Method and system for optimizing preventive maintenance strategy based on utilization rate of rental products

Abstract

The present invention belongs to the technical field of optimizing preventive maintenance strategies under the condition of uncertain utilization rate of leased products, and specifically relates to a method and system for optimizing preventive maintenance strategies based on the utilization rate of leased products. The preventive maintenance strategy optimization method includes the following steps: S1. Construct a failure rate function model of the leased product based on the utilization rate, where the utilization rate is the ratio of the usage amount to the usage duration, and construct a utilization rate distribution function of the leased product; S2. According to the failure rate function model, the utilization rate distribution function and in combination with preventive maintenance parameters, construct an optimization model for preventive maintenance strategies; S3. Use the optimization model for preventive maintenance strategies to calculate the optimal preventive maintenance strategy of the leased product. The present invention optimizes the preventive maintenance strategy of the leased product under the condition of uncertain utilization rate, improves the utilization efficiency of the product while considering the decisions of the lessee, and reduces costs at the same time.

Description

Technical Field

[0001] The present invention belongs to the technical field of preventive maintenance strategy optimization under the condition of uncertain utilization rate of leased products, and particularly relates to a preventive maintenance strategy optimization method and system based on the utilization rate of leased products. Background Art

[0002] At present, the leasing industry is developing rapidly and the competition is becoming increasingly fierce. Lessors generally provide free warranty periods for leased products and formulate maintenance plans during the warranty periods. Due to the lack of equipment utilization rate data or information asymmetry in utilization rate, there are situations where the utilization rate of leased products is uncertain. For example, a hospital leases a medical device, an X-ray machine, but since the hospital has not leased this product before, the utilization rate of the product after leasing is uncertain; another example is that a construction unit leases a bulldozer, and due to complex construction conditions, it is difficult to estimate the utilization rate of the product after leasing, and the utilization rate of the product is difficult to determine. Therefore, it is difficult for lessors to give maintenance strategies during the warranty period to ensure the reliability of products. In addition, leased products also need to be maintained outside the warranty period, and at this time, the maintenance costs are usually borne by the lessee. Considering the scenario where the maintenance strategy is decided by the lessee, the lessor needs to consider the impact on its costs caused by the lessee's maintenance decision outside the warranty period when making maintenance decisions during the warranty period. Moreover, lessors will carry out preventive maintenance to slow down the degradation process of products, so as to achieve the purpose of reducing maintenance costs and improving product availability. At the same time, considering that condition-based maintenance requires high monitoring costs, a more widely used periodic preventive maintenance strategy is adopted as the maintenance strategy for both lessors and lessees.

[0003] Therefore, there is an urgent need in this field to develop a preventive maintenance strategy optimization scheme applicable to uncertain utilization rates of leased products, so as to solve the problem of how to arrange preventive maintenance time points to improve the utilization efficiency of leased products and reduce costs on the premise of uncertain utilization rates of leased products. Summary of the Invention

[0004] Based on the above-mentioned drawbacks and deficiencies existing in the prior art, one of the purposes of the present invention is to at least solve one or more of the above problems existing in the prior art. In other words, one of the purposes of the present invention is to provide a preventive maintenance strategy optimization method and system based on the utilization rate of leased products that meet one or more of the foregoing requirements.

[0005] To achieve the above-mentioned invention purpose, the present invention adopts the following technical solutions:

[0006] A preventive maintenance strategy optimization method based on the utilization rate of leased products, comprising the following steps:

[0007] S1. Construct a failure rate function model of rental products based on the usage rate, where the usage rate is the ratio of the usage amount to the usage duration.

[0008] Construct the usage rate distribution function of rental products.

[0009] S2. Based on the failure rate function model, the usage rate distribution function, and combined with preventive maintenance parameters, construct an optimized model for preventive maintenance strategies.

[0010] S3. Use the optimized model for preventive maintenance strategies to calculate the optimal preventive maintenance strategy for rental products.

[0011] As an optimal solution, in step S1, the process of constructing the failure rate function model of rental products based on the usage rate includes the following steps:

[0012] S11. Statistically analyze the first failure time and cumulative usage amount of rental products at different usage rates.

[0013] Construct a failure rate function to describe the change of the failure rate of rental products over time and usage amount. The failure rate function is:

[0014] ;

[0015] Where is the th product reliability parameter of the rental product, ; and respectively represent the usage duration and cumulative usage amount of the rental product at time , represents the usage rate;

[0016] On the premise of ignoring the maintenance time, the converted failure rate function is:

[0017] ;

[0018] S12. Based on the first failure time and cumulative usage amount of rental products at different usage rates, perform parameter estimation on the converted failure rate function to obtain the failure rate function model.

[0019] As an optimal solution, in step S1, the process of constructing the usage rate distribution function of rental products includes the following steps:

[0020] S1a. Collect historical usage rate data of rental products.

[0021] S1b. Based on the historical usage rate data of rental products, respectively use different probability distribution functions for fitting, and perform parameter estimation and testing to obtain different distribution functions.

[0022] S1c. Calculate the sum of squared residuals of different distribution functions and historical usage rate data respectively, and select the distribution function with the smallest sum of squared residuals as the usage rate probability distribution function. .

[0023] As an optimal solution, in the step (2), the preventive maintenance strategy optimization model includes the total expected cost function of the lessor and the maintenance cost function of the lessee.

[0024] The total expected cost function of the lessor includes the maintenance cost during the warranty period, the penalty cost during the warranty period, and the maintenance profit outside the warranty period.

[0025] The maintenance cost function of the lessee includes the corrective maintenance cost outside the warranty period, the preventive maintenance cost outside the warranty period, and the failure loss outside the warranty period.

[0026] As an optimal solution, the calculation process of the total expected cost function of the lessor includes:

[0027] Define the decision variables as the total number of preventive maintenance times of the lessor and the total number of preventive maintenance times of the lessee ;

[0028] When the lessor conducts preventive maintenance during the warranty period, the failure rate function model of the leased product in the time interval of preventive maintenance is ;

[0029] ;

[0030] where represents the preventive maintenance time interval of the lessor, represents the preventive maintenance effect factor, represents the moment of the th preventive maintenance;

[0031] The preventive maintenance time intervals of the lessor are respectively:

[0032] ;

[0033] where represents the warranty period;

[0034] The maintenance cost during the warranty period is:

[0035] ;

[0036] where , are the lower and upper limits of the usage rate, , respectively represent preventive maintenance and corrective maintenance costs, represents the number of corrective maintenance times, as follows:

[0037] ;

[0038] The penalty cost during the warranty period is:

[0039] ;

[0040] Among them, represents the single penalty cost, represents the penalty probability;

[0041] The maintenance profit outside the warranty period is:

[0042] ;

[0043] Among them, , respectively represent the preventive maintenance price and the corrective maintenance price, represents the number of corrective maintenance times outside the warranty period;

[0044] ;

[0045] The total expected cost function of the lessor is:

[0046] .

[0047] As an optimal solution, the calculation process of the lessee's maintenance cost function includes:

[0048] When the lessee performs preventive maintenance outside the warranty period, the failure rate function model of the leased product in the time interval of preventive maintenance is: :

[0049] ;

[0050] ;

[0051] Among them, represents the preventive maintenance time interval of the lessee, represents the moment of performing the preventive maintenance;

[0052] The preventive maintenance time interval of the lessee is:

[0053] ;

[0054] Among them, Denote the lease term as;

[0055] Define the utilization rate as the preventive maintenance cost of the lessee outside the warranty period: ;

[0056] Define the utilization rate as the corrective maintenance cost of the lessee outside the warranty period: ; where, denotes the number of corrective maintenance times outside the warranty period;

[0057] Define the utilization rate as the failure loss of the lessee outside the warranty period: ; where, denotes the loss brought to the lessee by each failure of the leased product;

[0058] The maintenance cost function of the said lessee is:

[0059] .

[0060] As an optimal solution, the step S3 specifically includes:

[0061] S31. Take the derivative of the maintenance cost function of the lessee to obtain the optimal preventive maintenance times of the lessee;

[0062] Calculate the optimal corrective maintenance times of the lessee according to the optimal preventive maintenance times of the lessee;

[0063] S32. Based on the optimal preventive maintenance times of the lessee, the optimal corrective maintenance times, and the decision variable of the lessor within the preset value range, calculate the total expected cost function of the lessor and take the decision variable corresponding to the minimum total expected cost as the optimal preventive maintenance times of the lessor;

[0064] S33. Calculate the maintenance interval of the lessor according to the warranty period and the optimal preventive maintenance times of the lessor, that is, the optimal preventive maintenance strategy of the leased product.

[0065] As an optimal solution, in the step S31, the optimal preventive maintenance times of the lessee are:

[0066] ;

[0067] where, ;

[0068] The optimal corrective maintenance times of the said lessee are:

[0069] .

[0070] As a preferred solution, step S32 specifically includes:

[0071] If is non-zero, the optimal number of corrective maintenance for the lessee calculated is still expressed as ;

[0072] If is zero, the optimal number of corrective maintenance for the lessee calculated is expressed as ;

[0073] There are three forms of the lessor's total expected cost function:

[0074] (a) When the lessee performs preventive maintenance in the usage rate interval , the expression of the lessor's total expected cost function is:

[0075] ;

[0076] (b) When the lessee does not perform preventive maintenance in the usage rate interval and performs preventive maintenance in the usage rate interval , the expression of the lessor's total expected cost function is: ;

[0077] (c) When the lessee does not perform preventive maintenance in the usage rate interval , the expression of the lessor's total expected cost function is:

[0078] ; Among them, whether the lessee performs preventive maintenance is equivalent to or ;

[0079] Define the following parameters:

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] The sum of the maintenance cost and the failure loss brought to the lessee by each corrective maintenance after the warranty period is expressed as ;

[0085] If , the total expected cost function of the lessor is ;

[0086] If : When , the total expected cost function of the lessor is ; When , the total expected cost function of the lessor is ;

[0087] If : According to and being different in size, there are the following two cases:

[0088] The first case: , ; If , the total expected cost function of the lessor is ; If , the total expected cost function of the lessor is ; If , the total expected cost function of the lessor is ;

[0089] The second case: , ; The total expected cost function of the lessor is ;

[0090] If : When , the total expected cost function of the lessor is ; When , the total expected cost function of the lessor is ;

[0091] If , the total expected cost function of the lessor is ;

[0092] First, obtain the maximum value of the lessor's preventive maintenance times by calculating the ratio of the warranty period to the minimum maintenance time interval between the lessor's two preventive maintenances, and determine the preset value range of the decision variable ; Then, calculate the total expected cost of the lessor corresponding to each value in the preset value range of the decision variable ; Finally, compare the magnitudes of the total expected costs, and output the preventive maintenance times corresponding to the minimum total expected cost as the optimal preventive maintenance times of the lessor.

[0093] The present invention also provides a preventive maintenance strategy optimization system based on the usage rate of leased products, which applies the preventive maintenance strategy optimization method described in any one of the above solutions. The preventive maintenance strategy optimization system includes:

[0094] A building module, which is used to build a failure rate function model of a rental product based on the usage rate; is also used to build a usage rate distribution function of the rental product; and is further used to build an optimized preventive maintenance strategy model according to the failure rate function model, the usage rate distribution function and in combination with preventive maintenance parameters.

[0095] A calculation module, which is used to calculate the optimal preventive maintenance strategy of the rental product by using the optimized preventive maintenance strategy model.

[0096] Compared with the prior art, the present invention has the following remarkable advantages:

[0097] The optimized preventive maintenance strategy method and system based on the usage rate of the rental product of the present invention obtain the optimal number of preventive maintenance times of the lessee outside the warranty period from the perspective of the lessee, improve the usage efficiency of the rental product, and reduce the maintenance costs brought by preventive maintenance and corrective maintenance during the leasing process of the lessee as well as the losses when the product fails; from the perspective of the lessor, for the situation where the usage rate of the leased equipment is uncertain, while considering the decision-making of the lessee, it solves the technical problem of arranging the preventive maintenance time for the lessor, improves the usage efficiency of the rental product, and minimizes the cost of the lessor; from the perspective of data, according to the model, an algorithm applicable to different parameter data is designed, and an optimized preventive maintenance strategy design scheme of the lessor within the warranty period is obtained. Description of the Drawings

[0098] Figure 1 is a flowchart of the optimized preventive maintenance strategy method based on the usage rate of the rental product in an embodiment of the present invention;

[0099] Figure 2 is a schematic diagram of the preventive maintenance strategy design of the rental product in an embodiment of the present invention;

[0100] Figure 3 is a module architecture diagram of the optimized preventive maintenance strategy system based on the usage rate of the rental product in an embodiment of the present invention

[0101] Figure 4 is a curve relationship diagram between the total expected cost of the lessor and the number of preventive maintenance times in Application Example 1 of the present invention;

[0102] Figure 5 is a curve relationship diagram between the total expected cost of the lessor and the number of preventive maintenance times in Application Example 2 of the present invention. Detailed Embodiments

[0103] To more clearly illustrate the embodiments of the present invention, the specific implementation manners of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings, and other implementation manners can also be obtained.

[0104] As Figure 1 shown, the method for optimizing the preventive maintenance strategy based on the usage rate of rental products in the embodiments of the present invention specifically includes the following steps:

[0105] (1) Construct a failure rate function model of rental products based on the usage rate;

[0106] In this embodiment, the usage rate is the ratio of the usage amount to the usage duration of the rental product; based on the on-site data of the rental product, a failure rate function model under the set usage rate is established.

[0107] Specifically, based on the on-site data of the rental product, the first failure time and the cumulative usage amount of the rental product under different usage rates are statistically analyzed; a failure rate function is constructed to describe the change of the failure rate of the rental product with time and usage amount; among them, the failure rate function is:

[0108] ;

[0109] Among them, is the th product reliability parameter of the rental product, ; and respectively represent the usage duration and the cumulative usage amount of the rental product at time , represents the usage rate;

[0110] On the premise of ignoring the maintenance time, the converted failure rate function is obtained as:

[0111] ;

[0112] After that, based on the first failure time and the cumulative usage amount of the rental product under different usage rates, parameter estimation is performed on the converted failure rate function to obtain the failure rate function model.

[0113] Specifically, parameter estimation is performed on the converted failure rate function by using the maximum likelihood estimation method, specifically, a likelihood function is constructed according to the failure rate function and the first failure time and the cumulative usage amount under different usage rates, and the parameters are solved and the model is verified. Among them, the construction of the likelihood function and the solution of the parameters can specifically refer to the prior art and will not be elaborated here.

[0114] (2)Construct a utilization rate distribution function for the rental product based on the historical rental data of the rental product;

[0115] In the embodiments of the present invention, historical utilization rate data of the rental product is collected, including the first failure data of the rental product and the product status data at the end of the lease; different probability distribution functions such as uniform distribution, Weibull distribution, state distribution, etc. are used for fitting, and parameter estimation and testing are performed on the functions to obtain different distribution functions; for different distribution functions, by constructing a log-likelihood function, the parameters are solved and the accuracy of the model is verified; the most accurate distribution function is selected as the utilization rate distribution function . Specifically, calculate the sum of squared residuals of different distribution functions and the historical utilization rate data respectively, and select the distribution function with the smallest sum of squared residuals as the utilization rate distribution function .

[0116] (3)Construct an optimized preventive maintenance strategy model according to the failure rate function model, the utilization rate distribution function and in combination with the preventive maintenance parameters; specifically, the optimized preventive maintenance strategy model in the embodiments of the present invention includes the total expected cost function of the lessor and the maintenance cost function of the lessee;

[0117] Suppose the lessor leases the product to the lessee, and the lessor is responsible for all maintenance actions of the rental product during the lease period. The preventive maintenance and corrective maintenance costs within the warranty period are borne by the lessor, and the maintenance costs outside the warranty period are borne by the lessee. Since the time of preventive maintenance and corrective maintenance is much less than the time of the lease period, the time of preventive maintenance and corrective maintenance is ignored. Preventive maintenance can restore part of the equipment reliability, and corrective maintenance can make the failed equipment return to the normal working state. Due to reasons such as information asymmetry or lack of equipment usage data, the utilization rate of the product is uncertain before the lease, but generally remains unchanged after being leased to the lessee. After the end of the warranty period, since the lessee is the direct user of the equipment or has certain usage experience of the equipment, etc., the lessee understands the utilization rate of the product.

[0118] First, determine that the decision variables are the number of preventive maintenance times of the lessor and the number of preventive maintenance times of the lessee ;

[0119] The descriptions and calculation formulas of the intermediate variables to be calculated in the model are as follows:

[0120] Considering the effect of preventive maintenance, the failure rate function of the rental product in the time interval of the th preventive maintenance when the lessor performs preventive maintenance, and the failure rate function of the rental product in the Time intervals for preventive maintenance Failure rate functions are respectively:

[0121] ;

[0122] ;

[0123] ;

[0124] wherein, respectively represent the preventive maintenance time intervals of the lessor and the lessee, represents the effectiveness factor of preventive maintenance, respectively represent the moments when the lessor and the lessee perform preventive maintenance, represents the warranty period;

[0125] The preventive maintenance time intervals of the lessor and the lessee are respectively:

[0126] ;

[0127] ;

[0128] wherein, represents the lease term.

[0129] As an example, as shown in Figure 2 , the lessor makes a decision on the lessor's preventive maintenance PM during the warranty period , that is, the lessor's PM decision, and the lessee makes a decision on the lessee's preventive maintenance PM outside the warranty period during the lease term , that is, the lessee's PM decision, respectively represent the preventive maintenance time intervals of the lessor and the lessee.

[0130] Secondly, the objective function of the lessor is defined as the total expected cost, including the maintenance cost during the warranty period, the penalty cost during the warranty period, and the maintenance profit outside the warranty period;

[0131] Specifically, the maintenance cost during the warranty period in the embodiment of the present invention:

[0132] ;

[0133] wherein, , are the lower and upper limits of the usage rate of the leased product, , respectively represent the preventive maintenance and corrective maintenance costs, , can be obtained from historical cost data, represents the usage rate distribution function, represents the number of corrective maintenance times, as follows: ;

[0134] The penalty cost during the warranty period of the embodiment of the present invention:

[0135] ;

[0136] wherein, represents the single penalty cost obtained according to historical data, represents the penalty probability, which can be obtained from the maintenance time distribution and the maintenance time penalty threshold;

[0137] The maintenance profit outside the warranty period of the embodiment of the present invention:

[0138] ;

[0139] wherein, and respectively represent the prices of preventive maintenance and corrective maintenance, represents the number of corrective maintenance times outside the warranty period;

[0140] The total expected cost function of the lessor is obtained as:

[0141] .

[0142] Finally, the objective function of the lessee is defined as the maintenance cost, including the corrective maintenance cost outside the warranty period, the preventive maintenance cost outside the warranty period, and the failure loss outside the warranty period;

[0143] Specifically, the preventive maintenance cost outside the warranty period of the lessee with a usage rate of is defined as: ;

[0144] The corrective maintenance cost outside the warranty period of the lessee with a usage rate of is defined as: ;

[0145] wherein, represents the number of corrective maintenance times outside the warranty period, and the expression is:

[0146] ;

[0147] The failure loss outside the warranty period of the lessee with a usage rate of is defined as: ;

[0148] wherein, Represents the losses incurred by the lessee for each failure of the product.

[0149] Combining the above expressions, the cost function of the lessee is obtained:

[0150]

[0151] (4) Using the preventive maintenance strategy optimization model, the optimal preventive maintenance strategy of the leased product is calculated. The specific process includes the following steps:

[0152] First, take the derivative of the cost function of the lessee to obtain the optimal preventive maintenance times of the lessee : ;

[0153] Among them, ;

[0154] Next, calculate the optimal corrective maintenance times of the lessee according to the optimal preventive maintenance times of the lessee; specifically, substitute into to obtain the optimal corrective maintenance times of the lessee :

[0155] ;

[0156] Then, based on the optimal preventive maintenance times of the lessee, the optimal corrective maintenance times of the lessee, and the preset value range of the decision variable of the lessor, calculate the total expected cost function of the lessor and take the decision variable corresponding to the minimum total expected cost as the optimal preventive maintenance times of the lessor;

[0157] Specifically, when it is zero and non-zero, the expressions are different, and the total expected cost expression of the lessor is different;

[0158] Let represent the optimal corrective maintenance times of the lessee when it is non-zero, represent the optimal corrective maintenance times of the lessee when it is zero;

[0159] There are three forms of the total expected cost function of the lessor in the embodiments of the present invention:

[0160] First, when the lessee performs preventive maintenance in the usage rate interval , the expression of the total expected cost function of the lessor is:

[0161] ;

[0162] II. When the lessee does not perform preventive maintenance within the usage rate range and performs preventive maintenance within the usage rate range the expression of the lessor's total expected cost function is as follows:

[0163] ;

[0164] III. When the lessee does not perform preventive maintenance within the usage rate range the expression of the lessor's total expected cost function is as follows:

[0165] ;

[0166] Whether the lessee performs preventive maintenance is equivalent to or . By analyzing the expression, the corresponding relationship between whether the lessee performs preventive maintenance and can be obtained. Combining with the relationship between whether the lessor performs preventive maintenance and the lessor's total expected cost, the relationship between different parameters and and the total expected cost function is as follows:

[0167] Define the following parameters:

[0168] ;

[0169] ;

[0170] ;

[0171] ;

[0172] Among them, represents the threshold value of, which affects the corresponding relationship between the lessor's total expected cost function and other parameters. z = ), represents the threshold value between different lessor expected cost functions. represents the threshold value of the lessor's preventive maintenance times between different lessor expected cost functions. For the sake of easy expression, the sum of the maintenance cost borne by the lessee for each corrective maintenance outside the warranty period and the failure loss is expressed as ;

[0173] When the lessor's preventive maintenance times the lessor's total expected cost function is ;

[0174] When the number of preventive maintenance times of the lessor the total expected cost function of the lessor is ; When the total expected cost function of the lessor is ;

[0175] When according to and there are two cases as follows:

[0176] The first case: If then when when the number of preventive maintenance times of the lessor the total expected cost function of the lessor is ; When the total expected cost function of the lessor is ; When the total expected cost function of the lessor is ;

[0177] The second case: If then when when the number of preventive maintenance times of the lessor the total expected cost function of the lessor is ;

[0178] When when the number of preventive maintenance times of the lessor the total expected cost function of the lessor is ; When the total expected cost function of the lessor is ;

[0179] When when the number of preventive maintenance times of the lessor the total expected cost function of the lessor is .

[0180] The problem is solved by constructing an algorithm: First, the maximum value of the number of preventive maintenance times of the lessor is obtained by calculating the ratio of the warranty period to the minimum maintenance time interval between two preventive maintenances of the lessor to determine the value range of the solution; Then, each feasible solution is substituted into the expression of the lessor, and specifically, different lessor expected cost expressions are substituted according to the different values of the parameters and . Finally, compare the magnitudes of the expected costs of different preventive maintenance times, and output the preventive maintenance times corresponding to the minimum expected cost , by calculating , the maintenance interval of the lessor, i.e., the maintenance plan, is obtained. The specific process is as follows:

[0181] Determine The search interval of is , determine the search interval of the search interval , determine the parameter value , , , , , , , , ;

[0182] Initialize , according to the parameter and The different, select the corresponding total expected cost function of the lessor to calculate and save The size of the corresponding total expected cost;

[0183] Update , according to the parameter and The different, select the corresponding total expected cost function of the lessor to calculate and save The size of the corresponding total expected cost; until ;

[0184] Compare the sizes of all The corresponding total expected cost in the search interval, and find the one that minimizes the total expected cost And the lessor's expected cost, which is recorded as the optimal preventive maintenance times of the lessor And the lowest lessor's expected cost;

[0185] Finally, calculate the maintenance interval of the lessor according to the warranty period and the optimal preventive maintenance times of the lessor , that is, the optimal preventive maintenance strategy of the leased product.

[0186] Based on the above preventive maintenance strategy optimization method based on the usage rate of the leased product in the embodiment of the present invention, the embodiment of the present invention also provides a preventive maintenance strategy optimization system based on the usage rate of the leased product, as Figure 3 Shown, including the following functional modules: a construction module and a calculation module.

[0187] Specifically, the construction module of the embodiment of the present invention is used to construct a failure rate function model of the leased product based on the usage rate; is also used to construct a usage rate distribution function of the leased product; is also used to construct an optimal preventive maintenance strategy model according to the failure rate function model, the usage rate distribution function and in combination with the preventive maintenance parameters;

[0188] The calculation module of the embodiment of the present invention is used to calculate the optimal preventive maintenance strategy of the leased product by using the preventive maintenance strategy optimization model;

[0189] For the specific processing process of the above functional modules, reference can be made to the specific process of the above preventive maintenance strategy optimization method, which will not be elaborated here.

[0190] Applying the preventive maintenance strategy optimization method based on the usage rate of leased products in the embodiment of the present invention to an actual application case is as follows:

[0191] Application Example 1:

[0192] The lease period of a certain leased product is 2 years, the warranty period of the product is 1 year, the corrective maintenance cost and preventive maintenance cost of the product are 7,500 yuan and 3,000 yuan respectively, the fault penalty within the warranty period is 80,000 yuan per time, the preventive maintenance and corrective maintenance fees charged to the lessee outside the warranty period are 4,000 yuan and 8,000 yuan respectively, and each fault of the product will cause the lessee to lose 2,500 yuan. Due to reasons such as the product needs to undertake certain tasks or resource constraints, there is an upper limit of 20 times for the preventive maintenance times. According to parameter fitting, the usage rate interval of the lessee is uniformly distributed on [2.2, 3.4], the probability of occurrence of the penalty is 1, the effect factor of preventive maintenance is 0.01, and the failure rate function of the equipment is 。

[0193] According to the preventive maintenance strategy optimization method based on the usage rate of leased products in the embodiment of the present invention, as Figure 4 shown, the optimal preventive maintenance times of the lessor are obtained, that is, the optimal preventive maintenance plan of the lessor when the usage rate of the leased product is uncertain is: perform preventive maintenance 2 times within the warranty period, that is, perform preventive maintenance once every six months; at this time, the total expected cost of the lessor is 20,500 yuan.

[0194] Application Example 2:

[0195] The lease period of a certain leased automobile product is 2 years, the warranty period of the product is 0.5 year, the corrective maintenance cost and preventive maintenance cost of the product are 750 yuan and 400 yuan respectively, the fault penalty within the warranty period is 500 yuan per time, the preventive maintenance and corrective maintenance fees charged to the lessee outside the warranty period are 450 yuan and 800 yuan respectively, and each fault of the product will cause the lessee to lose 1,000 yuan. Due to reasons such as the product needs to undertake certain tasks or resource constraints, there is an upper limit of 12 times for the preventive maintenance times. According to parameter fitting, the usage rate interval of the lessee is uniformly distributed on [3.1, 4.2], the probability of occurrence of the penalty is 0.85, the effect factor of preventive maintenance is 0.1, and the failure rate function of the equipment is 。

[0196] According to the preventive maintenance strategy optimization method based on the usage rate of leased products in the embodiments of the present invention, as Figure 5 shown, the final optimal preventive maintenance times are obtained , that is, the optimal preventive maintenance plan for the lessor under the condition of uncertain usage rate of leased products is: conduct 7 preventive maintenances during the warranty period, that is, conduct a preventive maintenance every 25 days; at this time, the total expected cost of the lessor is 10,455 yuan.

[0197] 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 method for optimizing preventive maintenance strategies based on the usage rate of rental products, characterized in that It includes the following steps: S1. Construct a failure rate function model of the rental product based on the utilization rate, where the utilization rate is the ratio of the usage amount to the usage duration; Construct a utilization rate distribution function of the rental product; S2. Construct an optimized preventive maintenance strategy model according to the failure rate function model, the utilization rate distribution function and in combination with preventive maintenance parameters; S3. Use the optimized preventive maintenance strategy model to calculate the optimal preventive maintenance strategy of the rental product; In the step S1, the process of constructing a failure rate function model of the rental product based on the utilization rate includes the following steps: S11. Statistically analyze the first failure time and the cumulative usage amount of the rental product at different utilization rates; Construct a failure rate function to describe the change of the failure rate of the rental product with time and usage amount, where the failure rate function is: λ(t,r) = θ1 + θ2T(t) + θ3r + θ4X(t); where, θ k is the k-th product reliability parameter of the rental product, where k = 1, 2, 3, 4; T(t) and X(t) respectively represent the usage duration and cumulative usage of the rental product at time t, and r represents the usage rate; On the premise of ignoring the maintenance time, the converted failure rate function is: λ(t,r) = θ1 + θ2t + θ3r + θ4rt; S12. Conduct parameter estimation on the converted failure rate function based on the first failure time and the cumulative usage amount of the rental product at different utilization rates to obtain the failure rate function model; In the step S1, the process of constructing a utilization rate distribution function of the rental product includes the following steps: S1a. Collect the historical utilization rate data of the rental product; S1b. Based on the historical utilization rate data of the rental product, respectively use different probability distribution functions for fitting, and conduct parameter estimation and testing to obtain different distribution functions; S1c. Calculate the sum of squared residuals of different distribution functions and the historical utilization rate data respectively, and select the distribution function with the smallest sum of squared residuals as the utilization rate probability distribution function G(r); In the step S2, the optimized preventive maintenance strategy model includes the total expected cost function of the lessor and the maintenance cost function of the lessee; The total expected cost function of the lessor includes the maintenance cost during the warranty period, the penalty cost during the warranty period and the maintenance profit outside the warranty period; The maintenance cost function of the lessee includes the corrective maintenance cost outside the warranty period, the preventive maintenance cost outside the warranty period and the failure loss outside the warranty period; The calculation process of the total expected cost function of the lessor includes: Define the decision variable as the total number of preventive maintenance N for the lessor RP and the total number of preventive maintenance N for the lessee EP ; When the lessor conducts preventive maintenance during the warranty period, the failure rate function model λ i , T i+1 )(t, r) of the leased product during the time interval (T i+1 ) of the i-th preventive maintenance; λ i+1 (t,r) = λ(iaΔ R + t,r), t ∈ (0,Δ R ), i = 0, 1,..., N RP ; Among them, Δ R represents the preventive maintenance time interval of the lessor, a represents the effectiveness factor of preventive maintenance, and T i represents the time when the i-th preventive maintenance is carried out; The preventive maintenance time interval of the lessor is: Δ R = W / (N RP + 1); where W represents the warranty period; The maintenance cost during the warranty period is: where r L , r U are the lower and upper limits of the utilization rate, C P , C C represent the preventive maintenance and corrective maintenance costs respectively, N RC (N RP , r) represents the number of corrective maintenance times, as follows: The penalty cost during the warranty period is: Among them, C τ represents the single penalty cost, represents the penalty probability; The maintenance profit outside the warranty period is: where P P and P C represent the preventive maintenance price and the corrective maintenance price respectively, and N EC (N RP , N EP , r) represents the number of corrective maintenance times outside the warranty period; where L represents the lease period; The total expected cost function of the lessor is: The calculation process of the maintenance cost function of the lessee includes: When the lessee conducts preventive maintenance outside the warranty period, the failure rate function model λ j ,T j+1 )(t, r) of the leased product during the time interval (T j+1 ) of the jth preventive maintenance is as follows: λ j+1 (t, r) = λ((a - 1)N RP Δ R + W + t, r), t ∈ (0, Δ E ), j = 0; λ j+1 (t,r) = λ((N RP + 1)aΔ R + jaΔ E + t,r), t ∈ (0,Δ E ), j = 1,2,...,N EP ; Among them, Δ E represents the preventive maintenance time interval of the lessee, and T j represents the moment of the j-th preventive maintenance; The preventive maintenance time interval of the lessee is: Δ E =(L - W) / (N EP + 1); Define the preventive maintenance cost of the lessee with a usage rate of r outside the warranty period: P P N EP ; Define the corrective maintenance cost of the lessee with a utilization rate of r outside the warranty period: P C N EC (N RP ,N EP ,r); where N EC (N RP ,N EP ,r) represents the number of corrective maintenance times outside the warranty period; Define the failure loss of the lessee with a usage rate of r outside the warranty period: S C N EC (N RP ,N EP ,r); where S C represents the loss caused to the lessee by each failure of the leased product; The maintenance cost function of the lessee is: The step S3 specifically includes: S31. Take the derivative of the maintenance cost function of the lessee to obtain the optimal preventive maintenance times of the lessee; Calculate the optimal corrective maintenance times of the lessee according to the optimal preventive maintenance times of the lessee; S32. Calculate the total expected cost function of the lessor based on the optimal preventive maintenance times of the lessee, the optimal corrective maintenance times, and the decision variable N RP of the lessor, and take the decision variable N corresponding to the minimum total expected cost RP as the optimal preventive maintenance times of the lessor; S33. Calculate the maintenance interval of the lessor according to the warranty period and the optimal preventive maintenance times of the lessor, that is, the optimal preventive maintenance strategy of the rental product.

2. The preventive maintenance strategy optimization method according to claim 1, characterized in that In the step S31, the optimal preventive maintenance times of the lessee are: Among them, The optimal number of corrective maintenance for the lessee is as follows:

3. The preventive maintenance strategy optimization method according to claim 2, wherein The specific steps of S32 include: If is non - zero, the calculated optimal number of corrective maintenance for the lessee is still expressed as If is zero, the calculated optimal number of corrective maintenance times for the lessee is expressed as There are three forms of the lessor's total expected cost function: (a) When the lessee conducts preventive maintenance within the usage rate range [r L , r U , the expression of the lessor's total expected cost function is as follows: (b) When the lessee does not perform preventive maintenance in the usage rate interval [r L , r * (N RP )] and performs preventive maintenance in the usage rate interval (r * (N RP ), r U , the expression of the lessor's total expected cost function is as follows: (c) When the lessee does not perform preventive maintenance within the utilization rate range [r L , r U , the expression of the lessor's total expected cost function is as follows: Among them, whether the lessee conducts preventive maintenance is equivalent to or Define the following parameters: The maintenance cost P borne by the lessee for each corrective maintenance outside the warranty period C and the failure loss S C The sum is expressed as P S ; If the total expected cost function of the lessor is π1(N RP ); If When the lessor's total expected cost function is π1(N RP );When the lessor's total expected cost function is π2(N RP ); If According to B L and A U are of different sizes, there are the following two cases: The first case: If the total expected cost function of the lessor is π1(N RP );If the total expected cost function of the lessor is π2(N RP );If the total expected cost function of the lessor is π3(N RP ); The second case: The total expected cost function of the lessor is π2(N RP ) If When the lessor's total expected cost function is π2(N RP );When the lessor's total expected cost function is π3(N RP ); If the lessor's total expected cost function is π3(N RP ); First, the maximum value of the preventive maintenance times of the lessor is obtained by calculating the ratio of the warranty period to the minimum maintenance time interval between two preventive maintenances of the lessor, and the decision variable N RP is determined for its preset value range; then, the total expected cost of the lessor corresponding to each value in the preset value range of the decision variable N RP is calculated; finally, the sizes of the total expected costs are compared, and the preventive maintenance times corresponding to the minimum total expected cost are output as the optimal preventive maintenance times of the lessor.

4. A preventive maintenance strategy optimization system based on the usage rate of rental products, which applies the preventive maintenance strategy optimization method according to any one of claims 1-3, characterized in that The preventive maintenance strategy optimization system includes: A construction module, which is used to construct a failure rate function model of the leased product based on the usage rate; is also used to construct a usage rate distribution function of the leased product; and is also used to construct a preventive maintenance strategy optimization model according to the failure rate function model, the usage rate distribution function and in combination with preventive maintenance parameters; A calculation module, which is used to calculate the optimal preventive maintenance strategy of the leased product by using the preventive maintenance strategy optimization model.

Images