Method and system for determining extended warranty strategy for multi-component system

Abstract

The present invention relates to a method and system for determining an extended warranty strategy for a multi-component system, specifically to the technical field of military equipment maintenance. The method comprises: obtaining an extended warranty availability model for the multi-component system based on a failure correlation analysis, employing an incomplete preventive maintenance strategy and a minimum maintenance strategy based on a key component failure rate function and a subsystem failure rate function of the multi-component system; inputting a preset extended warranty period and preventive maintenance intervals for each iteration number into the multi-component system extended warranty availability model to obtain an extended warranty availability value for the multi-component system at each iteration number; and determining an extended warranty strategy for the multi-component system based on the preventive maintenance interval corresponding to the maximum extended warranty availability value among all the extended warranty availability values ​​for all iteration numbers. The present invention is used for extended warranty of a multi-component system, thereby optimizing the availability of the multi-component system of the equipment.

Description

Technical Field

[0001] The present invention relates to the technical field of military equipment maintenance, and in particular to a method and system for determining an extended warranty strategy for a multi-component system. Background Art

[0002] Extended warranty refers to a warranty service contract signed between the military and the contractor after the initial warranty period, which provides follow-up services for a certain period of time. How to scientifically formulate an extended warranty plan to maximize the availability of multiple component systems in equipment is a key concern for equipment support departments.

[0003] Currently, a large number of new weaponry and equipment are being deployed to the military. These devices are complex in structure and highly integrated, often integrating multiple mechanical, electrical, and hydraulic components. This increases the likelihood of fault correlations between components, complicating maintenance and daily management. During the initial warranty period, it is difficult for the military to independently maintain the maintenance capabilities of these complex equipment. Therefore, it is essential to rely on the contracting organization to provide extended warranty coverage for these equipment.

[0004] Song Zhijie developed an equipment maintenance plan with the goal of minimizing the equipment maintenance cost per unit time within the replacement cycle and using availability as a constraint, verifying the effectiveness of the model through case analysis. Yang Zhiyuan, while ensuring that the equipment availability met military requirements, aimed to minimize the equipment warranty cost during the extended warranty period and obtained the optimal preventive maintenance plan for equipment under both partial and full outsourcing models. Huang categorized users based on their usage during the initial warranty period and provided differentiated extended warranty plans for each type of user. By maximizing product availability during the extended warranty period, this approach improved consumer satisfaction and marketing competitiveness. Tong Peng, based on dynamic consumer usage, studied the optimal maintenance level during the extended warranty period with the goal of improving product extended warranty availability. Su Chun, building on Tong Peng's work, introduced a preventive maintenance strategy and optimized the maintenance strategy with the goal of maximizing product extended warranty availability. However, most of the aforementioned methods have been studied for single-component systems, with little research focusing on the extended warranty availability of multi-component systems with fault correlations. This, to a certain extent, has affected and constrained the development of extended warranty strategies for multi-component systems. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and system for determining an extended warranty strategy for a multi-component system, which is used for the extended warranty of the multi-component system and optimizes the availability of the multi-component system.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for determining an extended warranty policy for a multi-component system, comprising:

[0008] According to the failure rate function of key parts and subsystems of multi-component system, based on failure correlation analysis, the extended warranty availability model of multi-component system is obtained by adopting incomplete preventive maintenance strategy and minimum maintenance strategy.

[0009] Under the current iteration number, obtain the preventive maintenance interval under the previous iteration number;

[0010] Inputting a preset extended warranty period and the preventive maintenance interval at the previous iteration number into the multi-component system extended warranty availability model to obtain an extended warranty availability value of the multi-component system at the current iteration number;

[0011] Updating the preventive maintenance interval at the previous iteration number according to a preset update step size to obtain the preventive maintenance interval at the current iteration number;

[0012] Determine whether the preventive maintenance interval under the current number of iterations reaches a set threshold, and obtain a first determination result;

[0013] If the first judgment result is yes, determining an extended warranty policy for the multi-component system according to a preventive maintenance interval corresponding to a maximum extended warranty availability value in a set of extended warranty availability values, wherein the set of extended warranty availability values ​​includes extended warranty availability values ​​under all iteration numbers;

[0014] If the first judgment result is no, the number of iterations is updated and the next iteration is entered.

[0015] Optionally, the method of obtaining an extended warranty availability model for a multi-component system based on a failure correlation analysis, using an incomplete preventive maintenance strategy and a minimum maintenance strategy according to a key component failure rate function and a subsystem failure rate function of the multi-component system, specifically includes:

[0016] Using an incomplete preventive maintenance strategy to process the failure rate function of the key components of the multi-component system, to obtain the failure rate function of the key components of the multi-component system in each preventive maintenance interval;

[0017] Based on the failure correlation analysis, an incomplete preventive maintenance strategy is used to process the failure rate function of the subsystem of the multi-component system to obtain the failure rate function of the subsystem of the multi-component system in each preventive maintenance interval;

[0018] According to the failure rate function of the key component in each preventive maintenance interval and the failure rate function of the subsystem in each preventive maintenance interval, a minimum maintenance strategy is adopted to obtain a total expected downtime function of the multi-component system during the extended warranty period;

[0019] An extended warranty availability model for the multi-component system is obtained according to the total expected downtime function of the multi-component system within the extended warranty period.

[0020] Optionally, the failure rate function of the key components of the multi-component system during each preventive maintenance interval is specifically:

[0021] Among them, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ψ (t) represents the critical component failure rate function at time t, k represents the kth preventive maintenance interval, T represents the duration of the preventive maintenance interval, δ represents the improvement factor of incomplete preventive maintenance during the extended warranty period, W represents the initial warranty period, and v represents the maximum value of k.

[0022] Optionally, the failure rate function of the subsystems of the multi-component system during each preventive maintenance interval is specifically:

[0023] , where λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval, λ s (t) is the subsystem failure rate function at time t, θ represents the failure impact coefficient, m kψ represents the number of failures of key components during the kth preventive maintenance interval, m iψ represents the number of failures of key components during the i-th preventive maintenance interval.

[0024] Optionally, the total expected downtime function of the multi-component system during the extended warranty period is specifically:

[0025] , where ED(T,W,W e ) represents the total expected downtime of the multi-component system during the extended warranty period, T p represents the incomplete preventive maintenance time, n represents the number of preventive maintenance during the extended warranty period, T f1 Indicates the minimum maintenance time of key parts, T f2 represents the minimum maintenance time of the subsystem, W e represents the extended warranty period, λ xs (t) represents the failure rate function of the subsystem during the last preventive maintenance interval at time t, λ xψ (t) represents the failure rate function of key components during the last preventive maintenance interval at time t.

[0026] Optionally, the multi-component system extended warranty availability model is specifically:

[0027] Among them, EA(T,W,W e ) represents the extended warranty availability value for multi-unit systems.

[0028] A system for determining an extended warranty policy for a multi-component system, comprising:

[0029] A model building module is used to obtain an extended warranty availability model for a multi-component system based on the failure rate function of key components and subsystems of the multi-component system, failure correlation analysis, and the use of an incomplete preventive maintenance strategy and a minimum maintenance strategy;

[0030] An acquisition module is used to obtain the preventive maintenance interval under the previous iteration number under the current iteration number;

[0031] an availability value determination module, configured to input a preset extended warranty period and the preventive maintenance interval at the previous iteration number into the multi-component system extended warranty availability model to obtain an extended warranty availability value of the multi-component system at the current iteration number;

[0032] a preventive maintenance interval calculation module, configured to update the preventive maintenance interval at the previous iteration number according to a preset update step size to obtain the preventive maintenance interval at the current iteration number;

[0033] a judgment module, configured to judge whether the preventive maintenance interval under the current number of iterations reaches a set threshold, and obtain a first judgment result;

[0034] an extended warranty policy determination module configured to, if the first judgment result is yes, determine an extended warranty policy for the multi-component system based on a preventive maintenance interval corresponding to a maximum extended warranty availability value in a set of extended warranty availability values, wherein the set of extended warranty availability values ​​includes extended warranty availability values ​​at all iteration numbers;

[0035] The iteration module is used to update the number of iterations and enter the next iteration if the first judgment result is no.

[0036] Optionally, the model building module specifically includes:

[0037] a key component failure function processing unit, configured to process the key component failure rate function of the multi-component system using an incomplete preventive maintenance strategy to obtain a failure rate function of the key component of the multi-component system within each preventive maintenance interval;

[0038] a subsystem failure rate function processing unit, configured to process the subsystem failure rate function of the multi-component system using an incomplete preventive maintenance strategy based on a failure correlation analysis, to obtain a failure rate function of a subsystem of the multi-component system within each preventive maintenance interval;

[0039] a multi-component system total expected downtime function determination unit, configured to obtain a multi-component system total expected downtime function within the extended warranty period using a minimum maintenance strategy based on the failure rate function of the key component within each preventive maintenance interval and the failure rate function of the subsystem within each preventive maintenance interval;

[0040] The availability model determining unit is configured to obtain an extended warranty availability model for the multi-component system according to a total expected downtime function of the multi-component system within the extended warranty period.

[0041] Optionally, the failure rate function of the key components of the multi-component system during each preventive maintenance interval is specifically:

[0042] Among them, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ψ (t) represents the critical component failure rate function at time t, k represents the kth preventive maintenance interval, T represents the duration of the preventive maintenance interval, δ represents the improvement factor of incomplete preventive maintenance during the extended warranty period, W represents the initial warranty period, and v represents the maximum value of k.

[0043] Optionally, the failure rate function of the subsystems of the multi-component system during each preventive maintenance interval is specifically:

[0044] , where λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval, λ s (t) is the subsystem failure rate function at time t, θ represents the failure impact coefficient, m kψ represents the number of failures of key components during the kth preventive maintenance interval, m iψ represents the number of failures of key components during the i-th preventive maintenance interval.

[0045] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the present invention adopts an incomplete preventive maintenance strategy and a minimum maintenance strategy based on the failure correlation analysis of the key parts failure rate function and the subsystem failure rate function of the multi-component system to obtain an extended warranty availability model for the multi-component system. The multi-component system extended warranty availability model is used to obtain the availability values ​​corresponding to multiple preventive maintenance intervals within the preset extended warranty period. The extended warranty is performed according to the preventive maintenance interval corresponding to the maximum availability value, and an extended warranty plan is scientifically formulated to optimize the availability of the equipment multi-component system. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0047] Figure 1 A flowchart of a method for determining an extended warranty policy for a multi-component system provided by an embodiment of the present invention;

[0048] Figure 2 A schematic diagram of the virtual seniority method provided by an embodiment of the present invention;

[0049] Figure 3 A flowchart for processing using the extended warranty availability model for a multi-component system provided by an embodiment of the present invention;

[0050] Figure 4 An availability change trend graph obtained by processing the extended warranty availability model for a multi-component system provided by an embodiment of the present invention;

[0051] Figure 5 A graph showing the availability change curve calculated using the extended warranty availability model for a multi-component system provided by an embodiment of the present invention when T is fixed at 360 days;

[0052] Figure 6 This is a graph of availability variation calculated using the extended warranty availability model for a multi-component system provided by an embodiment of the present invention when We is fixed at 1080 days;

[0053] Figure 7 This is a curve diagram showing the change in extended warranty availability when only minimal repairs are performed;

[0054] Figure 8 The extended warranty availability value changes with the failure influence coefficient θ when We is fixed at 1080 days;

[0055] Figure 9 The extended warranty availability value changes with the failure impact coefficient θ when T is fixed at 360 days;

[0056] Figure 10 The curve of the extended warranty availability value changing with the improvement factor δ when We is fixed at 3600 days;

[0057] Figure 11 The graph shows the variation of the extended warranty availability value with the improvement factor δ when T is fixed at 36 days. DETAILED DESCRIPTION

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only 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 ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0059] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] The multi-component system processed in the embodiment of the present invention has the following characteristics: a fault-related multi-component system composed of key components and subsystems. The warranty strategy is to implement minimum maintenance after the failure of the multi-component system in the initial warranty stage, and to implement incomplete preventive maintenance on the system during the extended warranty period. The failure of key components will increase the failure rate of the subsystem to a certain extent (related to Class I failure), and the failure of the subsystem will directly lead to the failure of key components (related to Class II failure). At this time, the entire system will fail and require post-failure maintenance. Minimum maintenance is mainly used here. An availability model is established by adopting incomplete preventive maintenance and minimum maintenance strategies, with the preventive maintenance interval and the extended warranty period as decision variables, and the highest availability of the multi-component system during the extended warranty period as the decision goal. The establishment of the model is mainly based on the following conditions:

[0061] (1) The components of the system are connected in series.

[0062] (2) The system will only undergo minimal post-fault maintenance during the initial warranty period, and will use incomplete preventive maintenance during the extended warranty period. Failures within the preventive maintenance interval will be subject to minimal post-fault maintenance.

[0063] (3) The system failure rate increases with time.

[0064] (4) Preventive maintenance costs do not change with changes in the time and frequency of preventive maintenance.

[0065] (5) The minimum single maintenance cost is fixed and does not change with time or frequency.

[0066] (6) Minimal maintenance does not change the failure rate of components.

[0067] like Figure 1 As shown, an embodiment of the present invention provides a method for determining an extended warranty policy for a multi-component system, comprising:

[0068] Step 101: According to the failure rate function of the key parts and the failure rate function of the subsystem of the multi-component system, based on the failure correlation analysis, the incomplete preventive maintenance strategy and the minimum maintenance strategy are adopted to obtain the extended warranty availability model of the multi-component system. Fault correlation mainly means that in a multi-component system, the occurrence of a component failure will cause the overall environment of the system to change, which in turn affects the status of other components, resulting in an increase in failures. The "status" here includes various status metrics such as life and failure rate. For a multi-component system with fault correlation, the actual failure rate level of each component during operation is affected by two aspects, namely independent failure rate and correlated failure rate. Independent failure rate refers to the inherent failure rate of the component itself, which is determined by the design and manufacturing level; correlated failure rate refers to the failure rate caused by the failure or failure of other components in the system. Under the condition of fault correlation, the actual failure rate of each component can be expressed in the following matrix form:

[0069] [λ a (t)]=[I][λ a0 (t)]+[θ ab (t)][λ ba (t)] (1)

[0070] Among them, [λ a (t)], a=1,2,3,...,q is a q×1-dimensional vector, representing the actual failure rate of a single component; [λ a0 (t)] is a q × 1-dimensional vector, representing the independent failure rate of each component; [λ ba (t)] is a q×1-dimensional vector, where a,b=1,2,3,…,q and a≠b, representing the relative failure rate caused by component b to component a; [θ ab (t)] is a q×q dimensional non-negative real number matrix, representing the failure influence coefficient of component b on component a, 0≤θ ab (t)≤1,θ ab When the (t) value is 0, it means that there is no mutual influence between the components, and when the value is 1, it means that the failure of component b causes the failure of component a.

[0071] The effect of incomplete preventive maintenance is somewhere between "repair as good as new" and "repair as good as old." This paper uses a virtual service life method to describe the effect of incomplete preventive maintenance, meaning that each incomplete preventive maintenance reduces the actual service life of the product by a certain period of time. Let δ represent the improvement factor for incomplete preventive maintenance. Assuming the kth incomplete preventive maintenance is performed at time t, the product failure rate during the kth preventive maintenance interval can be expressed as:

[0072] λ(t)=λ(t-δ(k-1)T0) (2), where T0 is the interval of incomplete preventive maintenance. Using the virtual service life method, the change of product failure rate after each incomplete preventive maintenance is as follows: Figure 2 shown.

[0073] A minimum maintenance strategy is adopted for component failures during the initial warranty period and the preventive maintenance interval. The characteristic of minimum maintenance is that it follows a non-homogeneous Poisson process. The expected number of failures of the system over a period of time is: Where N(t) is the number of system failures within the time [0, t], and λ(s) is the system failure rate.

[0074] Step 102: Under the current iteration number, obtain the preventive maintenance interval under the previous iteration number.

[0075] Step 103: Input the preset extended warranty period and the preventive maintenance interval at the previous iteration number into the multi-component system extended warranty availability model to obtain the extended warranty availability value of the multi-component system at the current iteration number.

[0076] Step 104: updating the preventive maintenance interval at the previous iteration number according to a preset update step size to obtain the preventive maintenance interval at the current iteration number.

[0077] Step 105: Determine whether the preventive maintenance interval under the current number of iterations reaches a set threshold, and obtain a first determination result.

[0078] Step 106: If the first judgment result is yes, determining the extended warranty policy for the multi-component system based on the preventive maintenance interval corresponding to the largest extended warranty availability value in the extended warranty availability value set; the extended warranty availability value set includes extended warranty availability values ​​under all iteration numbers.

[0079] Step 107: If the first judgment result is no, update the number of iterations and enter the next iteration.

[0080] In practical applications, based on the failure correlation analysis of the key component failure rate function and the subsystem failure rate function of the multi-component system, an incomplete preventive maintenance strategy and a minimum maintenance strategy are adopted to obtain the extended warranty availability model of the multi-component system, which specifically includes:

[0081] An incomplete preventive maintenance strategy is adopted to process the failure rate function of the key components of the multi-component system to obtain the failure rate function of the key components of the multi-component system in each preventive maintenance interval.

[0082] Based on the failure correlation analysis, an incomplete preventive maintenance strategy is adopted to process the failure rate function of the subsystem of the multi-component system to obtain the failure rate function of the subsystem of the multi-component system in each preventive maintenance interval.

[0083] According to the failure rate function of the key component in each preventive maintenance interval and the failure rate function of the subsystem in each preventive maintenance interval, a minimum maintenance strategy is adopted to obtain a total expected downtime function of the multi-component system during the extended warranty period.

[0084] An extended warranty availability model for the multi-component system is obtained according to the total expected downtime function of the multi-component system within the extended warranty period.

[0085] In practical applications, the life distribution of key components is Weibull distribution, and its failure rate function is: Therefore, the failure rate function of the key components of a multi-component system during each preventive maintenance interval is specifically:

[0086] Among them, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ψ (t) represents the critical component failure rate function at time t, k represents the kth preventive maintenance interval, T represents the duration of the preventive maintenance interval, δ represents the improvement factor of incomplete preventive maintenance during the extended warranty period, W represents the initial warranty period, and v represents the maximum value of k. e , initial warranty period W, preventive maintenance interval T and incomplete preventive maintenance time T p , calculate the number of incomplete preventive maintenance of multi-component systems during the extended warranty period as follows: n = int[(W e -W) / (T+T p )] (6), where "int" means round down, T p Indicates the time required for a single incomplete preventive maintenance.

[0087] In practical applications, the failure rate function of the subsystems of the multi-component system during each preventive maintenance interval is specifically:

[0088]

[0089] Among them, λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval, λ s (t) is the subsystem failure rate function at time t, θ represents the failure impact coefficient, m kψ It represents the number of failures of key components during the kth preventive maintenance interval, which can be obtained by combining the minimum maintenance strategy theory. iψ represents the number of failures of key components during the i-th preventive maintenance interval. The life distribution of the subsystem is exponential distribution, and its failure rate function is:s =5×10 -4 / sky.

[0090] In practical applications, given the minimum maintenance time T for key parts f1 , the minimum maintenance time of the subsystem T f2 , combined with the minimum maintenance strategy, the minimum total maintenance downtime of the multi-component system in each preventive maintenance interval is calculated as:

[0091]

[0092] Given the minimum maintenance time T for key parts f1 , the minimum maintenance time of the subsystem T f2 , combined with the minimum maintenance strategy, find the multi-component system in [W+n(T+T p ),W e The expected minimum downtime for repair failure within ] is:

[0093]

[0094] In summary, the total expected downtime function of the multi-component system during the extended warranty period can be obtained, specifically:

[0095]

[0096] Among them, ED(T,W,W e ) represents the total expected downtime of the multi-component system during the extended warranty period, T p represents the incomplete preventive maintenance time, n represents the number of preventive maintenance during the extended warranty period, T f1 Indicates the minimum maintenance time of key parts, T f2 represents the minimum maintenance time of the subsystem, W e represents the extended warranty period, λ xs (t) represents the failure rate function of the subsystem during the last preventive maintenance interval at time t, λ xψ (t) represents the failure rate function of key components during the last preventive maintenance interval at time t.

[0097] In practical applications, the multi-component system extended warranty availability model is specifically as follows:

[0098] Among them, EA(T,W,W e ) represents the extended warranty availability value for multi-unit systems.

[0099] An embodiment of the present invention further provides a system for determining an extended warranty policy for a multi-component system corresponding to the above method, comprising:

[0100] The model building module is used to obtain the extended warranty availability model of the multi-component system based on the failure rate function of the key parts and the subsystem failure rate function of the multi-component system and the failure correlation analysis, and adopts the incomplete preventive maintenance strategy and the minimum maintenance strategy.

[0101] The acquisition module is used to obtain the preventive maintenance interval under the previous iteration number under the current iteration number.

[0102] The availability value determination module is configured to input a preset extended warranty period and a preventive maintenance interval at the previous iteration number into the multi-component system extended warranty availability model to obtain an extended warranty availability value of the multi-component system at the current iteration number.

[0103] The preventive maintenance interval calculation module is used to update the preventive maintenance interval under the previous iteration number according to a preset update step size to obtain the preventive maintenance interval under the current iteration number.

[0104] The judgment module is used to judge whether the preventive maintenance interval under the current number of iterations reaches a set threshold, and obtain a first judgment result.

[0105] an extended warranty policy determination module configured to, if the first judgment result is yes, determine an extended warranty policy for the multi-component system based on a preventive maintenance interval corresponding to a maximum extended warranty availability value in a set of extended warranty availability values, wherein the set of extended warranty availability values ​​includes extended warranty availability values ​​under all iteration numbers.

[0106] The iteration module is used to update the number of iterations and enter the next iteration if the first judgment result is no.

[0107] As an optional implementation, the model building module specifically includes:

[0108] The key component failure function processing unit is used to process the key component failure rate function of the multi-component system using an incomplete preventive maintenance strategy to obtain the failure rate function of the key component of the multi-component system in each preventive maintenance interval.

[0109] The subsystem failure rate function processing unit is used to process the subsystem failure rate function of the multi-component system based on failure correlation analysis and adopt an incomplete preventive maintenance strategy to obtain the failure rate function of the subsystem of the multi-component system in each preventive maintenance interval.

[0110] The multi-component system total expected downtime function determination unit is used to adopt a minimum maintenance strategy based on the failure rate function of the key component in each preventive maintenance interval and the failure rate function of the subsystem in each preventive maintenance interval to obtain the total expected downtime function of the multi-component system within the extended warranty period.

[0111] The availability model determining unit is configured to obtain an extended warranty availability model for the multi-component system according to a total expected downtime function of the multi-component system within the extended warranty period.

[0112] As an optional implementation, the failure rate function of the key components of the multi-component system during each preventive maintenance interval is specifically:

[0113] Among them, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ψ (t) represents the critical component failure rate function at time t, k represents the kth preventive maintenance interval, T represents the duration of the preventive maintenance interval, δ represents the improvement factor of incomplete preventive maintenance during the extended warranty period, W represents the initial warranty period, and v represents the maximum value of k.

[0114] As an optional implementation, the failure rate function of the subsystems of the multi-component system during each preventive maintenance interval is specifically:

[0115] Among them, λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval, λ s (t) is the subsystem failure rate function at time t, θ represents the failure impact coefficient, m kψ represents the number of failures of key components during the kth preventive maintenance interval, m iψ represents the number of failures of key components during the i-th preventive maintenance interval.

[0116] The present invention also provides a specific embodiment for applying the above method: the power unit of a certain type of equipment can be regarded as a multi-component system with fault correlation composed of a supercharger and a subsystem (the remaining components of the power unit). Through investigation, it was found that this type of equipment is a new type of high-tech complex equipment. During the initial warranty period, the troops cannot fully form an independent maintenance and support capability for the power unit. It is necessary to continue to introduce the maintenance and support force of the contracting unit to carry out technical services during the extended warranty period. Since the failure rate of new equipment is relatively low during the initial warranty period, it is considered to only adopt the minimum maintenance after the failure; during the extended warranty period, the equipment has been in service for a period of time, and the failure rate has increased significantly. On the basis of maintaining the minimum maintenance after the failure, it is very necessary to carry out incomplete preventive maintenance. Assume that the failure law of the supercharger obeys the following two-parameter Weibull distribution:

[0117] Among them, shape parameter α = 2, scale parameter β = 1000. It is known that the initial warranty period of the equipment is W = 2 years, and the failure rate of the subsystem is λ s =5×10 -4 / day, the minimum average maintenance time of the turbocharger is T f1 = 3 days. Minimum average maintenance time for power plant T f2 =5 days, average time for preventive maintenance T p = 2 days, and the improvement factor for incomplete preventive maintenance during the extended warranty period is δ = 0.8. Based on maintenance experience and data analysis, a supercharger failure increases the subsystem failure rate, with a failure impact coefficient θ = 0.5; a subsystem failure can lead to supercharger failure. Because the power unit plays a crucial role in providing kinetic energy for the entire equipment, the military attaches great importance to its availability. There is an urgent need to establish an extended warranty availability model for multi-component systems. By determining the optimal preventive maintenance intervals under different extended warranty periods, the power unit's availability can be maximized during the extended warranty period.

[0118] According to the maintenance experience of power plants, the preventive maintenance interval T is usually within 3 years, and too frequent preventive maintenance will increase warranty costs. Therefore, the value range of the preventive maintenance interval T is set to [0.1 year, 3 years]. According to the survey, the period for the troops to form independent maintenance capabilities for power plants is generally no more than 10 years, and generally no less than 3 years. Therefore, the extended warranty period W is set. e The range of values ​​is [3 years, 10 years]. The step length of the preventive maintenance interval and the extended warranty period is 0.1 year. The numerical algorithm is used to calculate any W e The availability of the multi-component system corresponding to the combination of T, the algorithm flow chart is as follows Figure 3 As shown, using the stored W e The combination of T and the availability of the multi-component system corresponding to the combination can be plotted. Figure 4 .

[0119] In order to study the relationship between power unit availability and extended warranty period W e and the change law of the preventive maintenance interval T, and respectively draw the change graph of availability with the extended warranty period when T = 360 days and W e = The graph of the change of availability with the preventive maintenance interval at 1080 days, such as Figure 5 and Figure 6 shown.

[0120] Depend on Figure 5 As can be seen, when the preventive maintenance interval is constant, the availability of multi-component systems generally decreases with the extension of the warranty period, but there are regular, small increases in some areas. This is mainly due to the increase in the number of incomplete preventive maintenance and the number of minimum maintenance as the extended warranty period increases, resulting in more downtime. Therefore, the longer the extended warranty period, the lower the availability. The small increases in some areas are mainly due to the fact that the implementation of preventive maintenance work has reduced the failure rate to a certain extent, resulting in a small increase in availability.

[0121] Depend on Figure 6 It can be seen that when the extended warranty period is determined, there is a multi-component system extended warranty strategy that maximizes system availability. Figure 6 In the ,system availability first increases and then decreases with the increase of preventive maintenance interval. This is mainly because when the preventive maintenance interval is short, preventive maintenance work will be carried out frequently, resulting in a large amount of downtime and lower availability. When the preventive maintenance interval is long, the system expects more failures, and the minimum maintenance after the failure will also cause frequent downtime, which will also lead to lower availability.

[0122] In order to determine the warranty plan under different extended warranty periods, based on the previous analysis of the incomplete preventive maintenance strategy, the availability (EA) of the multi-component system under the minimum failure maintenance strategy is calculated. The curve is as follows: Figure 7 shown.

[0123] from Figure 7 It can be found that, in the case of only minimal post-failure maintenance, the power unit availability decreases with the increase of the extended warranty period until it falls below 0.9. Figure 6 By comparison, it can be found that when the extended warranty period is the same, the availability when only minimal maintenance after failure is performed is lower than the availability when incomplete preventive maintenance is implemented.

[0124] Based on the above calculation results, combined with Figure 4 , we can solve the maximum availability of the power unit under different extended warranty periods and the corresponding extended warranty strategy for the multi-component system when considering both incomplete preventive maintenance and minimum maintenance after failure, as well as the availability when only the minimum maintenance strategy after failure is considered, as shown in Table 1.

[0125] Table 1 Availability of multi-component systems under different extended warranty periods

[0126]

[0127]

[0128] In Table 1, T* represents the extended warranty policy for multi-component systems, EA* is the optimal availability when both incomplete preventive maintenance and minimum maintenance after failure are considered, EA represents the availability of the power unit when only minimum maintenance after failure is performed, and RA represents EA * Percentage improvement in availability compared to EA. Based on Table 1, we conclude that adopting a partial preventive maintenance strategy can improve power unit availability within the extended warranty period, fully demonstrating the effectiveness of the model. Comparing the data in the RA column shows that the optimization effect of partial preventive maintenance on system availability gradually increases with the extension of the extended warranty period. This is because as the extended warranty period increases, partial preventive maintenance becomes increasingly effective in reducing the failure rate of multi-component systems, resulting in increasing system availability.

[0129] According to the scheme in Table 1, data such as the system availability and preventive maintenance interval within the extended warranty period can be obtained. This can provide information support and quantitative methods for both the contracting unit and the military to formulate extended warranty plans, thereby making extended warranty decisions more scientific and reasonable.

[0130] In the above model, system availability is related to factors such as the impact of correlated failures between components and the improvement factor for incomplete preventive maintenance. Different values ​​of these factors have different degrees of impact on system availability, which are analyzed below.

[0131] (1) Analysis of the impact degree of related faults θ

[0132] The basis of modeling fault-related multi-component systems is to construct a related failure rate formula. The parameter θ represents the degree of related failure influence between the components of the system. In order to further verify the influence of the failure influence coefficient θ on the system availability, Figure 4 Fixed at T = 360 days and W e = 1080 days, the availability change curve corresponding to different θ is calculated, such as Figure 8 and Figure 9 shown.

[0133] pass Figure 8 and Figure 9 It can be seen that the larger the fault impact coefficient θ, the lower the system availability. This is mainly because a larger fault impact coefficient increases the system's minimum maintenance downtime, which in turn reduces its availability. The fault correlation relationship is determined during the design and production phase, and the improvement of its coefficient needs to be fully considered at this stage.

[0134] (2) Analysis of the improvement factor δ of incomplete preventive maintenance

[0135] In order to further study the impact of improvement factor δ on system availability and make the difference in system availability under different improvement factors more obvious, the incomplete preventive interval T and the extended warranty period W are e Fixed at 36 days and 3600 days respectively, calculate the system availability corresponding to different δ, as follows Figure 10 and Figure 11 shown.

[0136] pass Figure 10 and Figure 11 It can be seen that the larger the improvement factor δ, the higher the system availability. This is mainly because a larger improvement factor reduces the number of system failures and the minimum repair time after failures during the extended warranty period, thereby improving system availability. The improvement factor is generally related to maintenance technology and the capabilities of maintenance personnel. In practice, improving the improvement factor and improving the technical level of maintenance personnel can improve system availability.

[0137] The present invention has the following technical effects:

[0138] The present invention conducts extended warranty research on fault-related multi-component systems, performs fault correlation analysis on the multi-component systems, adopts incomplete preventive maintenance and minimum maintenance strategies while considering the fault correlation between components, establishes an extended warranty availability model for the multi-component system, and solves the extended warranty strategy for the multi-component system under the extended warranty period, so as to maximize the availability of the system during the extended warranty period, and provide a quantitative basis for the formulation of the system extended warranty plan.

[0139] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0140] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for determining an extended warranty policy for a multi-component system, characterized in that: include: According to the failure rate function of key parts and subsystems of a multi-component system, based on the failure correlation analysis, the incomplete preventive maintenance strategy and the minimum maintenance strategy are adopted to obtain the extended warranty availability model of the multi-component system. Specifically, it includes: Using an incomplete preventive maintenance strategy to process the failure rate function of the key components of the multi-component system, to obtain the failure rate function of the key components of the multi-component system in each preventive maintenance interval; Based on the failure correlation analysis, an incomplete preventive maintenance strategy is used to process the failure rate function of the subsystem of the multi-component system to obtain the failure rate function of the subsystem of the multi-component system in each preventive maintenance interval; According to the failure rate function of the key component in each preventive maintenance interval and the failure rate function of the subsystem in each preventive maintenance interval, a minimum maintenance strategy is adopted to obtain a total expected downtime function of the multi-component system during the extended warranty period; Obtaining a multi-component system extended warranty availability model according to a total expected downtime function of the multi-component system during the extended warranty period; Under the current iteration number, obtain the preventive maintenance interval under the previous iteration number; Inputting a preset extended warranty period and the preventive maintenance interval at the previous iteration number into the multi-component system extended warranty availability model to obtain an extended warranty availability value of the multi-component system at the current iteration number; Updating the preventive maintenance interval at the previous iteration number according to a preset update step size to obtain the preventive maintenance interval at the current iteration number; Determining whether the preventive maintenance interval under the current number of iterations reaches a set threshold, and obtaining a first determination result; If the first judgment result is yes, determining an extended warranty policy for the multi-component system according to a preventive maintenance interval corresponding to a maximum extended warranty availability value in a set of extended warranty availability values, wherein the set of extended warranty availability values ​​includes extended warranty availability values ​​under all iteration numbers; If the first judgment result is no, the number of iterations is updated and the next iteration is entered; the total expected downtime function of the multi-component system during the extended warranty period is specifically: Among them, ED(T,W,W e ) represents the total expected downtime of the multi-component system during the extended warranty period, T p represents the incomplete preventive maintenance time, n represents the number of preventive maintenance during the extended warranty period, T f1 Indicates the minimum maintenance time of key parts, T f2 represents the minimum maintenance time of the subsystem, W e represents the extended warranty period, λ xs (t) represents the failure rate function of the subsystem during the last preventive maintenance interval at time t, λ xψ (t) represents the failure rate function of the key parts in the last preventive maintenance interval at time t, T represents the length of the preventive maintenance interval, W represents the initial warranty period, k represents the kth preventive maintenance interval, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval.

2. A method for determining an extended warranty policy for a multi-component system according to claim 1, characterized in that: The failure rate function of the key components of the multi-component system during each preventive maintenance interval is specifically: Among them, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ψ (t) represents the critical component failure rate function at time t, k represents the kth preventive maintenance interval, T represents the duration of the preventive maintenance interval, δ represents the improvement factor of incomplete preventive maintenance during the extended warranty period, W represents the initial warranty period, and v represents the maximum value of k.

3. The method for determining an extended warranty policy for a multi-component system according to claim 2, wherein: The failure rate function of the subsystems of the multi-component system during each preventive maintenance interval is specifically: ， Among them, λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval, λ s (t) is the subsystem failure rate function at time t, θ represents the failure impact coefficient, m kψ represents the number of failures of key components during the kth preventive maintenance interval, m iψ represents the number of failures of key components during the i-th preventive maintenance interval.

4. The method for determining an extended warranty policy for a multi-component system according to claim 1, wherein: The multi-component system extended warranty availability model is as follows: Among them, EA(T,W,W e ) represents the extended warranty availability value for multi-unit systems.

5. A system for determining an extended warranty policy for a multi-component system, characterized in that: include: A model building module is used to obtain an extended warranty availability model for a multi-component system based on the failure rate function of key components and subsystems of the multi-component system, failure correlation analysis, and the use of an incomplete preventive maintenance strategy and a minimum maintenance strategy; An acquisition module is used to obtain the preventive maintenance interval under the previous iteration number under the current iteration number; an availability value determination module, configured to input a preset extended warranty period and the preventive maintenance interval at the previous iteration number into the multi-component system extended warranty availability model to obtain an extended warranty availability value of the multi-component system at the current iteration number; a preventive maintenance interval calculation module, configured to update the preventive maintenance interval at the previous iteration number according to a preset update step size to obtain the preventive maintenance interval at the current iteration number; a judgment module, configured to judge whether the preventive maintenance interval under the current number of iterations reaches a set threshold, and obtain a first judgment result; an extended warranty policy determination module, configured to, if the first judgment result is yes, determine an extended warranty policy for the multi-component system according to a preventive maintenance interval corresponding to a maximum extended warranty availability value in a set of extended warranty availability values; The extended warranty availability value set includes extended warranty availability values ​​under all iteration numbers; an iteration module, configured to update the number of iterations and proceed to the next iteration if the first judgment result is no; The model building module specifically includes: a key component failure function processing unit, configured to process the key component failure rate function of the multi-component system using an incomplete preventive maintenance strategy to obtain a failure rate function of the key component of the multi-component system within each preventive maintenance interval; a subsystem failure rate function processing unit, configured to process the subsystem failure rate function of the multi-component system using an incomplete preventive maintenance strategy based on a failure correlation analysis, to obtain a failure rate function of a subsystem of the multi-component system within each preventive maintenance interval; a multi-component system total expected downtime function determination unit, configured to obtain a multi-component system total expected downtime function within the extended warranty period using a minimum maintenance strategy based on the failure rate function of the key component within each preventive maintenance interval and the failure rate function of the subsystem within each preventive maintenance interval; an availability model determining unit, configured to obtain an extended warranty availability model for a multi-component system according to a total expected downtime function of the multi-component system within the extended warranty period; The total expected downtime function of the multi-component system during the extended warranty period is specifically: ， Among them, ED(T,W,W e ) represents the total expected downtime of the multi-component system during the extended warranty period, T p represents the incomplete preventive maintenance time, n represents the number of preventive maintenance during the extended warranty period, T f1 Indicates the minimum maintenance time of key parts, T f2 represents the minimum maintenance time of the subsystem, W e represents the extended warranty period, λ xs (t) represents the failure rate function of the subsystem during the last preventive maintenance interval at time t, λ xψ (t) represents the failure rate function of the key parts in the last preventive maintenance interval at time t, T represents the length of the preventive maintenance interval, W represents the initial warranty period, k represents the kth preventive maintenance interval, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval.

6. A system for determining an extended warranty policy for a multi-component system according to claim 5, characterized in that: The failure rate function of the key components of the multi-component system during each preventive maintenance interval is specifically: Among them, λ kψ (t) represents the failure rate of key components in each preventive maintenance interval at time t, λ ψ (t) represents the critical component failure rate function at time t, k represents the kth preventive maintenance interval, T represents the duration of the preventive maintenance interval, δ represents the improvement factor of incomplete preventive maintenance during the extended warranty period, W represents the initial warranty period, and v represents the maximum value of k.

7. A system for determining an extended warranty policy for a multi-component system according to claim 6, characterized in that: The failure rate function of the subsystems of the multi-component system during each preventive maintenance interval is specifically: ， Among them, λ ks (t) represents the failure rate of the subsystem at time t during each preventive maintenance interval, λ s (t) is the subsystem failure rate function at time t, θ represents the failure impact coefficient, m kψ represents the number of failures of key components during the kth preventive maintenance interval, m iψ represents the number of failures of key components during the i-th preventive maintenance interval.

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