrective maintenance of dual-components with a refund system under the constraint of the refund period, uses preventive maintenance to reduce the product failure rate, reduce the risk of refund, and extend the product life cycle; uses Monte Carlo simulation to simulate component failures, so as to judge whether the refund condition is triggered; aims at minimizing the total maintenance cost during the entire warranty period, compares the objective functions corresponding to all feasible solutions through grid search, explores the best preventive maintenance reliability threshold, and obtains the optimal maintenance strategy design plan when the maintenance cost of the equipment manufacturer takes the minimum value; (2) The present invention selects dual-component equipment as the object, combines Monte Carlo simulation and grid search to design an optimization plan for the maintenance strategy of dual-component equipment under the refund system for the equipment manufacturer; considers the failure correlation between components, establishes a dual-component maintenance model under the refund system, optimizes the warranty maintenance strategy, so as to better balance the maintenance cost and equipment reliability, and improve the overall performance and operation efficiency of the equipment. Description of the Drawings

[0086] Figure 1 It is a flowchart of an optimization method for a dual-component maintenance strategy with fault interactivity provided by an embodiment of the present invention;

[0087] Figure 2 It is a schematic diagram of the change of the interactive failure rate of dual-components in the present invention;

[0088] Figure 3 It is a schematic diagram of two refund situations of dual-components in the present invention;

[0089] Figure 4 It is a schematic diagram of an imperfect preventive maintenance strategy centered on reliability for components in the present invention;

[0090] Figure 5 It is a schematic diagram of an optimal preventive maintenance strategy for dual components in the present invention;

[0091] Figure 6 It is a schematic diagram of the lowest total cost corresponding to different values of the decision variables of dual components in the present invention;

[0092] Figure 7 It is a principle block diagram of an optimization system for a dual-component maintenance strategy with fault interactivity provided by an embodiment of the present invention. Detailed implementation manners

[0093] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0094] The present invention will be further clarified below with reference to specific embodiments. Those skilled in the art should understand that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. Modifications of various equivalent forms of the present invention fall within the scope defined by the appended claims of this application.

[0095] Embodiment 1:

[0096] As Figure 1 shown, this embodiment provides an optimization method for a dual-component maintenance strategy with fault interactivity, including the following steps:

[0097] 1. Use the age-reducing and failure-rate-increasing model and the failure-rate correlation model to describe the independent failure-rate function and the interactive failure-rate function of the dual components;

[0098] 2. Determine the implementation methods of preventive maintenance and corrective maintenance strategies according to the independent failure-rate function, the interactive failure-rate function, and the reliability function of the dual components, and in combination with the relevant parameters of preventive maintenance;

[0099] 3. Obtain a maintenance cost plan based on the 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;

[0100] 4. Use Monte Carlo simulation and grid search to solve the maintenance optimization model and establish the optimal maintenance plan.

[0101] The following is a detailed description of each step.

[0102] Step 1 specifically includes the following steps:

[0103] 1-1. Use the 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 the th maintenance action changes from the original to . For the imperfect preventive maintenance strategy of the two-component equipment of the present invention, without considering the failure rate correlation between components, the independent failure rate of component in the th preventive maintenance cycle is obtained as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] where is the age reduction factor. When the equipment undergoes the th preventive maintenance, the equipment age is reduced from before preventive maintenance to , which can be understood as each preventive maintenance makes the equipment younger. is the failure rate increase factor. After the th preventive maintenance, the failure rate of the equipment changes from before preventive maintenance to , is the time of the th preventive maintenance of component .

[0108] 1-2. Establish the interaction relationship between the two components to obtain their respective interaction failure rates.

[0109] Regarding the failure rate correlation with interactivity of the two components, it is set that 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 is used to represent the degree of interaction between two related components. This means that the interaction between components causes changes in their interaction failure rates. The following are the expressions for the interaction failure rates of component 1 and component 2 under the failure interactivity between the two components:

[0110] ;

[0111] Among them, are the correlation coefficients when component 1 is affected by component 2 and the correlation coefficient when component 2 is affected by component 1, , taking 0 indicates no correlation between components, and taking 1 indicates complete correlation between components. The interactive failure rate of component 1 and component 2 is expanded as:

[0112] ;

[0113] Figure 2 is the change curve of the interactive failure rate of the two components. In the figure , , and are the moments when preventive maintenance is carried out on component 1 and component 2; the vertical coordinate is the failure rate. Figure 2 The influence of the age reduction factor and the failure rate increase factor is considered for both components. The solid line in the figure is the general trend of the failure rate when there is no interactive relationship within the two components. Due to the interactive influence of the failure rates between the two components, when one of the components is maintained, it will also cause a certain degree of decrease in the failure rate of the other component.

[0114] Step 2 specifically includes the following steps:

[0115] 2-1, description of the corrective maintenance strategy and description of the refund system;

[0116] When the system fails during the warranty period, the manufacturer or seller immediately starts to perform a minimal repair on the faulty system, that is, the corrective maintenance does not change the failure rate of the components, and the failures follow a non-homogeneous Poisson distribution. During the refund period ( ), the manufacturer or seller sets the failure times threshold of component as , as the maximum number of repair services to meet customer satisfaction. When the number of failures of component reaches , the warranty service stops and the equipment generates a refund. The manufacturer must refund a certain amount to the customer, and this amount is related to the moment when the refund is generated. During the warranty period, all the cost expenses mentioned in the present invention are borne by the equipment manufacturer.

[0117] Due to the limit on the number of fault repairs stipulated by the above clauses, the situation of generating a refund is that the number of failures of component reaches its threshold , and the number of failures of component reaches its threshold . Assume , Figure 3Two refund situations are shown, including the situation where a refund is generated due to the failure times of Component 1 reaching the threshold and the situation where a refund is generated due to the failure times of Component 2 reaching the threshold.

[0118] 2-2, Description of preventive maintenance strategy:

[0119] According to the theoretical relationship between system reliability and failure rate function, the reliability of Component the th preventive maintenance cycle is obtained , . Figure 4 Describes the preventive maintenance strategy. When the reliability of Component reaches the predetermined threshold , a preventive maintenance action is carried out on Component alone.

[0120] Therefore, based on , the reliability threshold is transformed into:

[0121] , is the th preventive maintenance cycle for Component

[0122] Taking the logarithm of the relationship formula between reliability and failure rate function gives:

[0123] ;

[0124] The length of the th preventive maintenance cycle of Component is obtained from the following formula:

[0125] .

[0126] Step 3 specifically includes the following steps:

[0127] 3-1, The cost generated by preventive maintenance activities at the end of a basic warranty period for a two-component device ;

[0128] Obtain the total maintenance cost of the two-component device composed of Component 1 and Component 2 within the warranty period from the perspective of the device manufacturer. The total cost consists of preventive maintenance cost , corrective maintenance cost , refund amount , and penalty cost and is composed of four parts:

[0129] ;

[0130] Set as the moment when a refund occurs for the device, , that is ; The actual length of the warranty period is , .

[0131] The preventive maintenance cost within the warranty period is:

[0132] ;

[0133] are the specific preventive maintenance costs of two components, is the fixed cost generated by the component maintenance action, including spare parts and delivery costs. is the number of preventive maintenance times of two components within , related to the failure rate function of the component i.e., its related factor, preventive maintenance threshold , the failure number threshold for triggering a refund , the length of the warranty period , the length of the refund period and so on.

[0134] Through the update of the failure rate function and the alternating calculation of the preventive maintenance cycle, on the premise of determining other parameters, the preventive maintenance times of component 1 and component 2 within the warranty period can be accurately calculated , and an optimal maintenance plan can be formulated:

[0135] .

[0136] 3 - 2, The cost generated by corrective maintenance activities at the end of a basic warranty period for a two-component device is expressed by probability formulas such as non-homogeneous Poisson distribution; According to the non-homogeneous Poisson distribution, the probabilities of various refund situations are given, and thus the corrective maintenance cost can be obtained:

[0137]

[0138] .

[0139] 3 - 3, The refund cost generated when the number of corrective maintenance activities of any component in a two-component device exceeds its threshold within a refund warranty period ;

[0140] When the device generates a refund, the manufacturer pays the customer a refund amount. Generally, the refund amount is related to the working time of the product during the warranty period. Assume the refund amount( ) is a linear function of the product working time:

[0141] ;

[0142] where and are two parameters of the refund warranty policy. If , = 1, then this system is a proportional refund warranty system; if , then this system is a one-time refund warranty system.

[0143] 3 - 4, the refund cost generated by a dual-component device at the end of a basic warranty period due to the number of corrective maintenance activities of any component exceeding its threshold.

[0144] During the warranty period, the device maintenance adopts the strategy of immediately performing minimal maintenance. Even if the duration of corrective maintenance and preventive maintenance is ignored in this process, the single maintenance time is very short for the entire warranty period, but frequent maintenance activities will lead to an increase in the cumulative downtime. The buyer has strict requirements on the downtime caused by maintenance actions when signing the warranty contract. Excessive maintenance activities will result in additional costs, which not only affect the seller's profit but may also affect its market competitiveness. Therefore, in order to ensure the stability of the device and prevent such situations that affect the interests of both parties of the warranty, the duration of maintenance actions is considered when calculating the cost. By setting penalty costs, the seller is forced to consider the overall downtime in the maintenance strategy and optimize the maintenance process.

[0145] If the total downtime of the device caused by 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 , and , , during which the device is unavailable. The downtime duration of the device during the warranty period can be expressed as: 。

[0146] The expected penalty cost during the warranty period is:

[0147] ;

[0148] where is the penalty cost per unit time.

[0149] Step 4 specifically includes the following steps:

[0150] 4-1. Implementation description of the maintenance strategy optimization algorithm

[0151] The optimization method uses Monte Carlo simulation. By random sampling estimation, the number of failures of the dual-component within each preventive maintenance cycle is estimated, and the accuracy of the value is increased through multiple simulations. The component failures follow a non-homogeneous Poisson distribution.

[0152] The following is a specific implementation case of the preventive maintenance strategy optimization plan for the dual-component equipment under the refund system using the optimization method of the present invention. Consider a repairable dual-component equipment with failure correlation, basic warranty period months, refund warranty period months. Assume that the independent failure rates of the dual-components in the first cycle follow a Weibull distribution, and the failure rate function is:

[0153] , ;

[0154] , is the scale parameter, , ; , is the shape parameter, , .

[0155] The following table 1 shows the specific parameters input for the maintenance strategy optimization algorithm:

[0156] Table 1 Data table of algorithm parameter settings

[0157]

[0158] 4-2. Set the number of simulation times of Monte Carlo simulation , and use the Monte Carlo simulation method to solve the corresponding maintenance cost for each set of decision variables. The specific process of Monte Carlo simulation is as follows;

[0159] The preventive maintenance threshold has upper and lower bound constraints: ;

[0160] 4-3. Based on the grid search method, within the set search space, search for the optimal maintenance strategy step by step , to obtain the optimal solution of the preventive maintenance strategy, including the optimal decision variable and the optimal preventive maintenance cycle.

[0161] The optimal solution is found through grid search, and the total cost model is solved. It is found that the best reliability threshold =0.36, = 0.44, the corresponding optimal preventive maintenance cycle is [7.9, 7.89, 6.78, 5.52, 4.44], [7.25, 7.23, 6.28, 5.17, 4.18, 3.39] (during the warranty period, the 5 maintenance operations to be performed on component 1 and the 6 maintenance operations to be performed on component 2), as Figure 5 and Figure 6 shown.

[0162] Embodiment 2:

[0163] As Figure 7 shown, this embodiment discloses a dual-component maintenance strategy optimization system with fault interactivity. Based on the method of Embodiment 1, it includes the following modules:

[0164] Failure rate function construction module, used to establish a dual-component failure rate function model with failure rate interaction according to the hybrid imperfect preventive maintenance model;

[0165] Non-homogeneous Poisson process description module, used to describe the process of component failures within the basic warranty period using the non-homogeneous Poisson process;

[0166] Maintenance strategy establishment module, used to establish the implementation methods of preventive maintenance and corrective maintenance strategies and the action mechanisms of the preventive maintenance and corrective maintenance strategies on dual-component failures;

[0167] Preventive maintenance strategy optimization plan acquisition module, used to establish an optimization model of the dual-component maintenance strategy considering interaction under the refund condition according to the dual-component failure rate function and reliability function within the basic warranty period and in combination with preventive maintenance-related parameters;

[0168] Optimal preventive maintenance plan determination module, used to determine the optimal preventive maintenance plan.

[0169] Other contents of this embodiment can refer to Embodiment 1.

[0170] The present invention selects dual-component equipment as the object, combines Monte Carlo simulation and grid search to design an optimization plan for the maintenance strategy of dual-component equipment under the refund system for equipment manufacturers; considering the fault correlation between components, establishes a dual-component maintenance model under the refund system, optimizes the warranty maintenance strategy, so as to better balance the maintenance cost and equipment reliability, and improve the overall performance and operation efficiency of the equipment.

[0171] The above is only a detailed description of the preferred embodiments and principles of the present invention. For those of ordinary skill in the art, according to the idea provided by the present invention, there will be changes in the specific implementation manners, and these changes should also be regarded as the protection scope of the present invention.

Claims

1. A dual-component maintenance strategy optimization method with fault interactivity, 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; 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 correlation of failure rates between components is not considered, the independent failure rate of component k in the i-th preventive maintenance cycle is obtained by the following formula: in, is the age reduction factor, is the failure rate increase factor; u∈(1,i-1); is the independent failure rate of component k after the i, i+1th preventive maintenance; T i k is the i-th preventive maintenance cycle of component k; 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 θ 12 ,θ 21 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, represents the interactive failure rate function of the i-th preventive maintenance cycle of component 1; represents the interactive failure rate function of the jth preventive maintenance cycle of component 2; represents the independent failure rate of component 1 after the i-th preventive maintenance; represents the independent failure rate of component 2 after the jth preventive maintenance; 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 W L The manufacturer or seller sets the failure threshold of component k to S k , when the number of component k failures reaches S k 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 reliability of component k in the i-th preventive maintenance cycle is obtained: is the interactive failure rate function of component k in the i-th preventive maintenance cycle; when the reliability of component k reaches a predetermined threshold When , a preventive maintenance action is performed on component k alone; based on Reliability Threshold is converted to: Among them, T i k is the i-th preventive maintenance cycle of component k; Length T of the i-th preventive maintenance cycle of component k i k It is derived from the following formula: Step S3 includes the following steps: S31, set the cost of preventive maintenance activities for dual-component equipment at the end of a basic warranty period W, expressed as follows: From the perspective of the equipment manufacturer, the total maintenance cost of the two-component equipment consisting of component 1 and component 2 within the basic warranty period W is obtained. The total maintenance cost C is composed of the preventive maintenance cost C PM , Corrective maintenance cost C CM 、Refund amount C r and the penalty cost C P It consists of four parts, namely: C=C PM +C CM +C r +C P ; Set W r When a refund occurs for a device, Right now The actual length of the warranty period is L W , Preventive maintenance cost during warranty period C PM for: in, is the specific preventive maintenance cost of the two components, C s The fixed costs incurred for component maintenance operations include spare parts and delivery costs; M1, M2 are the fixed costs of two components at (0, L W ) in the PM number; S32, the cost of corrective maintenance activities for dual-component equipment at the end of a basic warranty period W, is represented by a non-homogeneous Poisson distribution and other probability formulas; The intensity function used is The nonhomogeneous Poisson process N k (W L ) Analog component k is within the refund warranty period W L The randomness of the failures within the k (W L ) means that in the time interval (0,W L ]The total number of failures of component k, N k (W L ) is a non-negative random variable with the intensity function The non-homogeneous Poisson distribution of has a probability distribution function of: Wherein, l is an integer greater than or equal to 0; Finally get Where m k is the component k in (0,W L ) is the component k in (0,W L ) The time of the last preventive maintenance within 24 hours; Finally, the calculation formula for corrective maintenance cost is as follows: Among them, C CM1 ,C CM2 ,C CM3 is the cost corresponding to the three refund situations; n1, n2 are the costs of component 1 and component 2. Number of failures; They represent the single failure repair operation costs of component 1 and component 2 respectively; S1 represents the failure number threshold of component 1; S2 represents the failure number threshold of component 2; S33, dual component equipment within a refund warranty period W L The refund fee for any component corrective maintenance activities exceeding the corresponding threshold within the period is calculated as follows: When a refund is generated for a device, the manufacturer pays the customer a refund amount, which is related to the working time of the warranty product. Set the refund amount C r is a linear function of the product's operating time: in, and 0≤δ≤1 are two parameters of the refund strategy; S34, at the end of a basic warranty period W for a two-component device, 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 during the warranty period exceeds the specified contract threshold D Tmax , 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 downtime of the equipment during the basic warranty period W is expressed as: The expected penalty cost during the warranty period is: C P =c p (D T -D Tmax ) + ; where c p is the penalty cost per unit time.

2. The dual-component maintenance strategy optimization method with fault interactivity according to claim 1 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. The total maintenance cost under different combinations is obtained, where the total maintenance cost is the lowest. The value is the optimal reliability threshold combination required; S42, set the number of simulations Iter for Monte Carlo simulation max , 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 for step , R step 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.

3. A dual-component maintenance strategy optimization system with fault interactivity, based on the method described in any one of claims 1-2, 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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