Structure-related two-dimensional warranty equipment working age replacement decision-making method

Abstract

The invention provides a Copula function-based structure-related two-dimensional warranty equipment working age replacement method, which comprises the following steps of: 1, constructing a two-dimensional warranty multi-component system model according to specific equipment; 2, solving the two-dimensional warranty multi-component system model to obtain the total expected cost rate and the total expected availability of the system in the two-dimensional working age replacement interval, and taking the minimum cost-effectiveness ratio as an optimal objective function according to the obtained total expected cost rate and the total expected availability; 3, solving an optimal objective function with the minimum cost-effectiveness ratio based on a simulated annealing algorithm; and 4, formulating a two-dimensional warranty equipment working age replacement scheme according to the optimal cost-efficiency ratio calculated in the step 3. According to the method, the Copula function is used for describing the structural correlation of the components, the optimal decision scheme is solved by using the simulated annealing algorithm, and finally, the scheme result is used for reducing the cost and improving the availability of the structural correlation multi-component system.

Description

Technical Field

[0001] The present invention relates to the technical field of complex equipment, and in particular to a method for making decisions on the age replacement of structure-related two-dimensional maintenance equipment. Background Art

[0002] Complex equipment is usually composed of many multi-component systems with complex structures, more types of failures and more complex failure mechanisms, so higher requirements are placed on its maintenance guarantee. Warranty refers to a service commitment provided by a manufacturer or seller for a product due to quality problems or manufacturing defects within a certain period of time. At present, due to insufficient attention to warranty management, the problem of excessively high warranty costs for manufacturers or sellers still exists. To this end, it is necessary to establish a warranty decision model that pays attention to availability and warranty costs at the same time, so that the interests of both users and manufacturers are protected.

[0003] The life of a large number of complex equipment is jointly affected by factors such as calendar time and usage level. That is, too long usage time or too high usage intensity will accelerate the degradation rate of equipment systems or components, so a two-dimensional warranty method is usually adopted. Two-dimensional warranty means that the warranty period consists of two dimensions, one of which represents calendar time and the other represents the degree of usage. For example, a certain type of vehicle is equipped with a two-dimensional warranty period of up to 3 years and 25,000 kilometers. When any dimension reaches the upper limit, the warranty will be terminated. On the one hand, the two-dimensional warranty method conforms to the degradation law of equipment, and on the other hand, it can limit the high usage rate, which is beneficial for manufacturers to control warranty costs. In addition, manufacturers will also carry out regular and regular preventive maintenance work for equipment during the warranty period. Reasonable preventive maintenance can effectively avoid the occurrence of potential equipment failures. Therefore, it can save warranty costs, reduce downtime, and improve equipment availability to a certain extent. However, frequent preventive maintenance may lead to an increase in warranty costs and a decrease in availability. Therefore, determining the interval of regular preventive maintenance during the two-dimensional warranty period is a key issue.

[0004] In response to the current problems, the present invention takes complex equipment as the object, focuses on the parallel system in complex equipment, uses FGM Copula function to describe the correlation between component failure time and system failure time, comprehensively considers the expected cost rate and availability, takes the lowest cost-effectiveness as the decision-making goal, and adopts simulated annealing algorithm to obtain the optimal two-dimensional service life replacement plan of the system. Summary of the invention

[0005] In view of the shortcomings of the above-mentioned prior art, the present invention proposes a structure-related two-dimensional maintenance equipment service life replacement decision method, which includes the following steps:

[0006] Step 1: Construct a multi-component system model for two-dimensional warranty based on the structural correlation between the components;

[0007] Step 2: Solve the multi-component system model of two-dimensional maintenance to obtain the total expected cost rate and total expected availability of the system within the two-dimensional service life replacement interval, and use the minimum cost-effectiveness ratio as the optimization objective function based on the obtained total expected cost rate and total expected availability;

[0008] Step 3: Solve the optimization objective function with the minimum cost-effectiveness ratio based on the simulated annealing algorithm to obtain the optimal cost-effectiveness ratio;

[0009] Step 4: Based on the optimal cost-effectiveness calculated in step 3, formulate a replacement plan for the two-dimensional warranty equipment.

[0010] Furthermore, the specific steps of step 1 include:

[0011] Step 1.1: Give the model establishment assumptions;

[0012] Step 1.2: Based on the assumptions, build the following models:

[0013] 1) System life model

[0014] X TRS =min[χ(X1,X2,...,X N |r;α),T r ]

[0015] Among them, X TRS Indicates the actual life of the system, T r Indicates the time interval for replacing the actual service life of the system, x N represents the component life, α represents the component correlation parameter, r represents the system utilization rate, χ(X1,X2,...,X N |r; α) indicates that the life of the parallel system is determined by the component with the longest life in the system;

[0016] 2) Expected cost rate model

[0017]

[0018] Among them, C f represents the failure replacement cost, C p represents the preventive replacement cost;

[0019] and,

[0020]

[0021]

[0022] Among them, T0 and U0 represent the preventive maintenance intervals in terms of time and usage, respectively; F j represents the cumulative distribution function of component j’s life probability;

[0023] 3) Availability model

[0024]

[0025] Among them, T f Indicates the fault replacement time, T p Indicates preventive replacement time, 0 <T p <T f .

[0026] 4) Cost-effectiveness model

[0027] F=C a (T r ;α) / A(T r ; α)

[0028] Furthermore, the assumptions of step 1.1 include:

[0029] Assumption 1: The system consists of multiple components in parallel;

[0030] Assumption 2: Multi-component systems are unrepairable and have increasing failure rates;

[0031] Assumption 3: The usage rate of the same user remains unchanged; the usage rate of different users is a random variable that follows a distribution;

[0032] Assumption 4: Failure response time is negligible, that is, replacement is performed immediately after failure;

[0033] Assumption 5: The degradation of components and their corresponding degradation states are not considered;

[0034] Assumption 6: The replaced components are new and independent of each other.

[0035] Furthermore, the specific steps of step 2 include:

[0036] Step 2.1: Given a set (T0, U0), calculate r0 = U0 / T0;

[0037] Step 2.2: When r≤r0, T r =T0, the expected cost rate C at this time is solved by the following formula exp (1) and expected availability A exp (1):

[0038]

[0039]

[0040] Among them, r l is the lower limit of the utilization rate, G(r) is the cumulative probability distribution function that the utilization rate obeys;

[0041] Step 2.3: When r>r0, replace [r0,r u ] is evenly divided into k small intervals, where r u is the upper limit of utilization rate, and each small interval is [r a-1 ,r a ),a=1,2,...,k,r a It is expressed as:

[0042]

[0043] Among them, r a Indicates the upper limit of the utilization rate range, r l Indicates the lower limit of the utilization rate range;

[0044] Step 2.4: Replace each small interval with the average utilization rate of the interval. The average utilization rate of the interval can be expressed as:

[0045]

[0046] Among them, g(s) is the probability density function of the usage rate; s represents the usage rate in the interval [r a-1 ,r a ] the specific value obtained between;

[0047] Step 2.5: The probability that the usage rate falls in each interval is:

[0048] P a =G(r a )-G(r a-1 );

[0049] Step 2.6: Calculate the expected cost rate and expected availability of each cell using the following formula:

[0050]

[0051]

[0052] Step 2.7: Calculate the expected cost rate C at this time by the following formula: exp (2) and expected availability A exp (2) is:

[0053]

[0054]

[0055] Step 2.8: Based on C exp (1) A exp (1) C exp (2) and A exp(2), the total expected cost rate and total expected availability of the system within the two-dimensional service age replacement interval are obtained as follows:

[0056] C a = C exp (1) + C exp (2)

[0057] A = A exp (1) + A exp (2);

[0058] Step 2.9: Based on C a and A, establish an objective function with the minimum cost-effectiveness ratio:

[0059]

[0060] Furthermore, the specific operation steps for solving the minimum cost-effectiveness ratio in Step 3 include:

[0061] Step 3.1: Set the maximum number of iterations ψ max , let ψ = ψ0, where ψ0 is the initial temperature. Randomly generate a set of initial solutions (T0, U0) at temperature ψ0, and calculate the cost-effectiveness value f1(T0, U0) of this set of solutions through the calculation formula of the cost-effectiveness ratio F;

[0062] Step 3.2: Let the current temperature ψ be equal to the next value ψ1 in the cooling schedule;

[0063] Step 3.3: Calculate f1(T1, U1) under the current solution (T1, U1), and randomly generate a new solution (T2, U2) near this current solution, and calculate the cost-effectiveness value f1(T2, U2) of this set of solutions;

[0064] Step 3.4: If f1(T2, U2) < f1(T1, U1), then accept the new solution (T2, U2); if f1(T2, U2) ≥ f1(T1, U1), then calculate △f = f1(T2, U2) - f1(T1, U1), and let Then randomly generate a random number that follows a uniform distribution in the interval [0, 1] If Then accept the new solution (T2, U2);

[0065] Step 3.5: Repeat Steps 3.2 to 3.4 for L times;

[0066] Step 3.6: Determine whether the current iteration number L reaches the set maximum iteration number ψ max , if so, exit the iteration, otherwise return to Step 3.2 to continue the iteration.

[0067] Therefore, the present invention adopts the above-mentioned structure-related two-dimensional maintenance equipment service life replacement decision method, which has the following beneficial effects:

[0068] For multi-component systems with two-dimensional warranty, the present invention considers the structural correlation between components, uses the FGMCopula function to describe the dependency between component failure time and system failure time, proposes a two-dimensional service life replacement strategy optimization method based on the minimum cost-effectiveness ratio, and solves the optimal decision plan through the simulated annealing algorithm, so that manufacturers can use the plan results to reduce warranty costs and improve the availability of structurally related parallel systems. The warranty cost estimation, preventive maintenance interval determination, equipment availability assessment and other technologies proposed in the present invention can provide important support for the formulation of equipment warranty decision plans.

[0069] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 (a)-(b) are the actual system replacement moments; Figure 1 (a) is r≤U0 / T0, Figure 1 (b) r>U0 / T0;

[0071] Figure 2 A flowchart for solving a multi-component system model for two-dimensional warranty;

[0072] Figure 3 This is the structural diagram of the fuel fine filter;

[0073] Figure 4 is the expected cost rate change of the system;

[0074] Figure 5 is the change of system availability;

[0075] Figure 6 (a)-(b) are the dimensionality reduction analysis of expected cost rate;

[0076] Figure 7 (a)-(b) are the availability dimension reduction analysis;

[0077] Figure 8 (a)-(b) is (C p ,C f ) and (T p ,T f ) Sensitivity analysis;

[0078] in, Figure 3 1-filter element, 2-filter body, 3-center screw, 4-filter cover, 5-oil inlet, 6-oil outlet, 7-exhaust screw. DETAILED DESCRIPTION

[0079] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art make various changes or modifications to the present invention, and these equivalent forms also fall within the scope limited by the claims attached to the application.

[0080] 1. Related concepts of the present invention

[0081] (1) Seniority replacement strategy

[0082] Regular maintenance is a preventive maintenance strategy whose main goal is to prevent equipment failure before it actually occurs. According to the repair effect, regular maintenance can be divided into four categories: deterioration maintenance, minimum maintenance, imperfect maintenance and perfect maintenance. The two most common maintenance methods are imperfect maintenance and perfect maintenance. Imperfect maintenance is usually equipment inspection, partial or full overhaul of a specific period, oil change, lubrication and other activities. Perfect maintenance is usually to protect and enhance the reliability of equipment by replacing components before the components actually fail. Regular maintenance is essential to keep equipment, machines and working environments safe and reliable. Regular maintenance plans can prevent equipment failures and their serious consequences, but too frequent maintenance may cause costs to exceed benefits, resulting in increased maintenance costs or reduced system availability. Therefore, regular maintenance plans need to be carefully designed, and the most important issue is to determine the regular maintenance interval.

[0083] The service life replacement strategy is a popular regular replacement strategy. The service life replacement strategy mainly involves the planned replacement of products according to the preset service life to restore them to their original state. However, most of the current research on service life replacement strategies is conducted under a one-dimensional framework, and there is a lack of research on two-dimensional service life replacement strategies.

[0084] (2) Two-dimensional warranty

[0085] According to the number of variables covered by the warranty, warranties can be divided into one-dimensional warranties and two-dimensional warranties. A two-dimensional warranty is represented by an area on a two-dimensional plane, usually with one dimension representing calendar time and the other representing the intensity of use. Many capital-intensive products, such as automobiles, aircraft engines, and heavy equipment, have a two-dimensional warranty period. In recent years, scholars have widely discussed two-dimensional warranty decision models under different objectives, such as minimum cost, maximum profit, and maximum availability. The optimization of two-dimensional warranty schemes based on different maintenance strategies, such as incomplete maintenance, minimum maintenance, and complete maintenance, has been considered. Two-dimensional initial warranty and two-dimensional extended warranty have been proposed. However, current research assumes that most two-dimensional warranty products are single components or single systems, while ignoring the multi-component systems that are widely present in engineering practice. There are usually correlations between the components of a multi-component system. These correlations often have an important impact on two-dimensional warranty decisions.

[0086] (3) Maintenance relevance

[0087] In most cases, there are correlations between components within a system that make up a product, namely structural correlation, economic correlation, failure correlation, and resource correlation. Structural correlation exists between components when maintenance or replacement of one component requires removal or replacement of other components. Failure correlation means that the failure or degradation of one component will have an impact on the failure or degradation of other components. Economic correlation means that the cost of group maintenance is different from the cost of maintaining each component individually. Resource correlation exists between components when multiple systems or components share spare parts, tools, or maintenance personnel. Since structural correlation is easier to detect, it is usually considered first before making maintenance decisions. Series systems and parallel systems are the most common structurally correlated multi-component systems. For series systems, as long as one component fails, the entire system often requires preventive maintenance; for parallel systems, the maintenance time of the system depends on the last failed component.

[0088] (4) Copula function

[0089] Copula function is a function used to describe the interaction results of multiple correlated random variables. The parameter α in the Copula function represents the correlation of component failure times in the system. The joint distribution of multidimensional random variables can be represented by the one-dimensional marginal distribution of each random variable. Copula function provides a new method for reliability assessment and system maintenance decision-making.

[0090] 2. The structurally related two-dimensional maintenance equipment age replacement strategy based on Copula function proposed in this invention

[0091] Aiming at a multi-component system with two-dimensional maintenance, the present invention proposes a structure-related two-dimensional maintenance equipment service life replacement strategy based on Copula function. Copula function is used to describe the structural correlation between the components of the parallel system, and finally the optimal service life replacement decision scheme is obtained.

[0092] It includes the following steps:

[0093] Step 1, construct a multi-component system model for two-dimensional warranty;

[0094] (1) Model description

[0095] The multi-component system consists of several components connected in parallel. A two-dimensional service life replacement strategy is adopted for the system, that is, the system is replaced preventively when it reaches the specified two-dimensional preventive maintenance interval (T0, U0). If a fault occurs between the two-dimensional service life replacement intervals, a fault replacement is performed, and the new service life replacement period is recalculated from the time the system is replaced.

[0096] (2) Model assumptions

[0097] ①The system consists of multiple components in parallel.

[0098] ②Multi-component systems cannot be repaired and the failure rate increases.

[0099] ③ The usage rate of the same user remains unchanged; the usage rate of different users is a random variable and obeys a certain distribution.

[0100] ④ Fault response time is negligible, that is, replacement is carried out immediately after the fault.

[0101] ⑤ The degradation of components and their corresponding degradation states are not explicitly considered (only their lifetime and failure rate functions are used).

[0102] ⑥ The repair activities are perfect (the replaced components are brand new) and independent of each other.

[0103] (3) Model construction

[0104] ①System life model

[0105] Consider a system consisting of n components, each of which is connected in parallel. i is the life of the ith component, which is a random variable that obeys a certain distribution. Its probability density function, probability cumulative distribution function and failure rate function are: i (·), F i (·),λ i (·), where i = 1, 2, ..., n;

[0106] Based on the following Theorem 1-Theorem 3, the Copula function is used to describe the parallel structural correlation between components, and its expression is:

[0107] C(v1,v2,...,v n )=P(V1≤v1,V2≤v2,...,V n ≤v n ) (1)

[0108] Where C represents the Copula function; v n represents a standard uniformly distributed random variable, V n Denotes each random variable X i The cumulative distribution function of

[0109] Theorem 1: If H(x1,x2,...,x N ) is a continuous marginal distribution F1(x1), F2(x2), ..., F N (x N ), then there exists a unique Copula function C such that:

[0110] H(x1,x2,...,x N )=C[F1(x1),F2(x2),...,F N (x N )] (2)

[0111] Among them, F i (·) represents the cumulative distribution function of component i’s life probability, x N Represents component life;

[0112] Theorem 2: Given H(x1,x2,...,x N ) and F1(x1),F2(x2),...,F N (x N ), their Copula functions can be found.

[0113] It can be seen from Theorem 1 and Theorem 2 that the properties of a joint distribution with respect to correlation are completely determined by its Copula function.

[0114] Proof of Theorem 2: From Theorem 1, we know that H(x1,x2,...,x N )=C[F1(x1),F2(x2),...,F N (x N )],make:

[0115] F1(x1)=v1,F2(x2)=v2,...,F N (x N )=vn (3)

[0116] According to the properties of the inverse cumulative distribution function, we can get:

[0117]

[0118] Substituting formula (4) into formula (2) yields:

[0119]

[0120] Theorem 3: C(v1,v2,...,v n )=P(V1≤v1,V2≤v2,...,V n ≤v n ), v i is a standard uniformly distributed random variable.

[0121] Proof of Theorem 3: If X1, X2, ...X N are all random variables, and V1, V2, ...V N is the cumulative distribution function of each random variable, that is, V1=F(X1), V2=F(X2),..., V N =F(X N ), then:

[0122]

[0123] It is also known that 0≤F(v)≤1, so v i is a standard uniformly distributed random variable.

[0124] The life of a parallel multi-component system at a certain utilization rate is expressed as χ(X1,X2,...,X N |r; α), it is obvious that this is a random variable, and its probability density function, probability cumulative distribution function and failure rate function are: f χ (·|r;α),F χ (·|r; α) and λ χ (·|r; α), where α is the component correlation parameter and r is the utilization rate of the system.

[0125] For a parallel system, χ(X1,X2,...,X N |r;α)=X N:N , which means that the life of a parallel system is determined by the component with the longest life in the system. r is replaced when, or in χ(X1,X2,...,X N |r;α) is replaced at any given moment, depending on which event occurs first. Therefore, the actual life of a multi-component system can be expressed as:

[0126] X TRS =min[χ(X1,X2,...,X N |r;α),T r ] (7)

[0127] Among them, X TRS Indicates the actual life of the system, T r Indicates the time interval for replacing the actual service life of the system;

[0128] ② Two-dimensional expected cost rate model for replacement of service age

[0129] Since the defined two-dimensional preventive maintenance interval is (T0, U0), the actual system service life replacement time interval T r It varies depending on the usage rate and can be expressed as:

[0130]

[0131] Where T0 and U0 represent the preventive maintenance intervals in terms of time and usage, respectively.

[0132] According to the model's assumption ③, the usage U is a linear function of time T, and the coefficient of this function is the usage rate, that is, U = rT. Figure 1 As shown in (a), when r≤U0 / T0, since the utilization rate is at a relatively low value, the system is replaced first in the time dimension, that is, the replacement time interval T r =T0; Figure 1 As shown in (b), when r>U0 / T0, since the usage rate is at a relatively high value, the system is replaced first in the usage dimension, that is, the replacement time interval T r =U0 / r.

[0133] The reliability function of a multi-component system is:

[0134]

[0135] The average replacement time of the system is:

[0136]

[0137] The expected cost rate of a multi-component system during the replacement interval is:

[0138]

[0139] Among them, C f represents the failure replacement cost, C p represents the preventive replacement cost, 0 <C p <C f ; Eα Indicates the average replacement time of the system; C a represents the expected cost rate;

[0140] The FGM Copula function is used to describe the correlation between components, as shown in the following formula:

[0141]

[0142] Among them, 0 <v j <1, j = 1, 2, ..., n, and -1 < α < 1. In particular, when α = 0, it means that there is no correlation between the components.

[0143] Combining equation (9) with equation (12), we can get:

[0144]

[0145] in,

[0146] Combining equation (10) with equation (12), the average replacement time of the system can be obtained as:

[0147]

[0148] Among them, E α Indicates the average replacement time of the system;

[0149] The expected cost rate for a multi-component system between replacements is:

[0150]

[0151] ③ Two-dimensional service life replacement availability model

[0152] If MTTF is defined as the expected length of time the system will continue to operate (the average time the system is operating normally), and MTTR is defined as the expected time required to replace the system, then the system availability is:

[0153]

[0154] Among them, A represents the availability of the system;

[0155] Using a derivation method similar to the expected cost rate, based on the FGM Copula function, the system availability function is obtained as follows:

[0156]

[0157] Among them, T f Indicates the fault replacement time, T p Indicates preventive replacement time, 0 <T p <Tf ;

[0158] At this point, MTTR and MTTF can be expressed as:

[0159]

[0160]

[0161] Formula (17) can be rewritten as:

[0162]

[0163] ④ Cost-effectiveness model

[0164] The cost-effectiveness model that considers the expected cost rate and availability usually refers to a model used to evaluate the balance between cost and benefit of a project or system in a specific field (such as military, engineering projects, health economics, etc.). This model aims to help decision makers determine the most cost-effective solution by quantifying costs and benefits. Its basic model can be constructed using the following formula:

[0165]

[0166] In the present invention, the cost corresponds to the expected cost rate, and the benefit corresponds to the availability, so the cost-effectiveness model of the structure-related two-dimensional maintenance equipment age replacement is:

[0167]

[0168] With the goal of minimizing cost-effectiveness, we seek the best Minimize cost-effectiveness. This is the optimal two-dimensional length of service replacement plan.

[0169] Step 2, solving the constructed multi-component system model;

[0170] Since a two-dimensional service-year replacement strategy is adopted, the time of service-year replacement will change with the change of utilization rate. Figure 2 As shown, the specific steps for solving equation 22 are as follows:

[0171] Step 1: Given a set (T0, U0), calculate r0 = U0 / T0.

[0172] Step 2: When r≤r0, T r =T0, in this case the expected cost rate and expected availability are:

[0173]

[0174]

[0175] Among them, rl is the lower limit of the utilization rate, and G(r) is the cumulative probability distribution function that the utilization rate obeys.

[0176] Step 3: When r>r0, replace [r0,r u ] is evenly divided into k small intervals, where r u is the upper limit of utilization rate, and each small interval is [r a-1 ,r a ),a=1,2,...,k,r a It is expressed as:

[0177]

[0178] Among them, r a represents the upper limit of the utilization rate range, and ideal results can be obtained when a=20; r l Indicates the lower limit of the utilization rate range;

[0179] Step 4: Replace each small interval with the average usage rate of the interval, where the average usage rate of the interval is:

[0180]

[0181] Among them, g(s) is the probability density function of the usage rate; s represents the usage rate in the interval [r a-1 ,r a ] the specific value obtained between;

[0182] Step 5: Calculate the probability that the usage rate falls in each interval using the following formula:

[0183] P a =G(r a )-G(r a-1 ) (27)

[0184] Step 6: Calculate the expected cost rate and expected availability of each cell using the following formula:

[0185]

[0186]

[0187] Step 7: Calculate the interval [r0,r0 when r>r0 u The expected cost rate and expected availability of ] are:

[0188]

[0189]

[0190] Step 8: The total expected cost rate and total expected availability of the system during the two-dimensional service life replacement interval are:

[0191] C a = C exp (1) + C exp (2) (32)

[0192] A = A exp (1) + A exp (2) (33)

[0193] Step 9: Finally, based on C a and A, construct an objective function with the minimum cost - effectiveness ratio:

[0194]

[0195] Step 3, solve the objective function with the lowest cost - effectiveness ratio based on the simulated annealing algorithm;

[0196] The process of solving the above - mentioned minimum cost - effectiveness ratio optimization problem is to solve a global optimization problem with two variables (T0 and U0). The present invention uses the simulated annealing algorithm to solve the above - mentioned optimization problem and calculates the optimal value of F. The simulated annealing algorithm is used to solve the combinatorial optimization problem, and its starting point is based on the similarity between the annealing process of solid substances in physics and general optimization problems. The main steps of using the simulated annealing algorithm to solve the proposed optimization problem are as follows:

[0197] (1) Set the maximum number of iterations ψ max , let ψ = ψ0, where ψ0 is the initial temperature. Randomly generate a set of initial solutions (T0, U0) at the temperature ψ0, and calculate the cost - effectiveness ratio value f1(T0, U0) of this set of solutions through the calculation formula (Equation 34) of the cost - effectiveness ratio F;

[0198] (2) Let the current temperature ψ be equal to the next value ψ1 in the cooling schedule;

[0199] (3) Calculate f1(T1, U1) under the current solution (T1, U1), randomly generate a new solution (T2, U2) near the current solution, and calculate the cost - effectiveness ratio value f1(T2, U2) of this set of solutions;

[0200] (4) If f1(T2, U2) < f1(T1, U1), then accept the new solution (T2, U2); if f1(T2, U2) ≥ f1(T1, U1), then calculate △f = f1(T2, U2) - f1(T1, U1), let l = exp(-△f / ψ1), and then randomly generate a random number uniformly distributed in the interval [0, 1] If then accept the new solution (T2, U2);

[0201] (5) Repeat steps 4.2 to 4.4 for L times;

[0202] (6) Determine whether the current number of iterations L reaches the set maximum number of iterations ψ max , if yes, exit the iteration, otherwise return to step 4.2 to continue the iteration.

[0203] Below is pseudocode for the simulated annealing algorithm that solves this model.

[0204] Table 1 Pseudo code of simulated annealing algorithm

[0205]

[0206] Example

[0207] In order to verify the effect of the present invention, the following case is used for verification.

[0208] 1. Case Problem Description

[0209] Take a new equipment fuel filter as an example for analysis. The data in the case are all from the manufacturer and reliability test. The fuel filter is used to filter out fine impurities and water in the diesel, and provide clean diesel to the injection pump and injector to ensure their reliable operation. The fuel filter is composed of two filters in parallel. Each filter is composed of a filter cover (two made into one), a filter body, a filter element, a gasket, a spring and a sealing ring, etc. Figure 3 shown.

[0210] The main failure mode of the fuel filter is that the fuel filter becomes clogged and dirty, resulting in insufficient fuel supply, and ultimately insufficient starting power or even failure to start, causing the vehicle to become paralyzed. Therefore, the fuel filter should be replaced at regular intervals or after a certain mileage. This case is used to determine the optimal two-dimensional service life replacement interval for the fuel filter, so that the expected cost rate of the fuel filter is minimized or the availability is maximized.

[0211] This embodiment constructs the failure rate function of the filter based on the accelerated failure time (AFT) model. Lawless uses the concept of accelerated failure time and proportional hazards models to construct the impact of usage rate on system failure. This method has a certain theoretical basis and is relatively mature in application.

[0212] Assume T s and T r Respectively represent the design utilization rate r s and the time to first failure under utilization rate r, the relationship between them is:

[0213]

[0214] Assumptions The design utilization rate is r s The cumulative failure distribution function under s and represent the scale parameter and shape parameter of the fault distribution under the design utilization rate respectively.

[0215] When the utilization rate is r, the cumulative failure distribution function of the system is the same as the cumulative failure distribution function of the system under the design utilization rate, but the scale parameter has changed:

[0216]

[0217] Among them, the AFT parameter γ≥1.

[0218] Based on this, the cumulative failure distribution function of the system when the utilization rate is r is expressed as:

[0219]

[0220] There is a two-component system with two identical components connected in parallel, and the utilization rate of the system follows a uniform distribution. s Under this condition, the cumulative failure distribution function of a single component is:

[0221]

[0222] When the utilization rate is r, the cumulative failure distribution function of a single component is:

[0223]

[0224] The fuel fine filter is mainly composed of two filters connected in parallel. From formula (13), we can know:

[0225]

[0226]

[0227] The other parameter settings of the fuel filter are shown in Table 2.

[0228] Table 2 Parameter settings

[0229]

[0230] 2. System Optimal Two-Dimensional Service Length Replacement Solution

[0231] According to the parameter values ​​set in Table 2, according to the above model solving steps (step 1 to step 9), the expected cost rate and availability of the system during the replacement interval are obtained as follows: Figure 4 and Figure 5 shown.

[0232] Figure 4 The expected cost rate of the system during the replacement interval varies with the two-dimensional replacement interval. Figure 4 It can be seen that the expected cost rate of the system is jointly affected by T0 and U0, and there is an optimal two-dimensional replacement interval (T0, U0) that minimizes the expected cost rate of the system during the replacement interval. Figure 5 The variation of the system availability during the replacement interval with the two-dimensional replacement interval is shown. Similar to the expected cost rate, the system availability is affected by both T0 and U0. There is an optimal two-dimensional replacement interval (T0, U0) that makes the system availability the highest during the replacement interval.

[0233] In order to more intuitively show the changes of expected cost rate and availability with the 2D replacement interval, Figure 4 and Figure 5 Perform dimensionality reduction analysis, that is, fix one dimension of the two-dimensional replacement interval and observe how the expected cost rate or availability changes with the value of the other dimension. First, perform dimensionality reduction analysis on the expected cost rate, such as Figure 6 Then, the system availability is analyzed by dimensionality reduction, as shown in Figure 7 shown.

[0234] Figure 6 (a) shows the change of expected cost rate with T0 when U0 = 5000 km is fixed. When the value of T0 is 1.05 years, the expected cost rate reaches the minimum value of 69004 yuan / year. Figure 6 (b) shows the expected cost rate changes with U0 when T0 is fixed at 1 year. When the value of U0 is 13000 km, the expected cost rate reaches the minimum value of 64497 yuan / year.

[0235] Figure 7 (a) shows the variation of system availability with T0 when U0 = 5000 km. When T0 is 1.2 years, the system availability reaches a maximum value of 0.71106. Figure 7 (b) shows the variation of system availability with U0 when T0 is fixed to 1 year. When the value of U0 is 11000 km, the system availability reaches the maximum value of 0.693.

[0236] In order to find the optimal two-dimensional replacement interval of the system, the optimal two-dimensional service age replacement plan is solved based on the simulated annealing algorithm with the lowest cost-effectiveness as the decision-making goal. The basic parameter settings of the simulated annealing algorithm are shown in Table 3.

[0237] Table 3 Simulated annealing algorithm parameters

[0238]

[0239] The value range of U0 is (0KM, 10×104 KM), the range of T0 is (0 years, 5 years). Set the initial value of the two-dimensional service life replacement interval (T0, U0) to (5×10 4 KM, 2years). The simulated annealing algorithm search process is as follows Figure 8 As shown in the figure, the optimal two-dimensional service life replacement plan is (1×10 4 KM, 2years), as shown in Table 4.

[0240] Table 4 Cost-effectiveness ratio of different two-dimensional service life replacement schemes

[0241]

[0242] (Table 4 continued)

[0243]

[0244]

[0245] 2.C p , C f and T p 、T f Impact Analysis

[0246] In order to explore C p , C f The influence of the value of on the optimal two-dimensional service life replacement time, fixed U0 = 5000KM, changing C p , C f The expected cost rate of the system changes with the replacement time, as shown in the figure. Fix U0 = 5000KM again and change T p 、T f , and observe how the system availability changes with the replacement time, such as Figure 8 shown.

[0247] pass Figure 8 (a) It can be seen that as the preventive replacement cost increases, the system service life replacement time T0 becomes larger. That is to say, when formulating a maintenance plan, if the preventive replacement cost is high, the planned replacement time should be relatively delayed, because frequent replacement at this time will lead to an increase in the expected cost rate, which is not conducive to the manufacturer's saving of maintenance costs. As the corrective replacement cost increases, the system service life replacement time T0 becomes smaller. That is to say, when formulating a maintenance plan, if the corrective replacement cost is high, the planned replacement time should be relatively advanced. At the same time, it can be seen that higher corrective maintenance costs will cause the expected cost rate of system maintenance to increase.

[0248] pass Figure 8(b) It can be seen that as the preventive replacement time increases, the system service life replacement time T0 becomes larger. That is to say, when formulating a maintenance plan, if the preventive replacement time is long, the planned replacement time should be relatively delayed, because frequent replacement at this time will lead to a longer cumulative downtime and reduce system availability. As the corrective replacement time increases, the system service life replacement time T0 becomes smaller. That is to say, when formulating a maintenance plan, if the corrective replacement time is long, the planned replacement time should be relatively advanced. At the same time, it can be seen that a higher corrective maintenance time will cause a decrease in system availability.

[0249] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for decision-making on replacement of structure-related two-dimensional maintenance equipment based on service life, characterized in that: The following steps are involved: Step 1: Construct a multi-component system model for two-dimensional warranty based on the structural correlation between the components; Step 2: Solve the multi-component system model of two-dimensional maintenance to obtain the total expected cost rate and total expected availability of the system within the two-dimensional service life replacement interval, and use the minimum cost-effectiveness ratio as the optimization objective function based on the obtained total expected cost rate and total expected availability; Step 3: Solve the optimization objective function with the minimum cost-effectiveness ratio based on the simulated annealing algorithm to obtain the optimal cost-effectiveness ratio; Step 4: Based on the optimal cost-effectiveness calculated in step 3, formulate a replacement plan for the two-dimensional warranty equipment.

2. A method for decision-making on replacement of structure-related two-dimensional maintenance equipment according to claim 1, characterized in that: The specific steps of step 1 include: Step 1.1: Give the model establishment assumptions; Step 1.2: Based on the assumptions, build the following models: 1) System life model X TRS =min[χ(X1,X2,...,X N |r;a),T r ] Among them, X TRS Indicates the actual life of the system, T r Indicates the time interval for replacing the actual service life of the system, x N represents the component life, α represents the component correlation parameter, r represents the system utilization rate, χ(X1,X2,...,X N |r; α) indicates that the life of the parallel system is determined by the component with the longest life in the system; 2) Expected cost rate model Among them, C f represents the failure replacement cost, C p represents the preventive replacement cost; and, Among them, T0 and U0 represent the preventive maintenance intervals in terms of time and usage, respectively; F j represents the cumulative distribution function of component j’s life probability; 3) Availability model Among them, T f Indicates the fault replacement time, T p Indicates preventive replacement time, 0 <T p <T f . 4) Cost-effectiveness model F=C a (T r ;a) / A(T r ;a).

3. A method for decision-making on replacement of structure-related two-dimensional maintenance equipment according to claim 2, characterized in that: The assumptions for step 1.1 include: Assumption 1: The system consists of multiple components in parallel; Assumption 2: Multi-component systems are unrepairable and have increasing failure rates; Assumption 3: The usage rate of the same user remains unchanged; the usage rate of different users is a random variable that follows a distribution; Assumption 4: Failure response time is negligible, that is, replacement is performed immediately after failure; Assumption 5: The degradation of components and their corresponding degradation states are not considered; Assumption 6: The replaced components are new and independent of each other.

4. A method for decision-making on replacement of structure-related two-dimensional maintenance equipment according to claim 3, characterized in that: The specific steps of step 2 include: Step 2.1: Given a set (T0, U0), calculate r0 = U0 / T0; Step 2.2: When r≤r0, T r =T0, the expected cost rate C at this time is solved by the following formula exp (1) and expected availability A exp (1): Among them, r l is the lower limit of the utilization rate, G(r) is the cumulative probability distribution function that the utilization rate obeys; Step 2.3: When r>r0, replace [r0,r u ] is evenly divided into k small intervals, where r u is the upper limit of utilization rate, and each small interval is [r a-1 ,r a ),a=1,2,...,k,r a It is expressed as: Among them, r a Indicates the upper limit of the utilization rate range, r l Indicates the lower limit of the utilization rate range; Step 2.4: Replace each small interval with the average utilization rate of the interval. The average utilization rate of the interval can be expressed as: Among them, g(s) is the probability density function of the usage rate; s represents the usage rate in the interval [r a-1 ,r a ] the specific value obtained between; Step 2.5: The probability that the usage rate falls in each interval is: P a =G(r a )-G(r a-1 ); Step 2.6: Calculate the expected cost rate and expected availability of each cell using the following formula: Step 2.7: Calculate the expected cost rate C at this time by the following formula: exp (2) and expected availability A exp (2) is: Step 2.8: Based on C exp (1) A exp (1) C exp (2) and A exp (2), the total expected cost rate and total expected availability of the system during the two-dimensional service life replacement interval are obtained as follows: C a =C exp (1)+C exp (2) A=A exp (1)+A exp (2); Step 2.9: Based on C a and A, establish the objective function with the minimum cost-effectiveness ratio:

5. A method for decision-making on replacement of structure-related two-dimensional maintenance equipment according to claim 4, characterized in that: Step 3: The specific steps for solving the minimum cost-effectiveness ratio include: Step 3.1: Set the maximum number of iterations ψ max , let ψ=ψ0, where ψ0 is the initial temperature, randomly generate a set of initial solutions (T0, U0) at temperature ψ0, and calculate the cost-effectiveness value f1(T0, U0) of this set of solutions through the calculation formula of cost-effectiveness F; Step 3.2: Let the current temperature ψ be equal to the next value ψ1 in the cooling schedule; Step 3.3: Calculate f1(T1,U1) under the current solution (T1,U1), and randomly generate a new solution (T2,U2) near the current solution, and calculate the cost-effectiveness ratio f1(T2,U2) under this group of solutions; Step 3.4: If f1(T2, U2) < f1(T1, U1), then accept the new solution (T2, U2); if f1(T2, U2) ≥ f1(T1, U1), then calculate Δf = f1(T2, U2) - f1(T1, U1), let l = exp(-Δf / ψ1), and then randomly generate a random number that follows a uniform distribution in the interval [0, 1] If then accept the new solution (T2, U2); Step 3.5: Repeat steps 3.2 to 3.4 L times; Step 3.6: Determine whether the current number of iterations L reaches the set maximum number of iterations ψ max , if yes, exit the iteration, otherwise return to step 3.2 to continue the iteration.

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