CN113919204A

CN113919204A - Comprehensive importance analysis method for availability of multi-state manufacturing system

Info

Publication number: CN113919204A
Application number: CN202111272030.4A
Authority: CN
Inventors: 谷东伟; 钟宇虹; 许振�; 陈�光; 贾立刚; 聂瑞华
Original assignee: Changchun University of Technology
Current assignee: Changchun University of Technology
Priority date: 2021-10-29
Filing date: 2021-10-29
Publication date: 2022-01-11
Anticipated expiration: 2041-10-29
Also published as: CN113919204B

Abstract

The invention discloses an availability comprehensive importance analysis method for a multi-state manufacturing system, belongs to the field of reliability analysis, and provides an availability comprehensive importance (IAIM) analysis method based on a proportional risk model by taking the availability of integrated reliability and maintainability as a basis, considering the synergistic effect of time and state and combining the state probability, the state transfer rate, the repair rate and the repair transfer rate of components. The usability comprehensive importance of the components is analyzed through the numerical example of the multi-state system, the parameter sensitivity is analyzed, and the feasibility of a theoretical model is verified. The usability comprehensive importance model established by the invention fully examines information such as time parameters, state parameters, maintenance influence and the like of the multi-state system, comprehensively evaluates the relative importance of the components, provides theoretical basis for further making a reliability maintenance strategy and reducing maintenance cost, and indicates an improvement direction for further improving the reliability of the multi-state manufacturing system.

Description

Comprehensive importance analysis method for availability of multi-state manufacturing system

Technical Field

The invention belongs to the field of reliability analysis, and particularly relates to a method for analyzing the comprehensive importance of the usability of a multi-state manufacturing system.

Background

Manufacturing is an important manifestation of national competitiveness, and the reliability of manufacturing systems has a profound impact on manufacturing. With the increase of complexity of a manufacturing system, how to quickly and accurately determine weak links of the system becomes an urgent problem to be solved. In recent years, analyzing the importance of manufacturing systems and identifying key equipment has become an increasingly important topic and frontier of academic and industrial research. Importance is an important tool for evaluating the influence of an individual on a system according to a single index or multiple indexes, and is often used for identifying weak links of the system. Since Birbaum first proposed the concept of importance in 1969, Birbaum importance was expanded by many scholars both at home and abroad. In the importance analysis method, Miziula and Navarro utilize copula to establish a model related to components, and the importance of Birnbaum is popularized to the situation related to the components based on the contribution of the components to the reliability of the system. The Ahme and Liu provide a production quantity importance measure and a maintenance effect importance measure aiming at the problem that criticality of different components and successful maintenance activities have long-term influence on production system production in a certain period. In the application of importance analysis, Cho and Han propose a method for quantifying the importance of associated risks by using release frequency and Cs-137 radioactivity, and apply it to structures, systems and components (SSCs) for identifying nuclear power plant hazards. Zhou et al propose a global sensitivity index in order to measure the contribution of input variables to the system reliability and apply the index to identify significant and insignificant input variables of the aviation hydraulic piping system. Dui, etc. propose a new method for flexibly managing a multi-node system based on importance after a multi-node fault caused by natural disasters or artificial accidents, and apply the method to analyze the recovery sequence of the fault node of a Wind Power Generation System (WPGS) with the multi-node fault. Dui, etc., the comprehensive importance, the average absolute deviation and the differential importance are popularized and applied to the three-level inventory system, and the key parameters in the inventory system are determined, so that the inventory system with the minimum cost and the optimum cost is realized.

With the development of importance research, importance analysis is also gradually applied to reliability research of complex systems such as multi-state manufacturing systems. Zhang et al propose a repairable system importance method based on fault loss for piston production line, sequence the major failure modes and equipment which are easy to fail. Li et al have proposed a concept of time-varying importance in response to a problem of component importance change due to maintenance activities of a manufacturing system. Lu et al, which considers both quality and reliability improvements and maintenance cost reductions, introduce a cost-based improvement factor to identify the importance ranking of the PM group and apply it to the formulation of an optional repair strategy for a multi-stage manufacturing system.

In summary, the importance of manufacturing systems is mostly focused on two-state assumptions, and studies on multi-state systems are not uncommon. In order to more comprehensively analyze the relative importance of each component in the multi-state manufacturing system to the performance of the manufacturing system, the invention develops the availability model from the synergistic influence of time and state on the system, comprehensively considers the influence of reliability, maintainability and state factors, and provides an availability importance analysis method and a multi-state comprehensive importance analysis method which are expanded by taking the availability as an importance index. The state of each component has different influences on the availability of the component, and in order to measure the influence of the component state on the component, a state availability comprehensive importance (SIAIM) is constructed. The method can accurately quantify the difference of the influence of the components on the multi-state system, measure the improvement potential of the components, and provide theoretical basis for the reliability distribution, the reliability design and the reliability growth of the system.

Disclosure of Invention

The present invention is directed to a method for analyzing the comprehensive importance of the availability of a multi-state manufacturing system, so as to solve the above-mentioned technical problems.

In order to achieve the above purpose, the method for analyzing the comprehensive importance of the availability of the multi-state manufacturing system has the following specific technical scheme:

the invention uses one component X consisting of n components₁,X₂,L,X_nThe multi-state system is a research object, the states of the components and the system researched by the invention are identified by the performances of the components and the system, and each component Xi has Mi +1 states {0_i,L,M_iAnd the state of the system is composed of

Get, so the system has the same state space {0 } as the component_S,L,M_S}. There is a performance index (critical state K), K, for both components and systems_iAnd K_SRespectively represent a component X_iAnd critical states of the system S. States less than the critical state represent fault conditions and states greater than the critical state represent normal conditions. When the component and system states are in the failure state, they are repaired immediately, provided that the component and system can be restored to the normal state every maintenance, and the state transition of the component and system does not consider the current state transition to the same state.

Proportional risk model:

the proportional hazards model was a semi-parametric regression model proposed by statisticians d.r.cox in 1972, originally used for medical disease analysis. The expression is shown as formula (1).

h(t，x)＝h₀(t)g(γx) (1)

Wherein: h (t, x) is the risk rate of the system at time t under the influence of the covariate x. h is₀(t) is a baseline risk function. g (γ x) is a connecting function, γ is a regression coefficient, and x is (x)₁,x₂,L,x_n) Are covariates.

The natural aging, different state factors of the system, improper operation of workers and the like can influence the failure rate of the system over time, and the invention needs to utilize the state information of the system and analyze the relevant characteristics of the system by combining time, so the failure rate of the system can be modeled by utilizing a proportional risk model, and the expression is shown as follows.

h(t，Z)＝h₀(t)exp(γZ) (2)

Wherein h is₀(t) is a baseline failure rate function and Z is a state covariate. As the invention selects the reference fault rate function of the Weibull distribution construction system, at the moment, the fault rate function of the system can be changed into a form shown in an expression (3), wherein k and eta are the form parameter and the ruler parameter of the Weibull distribution respectively.

Constructing an availability comprehensive importance model based on a proportional risk model:

the method comprises the steps of constructing the availability comprehensive importance degree based on the proportional risk model, dividing the availability comprehensive importance degree into two parts, firstly expanding the traditional availability degree, secondly establishing the availability comprehensive importance degree model, and finally applying the established availability degree model to the comprehensive importance degree model to obtain the availability comprehensive importance degree model based on the proportional risk model.

(1) Usability model

The traditional availability is an important index for describing the reliability of a repairable system and only depends on time, but the system runs, and the state of the system is randomly changed due to any production factor, environmental factor and maintenance intervention. Component X_iIs expressed by the formula (4)

In the formula of_i(t) represents a module X_iFailure rate of (2), X_iTo take into account component state effects, among others, component X_iThe failure rate of (a) will be replaced with equation (3). Mu.s_i(t) represents a module X_iThe repair rate is the ratio of the repair density function to the unrepairable degree function, and the expression of the repair rate is shown in (5). Wherein f (t) -a repair density function; f (t) -maintenance function.

Substituting equations (3) and (5) into equation (4) can obtain component X under the proportional risk model_iIs shown in equation (6). Such availability models can describe the availability of the system under the influence of both time and status.

Since the complex system can be simplified into a plurality of series systems or parallel systems, the usability model is only built for the series systems and the parallel systems, as shown in formula (7).

(2) Usability comprehensive importance model

Usability importance was originally proposed by Barabady and Kumar for measuring subsystem or component X_iThe influence of the availability of (c) on the availability of the whole system is shown in formula (8).

For a component, changes in time and status will affect the performance of the component, resulting in a change in system availability. In order to clarify the synergistic influence of time and state on the component, the invention combines the state probability and the state transition rate to expand the usability importance model, namely the multi-state system component X_iFrom state m_iTransition to State g_iState availability synthesis ofThe importance, expressed as the product of the availability importance of the component and the state probability and all the state conditional probabilities making the system available, can be used to describe the impact of the component state transition on the availability of the component, as shown in equation (9).

Wherein the content of the first and second substances,

component Xi in m_iProbability of a state;

P(Φ(X)＞K_S|X_i＝m_i) Component Xi in m_iConditional probability of availability of the state system, K_SIs a critical state of the system;

component X_iFrom m_iSum of state transition rates of state transitions to the remaining states.

In series and parallel systems, the impact of the transfer of component states on system performance is different. In the series system, once the state of a component is lower than the critical value, the state of the system is directly below the critical value, but the parallel system does not exist, so that the formula (9) is different when being applied to the series system and the parallel system, and is specifically shown in an expression (10).

Component X_iState m_iThe status availability composite importance of is component X_iAll m_iThe sum of the state transition availability aggregate importance of the states may describe the effect of the state of the component on the component availability, as shown in equation (11). Component X_iIs component X_iSynthetic importance of all status availabilityAnd the sum is used for describing the influence of the components on the system usability, as shown in a formula (12).

The method for analyzing the comprehensive importance of the availability of the multi-state manufacturing system has the following advantages: the usability comprehensive importance model established by the invention fully examines information such as time parameters, state parameters, maintenance influence and the like of the multi-state system, comprehensively evaluates the relative importance of the components, provides theoretical basis for further making a reliability maintenance strategy, reducing maintenance cost and prolonging the service life of the system, and indicates an improvement direction for further improving the reliability of the multi-state manufacturing system.

Drawings

FIG. 1 is a block diagram of the reliability of a multi-state system of the present invention.

FIG. 2 is a comparison graph of status availability composite importance for the components of the present invention.

FIG. 3 is a comparison graph of the availability of the components of the present invention.

FIG. 4 shows an assembly X according to the invention₂Fault rate parameter k of₂The overall importance of the availability of the system under changing conditions (FIG. 4(a): k)₂1.2; in FIG. 4(b): k₂2.2; in FIG. 4(c): k ₂4; in FIG. 4(d): k₂＝8)。

FIG. 5 shows a component X₂Fault rate parameter η of₂The overall importance of the availability of the system under varying conditions (FIG. 5(a): η₂(ii) 5; eta in FIG. 5(b)₂10; eta. in FIG. 5(c)₂20; eta. in FIG. 5(d)₂＝60)。

FIG. 6 shows an assembly X according to the invention₂Fault rate parameter gamma of₂The overall importance of the availability of the system under varying conditions (FIG. 6(a): γ)₂3; FIG. 6(b): gamma₂1.5; FIG. 6(c): gamma₂＝1.5(ii) a FIG. 6(d): gamma₂＝3)。

FIG. 7 is a drawing of assembly X of FIG. 7 according to the present invention₂Repair rate parameter ω₂The overall importance of the availability of the system under changing conditions (FIG. 7(a): ω₂10.00; FIG. 7(b): ω₂0.69; FIG. 7(c): ω₂0.69; FIG. 7(d): ω₂＝10.00)。

FIG. 8 shows a block X₂Repair rate parameter σ of₂The overall importance of the availability of the system under changing conditions (FIG. 8(a): ω₂0.11; FIG. 8(b): ω₂0.77; FIG. 8(c): ω₂1.60; FIG. 8(d): ω₂＝8.00)。

FIG. 9 is a block diagram of a line architecture for an example analysis of integrated importance of multi-state manufacturing system availability.

FIG. 10 is a flowchart of the parameter estimation of the proportional risk model according to the present invention.

FIG. 11 is a state availability integrated importance comparison graph for a production line subsystem (FIG. 11(a): component X)₁(ii) a FIG. 11(b) Module X₂(ii) a FIG. 11(c) Assembly X₃(ii) a FIG. 11(d) Assembly X₄(ii) a FIG. 11(e) Module X₅)。

FIG. 12 is a comparison graph of the availability aggregate importance of production line subsystems.

Detailed Description

For a better understanding of the objects, structure and function of the present invention, a method for analyzing the comprehensive importance of the usability of a multistate manufacturing system according to the present invention will be described in detail with reference to the accompanying drawings.

The importance is widely applied to identifying weak links of a system in reliability engineering, but the existing importance mostly identifies the relative importance of components according to the change of reliability or the degradation of state. The multi-state manufacturing system can be subjected to maintenance activities along with the lapse of time, and the maintenance activities can cause the change of the state and the availability of the system, so the invention provides an availability integrated importance (IAIM) analysis method based on a proportional risk model by taking the availability of integrating the comprehensive reliability and the maintainability as a basis, considering the synergistic effect of time and the state and combining the state probability, the state transition rate, the repair rate and the repair transition rate of components. The usability comprehensive importance of the components is analyzed through the numerical example of the multi-state hybrid system, the parameter sensitivity is analyzed, and the feasibility of a theoretical model is verified.

And finally, taking a lithium battery pole piece production line as an example to analyze the comprehensive importance of the usability, and determining the key equipment of the system as a stirrer and a die cutting machine. The usability comprehensive importance model established by the invention fully examines information such as time parameters, state parameters, maintenance influence and the like of the multi-state system, comprehensively evaluates the relative importance of the components, provides theoretical basis for further making a reliability maintenance strategy, reducing maintenance cost and prolonging the service life of the system, and indicates an improvement direction for further improving the reliability of the multi-state manufacturing system.

1. Numerical calculation example:

suppose a set of 4 components { X }₁,X₂,X₃,X₄A reliability block diagram of a multi-state hybrid system is shown in fig. 1, wherein each component and the system has four states {0,1,2,3}, 0 is a fault state, 2 and 3 are normal states, 1 is a critical state, and state probabilities and state transition rates of components of the system are shown in tables 1 and 2.

TABLE 1 State probability tables for various components of a multi-state system

	0	1	2	3
					X₁	0.02	0.05	0.63	0.30
X₂	0.10	0.20	0.54	0.16
					X₃	0.06	0.18	0.43	0.33
X₄	0.18	0.25	0.37	0.30

TABLE 2 State transition Table for Components of a Multi-State System

	β^0,2	β^0,3	β^1,2	β^1,3	β^2,0	β^2,1	β^3,0	β^3,1	β^3,2
										X₁	0.120	0.080	0.150	0.100	0.170	0.100	0.050	0.110	0.120
X₂	0.070	0.110	0.085	0.090	0.130	0.100	0.120	0.150	0.145
										X₃	0.020	0.040	0.130	0.010	0.160	0.20	0.090	0.070	0.280
X₄	0.085	0.180	0.100	0.120	0.075	0.030	0.140	0.080	0.190

Assuming that the repair time of each component follows a lognormal distribution, there are two parameters for the repair rate, namely the mean value ω of the time logarithm and the standard deviation σ of the time logarithm. The failure rate parameters and repair rate parameters of each component of the multi-state system are shown in table 3.

TABLE 3 parameter Table for each component of the multi-state system

Since both the component and the system have 4 states, a state distribution as shown in table 4 can be derived, which records the probability that the component state will cause the system to be in a certain state. Taking the component X1 as an example, the conditional probability calculation formula of each state is shown in equation (13), and the conditional probabilities of the remaining states are shown in table 5.

TABLE 4 Multi-State System State distribution Table

TABLE 5 conditional probability distribution Table for multistate systems

	X₁	X₂	X₃	X₄
					0	0.605698	0.723431	0.720453	0.515035
1	0.600886	0.721213	0.718387	0.479032
					2	0.910592	0.852054	0.847710	1.000000
3	0.907355	0.835435	0.843451	1.000000

A comparison of SIAIM for different states of each component can be obtained using equation (11) is shown in FIG. 2.

Observing fig. 2, it can be seen that the combined importance of the status availability of the various components grows with time. Over time, the status availability composite importance rankings of component X1 and X4 are unchanged, while the status availability composite importance rankings of component X2 and X3 are changed. Only critical state 0 needs to be noted for component X1; only critical state 0 needs to be noted for component X4. While state 0 is noted for component X2 before 70h and component X3 before 90h, and state 1 is noted thereafter. Therefore, in increasing the availability of components, improvements are needed depending on the relative importance of their status availability.

A comparison graph of the availability integrated importance IAIM of the components is shown in fig. 3.

FIG. 3 shows that the availability aggregate importance of all components in the multi-state hybrid system is on the rising trend with time, the relative importance ranks of all components are unchanged, and the availability aggregate importance ranks of all components are X₁>X₄>X₂>X₃. Wherein the component X₁The greatest impact on the availability of the multi-state hybrid system,therefore, when reliability of the multi-state hybrid system is improved and a maintenance strategy is formulated, the component X needs to be focused₁。

In order to verify the effectiveness and novelty of the proposed IAIM, the present invention combines the IAIM with the documents Si S, Dui H, ZHao X, et al]The integrated importance I in IEEE Transactions on Reliability,2012,61(1):192-^IIM(i) And document Wu S, Chan L Y. Performance evaluation-analysis of Multi-state systems [ J]Performance utility importance I in Reliability, IEEE Transactions on,2003^UI(i) Comparative analysis was carried out, I^IIM(i) Calculating as shown in formula (14), I^UI(i) The calculation is shown in equation (15).

In the formula

From state m for component Xi_iIs transferred to_iTransfer rate of (a)_jFor the performance utility level when the system is in the j state, a of each state of the system_jAs shown in table 6.

TABLE 6 Multi-State System Performance utility levels

	0	1	2	3
					a_j	0	100	1000	3000

The availability composite importance ranking, the composite importance ranking, and the performance utility ranking for each component are shown in table 7.

TABLE 7 different importance rankings for various components of a multi-state system

It can also be seen from Table 7 that the ranking of the availability aggregate importance of the components is different from the ranking of the aggregate importance and the performance utility importance, since the availability aggregate importance of the present invention is based on availability and takes into account the impact of maintenance on the system; the comprehensive importance and the performance utility importance are based on the reliability, and the comprehensive importance only considers the influence of the degradation on the system.

In conclusion, the availability comprehensive importance degree comprehensively considering the reliability and the maintainability can more comprehensively analyze the multi-state system, and provide more accurate theoretical basis for the subsequent system reliability improvement and maintenance strategy formulation.

2. And (3) analyzing the parameter sensitivity:

there are a number of parameters in the component state availability composite importance and the availability composite importance, k, η, γ in the failure rate function and ω, σ in the repair rate function, respectively. To further investigate the effect of each parameter on the relative importance of the components, a multi-state system was performedAnd (5) analyzing system parameter sensitivity. The invention uses a component X₂The state availability comprehensive importance of each component and the change rule of the availability comprehensive importance are researched, and therefore the improvement direction of the system availability is sought.

(1) Failure rate function parameter sensitivity analysis

To observe X₂The influence of the fault rate parameter change on the comprehensive importance of the component availability is achieved, and the parameter change values are selected through an orthogonal test method, as shown in table 8. And obtaining a component availability comprehensive importance contrast chart after the failure rate function parameters are changed as shown in the figures 4-6 through calculation.

Table 8 fault rate parameter table

Viewing FIG. 4, it can be seen that the parameters affect the relative importance ranking of the components, where component X is paired with component X₃Has the greatest influence on the overall importance of availability and is dependent on the parameter k₂Increase in value, component X₃The greater the overall importance of availability of (c).

It can be appreciated from FIG. 5 that the change in the parameter has an effect on the aggregate importance ranking of the availability of the components, where component X is₃The overall importance of usability of (2) is most influential. Parameter eta₂The larger, the component X₃The smaller the availability composite importance of, component X₁The greater the overall importance of availability of (c).

From the observation of FIG. 6, the parameter γ can be found₂To the component X₃Has the greatest influence on the overall importance of the usability of the system, when the parameter gamma is₂When negative, the component X₃Minimum overall importance of availability of; when the parameter gamma₂When positive, the component X₃The overall importance of availability of (a) is promoted to the second. It can also be seen from the figure that the parameter γ is not the same₂Whether positive or negative, the greater the value of the component X₃The greater the overall importance of availability of (c).

(2) Repair rate function parameter sensitivity analysis

The repair rate parameter change values shown in table 9 were selected by an orthogonal test method, and the influence of the repair rate parameters on the comprehensive importance of the component availability was observed. The composite importance contrast map of the usability of the components with changed parameters shown in fig. 7 and 8 is obtained through calculation.

TABLE 9 repair Rate parameters Table

From the observation of FIG. 7, the parameter ω can be found₂Aggregate importance ranking affecting availability of components, with the most influential being component X₃The availability of (2) integrates the importance. When parameter ω₂When negative, the larger the value, the component X₃The smaller the overall importance of availability of (c); when parameter ω₂When it is positive, the larger the value is, the component X₃The greater the overall importance of availability of (c). Parameter omega₂To the component X₁And component X₄The availability aggregate importance value of (c) has an effect but does not affect its ranking.

From fig. 8, the parameter σ can be derived₂The change in (b) has an effect on the overall importance of the availability of the component, and the effect is regular. From the graph can follow the parameter σ₂Increase of (2), component X₃And component X₄The overall importance of availability of (A) shows a trend of decreasing first and then increasing, component X₁The comprehensive importance of the usability of (2) shows a trend of increasing first and then decreasing.

Through sensitivity analysis of failure rate and repair rate parameters, the following results can be obtained: for the same structure, when the parameter of a certain component is changed, the relative importance of the rest of the components in the system is also changed, so the setting of the parameter is also emphasized in the product design process.

3. Multi-state manufacturing system availability integrated importance instance analysis:

the production line of the lithium battery pole piece shown in figure 9 is taken as a research object and comprises a stirrer X₁Coating machine X₂Roller press X₃Die cutting machine X₄And is divided intoStrip machine X₅A system formed by connecting in series. The state space of the production line and the subsystems thereof is Z ═ {0,1,2,3}, the state of "0" represents the serious state, and the state of "3" represents the normal state. When one subsystem breaks down, the system is in a fault state, at the moment, maintenance personnel repair the production line immediately, and during the repair period, the rest subsystems are in a shutdown state.

3.1 proportional risk model parameter estimation:

and analyzing the operation and maintenance data of the lithium battery production line in 2018 to obtain the fault interval time of each device and using the fault interval time for model construction. According to the formula (3), the fault rate of the production line is the product of a function related to time and a function related to state, so that the invention is based on a transformer failure probability model [ J ] with coordination of the literature Liuning, Liyuan, Xuyaoyu, Zhang Guanjun, work age accumulation and state inducement]The idea of the Chinese Motor engineering report, 2019,39(22): 6783-. First, to highlight the effect of time on failure rate, state averages may be used for state variables

Instead, the state connecting function portion can be regarded as a constant α at this time, as shown in equation (16). Second, to highlight the effect of the state on the failure rate, the time variable may be averaged over time

Instead, the reference failure rate function portion can be regarded as a constant τ at this time, as shown in equation (17).

The formula (16) is a reference fault rate function model, and a certain error epsilon exists between the reference fault rate function model and the actual fault rate. To make the model more stableIn accordance with the practice, the sum of the required errors ε_SThe smaller the better.

Wherein λ_iFor production line subsystem X_iMay be expressed as a ratio of downtime to system load time.

From the above analysis, it can be seen that when k and η in the formula (16) are solved, the process can be converted to seek ε_SMinimum value of (c). Due to the leap nature of the particle swarm optimization, the particle swarm optimization is easier to obtain the global optimal value and cannot be trapped in the local optimal value, so that the shape parameters and the scale parameters of the reference fault rate function are optimized and solved by the particle swarm optimization. Using the idea of linear regression to make the parameter alpha gradually approximate to that in equation (17)

The parameters k, η and γ are finally estimated. The flowchart is shown in fig. 10, and the specific steps are as follows.

1. And (5) initializing. And setting the precision theta, and calculating the state average value and the average time.

2. The parameters k and η are solved. Solving by adopting a particle swarm algorithm to obtain the sum in the formula (16), and ordering

3. And solving the parameter gamma. The parameters can be solved according to the definition of the mean failure rate (the ratio of the number of failures in the investigation time to the accumulated working time).

D is the number of subsystem faults; t is the cumulative working time in a year, the line works eight hours a day, two shifts, 260 days a year, so T is 4160 h. N is a radical of_pFor the subsystem to be in

Fault samples of the state.

4. And (5) carrying out iterative judgment. Judgment of

If yes, the iteration is terminated, and a parameter k is output_j、η_jAnd gamma_j(ii) a If not, then order

And the iteration continues from step 2.

The failure rate parameters of each subsystem of the production line calculated by the parameter estimation process are shown in table 10:

TABLE 10 failure rate parameter table for each subsystem of production line

Sub-system	k_i	η_i	γ_i
				X₁	2.2035	46.2472	-1.4836
X₂	1.7175	69.4702	-0.4907
				X₃	2.1361	41.7805	-1.3474
X₄	1.7880	31.2055	-0.3266
				X₅	1.9234	28.1332	-1.4077

3.2 repair rate model parameter estimation:

according to the operation and maintenance data of the lithium battery production line in 2018, the maintenance samples are found to be in accordance with the log-normal distribution, so that the maintenance samples of the production line are modeled by the log-normal distribution, a maintenance density function and a maintenance degree function of the samples are shown as formulas (21) and (22), wherein omega is an average value of time logarithms, and sigma is a standard deviation of the time logarithms.

The method adopts a maximum likelihood estimation method to estimate parameters omega and sigma of the repair rate model. The principle of maximum likelihood estimation is that after many times of experiments, a certain parameter is obtained to enable the occurrence probability of a sample to be maximum, and the result is used as the true value of the sample parameter. When r maintenance samples of the production line are known, the likelihood function and the maximum likelihood equation are shown in the formula (23) and the formula (24).

The expressions for parameters ω and σ are available according to equation (24):

the parameters of the repair rate of each subsystem of the production line can be obtained by the above parameter estimation method, as shown in table 11.

Table 11 repair rate parameter table for each subsystem of production line

Sub-system	ω_i	σ_i
			X₁	-0.1857	0.6940
X₂	-0.6945	0.7679
			X₃	0.3104	0.9911
X₄	-0.4150	0.8459
			X₅	-0.0835	0.9751

3.3 component availability comprehensive importance analysis:

the state probabilities of the various subsystems of the production line can be calculated based on the number of times that the state occurs during the entire observation period, as shown in table 12. The state transition rates of the subsystems are obtained according to the operation data and the expert scores of the enterprise engineers as shown in table 13. The conditional probabilities for the various subsystems of the production line obtained according to equation (13) are shown in table 14.

Table 12 probability table of states of subsystems in production line

	0	1	2	3
					X₁	0.20	0.20	0.20	0.40
X₂	0.07	0.13	0.27	0.53
					X₃	0.16	0.17	0.17	0.50
X₄	0.08	0.09	0.33	0.50
					X₅	0.05	0.13	0.31	0.51

Table 13 status transition table for each subsystem of production line

	β^0,2	β^0,3	β^1,2	β^1,3	β^2,0	β^2,1	β^3,0	β^3,1	β^3,2
										X₁	0.12	0.08	0.15	0.10	0.17	0.10	0.05	0.11	0.12
X₂	0.07	0.11	0.085	0.09	0.13	0.10	0.12	0.15	0.145
										X₃	0.02	0.04	0.13	0.01	0.16	0.2	0.09	0.07	0.28
X₄	0.085	0.18	0.10	0.12	0.03	0.075	0.08	0.14	0.19
										X₅	0.15	0.07	0.10	0.08	0.15	0.15	0.09	0.10	0.11

TABLE 14 conditional probability distribution table for each subsystem of production line

	X₁	X₂	X₃	X₄	X₅
						0	0	0	0	0	0
1	0	0	0	0	0
						2	0.364086	0.2736012	0.326688	0.263712	0.266928
3	0.364086	0.2736012	0.326688	0.263712	0.266928

According to the above-mentioned method for analyzing the comprehensive importance of availability and the data in tables 10 to 14, the comprehensive importance of availability of each subsystem of the production line can be obtained, so that the relative importance of each subsystem in availability under the synergistic influence of time and state can be known. The status availability integrated importance and the availability integrated importance of each subsystem are shown in fig. 11 and 12, respectively.

It can be observed from fig. 11 that the status availability composite importance rankings for each subsystem are 3 states >2 states >1 state >0 states, i.e. each subsystem state 3 is more important than the remaining states. As time goes on, SIAIM of each subsystem is in a descending trend, and SIAIM ordering of each component is unchanged. The key state of each subsystem is found to be state 3, so that the state transition rate of the state 3 can be reduced by means of preventive maintenance and the like, and the aim of improving the reliability of each subsystem is fulfilled.

From FIG. 12, the availability aggregate importance of each subsystem within 0h-20h is ranked as follows. After 40h the relative importance ranking of the subsystems of the production line becomes. During the whole investigation time, X₂System, X₃System and X₅The comprehensive importance of the availability of the system is very close, and the trend is very similar. Viewing fig. 12, it can be seen that the key subsystem was a blender 30h, and after 30h, the key subsystem became a die cutter. Of the above-mentioned critical sub-systemsThe change in state affects the availability of the production line, and therefore, when a maintenance strategy is formulated for the production line, preventive maintenance needs to be added to the blender and the die cutting machine to prevent the degradation of the key state from affecting the availability of the production line.

The availability comprehensive importance analysis of the production line can be known as follows:

(1) from the effect of the state: in the comparison graph of the relative importance of the states of the subsystems, the influence of each state on the subsystems is different, and when the state of the subsystems is changed, the availability of the subsystems is influenced, so that the critical state of the subsystems needs to be concerned, and strict clearance needs to be carried out in the initial design or subsystem model selection stage, so that the reduction of the availability of the system caused by the change of the state is avoided.

(2) From the influence of the time history: since the aggregate importance ranking of the availability of the production lines by the subsystems varies over time, time considerations are taken into account when developing maintenance strategies for the manufacturing system. Corresponding maintenance strategies are made according to different operation stages of the manufacturing system, so that the problem that the availability of the system is reduced due to the fact that only key equipment at a certain time is concerned and key equipment at the rest time is ignored is avoided.

In summary, when analyzing the comprehensive importance of availability of the multi-state manufacturing system, the synergistic effect of time and state needs to be considered sufficiently, so as to evaluate the relative importance of each subsystem more comprehensively.

The invention analyzes the comprehensive importance of the availability aiming at the multi-state manufacturing system and obtains the following conclusion:

(1) aiming at a multi-state manufacturing system, the cooperative influence of time and state is comprehensively considered, and a comprehensive usability importance degree analysis method based on a proportional risk model is provided;

(2) the feasibility of the availability comprehensive importance model based on the proportional risk model is verified by carrying out numerical example analysis on the multi-state hybrid system, and meanwhile, the change rule of the component importance influenced by related parameters is analyzed, so that a theoretical basis is provided for further improving the system;

(3) the method has the advantages that the comprehensive importance degree analysis of the usability is carried out by taking the lithium battery pole piece production line as an example, the key subsystems of the production line under the synergistic influence of time and state are obtained to be the stirrer and the die cutting machine, the key state is 3, and a more definite target is provided for the follow-up reliability improvement of the manufacturing system and the establishment of the maintenance strategy.

It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims

1. A comprehensive importance analysis method for availability of a multi-state manufacturing system is characterized in that relative importance of components can be more comprehensively analyzed, and the method comprises the following steps which are sequentially carried out:

s1, constructing a reference fault rate function of the system by utilizing the proportional risk model and selecting Weibull distribution, wherein the fault rate function of the system is in a form shown in formula (3), and k and eta are respectively a form parameter and a scale parameter of the Weibull distribution

S2, building availability comprehensive importance based on a proportional risk model;

step S2-1, expanding the traditional availability;

s2-2, establishing an availability comprehensive importance model;

and S2-3, applying the established availability model to the comprehensive importance model to obtain an availability comprehensive importance model based on the proportional risk model.

2. The method for analyzing the comprehensive importance of the availability of the multistate manufacturing system according to claim 1, wherein the step S2-1 of expanding the traditional availability specifically comprises the following steps:

component X_iIs expressed by the formula (4)

In the formula of_i(t) represents a module X_iIn order to take into account the component state influence, component X_iThe failure rate of (a) will be replaced with equation (3); mu.s_i(t) represents a module X_iThe repair rate is the ratio of a repair density function to an unrepairable degree function, and the expression of the repair rate is shown as (5); wherein f (t) -a repair density function; f (t) -maintenance function:

substituting equations (3) and (5) into equation (4) can obtain component X under the proportional risk model_iIs shown in equation (6):

3. the method for analyzing comprehensive importance of availability of a multi-state manufacturing system according to claim 2, wherein the step S2-1 is to construct the availability model only for the series connection system and the parallel connection system, as shown in formula (7):

4. the method for analyzing the comprehensive importance of availability of a multi-state manufacturing system according to claim 1, wherein the step S2-2 of establishing the comprehensive importance of availability model comprises the following steps:

the expression of the usability importance is shown in formula (8);

extending equation (8) in conjunction with state probabilities and state transition rates, the Multi-State System component X_iFrom state m_iTransition to State g_iThe composite importance of state availability of (a) is expressed as the product of the availability importance of the component and the state probability and the conditional probability of all states making the system available, and can be used to describe the effect of component state transition on the availability of the component, as shown in equation (9):

wherein the content of the first and second substances,

is a component X_iAt m_iProbability of a state; p (phi (X) > K_S|X_i＝m_i) Is a component X_iAt m_iConditional probability of availability of the state system, K_SIs a critical state of the system;

is a component X_iFrom m_iSum of state transition rates of state transitions to the remaining states.

5. The method for analyzing integrated importance of availability of a multi-state manufacturing system according to claim 4, wherein the step S2-2 is represented by expression (10) when applying the formula (9) to the series and parallel systems in the series system, respectively:

component X_iState m_iThe status availability composite importance of is component X_iAll m_iThe sum of the state transition availability comprehensive importance of the state can describe the influence of the state of the component on the availability of the component, as shown in formula (11); component X_iIs component X_iThe sum of the comprehensive importance of all the state availability is used for describing the influence of the components on the system availability, as shown in formula (12):