CN108171435B - Production plan decision method considering preventive maintenance - Google Patents
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Abstract
The invention discloses a production plan decision method considering preventive maintenance, which relates to the field of production plan decision, and comprises the following steps: obtaining a production plan output function; and making a production plan decision according to the production plan output function. The production plan yield function also takes into account preventative maintenance. Obtaining a production plan yield function that accounts for preventative maintenance includes: establishing a simulation model; collecting and processing data; and fitting a yield function and establishing parameters of the yield function. The invention also provides a specific method for piecewise linearization of the output function. The production plan output function considering preventive maintenance provided by the invention is more suitable for the actual situation, and the influence of maintenance is taken into consideration, so that the production plan is more accurate. Aiming at the output function considering the influence of maintenance, the piecewise fitting mode provided by the invention has higher fitting precision and can reflect the essence of the output function better.
Description
Technical Field
The invention relates to the field of production plan decision-making methods under a non-fixed advance period, in particular to a production plan decision-making method considering preventive maintenance as a related variable.
Background
The yield function is a constraint in the production plan, and the specific law indicates that functional relationships exist among yield, load and lead period. The existing yield function (also called clean function) does not consider the influence of maintenance on the yield function, and the accuracy of the production plan is influenced.
When the production planning method treats the capacity, the current method mainly assumes that the equipment capacity is infinite, and uses a fixed lead time. However, in reality, the lead period is a quantity that changes dynamically with the load, and from the theoretical analysis of the queuing theory, the lead period is also a quantity that changes dynamically, and needs to be adjusted dynamically according to the current load of the system.
When the production plan is decided, the decision is separated from the maintenance activities at present, and the fact that the two activities act on the same equipment and can affect each other is often ignored. Excessive maintenance can reduce equipment utilization, insufficient maintenance can increase equipment failure rate, and production planning accuracy can be affected.
Specifically, existing production plans suffer from the following disadvantages in decision making:
1. the existing achievement does not consider the mutual influence of the maintenance plan and the production plan, so that the representation of the output function is not accurate enough and is not in accordance with the reality;
2. the existing achievement does not consider the change of the production lead time of the product due to the fact that the maintenance occupies the capacity of equipment, and therefore the accuracy of a production plan is affected;
3. the existing achievement does not consider the influence of the reliability change of the equipment after maintenance on the load of the equipment, and the lead period is associated with the load, so the change of a production plan can be caused;
4. existing efforts do not account for changes in functional form caused by dimensional increases in constraints-yield functions in production plans due to maintenance variables;
5. existing efforts do not take into account the changes in the nonlinear function linearization method caused by the maintenance variables causing the constraints in the production plan-the dimensionality of the yield function-to increase.
At present, no multidimensional yield function achievement considering maintenance exists. As dimensions increase, the complexity of production planning decisions also increases, requiring new methods to derive the specific parameters of the yield function.
Disclosure of Invention
In view of the above defects in the prior art, the invention selects appropriate maintenance-related decision variables to be introduced into the existing production plan constraints, and obtains the influence of the maintenance variables on the load and the output through the correlation between the load and the lead period and the output.
To achieve the above object, the present invention provides a production plan decision method considering preventive maintenance, characterized in that the method comprises the steps of:
and 2, making a production plan decision according to the production function of the production plan.
Further, said step 1 also allows for preventive maintenance.
Further, the step 1 further comprises:
step 1.1, establishing a simulation model;
step 1.2, data collection and processing;
and 1.3, fitting a yield function and determining yield function parameters.
Further, the theoretical basis of the simulation model in step 1.1 is a specific law, and a functional relationship exists among yield, load and lead period.
Further, the simulation model of step 1.1 also considers the equipment degradation, preventive maintenance and proportional-based first-in first-out scheduling rules.
Furthermore, the preventive maintenance decision is taken at the beginning of a period, either perfect maintenance is carried out or no measures are taken, the maintenance decisions in the simulation period form a sequence, the sequence is randomly generated, each sequence can correspond to a preventive maintenance strategy, the service life of the equipment subjected to preventive maintenance is the original service life multiplied by a repair factor, if the equipment is perfect maintenance, the repair factor is 0, and if the equipment is minimum maintenance, the repair factor is 1; and various preventive maintenance strategies such as a service life-based preventive maintenance strategy, a failure number-based preventive maintenance strategy, a periodic preventive maintenance strategy, a sequential preventive maintenance strategy, a maintenance restriction strategy, a failure restriction strategy, and the like can be considered.
Further, the step 1.3 further includes:
step 1.3.1, fitting a yield function by adopting piecewise linear regression;
1.3.2, searching the break points in the segmented linear regression by utilizing various optimization algorithms;
step 1.3.3, carrying out binary linear fitting on the collected data under the condition that the confidence coefficient is 90%;
and 1.3.4, comparing the fitting effects of the different models to obtain an output function considering preventive maintenance.
Further, in the piecewise linear regression of step 1.3.1, determining the number and value of breakpoints is the most critical step, and the whole piecewise model should have the largest decision coefficient R under the condition of the optimal breakpoint combination2：
Two independent variables x and z exist in the data set, the dependent variable is y, and the break points of the independent variables are arranged from large to small as follows:
the optimal breakpoint combination can be found by the following mathematical model:
N is the total number of dots
Further, said step 1.3.2 searches for breakpoints in the segmented linear regression using genetic algorithms.
Further, said step 1.3.4 compares the decision coefficients (coefficients of determination) R of the different models2The method comprises the following steps of determining the fitting precision of function parameters by comparing the sizes of judgment coefficients of a model according to three indexes of Mean absolute error (MAD) and Mean Absolute Percentage Error (MAPE), wherein the larger the judgment coefficient is, the better the fitting effect is; carrying out variance analysis on the model, and carrying out significance test and residual error test of the model; and meanwhile, determining parameters and confidence intervals of piecewise linear fitting according to the model, thereby obtaining an output function considering preventive maintenance.
The production plan output function considering preventive maintenance provided by the invention is more suitable for the actual situation, and the influence of maintenance is taken into consideration, so that the production plan is more accurate. Aiming at the output function considering the influence of maintenance, the piecewise fitting mode provided by the invention has higher fitting precision and can reflect the essence of the output function better.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a flow chart of a method in accordance with a preferred embodiment of the present invention;
FIG. 2 is a model in a simulation platform of a preferred embodiment of the present invention;
FIG. 3 is a schematic of the equipment degradation flow and preventive maintenance of a preferred embodiment of the present invention;
FIG. 4 is a graphical representation of the yield function in a three-dimensional coordinate system in accordance with a preferred embodiment of the present invention.
Detailed Description
A preferred embodiment of the present invention will be described below with reference to the accompanying drawings for clarity and understanding of the technical contents thereof. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
As shown in fig. 1, the production plan decision method includes two steps:
step 1: obtaining a production plan outcome function that takes into account preventative maintenance;
step 2: and making a production plan decision according to the production plan output function.
In step one, the existing achievement does not consider the influence of the equipment reliability change after maintenance on the equipment load, and the lead time is related to the load, so the production plan is changed.
And drawing a graph of the relationship among the maintenance variable, the load and the output through simulation to establish the shape of the output function relationship.
And carrying out proper linearization on the multidimensional nonlinear functional relation according to the characteristic of the multidimensional nonlinear functional relation, establishing parameters of the multidimensional nonlinear functional relation, obtaining the functional relation, and further obtaining an output function of the novel production plan introducing the maintenance factors.
Specifically, the process of obtaining the new production plan output function includes the following steps:
step one, establishing a simulation model
1.1 simulation theoretical basis of yield function
According to the Rispelt law, a functional relationship exists among yield, load and lead period. The lead period and the load are dynamically influenced mutually, for a complex system, the output function is particularly complex in mathematical representation and difficult to model, and the parameter acquisition mainly adopts an empirical data estimation method, so that the output function is obtained by estimating empirical data through establishing a simulation model.
1.2 principles and methods of model building
And establishing an abstracted simulation model aiming at the production system. The model should establish:
the simulation software and the software version are used;
product combination, and proportion distribution among products;
establishing various times, including but not limited to equipment processing time, downtime, maintenance time;
establishing equipment degradation parameters and simulating a maintenance strategy;
establishing a simulation period, establishing a total simulation time and setting the simulation repetition number.
As shown in fig. 2, the simulation model established by the present invention has the following main features:
device degradation is considered: in the wafer production simulation model, although unreliable equipment exists, the availability of the equipment is a fixed external parameter and does not change along with the increase of time, which is not true. In the model established by the invention, the reliability of the equipment can be degraded along with the simulation time, and the failure rate function follows Weibull distribution;
secondly, preventive maintenance: preventive maintenance activities exist in the simulation model, maintenance decisions occur at the beginning of a period, either perfect maintenance is carried out, or no measures are taken, the maintenance decisions form a sequence in the simulation period, the sequence is randomly generated, and each sequence can correspond to a preventive maintenance strategy. Multiplying the original service life by a repair factor after preventive maintenance, wherein the repair factor is 0 if the original service life is perfect maintenance, and the repair factor is 1 if the original service life is minimum maintenance;
the first-in first-out scheduling rule based on proportion: since wafer production is a reentrant system, simply adopting the first-in first-out rule under the condition of multiple products can make the workpiece processing priority in the later link lower, resulting in a large amount of work-in-process inventory in the system. Therefore, the capacity of the equipment is distributed according to the proportion of the types of the workpieces in the cache region, and products from the same process and the same type of products are subject to the first-come-first-served scheduling rule. The specific degradation procedure and preventive maintenance procedure are shown in fig. 3.
Step two: data collection process
2.1 data gathering method
The multi-dimensional production function achievement object considering preventive maintenance in the invention is a single machine. Wherein the load is the sum of work in process in inventory (WIP) at the beginning of the cycle and the number of newly arrived workpieces in the cycle. Load and output data in each simulation period are obtained through simulation software, and expected failure times are adopted for measuring the reliability level of the equipment. The expected number of failures within a cycle is therefore calculated from the failure rate distribution function of the device.
2.2 data processing method
The number of experimental replicates was established and several sets of data were obtained. And processing the abnormal data value according to the data characteristics, and establishing final valid data. As shown in fig. 4, the load, the yield and the expected failure times are plotted in the same coordinate system to obtain an expression form of a multidimensional yield function.
Step three: fitting a yield function and establishing yield function parameters
3.1 theoretical basis for fitting of yield function
When the equipment utilization rate is low, the capacity is sufficient, the nonlinearity of the output function is not obvious, when the equipment utilization rate is high, the nonlinear characteristic of the output function is obvious due to the blocking effect caused by maintenance, random downtime and the like, meanwhile, unreliable equipment exists due to maintenance consideration, and the output function has an obvious critical value, so that the whole function is respectively composed of two functions, and therefore, the segmentation is very necessary by combining the characteristics of the output function line at different stages. The obtained output function is a nonlinear complex curved surface and is multivariate, so that the solution is not facilitated. Therefore, the invention adopts a piecewise linear regression to fit the obtained yield function. The piecewise linear regression is mainly applied to the regression problem of the data set with the nonlinear relation, and linear fitting is carried out on data in a plurality of intervals respectively after the dependent variable data are divided into the intervals by introducing one or more break points.
In the unary second-order linear model, the data set is (x, y), where y is a dependent variable, x is an independent variable, and BP is a breakpoint. The piecewise function at this time can be expressed as:
y＝As(x-xs)+ys+Vy x＜BP
y＝Ag(x-xg)+yg+Vy x＞BP
where the breakpoint BP can be expressed as
Wherein xs, ys, As and Vy are respectively the mean value of x when x is less than BP, the mean value of y, the slope of the regression function and the error of the regression function;
xg, yg, Ag and Vy are the mean value of x, the mean value of y, the slope of the regression function and the error of the regression function when x is larger than BP. When an argument z is added to the system, the piecewise function form when x, z have only one breakpoint is as follows:
y＝Asx+ys+Vy x＜BPx
y＝Agx+yg+Vy x＞BPx
Vy＝Csz+Ds z＜BPz
Vy＝Cgz+Dg z＞BPz
wherein, BPxAnd BPzBreak points of x and z, respectively, Cs、DsRespectively, the mean value of z and the mean value of y when x is less than BP; cg、DgThe mean value of z and the mean value of y when x > BP, respectively. The general expression of the segmented yield function is as follows:
wherein x is less than BPx and z＜BPzWhen, A is not As,
C＝Cs,D＝Ds；
x＜BPx and z＞BPzwhen, A is not As,
C＝Cg,D＝Dg；
x＞BPx and z＜BPzwhen the compound is represented by formula (I), A is Ag,
C＝Cs,D＝Ds；
x＞BPx and z＞BPzwhen the compound is represented by formula (I), A is Ag,
C＝Cg,D＝Dg；
3.2 introduction to piecewise Linear regression method
In the segmentation regression, the number of breakpoints needs to be established, and how to determine the breakpoint value is the most critical step. The whole segmented model under the condition of optimal breakpoint combination should have the maximum judgment coefficient R2。
Two independent variables x and z exist in the data set, the dependent variable is y, and the break points of the independent variables are arranged from large to small as follows:
the optimal breakpoint combination can be found by the following mathematical model:
N is the total number of dots
3.3 breakpoint search
Various optimization algorithms can be used for searching the breakpoint, and the invention provides a breakpoint searching example under the condition of a genetic algorithm:
the piecewise linear regression mainly uses a statistical analysis means to obtain a function expression so as to put a complex nonlinear relation into a production plan model for solving by linear approximation. In piecewise linear regression, it is most critical to find the appropriate break points to fit the curve piecewise. Therefore, the present invention will use genetic algorithm to search for the case where X has two breakpoints and Z has 1 breakpoint as an example for explaining the search process. First, a series of breakpoint combinations (X) is determineds,Xg,Z0) As starting population, wherein XsFor small X breakpoints, XgThe larger X break point (the initial point can be determined based on an evenly distributed rule to speed up the search). And carrying out binary coding on the combination to obtain a chromosome of the genetic algorithm. The fitness function being a decision coefficient, i.e. the overall R2. The population number was set to 50 and the number of iterations was set to 20. It should be noted that, since the decision coefficient is a number smaller than 1 and larger than 0, when the iteration is performed in the second half, the difference between the chromosome with the largest decision coefficient and the chromosome fitness function with the smallest decision coefficient in the population is less than 1%, and the probability of selecting the superior parent is very low when the conventional roulette is used for selection. The solution is as follows: when the maximum fitness differs from the minimum fitness by less than 2% of the chromosomes in the population, the fitness function is redefined: and sequencing the fitness from small to large, and replacing the sequence number of each chromosome with a new fitness function.
3.4 piecewise regression
After the algorithm design is completed, the invention carries out binary linear fitting on the collected data under the condition that the confidence coefficient is 90%, and discusses the following segmented model of 3 breakpoint combinations:
model one: x (production load) is a unary linear Function of Y (output) when 2 breakpoints exist, namely a traditional cleaning Function model;
model two: x (production load) is two breakpoints, and Z (expected failure frequency) is a binary linear function of Y (output) when 1 breakpoint;
and (3) model III: x (production load) and Z (expected failure times) are each a binary linear function of Y (yield) at 2 breakpoints.
In order to measure the fitting effect of the data, the invention respectively calculates and compares the judgment coefficients (Coefficient of determination) R of the three models2Mean absolute error (Mean absolute deviation) MAD, Mean absolute percentage error (Mean average percentage error) MAPE. The fitting precision of the function parameters is mainly determined by comparing the sizes of the judgment coefficients of the models, and the larger the judgment coefficient is, the better the fitting effect is.
Subsequently, the model was analyzed for variance, and a significance check and a residual check of the model were performed.
And meanwhile, determining parameters and confidence intervals of piecewise linear fitting according to the model, thereby obtaining an output function considering preventive maintenance.
The output function related to the invention selects a preventive maintenance strategy, and various preventive maintenance strategies such as a preventive maintenance strategy based on service life, a preventive maintenance strategy based on failure times, a periodic preventive maintenance strategy, a sequential preventive maintenance strategy, a maintenance limit strategy, a failure limit strategy and the like can be considered when the output function is established.
The reliability measurement indexes related by the invention select expected failure times, and any reliability measurement indexes such as average failure interval time, equipment availability, expected failure times and the like can be considered when establishing the output function.
The piecewise linear regression of the yield function related by the invention obtains the function parameters, and any other function parameter obtaining method can be considered when the yield function is established.
The breakpoint of the output function in the segmentation process adopts a genetic algorithm, and if the piecewise linear regression is adopted, other optimization algorithms (or intelligent algorithms) in any form such as the genetic algorithm, a simulated annealing algorithm, tabu search and the like can be considered.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (6)
1. A method of production plan decision making taking into account preventative maintenance, the method comprising the steps of:
step 1, obtaining a production plan output function;
the step 1 specifically comprises the following steps:
step 1.1, establishing a simulation model;
the simulation model of step 1.1 also considers equipment degradation, preventive maintenance and proportion-based first-in first-out scheduling rules;
step 1.2, data collection and processing;
step 1.3, fitting a yield function and determining yield function parameters;
the step 1.3 specifically comprises the following steps:
step 1.3.1, fitting a yield function by adopting piecewise linear regression;
1.3.2, searching the break points in the segmented linear regression by utilizing various optimization algorithms;
step 1.3.3, carrying out binary linear fitting on the collected data under the condition that the confidence coefficient is 90%;
step 1.3.4, comparing the fitting effects of different models to obtain an output function considering preventive maintenance;
and 2, making a production plan decision according to the production function of the production plan.
2. A method for decision making on a production plan with consideration for preventive maintenance as claimed in claim 1, wherein the theoretical basis of the simulation model of step 1.1 is the rieci law, and there is a functional relationship among yield, load and lead period.
3. A method of decision making for a production plan that considers preventative maintenance as in claim 1, wherein the decision for preventative maintenance occurs at the beginning of the cycle, either perfect maintenance is performed or no action is taken, the maintenance decisions within the simulation cycle form a sequence, the sequences are randomly generated, each sequence corresponds to a preventative maintenance policy, the service life of the equipment after preventative maintenance is the original service life multiplied by a repair factor, the repair factor is 0 for perfect maintenance and 1 for minimum maintenance; and various preventative maintenance strategies are considered including a life-based preventative maintenance strategy, a failure number-based preventative maintenance strategy, a periodic preventative maintenance strategy, a sequential preventative maintenance strategy, a maintenance limit strategy, a failure limit strategy.
4. The method of claim 1, wherein in the piecewise linear regression of step 1.3.1, determining the number and value of breakpoints is the most critical step, and the whole piecewise model has the largest decision coefficient R under the condition of the optimal breakpoint combination2：
Two independent variables x and z exist in the data set, the dependent variable is y, and the break points of the independent variables are arranged from large to small as follows:
the optimal breakpoint combination can be found by the following mathematical model:
N is the total number of dots
5. A method of production plan decision making taking into account preventative maintenance as claimed in claim 1, characterized by said step 1.3.2 of searching for breakpoints in segmented linear regression using genetic algorithms.
6. A method for production plan decision making taking into account preventative maintenance as claimed in claim 1 wherein said step 1.3.4 compares the decision coefficients R of different models2Determining the fitting precision of the function parameters by comparing the judging coefficients of the models according to three indexes of the average absolute error MAD and the average absolute percentage error MAPE, wherein the larger the judging coefficient is, the better the fitting effect is; carrying out variance analysis on the model, and carrying out significance test and residual error test of the model; and meanwhile, determining parameters and confidence intervals of piecewise linear fitting according to the model, thereby obtaining an output function considering preventive maintenance.
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