Continuous production system cost-effectiveness optimal life dynamic evaluation method considering performance degradation

Abstract

The invention discloses a continuous production system cost-effectiveness optimal life dynamic evaluation method considering performance degradation, and relates to the technical field of production system economic affordability design optimization. The method comprises the following steps: 1, modeling and evaluating production performance based on instantaneous yield; 2, life cycle cost decomposition and dynamic calculation; 3, performing performance-cost coupling analysis, defining a calculation model of the cost-effectiveness ratio and the cost-effectiveness optimal life, constructing an optimization framework of maximizing the cost-effectiveness ratio, and analyzing a dynamic change rule of the cost-effectiveness ratio of the production system; and step 4, performing dynamic cost-effectiveness optimal life evaluation based on the model, establishing a mixed integer programming model with maximization of the cost-effectiveness ratio as a target, and performing optimization solution to obtain the optimal cost-effectiveness and the optimal life. According to the method, the performance degradation and cost accumulation characteristics of the production system in the operation process can be accurately described, a more reasonable cost-effectiveness optimal life evaluation method is provided, and the economic affordability of the production system and the scientificity of using an optimization decision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field related to the economic evaluation of production systems, and in particular provides a method for dynamically evaluating the cost-effective optimal life of a continuous production system taking into account performance degradation, that is, a method for dynamically evaluating the cost-effective optimal life that combines the dynamic changes of the dual dimensions of performance and cost of the continuous production system. The present invention relates to a method for dynamically evaluating the cost-effective optimal life of a continuous production system based on performance degradation, life cycle costs, economic engineering applications, and cost-performance convolution. This method is centered on cost-effectiveness and driven by technological updates. It establishes a production performance model based on output value for a continuous production system based on a typical production system architecture and performance degradation laws, and quantitatively obtains the time-varying dynamic laws of its production performance. Based on the cost elements of the entire life cycle and data analysis, a relationship model between various costs of the life cycle is comprehensively established, and the performance-cost relationship is used to dynamically evaluate the cost-effectiveness ratio. Through this framework, the cost-effectiveness ratio results under different usage stages are finally evaluated, and the dynamic cost-effectiveness optimal life evaluation results are given. Background Art

[0002] Continuous production systems are widely used in various industries, including the chemical and pharmaceutical industries. Their production efficiency and economic benefits directly impact a company's market competitiveness. However, during the long-term operation of continuous production systems, core equipment and key components inevitably suffer from performance degradation, leading to decreased production efficiency and increased operating costs, impacting the stability and economics of the production system. Therefore, studying the performance degradation and cost patterns in historical data of continuous production systems and conducting cost-effective optimal lifecycle assessments based on their dynamic evolution is of great significance and application value. Currently, economic assessment methods for continuous production systems primarily focus on static, single-line economic analysis and fixed lifecycle cost assessment methods. However, such methods often overlook the dynamic degradation characteristics of production system performance during operation and fail to explore the joint impact of performance and cost, making it difficult to accurately assess the cost-effectiveness ratio at different stages of use. Furthermore, these methods fail to fully consider the time-varying nature of production system performance and its impact on the cost-effectiveness ratio, making it impossible to consider the long-term cost-effectiveness ratio of continuous production systems. Therefore, a cost-effective optimal lifecycle assessment method for continuous production systems that integrates performance degradation characteristics, full lifecycle cost analysis, and dynamic economic assessment is needed. This method should comprehensively consider the dynamic performance evolution of production systems, establish a correlation between production performance and cumulative costs, accurately quantify the time-varying characteristics of the cost-effectiveness ratio, and utilize a performance-cost convolution method to assess the evolution of the cost-effectiveness ratio over time. Ultimately, this method should provide a reliable basis for cost-effectiveness analysis at different stages of use and produce a dynamic cost-effectiveness optimal lifespan assessment of the system, providing scientific decision-making support for enterprises' technological upgrades and equipment management. Summary of the Invention

[0003] (1) Objects of the present invention:

[0004] The present invention aims to provide a dynamic assessment method for the cost-effective optimal lifespan of continuous production systems, taking into account performance degradation. This method addresses the shortcomings of previous economic assessment methods for production systems, which have insufficiently considered the impact of system performance degradation, lacked quantitative analysis of the dynamic changes in lifecycle costs, and failed to effectively integrate production performance and cost consumption. Instead, it proposes a dynamic assessment method that comprehensively considers performance degradation, lifecycle costs, and economic engineering applications. The method comprises four core steps: production performance modeling and evaluation based on instantaneous yield, lifecycle cost decomposition and dynamic calculation of lifecycle costs, performance-cost coupling analysis, and dynamic cost-effective optimal lifespan assessment. By considering the differences in performance degradation and cost components of continuous production systems at different stages of use, the method quantitatively analyzes the time-dependent performance decay patterns. A cost model is constructed based on the lifecycle costs, analyzing the dynamic relationships between different cost elements. Based on this, the cost-effectiveness ratio of the system is evaluated using the performance-cost relationship, forming a calculation framework for the dynamic cost-effective optimal lifespan. Ultimately, the method enables accurate assessment of the cost-effective optimal lifespan of continuous production systems, supports lifespan design and technology upgrades for cost-effective optimization, and provides a scientific and effective method for quantitatively analyzing and determining the cost-effective optimal lifespan for the lifecycle management of industrial production systems.

[0005] (2) Technical Solution: Based on the above theories and ideas, the present invention provides a dynamic evaluation method for the cost-effective optimal lifespan of a continuous production system taking into account performance degradation. This method is a cost-effective optimal lifespan evaluation method that combines the dynamic changes of both performance and cost of a continuous production system. The specific implementation steps are as follows:

[0006] Step 1: Production performance modeling and evaluation based on instantaneous yield

[0007] The cost-effectiveness of the production system is in a dynamic and continuous relationship with the production performance over time t, so the present invention constructs a production performance evaluation model based on instantaneous yield. Typical physical parameters that can reflect the degradation law of system performance, such as power output, availability or effective working time, are selected as core measurement indicators of the instantaneous production performance of the system. Let the instantaneous production performance be e(t), and its specific manifestations may include but are not limited to using the conversion relationship between the input and output of the system as a production performance measurement standard; based on the availability or effective working time of the system, combined with the empirical degradation function, the production performance is quantified; by regularly collecting the output or output rate data of the system / equipment, and using regression analysis methods to fit the instantaneous production performance function. Instantaneous production performance is also affected by multiple parameters, and the modeling expression is e(p1, p2,…, t).

[0008] After the instantaneous production performance is determined, the system's cumulative production performance is defined as E(t) as the integral of the instantaneous production performance over time, that is:

[0009]

[0010] Where p1 and p2 are parameters to be estimated, t is the continuous working time of the production system, e(p1, p2,…, t) represents the instantaneous production performance function of the system, and E(t) represents the cumulative production performance of the system.

[0011] Step 2: Life cycle cost decomposition and dynamic calculation

[0012] Establish a life cycle decomposition model based on the production and maintenance characteristics of the overall integrated continuous production system, that is, a cost decomposition model with integrated machine procurement, continuous production, breakdown maintenance, and preventive maintenance as the main cost elements, in order to dynamically calculate the cost elements that change with the continuous working time of the production system, namely:

[0013] The purchase cost of the whole machine (including the amortized research and development cost of each machine):

[0014] C1(t)=CP, (2)

[0015] Cumulative usage fees:

[0016] C2(t)=U(t), (3)

[0017] Accumulated breakdown repair costs:

[0018] C3(t)=c f N f , (4)

[0019]

[0020] Cumulative preventive maintenance costs:

[0021] C4(t)=c p N p , (6)

[0022]

[0023] The total cost is dynamically accumulated as follows:

[0024]

[0025] Where c f , c p is the unit failure / preventive maintenance cost, t is the continuous working time of the production system, CP represents the purchase cost of a single production system (including the amortized single unit development cost), U(t) represents the usage cost function accumulated over time, N f and Np are the cumulative number of failure / preventive maintenance times of the continuous production system working until time t, MTBF is the mean time between failures, which represents the failure maintenance cycle, t p It is the prescribed preventive maintenance period.

[0026] Step 3: Performance-Cost Coupling Analysis

[0027] Based on the cumulative output of instantaneous production performance and cost, the coupling effect between the two can be evaluated from the perspective of cost-effectiveness, that is, the concepts of cost-effectiveness and cost-effectiveness optimal life are proposed. Cost-effectiveness refers to the quotient of the specified performance output of the production system and the total cost under specified parameter settings and within a specified time, denoted as w(p1, p2, …, t), and is expressed as follows:

[0028]

[0029] Where p1 and p2 are parameters to be estimated, t is the continuous working time of the production system, w(p1, p2, ..., t) represents the cost-effectiveness ratio of the system at time t, e(p1, p2, ..., t) represents the instantaneous production performance function of the system, E(p1, p2, ..., t) represents the cumulative production performance of the system, t is the continuous working time of the production system, C i (p1, p2, …, t) represents the i-th cost component of the system, and C(p1, p2, …, t) represents the cumulative cost of the system.

[0030] The aforementioned cost-effectiveness evaluation process couples the relationship between performance and cost, transforming the min-max trade-off between maximizing performance and minimizing cost into a single-objective optimization problem focused on maximizing the cost-effectiveness ratio. Therefore, using the dynamic calculation results of the production system's instantaneous performance and costs in steps one and two, the dynamic cost-effectiveness ratio of the production system can be calculated in real time to assess its economic affordability and current economic performance.

[0031] In the initial stages of a production system's operation, as components adjust and the learning rate curve influences them, the system's instantaneous production performance stabilizes or even increases. The cumulative production performance (E(p1, p2, …, t)) increases steadily, and the cost accumulation process shows a cyclical increase with preventive maintenance parameters. However, as the production system's operating time increases, performance degradation becomes increasingly apparent, causing the cumulative production performance (E(p1, p2, …, t)) to slow down. During this process, the accumulated operating costs and fault repair costs increase due to cost-amplifying factors such as technological backwardness and wear and fatigue, resulting in an increase in the cumulative system cost (C(p1, p2, …, t).

[0032] That is, as the design / service life x increases, its technical performance will gradually decline due to physical wear and invisible wear caused by the emergence of new technologies, and the cumulative cost will also increase rapidly. Although the production system can continue to be used, its cost-effectiveness may be significantly reduced. The optimal cost-effectiveness life T is defined as: the service life of the system when the cost-effectiveness reaches the highest value, starting from the time the system is put into use in a brand new state, using the cost-effectiveness as the evaluation indicator of the use effect. The core of the optimal cost-effectiveness life is to maximize the "production performance per unit cost" of the equipment, which is expressed as follows:

[0033]

[0034] Among them, T is the optimal lifespan result of the cost-effectiveness, and the cost-effectiveness ratio function is w(p1, p2,…, t). It represents a subset of the domain, any element in which can make the function take the maximum value. It can be obtained by differentiating the cost-effectiveness function:

[0035]

[0036] Step 4: Model-based dynamic cost-effective optimal lifespan assessment

[0037] The analysis process of steps one to three can be expressed as a mixed integer programming (MILP) model. Based on the relationship between parameters, decision variables and constraints in the model, the cost-effective optimal lifespan result with the maximum cost-effectiveness ratio as the objective function is determined.

[0038] First, establish the objective function of "maximizing the cost-effectiveness ratio"

[0039]

[0040] Then the optimization model constraints are established in linear form

[0041] 1. Constraints on the calculation of cumulative production performance of continuous production systems:

[0042]

[0043] 2. Constraints on the calculation of cumulative production performance of continuous production systems:

[0044]

[0045] 3. Purchase cost parameter conversion constraints:

[0046] C1(t)=CP, (15)

[0047] 4. Constraints on calculation of accumulated usage fees:

[0048] C2(t)=U(t), (16)

[0049] 5. Constraints on cumulative breakdown repair costs:

[0050] C3(t)=c f N f , (17)

[0051] 6. Calculation constraints for the cumulative number of failures, with upper and lower bounds:

[0052]

[0053]

[0054] 7. Constraints on calculation of cumulative preventive maintenance costs:

[0055] C4(t)=c p N p , (20)

[0056] 8. Calculation constraints for cumulative preventive maintenance times, with upper and lower bounds:

[0057]

[0058]

[0059] Based on this model, the dynamically generated performance-cost parameters can be quickly processed. According to the relationship between variables, the current cost-effectiveness ratio and the time corresponding to the maximum cost-effectiveness ratio point, that is, the cost-effectiveness optimal lifespan, can be planned and solved under the constraints of linear constraints.

[0060] Through the above steps, the present invention proposes a dynamic evaluation method for the cost-effective optimal life of a continuous production system taking into account performance degradation. Compared with most economic evaluation methods, this method not only takes into account the performance degradation and cost convolution effects during the use process, but also focuses on the dynamic changes in the dual dimensions of performance and cost of the continuous production system. It proposes the concepts of cost-effectiveness and optimal life and provides a new economic dynamic evaluation method based on this, which helps to more accurately capture the changes in the economic efficiency of the production system and the timing of technological iteration. This method is simple to calculate, easy to implement, and more in line with engineering practice.

[0061] (3) Advantages and effects:

[0062] ① The present invention proposes a life assessment method for continuous production systems based on cost-effectiveness optimization by quantitatively constructing a dynamic coupling model of instantaneous production performance and cumulative costs. This method can accurately characterize the performance degradation trend and cost accumulation effect of the production system at different operating stages, and establishes a calculation framework for the cost-effectiveness optimal life. Compared with existing life assessment methods, the present invention not only takes into account the performance degradation characteristics and maintenance cost changes of the production system, but also focuses on the dynamic coupling effect of technology iteration and economic evaluation, and proposes a new cost-effectiveness optimal life optimization method, which helps to more accurately identify the optimal service life and the timing of technology replacement.

[0063] ② The proposed method is computationally simple and based on a mixed integer programming (MILP) model. It achieves optimal cost-effective lifespan decisions while maintaining computational efficiency. This method is applicable to various types of continuous production systems and can dynamically adjust optimization objectives to meet actual engineering needs. It is easy for engineers to master and use, featuring a scientific approach and excellent manufacturability. It has strong engineering practical value and potential for widespread application. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is a flow chart of the method of the present invention.

[0065] Figure 2 It is a production performance-time relationship diagram proposed by the present invention.

[0066] Figure 3 This is the cost-effective optimal life calculation principle proposed by the present invention.

[0067] Figure 4 It is the instantaneous performance and cumulative performance curve of a continuous production system.

[0068] Figure 5 It is the dynamic cost-effectiveness optimal curve of a continuous production system. DETAILED DESCRIPTION

[0069] The following is an example of the performance and cost data of a continuous production system in my country for the purpose of preparing chemical raw materials. Figure 1 , the present invention is described in further detail.

[0070] The purchase price of a continuous production system (including amortized development costs) is 1 million yuan, the mean time between failures (MTBF) is 2000 hours, the preventive maintenance cycle is 720 hours, the cost of a single failure repair is 30,000 yuan, and the cost of a single preventive maintenance is 10,000 yuan. The function of the cost of using the production system as it changes with the use time is U t =1.5t×10 -3(10,000 yuan), where t is the usage time. The cost data information is shown in Table 1. A typical performance is used as a case, and its instantaneous production performance function is See Figure 4 As shown in (a). Table 1 Cost data information Purchase cost CP <![CDATA[Single fault repair cost c f > <![CDATA[Single preventive maintenance cost c p > <![CDATA[Using cost function c p > Cost / 10,000 yuan 100 3 1 <![CDATA[1.5t×10 -3 ]]>

[0071] The present invention proposes a dynamic evaluation method for the cost-effective optimal life of a continuous production system considering performance degradation. Figure 1 As shown, the specific implementation steps are as follows:

[0072] Step 1: Production performance modeling and evaluation based on instantaneous yield

[0073] By calculating and sorting out some of the data obtained, the cumulative production performance output function can be obtained as follows:

[0074]

[0075] The cumulative production performance output obtained according to the performance degradation law is an intuitive expression of the production system's efficiency. Its growth rate decreases gradually with time. Figure 4 As shown in (b), this reflects that the components contained in the continuous production system have obvious wear and aging phenomena during use.

[0076] Step 2: Life cycle cost decomposition and dynamic calculation

[0077] The cost at time variable t is used as the calculation basis.

[0078] Based on the MTBF of the production system and its single failure maintenance cost, the cumulative failure maintenance cost function during the life cycle can be obtained as follows:

[0079]

[0080] Based on the preventive maintenance cycle of the production system and the single preventive maintenance cost of the equipment, the cumulative preventive maintenance cost function within the design life can be obtained as follows:

[0081]

[0082] Combining the production system procurement cost and cumulative usage cost functions, the cumulative cost dynamic consumption function within a certain specified design life can be obtained as follows:

[0083]

[0084] Step 3: Performance-Cost Coupling Analysis

[0085] Combining the production performance and life cycle cost results obtained in steps one and two, respectively, with the cost-benefit ratio concept proposed in the present invention, a dynamic cost-benefit ratio function after performance-cost coupling can be obtained:

[0086]

[0087] Step 4: Model-based dynamic cost-effective optimal lifespan assessment

[0088] To determine the cost-effective lifespan of a production system, continuous or discrete lifespan values ​​can be listed and optimized based on the model. Taking the discrete lifespan values ​​as an example, as shown in Table 2, the optimal cost-effective lifespan solution can be determined from the range of 4320 to 86400 hours. Table 2 Design life values ​​of production systems for different discrete design schemes (hours) plan 1 2 3 4 5 6 7 8 9 life 4320 8640 12960 17280 21600 25920 30240 34560 38880 plan 10 11 12 13 14 15 16 17 18 life 43200 47520 51840 56160 60480 64800 69120 73440 77760 plan 19 20 life 82080 86400

[0089] Substituting the life design values ​​of each design scheme into the model, the cost-effectiveness of the production system under each design life scheme can be calculated. The specific calculation results are shown in Table 3, and the comparison curve of the dynamic cost-effectiveness under each scheme is shown in Figure 5 . Table 3 Calculation results of production system cost-effectiveness ratio under different design schemes

[0090] Therefore, according to the various life design schemes given in the data set, the cost-effectiveness results under this life can be dynamically calculated. After comparison, the cost-effectiveness optimal life can be determined to verify the effectiveness of the model and method. The results are as follows Figure 5 As shown. From the detailed results, design scheme 6, that is, the design scheme with a duration of 25920 hours, has the highest cost-effectiveness output. Before this scheme, the cost-effectiveness of the production system has continued to increase with time. The calculation logic behind it shows that under the coupling of performance degradation and cost convolution, the degradation rate and cost growth rate are within a controllable range, the degradation effect is not obvious, and the cost increase is small. After this scheme, the degradation rate and cost growth rate began to deviate from the control of technology and management, and the cost-effectiveness of the output continued to decrease until it reached a certain acceptable range. The production system needs to undergo technology updates, parts replacements, and even overall upgrades to improve performance output and reduce cost accumulation, ultimately achieving the goal of improving cost-effectiveness and extending the cost-effectiveness optimal life. Therefore, it can be considered that the method proposed in the present invention can accurately judge the cost-effectiveness status of the continuous production system, obtain sufficiently accurate cost-effectiveness optimal life information, and help to more accurately identify the optimal service life and the timing of technology replacement.

[0091] In summary, the present invention relates to a dynamic evaluation method for the cost-effective optimal life of a continuous production system taking into account performance degradation. The method comprehensively utilizes instantaneous production performance modeling, life cycle cost decomposition, performance-cost coupling analysis and optimization solution technology to quantitatively establish the dynamic relationship between performance degradation and cost accumulation of the production system. By constructing a production performance evaluation model based on instantaneous yield, the performance degradation characteristics of the production system during operation are systematically analyzed; at the same time, based on the life cycle cost decomposition, the cost change trend of the system at different stages of use is dynamically calculated, and further combined with the cost-effectiveness concept, a cost-effectiveness optimal life optimization model is constructed. Finally, the optimal cost-effectiveness optimal life is solved by the mixed integer programming (MILP) method, providing a scientific basis for the economic affordability of the production system and the use optimization decision. The present invention effectively improves the accuracy and applicability of cost-effectiveness evaluation, improves the traditional economic evaluation method, and can provide more scientific guidance for the design, operation and maintenance and upgrading of continuous production systems.

Claims

1. A method for dynamically evaluating the cost-effective lifespan of a continuous production system considering performance degradation, comprising the following steps: (1) Production performance modeling evaluation based on instantaneous yield: The cost-effectiveness of the production system is in a dynamic and continuous relationship with the production performance over time t, so the present invention constructs a production performance evaluation model based on instantaneous yield. Typical physical parameters that can reflect the degradation law of system performance, such as power output, availability or effective working time, are selected as core measurement indicators of the instantaneous production performance of the system. Let the instantaneous production performance be e(t), and its specific manifestations may include but are not limited to using the conversion relationship between the input and output of the system as a production performance measurement standard; based on the availability or effective working time of the system, combined with the empirical degradation function, the production performance is quantified; by regularly collecting the output or output rate data of the system / equipment, and using regression analysis methods to fit the instantaneous production performance function. Instantaneous production performance is also affected by multiple parameters, and the modeling expression is e(p1, p2,…, t). After the instantaneous production performance is determined, the cumulative production performance of the system is defined as E(t) as the integral of the instantaneous production performance over time. (2) Life cycle cost decomposition and dynamic calculation: Establish a life cycle decomposition model based on the production and maintenance characteristics of the overall integrated continuous production system, that is, a cost decomposition model with integrated machine procurement, continuous production, fault maintenance, and preventive maintenance as the main cost elements, in order to dynamically calculate the cost elements that change with the continuous working time of the production system, namely: (2.1) Purchase cost of the complete machine (including the amortized development cost of each machine): C1(t)=CP, (2.2) Cumulative usage fees: C2(t)=U(t), (2.3) Accumulated breakdown repair costs: C3(t)=c f N f , (2.4) Cumulative preventive maintenance costs: C4(t)=c p N p , (2.5) Dynamic accumulation of total expenses Where c f , c p is the unit failure / preventive maintenance cost, t is the continuous working time of the production system, CP represents the purchase cost of a single production system (including the amortized single unit development cost), U(t) represents the usage cost function accumulated over time, N f and N p are the cumulative number of failure / preventive maintenance times of the continuous production system working until time t, MTBF is the mean time between failures, which represents the failure maintenance cycle, t p It is the prescribed preventive maintenance period. (3) Performance-cost coupling analysis: (3.1) Based on the instantaneous production performance and cumulative cost output, the coupling effect between the two can be evaluated from the perspective of cost-benefit ratio, that is, the concept of cost-benefit ratio and cost-benefit optimal life is proposed. Cost-benefit ratio refers to the quotient of the specified performance output of the production system and the total cost under specified parameter settings and within a specified time, denoted as w(p1, p2, …, t). Where p1 and p2 are parameters to be estimated, t is the continuous working time of the production system, w(p1, p2, ..., t) represents the cost-effectiveness ratio of the system at time t, e(p1, p2, ..., t) represents the instantaneous production performance function of the system, E(p1, p2, ..., t) represents the cumulative production performance of the system, t is the continuous working time of the production system, C i (p1, p2, …, t) represents the i-th cost component of the system, and C(p1, p2, …, t) represents the cumulative cost of the system. The aforementioned cost-effectiveness evaluation process couples the relationship between performance and cost, transforming the min-max trade-off between maximizing performance and minimizing cost into a single-objective optimization problem focused on maximizing the cost-effectiveness ratio. Therefore, using the dynamic calculation results of the production system's instantaneous performance and costs in steps one and two, the dynamic cost-effectiveness ratio of the production system can be calculated in real time to assess its economic affordability and current economic performance. (3.2) In the initial stages of a production system's operation, as components adjust and the learning rate curve influences them, the system's instantaneous production performance stabilizes or even increases. The cumulative production performance E(p1, p2, …, t) grows steadily, and the cost accumulation process shows a cyclical increase with the preventive maintenance parameters. However, as the production system's operating time increases, performance degradation becomes increasingly apparent, causing the cumulative production performance E(p1, p2, …, t) to grow at a slower rate. During this process, the cumulative operating costs and fault repair costs increase due to cost-amplifying factors such as technological backwardness and wear and fatigue, resulting in an increase in the cumulative system cost C(p1, p2, …, t). That is, as the design / service life x increases, its technical performance will gradually decline due to physical wear and intangible wear caused by the emergence of new technologies, and cumulative costs will also increase rapidly. Although the production system can continue to be used, its cost-effectiveness may be significantly reduced. The optimal cost-effectiveness life T is defined as: the service life of the system, starting from a brand new state, with the cost-effectiveness as the evaluation indicator of its effectiveness, and the service life during which the cost-effectiveness reaches its highest value. The core of the optimal cost-effectiveness life is to maximize the equipment's "production performance per unit cost", which is expressed as follows: in, T is the optimal lifespan result of the cost-effectiveness, and the cost-effectiveness function is w(p1, p2,…, t). It represents a subset of the domain, any element in which can make the function take the maximum value. It can be obtained by differentiating the cost-effectiveness function: (4) Model-based dynamic cost-effective optimal lifespan assessment The analysis process of steps one to three can be expressed as a mixed integer programming (MILP) model. Based on the relationship between parameters, decision variables and constraints in the model, the cost-effective optimal lifespan result with the maximum cost-effectiveness ratio as the objective function is determined. (4.1) First, establish the objective function of "maximizing the cost-effectiveness ratio" Establishing optimization model constraints in linear form (4.2) Constraints on the calculation of cumulative production performance of continuous production systems: (4.3) Constraints on the calculation of cumulative production performance of continuous production systems: (4.4) Purchase cost parameter conversion constraints: C1(t)=CP, (4.5) Constraints on calculation of cumulative usage fees: C2(t)=U(t), (4.6) Cumulative breakdown repair cost constraints: C3(t)=c f N f , (4.7) The calculation constraints of the cumulative number of failures are respectively limited to the upper and lower bounds: (4.8) Constraints on calculation of cumulative preventive maintenance costs: C4(t)=c p N p , (4.9) The calculation constraints of the cumulative number of preventive maintenance are as follows: Based on this model, the dynamically generated performance-cost parameters can be quickly processed. According to the relationship between variables, the current cost-effectiveness ratio and the time corresponding to the maximum cost-effectiveness ratio point, that is, the cost-effectiveness optimal life span, can be planned and solved under the constraints of linear constraints.

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