A Joint Decision-Making Method for Preventive Maintenance and Production Scheduling in a Hybrid Flow Shop

Abstract

The present invention discloses a joint decision-making method for preventive maintenance and production scheduling in a hybrid flow shop, which relates to a data processing method and an optimization solution method for a joint scheduling model of a hybrid assembly line. The present invention aims at low total costs of machine maintenance costs and workpiece earliness / tardiness penalties, few system downtime periods, and relatively small impacts of unexpected machine failures; by comprehensively considering the different impacts of unexpected failures of different machines on production and the impact of economic correlation between equipment on maintenance costs during the joint scheduling process of the hybrid assembly line, taking the sum of equipment maintenance costs and workpiece earliness / tardiness penalty costs as the objective function, an embedded simulation particle swarm-genetic algorithm is used to solve the scheduling order of each workpiece and the maintenance time points of each equipment, which can reduce the number and cost of system maintenance and improve the on-time completion rate of workpieces.

Description

Technical Field

[0001] The present invention relates to the field of preventive maintenance and production joint scheduling in a hybrid flow shop, and specifically to a joint scheduling method for production and maintenance of a mixed-flow production line that simultaneously considers preventive opportunistic maintenance and production scheduling. Technical Background

[0002] The maintenance and scheduling management of a hybrid flow shop are two important execution links that affect the performance of the production line. To enable the sound development of China's manufacturing industry, in addition to expanding the production scale of each industry, it is also necessary to pay attention to the production efficiency of the production system and strengthen the two core technologies of production system maintenance management and scheduling management. Production scheduling and equipment maintenance directly affect key factors such as the production cost, delivery date, and product quality of an enterprise. For a long time, the maintenance management and production scheduling management of a hybrid flow shop have been considered separately, but there is an inseparable connection between equipment maintenance and production scheduling. Production scheduling affects the failure rate of equipment, while equipment maintenance activities affect normal production activities. Considering these two parts separately may lead to problems such as management conflicts and increased production costs. Therefore, it is very necessary to consider equipment maintenance and production scheduling simultaneously.

[0003] The current research on the preventive maintenance and production joint scheduling of a hybrid flow shop mainly combines the individual preventive maintenance of equipment with production scheduling. This model has poor flexibility and unsatisfactory optimization effects. The existing joint scheduling models for hybrid flow shops do not consider the impact of different costs when different equipment fails unexpectedly on the maintenance cost. The prior art discloses Li Youtang, Huang Zhaokun. Multi-objective dynamic maintenance of series-parallel production systems under multi-resource constraints [J]. Journal of Lanzhou University of Technology, 2021, 47(02): 26-31, which only considers the impact of differences in human resources, spare parts inventory, and the key degree of the process where the equipment is located on the maintenance cost after equipment failure. At the same time, the existing joint scheduling models do not consider the difference in the maintenance resource scheduling cost between equipment preventive maintenance and post-failure minor repair, so that the joint scheduling scheme is not ideal in practical applications. Summary of the Invention

[0004] Aiming at the deficiencies of the existing joint decision-making model for preventive maintenance and production scheduling in a hybrid flow shop, the present invention proposes a joint scheduling method for opportunistic maintenance and production of a mixed-flow production line. This method takes minimizing the equipment maintenance cost and minimizing the total workpiece earliness / tardiness penalty cost as the optimization objectives, establishes a mathematical model, and optimizes and solves to obtain the production scheduling scheme and the equipment maintenance time points during the scheduling period, realizing the joint management of maintenance and production scheduling in a hybrid flow shop.

[0005] The technical solution of the present invention is a joint decision-making method for preventive maintenance and production scheduling in a hybrid flow shop, which includes the following steps:

[0006] Step 1: Based on the collected equipment performance degradation data, obtain the reliability function and failure rate function of the equipment;

[0007] Step 2: Calculate the equipment maintenance priorities among different processes according to the equipment differences;

[0008] Step 3: Establish a joint scheduling model for the hybrid flow shop according to the equipment maintenance requirement priorities obtained in Step 2;

[0009] Step 3.1: Determine the constraints of the joint scheduling model;

[0010] Step 3.2: Conduct preventive maintenance modeling and update the initial scheduling sequence;

[0011] Step 3.2.1: Assume that the machine failure rate function follows a two-parameter Weibull distribution: Then the machine reliability function is: where t represents the equipment service age. Assume that when there is Then the system performs the j-th maintenance shutdown. Denote β j,xy = 1, T j = t, n s = n s + 1. Conduct opportunistic maintenance judgment for all processes where o i ≥ o x :

[0012]

[0013] The equipment status factor β j,xy represents whether the equipment E xy performs maintenance activities during the j-th shutdown maintenance of the system. Among them, for all processes with order o i < o x let β j,xy = 0;

[0014] Among them, represents taking any value. φ represents the shape parameter in the Weibull distribution, φ > 0, η represents the scale parameter in the Weibull distribution, η > 0, R xy (t) represents the reliability function of the equipment E xy , C xy[l] represents the end time of the O xy[l] process, R pt represents the equipment preventive maintenance threshold, T j represents the j-th preventive maintenance time of the system, E xy represents the y-th equipment of the x-th process, n s represents the total number of system shutdowns, with an initial value of 0, represents the service life of the yth equipment in process x at time t, R ot Indicates the equipment opportunity maintenance threshold;

[0015] Step 3.2.2: Use the virtual age model to model the maintenance effect. After the jth shutdown maintenance of the system, according to the equipment status factor β j,xy Update after the jth maintenance t=t+T m The virtual service life of the equipment at a certain time, T m Indicates the average maintenance time of equipment:

[0016] ①β j,xy =0, that is, during the jth system maintenance, the device E xy No maintenance:

[0017]

[0018] ②β j,xy =1, that is, during the jth system maintenance, the device E xy To perform maintenance:

[0019]

[0020] ε x is the service life improvement factor, which is used to describe the reliability change of equipment after imperfect maintenance. x The same and constant value, 0<ε x <1;

[0021] Step 3.2.3: Start processing time S xy[l] and completion time C xy[l] renew:

[0022]

[0023]

[0024] Among them, T j represents the jth preventive maintenance time of the system;

[0025] Step 3.3: Construct the joint scheduling model objective function;

[0026] (1) Calculate the total equipment maintenance cost C m :

[0027] C m =C dm +C pm

[0028] in,

[0029]

[0030]

[0031] Among them, c us When representing the minor repair cost of the equipment, the emergency scheduling cost for minor repair after a failure needs to be considered. c s When representing the preventive maintenance cost of the equipment, the preventive maintenance scheduling cost needs to be considered. C dm Represents the total cost of minor repair after the event. C pm Represents the total cost of preventive maintenance. m represents the total number of processes, and n x Represents the total number of equipment. n xy Represents the expected number of accidental failures of the y-th equipment in process x, with an initial value of 0. Represents the minor repair cost of the equipment in process x. c s Represents the single maintenance scheduling cost. Represents the equipment maintenance cost in process x;

[0032] (2) Calculate the total earliness / tardiness penalty cost C ta :

[0033]

[0034]

[0035] Among them, Represents the expected completion time of workpiece J i . Represents the unit tardiness penalty cost of workpiece J i . Represents the unit earliness penalty cost of workpiece J i . x ixy[l] Represents workpiece J i Is 1 when processed at the l-th position of the y-th equipment in process x, otherwise 0;

[0036] (3) Objective function:

[0037] min(Cost) = min(C ta + C m ) ;

[0038] Step 4: Calculate the workpiece scheduling sequence and maintenance time point when the objective function is minimized. The workpiece scheduling sequence is determined by the start processing time S xy[l] and the completion time C xy[l] of each workpiece. The equipment maintenance time point is jointly determined according to T j and β j,xy ;

[0039] Furthermore, the specific method of Step 1 is:

[0040] Step 1.1: Analyze the failure mechanism of the device, and determine the degradation characteristic quantity and failure threshold D that can reflect the performance degradation of the product f ;

[0041] Step 1.2: Collect the degradation data of n devices at times t 1 , t 2 ......, t m . According to the trend of the performance degradation curve, select an appropriate degradation model to describe it;

[0042] Step 1.3: According to the collected device performance degradation data, use the least squares method to estimate the parameters of each sample performance degradation model, and obtain the degradation trajectory of each sample;

[0043] Step 1.4: According to the failure threshold D f and the obtained degradation models of each sample, extrapolate to find the failure time T 1 , T 2 ....., T n ;

[0044] Step 1.5: Use the Weibull distribution to fit the probability density function f(t) of the failure time of the device; according to the extrapolated failure time data, find the shape parameter φ and scale parameter η in the Weibull distribution by the maximum likelihood estimation method:

[0045] Step 1.5.1: Probability density function f(t):

[0046]

[0047] Step 1.5.2: Construct the likelihood function:

[0048]

[0049] where T n represents the failure time of the nth sample obtained by extrapolation;

[0050] Step 1.5.3: Parameter calculation:

[0051]

[0052]

[0053] From this calculation, the maximum likelihood estimators of η and φ can be obtained Then:

[0054]

[0055] Step 1.6: Device reliability function and failure rate function;

[0056] Calculate the reliability function according to the reliability theory:

[0057]

[0058] Failure rate function:

[0059]

[0060] Furthermore, the specific method of step 2 is as follows:

[0061] Step 2.1: Construct a judgment matrix among the differential elements of the equipment;

[0062] In a mixed flow shop, the consequences of unexpected failures of different equipment mainly consider the following three elements: the impact of equipment failures in different processes on product quality is different, the minor repair prices are different, and the difficulty of purchasing parts is different; through the analytic hierarchy process, the above three equipment differential elements are integrated, the weight coefficients of each element are solved, and the judgment matrix J of the relative importance among each element is constructed as follows:

[0063]

[0064] Among them, each element in J represents the importance of one equipment differential element relative to another equipment differential element. For example, u 12 represents the importance of the impact of equipment failure on product quality relative to the minor repair price of the equipment;

[0065] Step 2.2: Calculate the maintenance priorities of the equipment for each process;

[0066] After constructing the judgment matrix among the differential elements of the equipment, calculate the maximum eigenvalue ζ max , and substitute it into the system of equations:

[0067]

[0068] Among them, ζ represents the maximum eigenvalue of the judgment matrix J, and α 1 , α 2 , α 3 represent the weight coefficients of the three equipment differential elements;

[0069] Solve the eigenvector corresponding to ζ max through this system of equations, and normalize the eigenvector, that is, obtain the weight coefficients of the equipment differential elements. Then the equipment maintenance demand coefficient is:

[0070] γ x =q x α 1 +p x α 2 +b x α3

[0071] Among them, q x represents the impact factor of equipment failure in process x on product quality, and p x represents the minor repair price factor of the equipment in process x, and b x represents the difficulty factor of purchasing equipment parts in process x;

[0072] Maintenance requirement coefficient γ x The larger it is, the more serious the consequences are after the equipment in this process has a random failure. Therefore, its maintenance priority is higher, and when performing preventive maintenance, it is necessary to give priority to opportunistic maintenance of the equipment in this process; for [γ 1 , γ 2 , γ 3 .....γ m is sorted, and o x represents the maintenance priority of the equipment for each process. The larger γ x , the higher o x . According to the sorting, the maintenance priorities corresponding to the equipment for each process are obtained.

[0073] Furthermore, the specific calculation method of the adaptive population allocation factor and the parallel particle swarm-genetic hybrid algorithm for the adaptation problem model in step 4 are as follows:

[0074] Step 4.1: Use the double-chromosome form to represent the encoding of the feasible solution. Initialize the population according to step 3.1. At the same time, divide the population into two sub-populations according to the adaptive population allocation factor. One sub-population is updated using the particle swarm algorithm, and one sub-population is updated using the genetic algorithm. The calculation formula of the adaptive population allocation factor is as follows:

[0075]

[0076]

[0077] When the population size is N, KN individuals in the population form sub-population 1 and enter the particle swarm algorithm for update, and the remaining individuals form sub-population 2 and enter the genetic algorithm for update;

[0078] Step 4.2: Construct an improved particle swarm algorithm to optimize sub-population 1 in step 4.1;

[0079] Step 4.2.1: Calculate the fitness of each particle through the preventive maintenance model simulation established in step 3.2 according to the maintenance threshold combination and update the start / finish time of each workpiece obtained by decoding;

[0080] Step 4.2.2: Adaptive weight update;

[0081] Step 4.2.3: Particle velocity update and position update;

[0082] Step 4.3: Construct an improved genetic algorithm to optimize sub-population 2 in Step 4.1;

[0083] Step 4.3.1: According to the maintenance threshold combination, simulate and calculate the fitness of each chromosome through the preventive maintenance model established in Step 3.2, and update the start / finish time of each workpiece obtained by decoding;

[0084] Step 4.3.2: Use the method of stochastic competitive selection for chromosome selection operation and introduce the elite retention strategy;

[0085] Step 4.3.3: Use the single-point crossover method for crossover operation;

[0086] Step 4.3.4: Chromosome mutation operation;

[0087] Step 4.4: Merge sub-population 1 and sub-population 2;

[0088] Step 4.5: Determine whether the current population has reached the maximum number of iterations. If so, execute Step 4.6; otherwise, continue with Step 4.1;

[0089] Step 4.6: Obtain the workpiece scheduling sequence and maintenance time points under the optimal maintenance threshold combination.

[0090] The present invention proposes a method for joint decision-making of preventive opportunistic maintenance and production scheduling in a hybrid flow shop. Based on considering different maintenance resource scheduling costs, this method establishes a preventive opportunistic maintenance strategy based on maintenance priorities according to the impact degree of unexpected failures of different equipment on production, and integrates it into the production scheduling model to form a joint scheduling model. At the same time, according to the characteristics of the model, a parallel adaptive particle swarm-genetic hybrid algorithm embedded with simulation is designed to optimize the equipment maintenance cost and the workpiece earliness / tardiness penalty cost, so as to realize the optimal management of the hybrid flow shop. Description of the Drawings

[0091] Figure 1 It is a flow chart of the particle swarm-genetic algorithm embedded with simulation;

[0092] Figure 2 It is a flow chart of the simulation algorithm;

[0093] Figure 3 It is a flow chart of the specific implementation manner of the method of the present invention. Detailed Description of the Invention

[0094] The following is a detailed description of the embodiments of the present invention ( Figure 3) This example routine is implemented on the premise of the technical solution of the present invention, and detailed implementation methods and specific operation processes are given. However, the protection scope of the present invention is not limited to the following example routine.

[0095] The example routine can be mainly divided into the following steps:

[0096] Step 1: Obtain the reliability function based on the historical degradation data of each device.

[0097] Step 1.1: Analyze the failure mechanism of the device, and determine the degradation characteristic quantity and failure threshold D that can reflect the performance degradation of the product f .

[0098] Step 1.2: Collect the degradation data of n devices at times t 1 , t 2 ......, t m . According to the trend of the performance degradation curve, select an appropriate degradation model to describe it.

[0099] Step 1.3: According to the collected device performance degradation data, use the least squares method to estimate the parameters of each sample performance degradation model, and obtain the degradation trajectory of each sample.

[0100] Step 1.4: According to the failure threshold D f and the obtained degradation models of each sample, extrapolate to find the failure time T 1 of each sample, T 2 ....., T n .

[0101] Step 1.5: Use the Weibull distribution to fit the failure time probability density function f(t) of the device. According to the extrapolated failure time data, find the shape parameter φ and scale parameter η in the Weibull distribution by the maximum likelihood estimation method:

[0102] (1) Probability density function f(t)

[0103]

[0104] (2) Construct the likelihood function

[0105]

[0106] (3) Parameter calculation

[0107]

[0108] From this calculation, the maximum likelihood estimators of η and φ can be obtained Then:

[0109]

[0110] Step 1.6: Equipment reliability function and failure rate function

[0111] According to reliability theory, the reliability function can be obtained as follows:

[0112]

[0113] Step 2: Calculate the equipment maintenance priority.

[0114] Step 2.1: Construct a judgment matrix among the three elements of the impact degree of equipment failure on product quality, the price of minor repairs, and the difficulty of purchasing parts;

[0115]

[0116] where u ij represents the importance degree of the difference of the i-th equipment compared to the difference of the j-th equipment. u ij The value scale and meaning are as follows:

[0117]

[0118] Step 2.2: Calculate the maximum eigenvalue ζ max ;

[0119] Step 2.3: Substitute the maximum eigenvalue ζ max into the system of equations:

[0120]

[0121] Solve for the eigenvector corresponding to the maximum eigenvalue, and normalize the eigenvector to obtain the weight coefficient of the equipment difference elements.

[0122] Step 2.4: According to the normalized values of the three elements of each equipment, the maintenance requirement coefficient of each equipment is obtained as:

[0123] γ x = q x α 1 + p x α 2 + b x α 3

[0124] Step 2.5: Sort [γ 1 , γ 2 , γ 3 .....γ m , and use o x (o x ∈{0, 1....m - 1}) to represent the maintenance priority of each process equipment. The larger γ x , the larger o xThe higher it is, the maintenance priorities corresponding to the equipment of each process can be obtained according to the sorting.

[0125] Step 3: Determine the model constraints.

[0126] (1) In any process, each workpiece can only occupy one processing position of one machine

[0127]

[0128] (2) In any process, any position of any machine can only process one workpiece

[0129]

[0130] (3) The standard processing time of the workpiece process corresponding to the l-th processing position of the y-th equipment in process x

[0131]

[0132] (4) The start processing time of a process shall not be earlier than the completion time of the previous process on this equipment

[0133]

[0134] (5) The start processing time of a process shall not be earlier than the completion time of the previous process of this workpiece

[0135]

[0136] (6) The end time of the workpiece process corresponding to the l-th processing position of the y-th equipment in process x

[0137] C xy[l] ≥S xy[l] +p xy[l]

[0138] (7) Equipment preventive maintenance threshold and opportunistic maintenance threshold constraints

[0139] 0≤R pt ,R ot ≤1

[0140] R pt <R ot

[0141] (8) System maximum completion time

[0142] C mk =max{C my[l]}

[0143] Step 4: Construct a parallel particle swarm-genetic algorithm with embedded simulation for optimization and solution ( Figure 1 )。

[0144] Step 4.1: Initialize the maintenance threshold combination according to the model constraints determined in Step 3;

[0145] Step 4.2: Initialize the scheduling scheme population according to the model constraints determined in Step 3;

[0146] Step 4.3: Divide the population into two sub - populations. One sub - population is updated using the particle swarm algorithm, and the other sub - population is updated using the genetic algorithm. In order to improve the local search ability of the algorithm when the population is relatively dispersed and improve the global search ability of the algorithm when the population is relatively concentrated, an adaptive allocation factor is used for population division:

[0147]

[0148]

[0149] When the population size is N, KN individuals in the population enter the particle swarm algorithm for updating, and the remaining individuals enter the genetic algorithm for updating.

[0150] Step 4.4: Sub - population 1 iterates using the improved particle swarm algorithm;

[0151] Step 4.4.1: Calculate the fitness of each particle through simulation ( Figure 2 );

[0152] (1) When , there is Then the system performs the j - th maintenance shutdown, record T j = t, n s = n s +1, and perform opportunistic maintenance judgment on all processes where o i ≥ o x :

[0153]

[0154] The equipment status factor β j,xy represents whether the equipment E xy performs maintenance activities during the j - th shutdown maintenance of the system. Among them, for all processes with order o i < o x , let β j,xy = 0.

[0155] (2) After the j - th shutdown maintenance of the system, update the service age of the equipment at time t = t + T j,xy after the j - th maintenance according to the equipment status factor β m :

[0156] ①β j,xy = 0, that is, during the j - th system maintenance, the equipment E xyNo maintenance:

[0157]

[0158] ②β j,xy = 1, that is, during the jth system maintenance, equipment E xy Performs maintenance:

[0159]

[0160] ε x Is the service age improvement factor, used to describe the reliability transformation situation after imperfect maintenance of the equipment. The equipment ε within the same process x Is the same and is a fixed value, 0 < ε x < 1.

[0161] (3) Start processing time S xy[l] And completion time C xy[l] Update:

[0162]

[0163]

[0164] (4) Expected number of accidental failures of equipment E xy :

[0165]

[0166] Among them Represents the service age of machine E xy At time C mk Service age.

[0167] Calculate the total cost of machine maintenance C m :

[0168] C m = C dm + C pm

[0169] Among them:

[0170]

[0171]

[0172] (6) Calculate the total earliness / tardiness penalty cost C of the workpiece ta :

[0173]

[0174] Among them:

[0175]

[0176] (7) Calculate the fitness f:

[0177] f = C ta + C m

[0178] Step 4.4.2: Update ω using a non - linear dynamic inertia weight coefficient formula:

[0179]

[0180] Step 4.4.3: Update the particle velocity and position:

[0181]

[0182] x id (t + 1)= x id (t)+ v id (t + 1)

[0183] Step 4.4.3: Since the particle swarm algorithm is for continuous variables, real numbers will be generated during the search process, and illegal solutions often occur. Therefore, after one optimization operation, the updated particles need to be adjusted to correct the illegal solutions:

[0184] (1) Round down each encoding

[0185] (2) Remove the still illegal solutions in the encoding

[0186] (3) Randomly generate chromosome pairs according to the encoding rules to complete the solutions removed in (2)

[0187] Step 4.5: Sub - population 2 iterates using the improved genetic algorithm;

[0188] Step 4.5.1: Calculate the fitness of each chromosome through simulation, and the calculation method is the same as that in Step 4.4.1;

[0189] Step 4.5.2: Use the method of random competition selection for the selection operation, so that the greater the fitness of the chromosome, the greater the probability of being retained. Randomly select a certain number of chromosomes as the new parents, and at the same time introduce the elite retention strategy to directly introduce a certain number of high - quality solutions into the next generation to accelerate the convergence speed of the algorithm;

[0190] Step 4.5.3: Perform the crossover operation using the single-point crossover method. Since the encoding in this paper needs to maintain certain constraints: the first-dimensional encoding, which represents the processing equipment codes selected by the workpiece at each process, requires that the values of each element are not greater than the number of equipment in its corresponding process; the second-dimensional encoding, which represents the processing sequence codes of the workpiece at each process, requires that the values of each element are unique in its corresponding column. Therefore, for the first-dimensional encoding, randomly select the vertical crossover and horizontal crossover methods for the single-point crossover operation, and for the second-dimensional encoding, use the vertical crossover method for the single-point crossover operation;

[0191] Step 4.5.4: Randomly select two genes to exchange their order to achieve the mutation effect. From the above encoding constraints, it can be seen that only row gene mutation can be performed on the first-dimensional encoding, and both row and column mutations can be performed on the second-dimensional encoding;

[0192] Step 4.6: Merge population 1 and population 2 and determine whether the current population meets the termination condition. If not, continue with step 4.3; otherwise, stop the iteration;

[0193] Step 4.7: Output the optimal combined scheduling plan.

Claims

1. A joint decision-making method for preventive maintenance and production scheduling in a hybrid flow shop, the method comprises the following steps: Step 1: According to the collected equipment performance degradation data, obtain the reliability function and failure rate function of the equipment; Step 2: Calculate the equipment maintenance priorities between processes according to equipment differences; Step 3: Establish a joint scheduling model for the hybrid flow shop according to the equipment maintenance requirement priorities obtained in Step 2; Step 3.1: Determine the constraints of the joint scheduling model; Step 3.2: Conduct preventive maintenance modeling and update the initial scheduling order; Step 3.2.1: Assume that the machine failure rate function follows a two-parameter Weibull distribution: Then the machine reliability function is: where t represents the equipment service age. Assume that when there is Then when the system performs the j-th maintenance shutdown, denote β j,xy = 1, T j = t, n s = n s + 1, and perform opportunistic maintenance judgment on all processes where o i ≥ o x : Device status factor β j,xy Indicates that when the system performs the j-th shutdown maintenance, device E xy Whether maintenance activities are carried out, where for order o i <o x All process orders β j,xy = 0; Among them, represents taking any value, φ represents the shape parameter in the Weibull distribution, φ > 0, η represents the scale parameter in the Weibull distribution, η > 0, R xy (t) represents the reliability function of device E xy ; C xy[l] represents the end time of operation O xy[l] ; R pt represents the preventive maintenance threshold of the device; T j represents the time of the jth preventive maintenance of the system; E xy represents the yth device of process x; n s represents the total number of system downtimes, with an initial value of 0; represents the age of the yth device of process x at time t; R ot represents the opportunistic maintenance threshold of the device; Step 3.2.2: Model the maintenance effect using the virtual service age model. After the j-th shutdown maintenance of the system, according to the equipment status factor β j,xy Update the virtual service age of the equipment at time t = t + T after the j-th maintenance, where T m represents the average maintenance time of the equipment: m ​ ①β j,xy = 0, that is, during the j-th system maintenance, device E xy is not maintained: ②β j,xy = 1, that is, during the j-th system maintenance, device E xy is maintained: ε x is the age improvement factor, used to describe the reliability transformation after imperfect maintenance of the equipment. The equipment ε within the same process x is the same and is a fixed value, 0 < ε x < 1; Step 3.2.3: Start processing time S xy[l] and completion time C xy[l] Update: Among them, T j represents the j-th preventive maintenance time of the system; Step 3.3: Construct the objective function of the joint scheduling model; (1) Calculate the total maintenance cost C of the computing device m : C m = C dm + C pm wherein, Among them, c us represents the emergency scheduling cost for minor repairs after a failure that needs to be considered when calculating the minor repair cost of the equipment. C dm represents the total cost of minor repairs after the event. C pm represents the total cost of preventive maintenance. m represents the total number of processes, and n x represents the total number of equipment, and n xy represents the expected number of accidental failures of the y-th equipment in process x, with an initial value of 0. represents the minor repair cost of the equipment in process x. c s represents the single maintenance scheduling cost. represents the equipment maintenance cost in process x. (2) Calculate the total earliness / tardiness penalty cost C of the workpiece ta : Among them, represents the expected completion time of workpiece J i ; represents the unit tardiness penalty cost of workpiece J i ; represents the unit earliness penalty cost of workpiece J i ; x ixy[l] represents that workpiece J i is processed at the l-th position of the y-th device in process x as 1, otherwise 0; (3) Objective function: min(Cost)=min(C ta +C m ); Step 4: Calculate the workpiece scheduling order and maintenance time points when the objective function is minimized. The workpiece scheduling order is determined by the start processing time S xy[l] and the completion time C xy[l] of each workpiece. The equipment maintenance time points are jointly determined according to T j and β j,xy .

2. A joint decision-making method for preventive maintenance and production scheduling in a hybrid flow shop as claimed in claim 1, characterized in that the specific method of Step 1 is: Step 1.1: Analyze the failure mechanism of the device to determine the degradation characteristic quantity and failure threshold D that can reflect the performance degradation of the product f ; Step 1.2: Collect the degradation data of n devices at time t 1 , t 2 ......, t m ; according to the trend of the performance degradation curve, select an appropriate degradation model to describe it Step 1.3: According to the collected equipment performance degradation data, use the least squares method to estimate the parameters of each sample performance degradation model, and obtain the degradation trajectories of each sample; Step 1.4: According to the failure threshold D f and the obtained degradation models of each sample, extrapolate to obtain the failure time T of each sample 1 , T 2 ....., T n ; Step 1.5: Use the Weibull distribution to fit the probability density function f(t) of the equipment failure time; According to the extrapolated failure time data, use the maximum likelihood estimation method to find the shape parameter φ and scale parameter η in the Weibull distribution: Step 1.5.1: Probability density function f(t): Step 1.5.2: Construct the likelihood function: Among them, T n represents the failure time of the nth sample obtained by extrapolation; Step 1.5.3: Parameter calculation: The maximum likelihood estimators of η and φ can be obtained by calculation Then: Step 1.6: Equipment reliability function and failure rate function; Calculate the reliability function according to reliability theory: Failure rate function:

3. A joint decision-making method for preventive maintenance and production scheduling in a hybrid flow shop as claimed in claim 1, characterized in that the specific method of Step 2 is: Step 2.1: Construct a judgment matrix between equipment difference factors; In a hybrid flow shop, the accidental failure consequences of different equipment mainly consider the following three factors: the impact of equipment failures in different processes on product quality is different, the minor repair prices are different, and the difficulty of purchasing parts is different; Through the analytic hierarchy process, the above three equipment difference factors are integrated, the weight coefficients of each factor are solved, and the judgment matrix J of the relative importance degree between each factor is constructed as follows: wherein, each element in J represents the importance degree of one equipment difference factor relative to another equipment difference factor; Step 2.2: Calculate the equipment maintenance priorities of each process; After constructing the judgment matrix among the device difference factors, calculate the maximum eigenvalue ζ of the judgment matrix max , and substitute it into the system of equations: Among them, ζ represents the largest eigenvalue of the judgment matrix J, and α 1 , α 2 , α 3 represent the weight coefficients of the three equipment difference factors; Solve for ζ through this system of equations max The corresponding eigenvector, and normalize the eigenvector, that is, obtain the weight coefficient of the equipment difference factor, then the equipment maintenance requirement coefficient is: γ x = q x α 1 + p x α 2 + b x α 3 Among them, q x represents the impact factor of equipment failure in process x on product quality, p x represents the minor repair price factor of equipment in process x, b x represents the difficulty factor of equipment part procurement in process x; Maintenance requirement coefficient γ x The larger it is, the more serious the consequences are after a random failure occurs to the equipment of this process. Therefore, its maintenance priority is higher, and when performing preventive maintenance, it is necessary to give priority to opportunistic maintenance of the equipment of this process; for [γ 1 , γ 2 , γ 3 .....γ m , perform sorting, and use o x to represent the maintenance priorities of the equipment of each process. The larger γ x is, the higher o x is. According to the sorting, obtain the maintenance priorities corresponding to the equipment of each process.

4. A joint decision-making method for preventive maintenance and production scheduling in a hybrid flow shop as claimed in claim 1, characterized in that the specific calculation method of the adaptive population allocation factor and the parallel particle swarm-genetic hybrid algorithm for the adaptation problem model in Step 4 are as follows: The algorithm flow is as follows: Step 4.1: Use a double-chromosome form to represent the encoding of the feasible solution. Initialize the population according to Step 3.

1. At the same time, divide the population into two sub-populations according to the adaptive population allocation factor. One sub-population is updated using the particle swarm algorithm, and one sub-population is updated using the genetic algorithm. The calculation formula of the adaptive population allocation factor is as follows: When the population size is N, KN individuals in the population form sub-population 1 and enter the particle swarm algorithm for update, and the remaining individuals form sub-population 2 and enter the genetic algorithm for update; Step 4.2: Construct an improved particle swarm optimization algorithm to optimize sub-population 1 in Step 4.1; Step 4.2.1: According to the maintenance threshold combination, simulate and calculate the fitness of each particle through the preventive maintenance model established in Step 3.2, and update the start / finish times of each workpiece obtained by decoding; Step 4.2.2: Adaptive weight update; Step 4.2.3: Particle velocity update and position update; Step 4.3: Construct an improved genetic algorithm to optimize sub-population 2 in Step 4.1; Step 4.3.1: According to the maintenance threshold combination, simulate and calculate the fitness of each chromosome through the preventive maintenance model established in Step 3.2, and update the start / finish times of each workpiece obtained by decoding; Step 4.3.2: Use the method of stochastic tournament selection for chromosome selection operation and introduce the elite retention strategy; Step 4.3.3: Use single-point crossover for crossover operation; Step 4.3.4: Chromosome mutation operation; Step 4.4: Merge sub-population 1 and sub-population 2; Step 4.5: Determine whether the current population has reached the maximum number of iterations. If so, execute Step 4.6; otherwise, continue with Step 4.1; Step 4.6: Obtain the workpiece scheduling order and maintenance time points under the optimal maintenance threshold combination.

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