CN112084677A - Preventive maintenance and control chart combined availability optimization method suitable for emergency production system - Google Patents
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Abstract
The invention relates to a combined availability optimization method for preventive maintenance and control charts, which is suitable for an emergency production system, effectively solves the problem of combined availability optimization for preventive maintenance and control charts in the emergency production system, and comprises the steps of I, determining six updating situations of the system; defining the mean value to control the occurrence probability of two types of errors; step three, solving the occurrence probability of each scene; solving the normal operation expected time, the system expected period, the system expected cost, the availability objective function and the economic constraint function of each updating situation; step five, improving the genetic algorithm by combining a simulated annealing algorithm, adding a constraint matrix to establish an algorithm model, and step six, carrying out sensitivity analysis on 12 model parameters by adopting an orthogonal test design and regression analysis method; and seventhly, researching distribution parameters by using two parameters of Weibull distribution, wherein the distribution parameters guarantee normal operation of the emergency supply chain and have important practical value.
Description
Technical Field
The invention relates to the technical field of system optimization, in particular to a combined availability optimization method for preventive maintenance and control charts, which is suitable for an emergency production system.
Background
A novel coronavirus (COVID-19, Corona Virus Disease 2019) which is outbreaked at the end of 2019 makes medical supplies such as a mask, a protective clothing and a protective mask be in short emergency, and in the face of the sudden epidemic situation, many enterprises actively respond to national policies and enter a medical supplies emergency production mode. The capacity of the system is firstly ensured in the emergency production process rather than the pursuit of the system economy, and the availability of the system is used as the proportion of the effective operation time of the system, which is the key factor for restricting the capacity of the system.
Regarding the joint decision problem of preventive maintenance and control chart, the current research mainly starts from the economic aspect, and achieves the purpose of reducing the system operation cost by optimizing and improving the model, however, under the emergency production mode in the presence of sudden disasters such as epidemic situation, earthquake or seasonal demand, the system availability becomes the primary consideration target of replacing economy, and the integrated model construction idea based on economy is no longer applicable. Even under general non-emergency production conditions, the single economic model may reduce the availability of the system, and stealth losses such as delivery delay and user satisfaction reduction caused by low availability of the system may offset or even exceed the benefits of the single economic model. In addition, considering that the system has low abnormal occurrence probability in the initial operation stage in actual production, the delay monitoring is adopted to better ensure that the system availability reaches the maximum under the constraint of economic cost, and is favorable for the turnover of technicians and monitoring equipment under an emergency production system to a certain extent.
Therefore, the invention aims at the emergency production system, researches the integrated decision problem of preventive maintenance and control chart with delay monitoring based on the availability of the system under the condition of considering economic constraint, and provides theoretical and method support for the process quality monitoring and preventive maintenance integrated decision of the maximum capacity target of the production system under the emergency condition.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a combined availability optimization method for preventive maintenance and control chart applicable to an emergency production system, and the problem of combined availability optimization for preventive maintenance and control chart in the emergency production system is effectively solved.
The combined availability optimization method for preventive maintenance and control charts applicable to emergency production systems is characterized by comprising the following steps of:
firstly, setting that the repairable system only has controlled and out-of-control states, wherein the initial states of the system are controlled states, and the average value can drift due to system abnormality;
analyzing and defining the occurrence probability of two types of errors of the mean control chart;
step three, according to the step one and the step two, a combined availability model of preventive maintenance and mean value control chart based on delay monitoring is constructed; respectively establishing integrated models of preventive maintenance and control charts under six scenes of S1-S6, and solving the occurrence probability of each scene;
respectively solving the normal operation expected time, the system expected period, the system expected cost, the availability objective function and the economic constraint function of each updating situation according to the obtained six scene occurrence probabilities;
step five, combining a simulated annealing algorithm to improve a genetic algorithm, adding a constraint matrix to establish an algorithm model, and verifying the effectiveness of the model by adopting Python language and combining the production process of a certain steel pipe manufacturing enterprise;
sixthly, in order to provide guidance for the improved practice of system operation and maintenance management, sensitivity analysis is carried out on 12 model parameters by adopting an orthogonal test design and regression analysis method, and different influences of the model parameters on a target function are explained;
and seventhly, taking two parameters of Weibull distribution as an example, and researching the influence of the distribution parameters on the delay monitoring strategy selection through contrastive analysis of system availability change brought by different monitoring strategy selections under the same distribution parameters.
The invention expands the integrated optimization of preventive maintenance and control charts from a general production system taking economy as a decision-making target to an emergency production system taking availability as a decision-making target, can help the emergency production system to further improve the production capacity, strengthen the production management level, ensure the normal operation of an emergency supply chain, and has important practical value.
Drawings
FIG. 1 is a block diagram of the steps of the present invention.
FIG. 2 is a diagram of the system operation of the test production system of the present invention.
FIG. 3 is a table of model parameter descriptions for a test production system according to the present invention.
FIG. 4 is a system operating diagram of a test production system scenario S1 according to the present invention.
FIG. 5 is a system operating diagram of a test production system scenario S2 according to the present invention.
FIG. 6 is a diagram of a production system scenario S3 for testing according to the present invention.
FIG. 7 is a diagram of a production system scenario S41 for testing according to the present invention.
FIG. 8 is a production system scenario S42 system operational diagram for testing in accordance with the present invention.
FIG. 9 is a system operating diagram of a test production system scenario S5 according to the present invention.
FIG. 10 is a diagram of a production system scenario S6 for testing according to the present invention.
FIG. 11 is a table of equations for production system expectations for testing in accordance with the present invention.
FIG. 12 is a flow chart of a production system genetic annealing algorithm for testing in accordance with the present invention.
FIG. 13 is a table of production system parameter levels for testing in accordance with the present invention.
FIG. 14 is a table of orthogonal design and optimization results for a test production system according to the present invention.
FIG. 15 is a table of regression analysis of production systems for testing in accordance with the present invention.
FIG. 16 is a table of the sensitivity analysis of the model parameters of the test production system according to the present invention.
FIG. 17 is a system availability table for a delay monitoring strategy of a production system for testing in accordance with the present invention.
FIG. 18 is a table of system availability under the strategy of no-delay monitoring of the production system for testing according to the present invention.
FIG. 19 is a table of the system availability of the test production system according to the present invention.
FIG. 20 is a diagram of the system availability difference main effect analysis of the test production system of the present invention.
Detailed Description
The foregoing and other aspects, features and advantages of the invention will be apparent from the following more particular description of the embodiments, as illustrated in the accompanying drawings in which reference is made to figures 1-20. The structural contents mentioned in the following embodiments are all referred to the attached drawings of the specification.
Exemplary embodiments of the present invention will be described below with reference to the accompanying drawings.
Step one, because the occurrence probability of the abnormity at the initial operation stage of the system is low, and the process quality mean value drift amount is small, the implementation of delay monitoring on the system can save manpower and material resources, and can better pursue the maximum availability of the system under the condition of considering economic constraint. Therefore, a delay monitoring strategy is adopted for the system, namely, the control chart is not developed for monitoring from the beginning of the operation of the system, but enters a control chart monitoring period after the system operates for a period of time.
Considering that only two states of controlled state and out-of-control state exist in a production system, the initial state of the system is the controlled state, and the mean value can drift due to system abnormity. Because the production process of the system is monitored through the control chart, the invention adopts the mean value control chart to monitor the quality of the production process. Considering two types of error occurrence probabilities of the control chart and the fact that a preventive maintenance strategy is required to be carried out on the system regularly, when the control chart is alarmed, the system is stopped to be maintained immediately, otherwise, the system is operated to a preventive maintenance point to be maintained. Assuming that each repair is "repaired as new," the operation of the system belongs to an update process, the operation process being shown in FIG. 2.
In fig. 2, o denotes a system abnormality time point, × denotes a control map false alarm time point, ● denotes a control map found abnormality and correct alarm time point; PM (PM) indicates that Preventive Maintenance is performed, CM (complementary Maintenance) indicates that Compensatory Maintenance is performed, and RM (Reactive Maintenance) indicates that restorative Maintenance is performed; t isdIndicating a delay monitoring point, TpIndicating a preventive maintenance point.
In the scenarios S1 and S2, no abnormality occurs in the system during operation. When the control chart is not in false alarm in normal operation, the system is operated to a preventive maintenance point TpPerforming a shutdown check and performing preventive maintenance (S1); when a false alarm occurs in the control map, the system immediately stops checking and performs compensatory repairs at the alarm point (S2).
In scenarios S3 and S4, the system is abnormal during the control chart monitoring period. Control picture hairIf the abnormality occurs, the system is immediately stopped for inspection and recovery maintenance is carried out (S3); if the control chart is not abnormal, the system runs to a preventive maintenance point TpA shutdown check is performed, a system abnormality is found, and recovery maintenance is performed (S4).
In scenarios S5 and S6, the system has experienced an anomaly during the delayed monitoring period. When the system enters a control chart monitoring period, if the control chart is abnormal and alarmed, the system is immediately stopped for inspection and recovery maintenance is carried out (S5); if the control map is not abnormal, the system runs to a preventive maintenance point Tp for shutdown check, the system is abnormal and recovery maintenance is performed (S6), and the model parameters are described as shown in FIG. 3.
And step two, recording the occurrence probability of the first type of false alarm and the second type of false negative of the control chart as alpha, wherein n represents the sample amount of each sampling of the control chart, h represents the interval of the sampling, and k represents the control chart control line parameter. Assuming that the quality characteristic X when the system is controlled follows a normal distribution
Mean shift to mu when system is out of control0B, wherein μ0And σ0Mean value and standard deviation when the system is normal, mean value drift amount when the system is abnormal, phi represents a numerical value in brackets and follows standard normal distribution.
At this time, control lines on the diagram: UCL ═ mu0+kσ0And (3) controlling the following lines: LCL ═ mu0-kσ0。
Probability of occurrence of a first type of false error: α is 2-2 φ (k) (1)
Probability of occurrence of false negative report of the second kind:
and step three, constructing a preventive maintenance and mean value control chart integrated model based on delay monitoring according to the step one and the step two. And respectively establishing a preventive maintenance and control chart integrated model under six scenes of S1-S6, and solving the occurrence probability of each scene.
(1) S1: the system operates normally, and the control chart is normal.
Under the situation, the system always operates normally, the control chart also always operates normally and does not give an alarm, and the system is arranged at a preventive maintenance point TPPreventive maintenance is performed as shown in fig. 4. Defining event A1For normal operation of the system to a preventive maintenance point, event B1If the control chart is not in normal operation and is not alarmed, the occurrence probability of S1 is as follows:
P1＝P(A1∩B1)＝P(A1)P(B1|A1)＝[1-F(TP)]·(1-α)L (3)
(2) s2: the system operates normally, and false alarm of control chart
Under the condition, the system runs normally, false alarm occurs in the monitoring period of the control chart, and compensatory maintenance is executed at the alarm point by the system. Suppose a control chart is at tiFalse alarms occur during sub-sampling, at which time the system is shut down to perform compensatory repairs, as shown in FIG. 5. Defining event A2For the system to normally run to tiSample point, event B2At t for control ofiFalse alarm occurs at the sampling point. The probability of occurrence of S2 is:
the system normal operation time is T at the momentd+ i.h, no abnormal operation time, system down maintenance time TCM(ii) a The quality loss in normal operation of the system is (T)d+i·h)·Cl1(ii) a Shutdown loss of TCMCd, the sampling detection cost is i.Cs, the system executes compensatory maintenance, and the maintenance cost is CCM。
(3) S3: the system starts to generate abnormity in the monitoring period of the control chart, and the control chart alarms correctly
Under the condition, the system abnormity occurs in the control chart monitoring period, the control chart finds the abnormity and gives an alarm, and the system executes recovery maintenance at an alarm point. Suppose a system anomaly point u3Occurs at ti-1To tiStage, control chart at tjThe point detects a system anomaly and raises an alarm and the system is immediately shut down for restorative maintenance RM, as shown in fig. 6. Defining event A3For the system during the sampling interval (t)i-1-ti) Very short time (u)3,u3+ du) occurrence of an exception, event B3At t for control ofjThe sampling point finds abnormality and gives an alarm correctly. The probability of occurrence of S3 is:
the system uptime is u at this time3The abnormal operation time is Td+j·h-u3And the system is stopped for maintenance time TRM(ii) a The quality loss is u when the system operates normally3·Cl1The abnormal operation process has a mass loss of (T)d+j·h-u3)·Cl2Shutdown loss of TRMCd, sampling detection cost j.Cs, system execution recovery maintenance, maintenance cost CRM。
(4) S4: the system is abnormal in the monitoring period, and the control chart is not alarmed
Such a scenario can be further discussed in two cases, S41 and S42, below, according to the difference in the positions where the abnormality occurs.
S41: system anomaly point u41T occurring during control chart monitoring period before last samplingi-1To tiStage, controlling missed alarm and running the system to the preventive maintenance point TPA restorative repair RM is performed as shown in fig. 7. Defining event A41For the system during the sampling interval (t)i-1-tii.ltoreq.L) of very short time (u)41,u41+ du) occurrence of an exception, event B41To control the alarm leakage. The probability of occurrence of S41 is:
the system uptime is u at this time41Abnormal operationTime is Tp-u41And the system is stopped for maintenance time TRM(ii) a The quality loss is u when the system operates normally41·Cl1The abnormal operation process has a mass loss of (T)p-u41)·Cl2Shutdown loss of TRMCd, sampling detection cost L.Cs, system execution recovery maintenance, maintenance cost CRM。
S42: system anomaly point u42The system is operated to a preventive maintenance point T between the last sampling and the preventive maintenance pointPAnd performs a restorative repair RM. The system operates as shown in FIG. 8, defining event A42Is a system in (t)L～Tp) Very short time of phase (u)42,u42+ du) occurrence of an exception, event B42No alarm is provided for controlling normal operation. The probability of occurrence of S42 is:
the system uptime is u at this time42The abnormal operation time is Tp-u42And the system is stopped for maintenance time TRM(ii) a The quality loss is u when the system operates normally42·Cl1The abnormal operation process has a mass loss of (T)p-u42)·Cl2Shutdown loss of TRMCd, sampling detection cost L.Cs, system execution recovery maintenance, maintenance cost CRM。
(5) S5: the system is abnormal in the delayed monitoring period, and the control chart alarms correctly
In this case, the system abnormality occurs in the delay monitoring period, and after the system enters the control chart monitoring period, the control chart detects a fault and gives an alarm, and the system is immediately shut down for recovery maintenance RM, as shown in fig. 9. Defining event A5For the system during the sampling interval (0, T)d) Very short time (u)5,u5+ du) occurrence of an exception, event B5At t for control ofiThe sampling point finds abnormality and gives an alarm correctly. The probability of occurrence of S5 is:
the system uptime is u at this time5The abnormal operation time is i.h + Td-u5And the system is stopped for maintenance time TRM(ii) a The quality loss is u when the system operates normally5·Cl1The mass loss in the abnormal operation process is (i.h + T)d-u5)·Cl2Shutdown loss of TRMCd, the sampling detection cost is i.Cs, the system executes the recovery maintenance, and the maintenance cost is CRM。
(6) S6: the system is abnormal in the delayed monitoring period to control the missed alarm
In this case, the system abnormality occurs in the delayed monitoring period, after the system enters the control chart monitoring period, the control chart does not send an alarm and the missed detection occurs, and the system runs to the preventive maintenance point to perform the recovery maintenance RM, as shown in fig. 10. Defining event A6For the system during the sampling interval (0, T)d) Very short time (u)6,u6+ du) occurrence of an exception, event B6To control the alarm leakage. The probability of occurrence of S6 is:
the system uptime is u at this time6The abnormal operation time is Tp-u6And the system is stopped for maintenance time TRM(ii) a The quality loss is u when the system operates normally6·Cl1The abnormal operation process has a mass loss of (T)p-u6)·Cl2Shutdown loss of TRMCd, sampling detection cost L.Cs, system execution recovery maintenance, maintenance cost CRM。
Step four: the system operation period consists of the normal operation time of the system, the abnormal operation time of the system and the shutdown maintenance time; the system running cost is determined by the maintenance cost and the normal running quality of the systemThe system comprises five parts of volume loss, system abnormal operation quality loss, shutdown loss and sampling cost. Suppose ZiIndicating scenario i System uptime, TiIndicating scenario i System update period, CiRepresents scenario i System update cost, PiRepresenting the probability of occurrence of scenario i, E (Z)i)＝Zi·PiIndicating the expected time of normal operation of the system, E (T), of scenario ii)＝Ti·PiIndicating scenario i System expectation period, E (C)i)＝Ci·PiRepresenting the scenario i system expected cost.
According to the theory of the updating process, the expected availability of the system under the long-term use condition is equal to the expected availability of one updating period, namely the system availability is expressed as the expected time E (Z) for normal operation of the system under six updating situationsi) Sum and desired period E (T)i) The ratio of the sums; the expected cost of the system under long-term use conditions is equal to the expected cost of one update cycle, i.e. the expected cost per unit time of the system is expressed as the expected cost E (C) in six scenariosi) Sum and desired period E (T)i) The ratio of the sums. E (Z) under six scenesi)、E(Ti)、E(Ci) Solving formula as shown in fig. 11, it can be known from the theory of the desired solving formula and the updating process of fig. 11 that the system availability and the desired cost per unit time of the system can be expressed as:
and (3) combining the availability of the system and the expected cost model in unit time, establishing a preventive maintenance and mean value control chart combined optimization model which takes the availability as the maximum decision target and considers economic constraint under delayed monitoring:
n, h, k, T in the formulae (10) and (12)p、TdAll are decision variables and are respectively expressed as sample capacity, sampling interval, control line coefficient, preventive maintenance period and delayed monitoring period of the control chart, ECTERepresenting a cost per unit time constraint value.
Step five: because the genetic algorithm is easy to fall into local optimum, and the simulated annealing algorithm can accept the solution worse than the current solution with a certain probability along with the continuous reduction of the temperature when the feasible solution is updated iteratively, the local optimum can be skipped to achieve the global optimum, therefore, the invention mainly combines the simulated annealing algorithm to improve the genetic algorithm and adds a constraint matrix to establish an algorithm model. The algorithm model can be ensured to rapidly process complex constraints, meanwhile, the efficiency and the accuracy of the algorithm can be improved, and the flow of the genetic annealing algorithm model is shown in FIG. 12.
First, a decoding matrix is created. Inputting a decision variable value range: n to [3, 30%]、h～[1,240]、TP～[240,2400]、Td～[0，TP-H](if result T is optimized)dWhen the value is taken to the upper and lower boundaries, the model is invalid), K- [1.6, 4.6 ]]. The coding mode adopts binary coding and arithmetic graduation;
and secondly, setting parameters of the genetic simulated annealing algorithm. The population scale is 50, the maximum genetic algebra is 50, two points are crossed by random sampling, the crossing probability is 0.6, the variation probability is 0.01, the initial temperature is 100, the maximum temperature iteration number is 10, the iteration number at each temperature is 20, and the boltzmann constant is 0.9;
thirdly, establishing an initial population, and calculating a population fitness value according to a constraint matrix;
fourthly, carrying out genetic algorithm evolution operation: selecting, recombining and mutating, and reserving the paternal elite individuals to form a new population;
fifthly, performing simulated annealing on the whole new population to form a new population, calculating a population fitness value, and recording optimal individuals;
and sixthly, circulating operation and program output. And repeating the three-five steps until the traversal is completed, and outputting the optimal variable value.
And seventhly, verifying the process. It is known that the key quality characteristic of the output product of this system is heat tolerance (X), and the key component is Z when the system is controlled, X obeys the mean value mu 0600, standard deviation σ0Normal distribution of 28, i.e. X to N (600, 28)2) When the critical component Z is abnormal to cause the system to be out of control, the mean value of X is shifted to 584, that is, the mean value shift amount is-16. According to historical data analysis, the fault occurrence time of the key component Z follows a Weibull distribution of a scale parameter theta 100 and a shape parameter eta 2. In the operation process of the system in 2019, a planned and set control chart parameter n is 5, h is 48h, and k is 3; the system does not perform delay monitoring, i.e. Td0h, preventive maintenance planning interval TP2160 h; the maintenance cost and time of the year are respectively counted as CCM62 yuan, TCM＝4.8h、CRM730 yuan, TRM＝19.2h、CPM325 Yuan, TPM7.2h, loss of product quality is Cl116.25 yuan/h, Cl222.083 yuan/h, the shutdown loss is CdFixed cost C of each sampling test is 12.5 yuan/h f20 yuan, variable cost Cq4-membered.
The operation parameters of the enterprise system are substituted into a usability formula (10) and a cost model formula (11), and A is obtained through calculation0＝0.823，ECT0242.126 yuan/day; based on field data, statistical analysis can obtain that the availability of the system in 2019 is 0.8, the total production cost is 92354 yuan, and the average daily cost is 92354/365-253.025 yuan. Model calculation value A0Relative deviation from actual value of 0.029, ECT0The relative deviation from the actual value is 0.043, and the model has good consistency, so that the model can better depict the actual production condition.
Suppose the enterprise wishes to increase production system availability while keeping production costs within 200 dollars per day. Performing genetic simulation annealing optimization based on python language by using a preventive maintenance and control chart integrated optimization model based on delay monitoring, and calculating to obtain an optimized resultComprises the following steps: 22, 58.287h, 2.695 k, TP＝576h，Td135.402h, the availability of the system is 0.98 and the cost per unit time is 199.724 yuan/day. Compared with A before optimization0And ECT0The availability is improved by 0.157, and the cost is reduced by 42.402 yuan/day.
Step six, in order to provide guidance for the improvement practice of system operation and maintenance management, step C is further described belowCM、TCM、CRM、TRM、CPM、TPM、Cl1、Cl2、Cd、Cf、CqA total of 12 model parameters were analyzed for sensitivity. Considering that the number of the test factors is large, the test design adopts a Taguchi design method, and 12 model parameters are horizontally set according to the actual production situation, as shown in FIG. 13. Construction of L Using minitab software16(212) And solving 16 sets of parameters based on Python language according to an improved genetic simulated annealing algorithm by using an orthogonal table, wherein the calculated values of the orthogonal table, various decision variables, availability, cost and the like are shown in FIG. 14.
Regression analysis was performed on the 16 sets of usability optimization results in fig. 14 using minitab software (fig. 15), where R-Sq represents the correlation coefficient (the larger the value is, the better the model fits the data), and R-Sq (adjustment) represents the corrected correlation coefficient (the closer the value is to the value of R-Sq, the more reliable the model), and as can be seen from fig. 15, the model is reliable when R-Sq (adjustment) is 97.4% and the difference is not much from R-Sq to 98.4%; p is the test significance value, P ═ 0, and the presence parameter had a significant effect on the availability a.
The sensitivity analysis of the model parameters obtained by regression analysis is shown in FIG. 16. As can be seen from the parameter coefficients and P values in FIG. 16, TCM、TRM、TPM、Cl1、Cl2、CqAll have a significant effect on the availability, which is manifested as a very significant positive effect, Cl1It is shown as a very marked negative effect, TCM、TRM、TPM、Cl2、CqShowing a significant negative effect.
As can be seen from the view in figure 16,the mean shift quantity has very obvious positive influence on the availability, because the larger the mean shift quantity is, the more beneficial the control chart can find the abnormal phenomenon existing in the system operation in time and send out an alarm, the abnormal operation time of the system is effectively reduced, and the system availability is further improved. Mass loss Cl per unit time during normal operation of system1Shows a very significant negative effect on the availability with a loss of mass Cl per unit time in abnormal operation2Shows a significant negative effect on the availability, due to Cl1The increase will result in a large increase in system operating cost due to cost constraints in the decision model when Cl is present1When added, shorter uptime has to be chosen to meet cost constraints, resulting in reduced availability. In the same way, Cl2The increase will also result in increased system operating costs and thus reduced system availability, but since the main operating mode of the system is normal in general, Cl is the operating mode of the system1Is shown to be very remarkable as Cl2The appearance was significant. Variable cost per spot check CqThe system availability is shown to be significantly negatively affected, while the cost C is fixed for each spot checkfThe effect is insignificant, because of the total cost C of each spot tests＝n×Cq+CfWhen each sampling inspection is carried out, the cost is variable CqWhen the sampling rate is increased, the single sampling cost of the system is greatly increased, so that the model can selectively reduce the sample sampling amount to ensure that the total cost is still in the economic constraint, the missing detection probability of the abnormity is increased, and the usability of the system is reduced. T isCM、TRM、TPMThe three parameters have a significant negative impact on the availability, since an increase in the three maintenance times will directly result in an increase in the system operating period, which in turn reduces the system availability.
Based on the above analysis results, in order to improve the availability of the system, the key direction of improving the operation and maintenance of the system should focus on the two aspects of reducing the maintenance time and the operation and maintenance cost. In the aspect of maintenance time, the technical level of maintenance personnel can be improved by strengthening the technical training of the maintenance personnel, so that the maintenance time of compensatory maintenance, restorative maintenance and preventive maintenance is continuously shortened, and the system can be ensured to operate more quickly and stably. In the aspect of maintenance cost, because the normal operation cost and the abnormal operation cost of the system have obvious influence on the availability, the operation process of the system needs to be optimized, and the operation cost of the system is further controlled, the availability of the system is improved and the capacity of the system is ensured by improving and optimizing the production process; meanwhile, the variable cost of the spot check is controlled well, and the increase of the probability of the occurrence of the missed inspection event caused by overhigh cost of the spot check is avoided. In addition, the mean shift amount has a very significant positive influence on the availability, and the availability of the system can be improved by increasing the process quality shift amount caused by system abnormity through technical improvement, but the increase generally causes the increase of quality loss, so the quality cost is comprehensively weighed when the availability of the system is improved through the method.
Step seven, the Weibull distribution of the two parameters is the common distribution of the system reliability and is widely applied in production practice. The invention mainly takes two parameters of Weibull distribution as an example, and researches the influence of the distribution parameters on the selection of the delay monitoring strategy by comparing and analyzing the change of the system availability caused by the selection of different monitoring strategies under the same distribution parameters.
As can be seen from fig. 14, the system achieved the maximum availability at the parameter settings of the test set 15. The system availability results of the delayed monitoring and non-delayed monitoring strategies under different level combination conditions of the scale parameter theta and the shape parameter eta are calculated by using the set of parameter values such as cost and time as input data of the model parameters, and are respectively shown in fig. 17 and fig. 18. Based on the availability data in fig. 17 and fig. 18, the availability difference between the delay monitoring system and the non-delay monitoring system under different values of the distribution parameter (system availability difference between the system availability under the delay monitoring strategy and the system availability under the non-delay monitoring strategy) is calculated, and the result is shown in fig. 19.
The main effect analysis was performed on the system availability difference values of fig. 19, and a main effect analysis result graph was plotted (fig. 20). As can be seen from fig. 20, the difference in the availability of delay monitoring and no-delay monitoring increases with increasing values of the shape parameter and the scale parameter. That is, whether for shape parameters or scale parameters, larger parameter values are more desirable to employ a delay monitoring strategy. This is mainly because, for a weibull distribution, the larger the shape and scale parameters, the lower the early failure rate. The lower the early failure rate of the system, the lower the availability benefit brought by correct alarm of the control diagram on one hand, and on the other hand, the higher the probability of false alarm of the control diagram at the moment, which is known by the formula (4), and the higher the loss of the system availability caused by the probability is. Therefore, the lower the system failure rate, the greater the utility of the availability enhancement brought by the delay monitoring, i.e. for a system whose reliability complies with the weibull distribution, the larger the shape parameters and the scale parameters, the more suitable the delay monitoring strategy is to be adopted.
The invention provides a preventive maintenance and control chart combined availability optimization method considering a delay monitoring strategy aiming at emergency production and a high availability requirement system. Compared with the traditional economic model, the model can effectively improve the availability of the system, better guarantee the productivity of the system and control the cost economy.
The invention expands the integrated optimization of preventive maintenance and control charts from a general production system taking economy as a decision-making target to an emergency production system taking availability as a decision-making target, can help the emergency production system to further improve the production capacity, strengthen the production management level, ensure the normal operation of an emergency supply chain, and has important practical value.
Claims (5)
1. The combined availability optimization method for preventive maintenance and control charts applicable to emergency production systems is characterized by comprising the following steps of:
firstly, setting that the repairable system only has controlled and out-of-control states, wherein the initial states of the system are controlled states, and the average value can drift due to system abnormality;
analyzing and defining the occurrence probability of two types of errors of the mean control chart;
step three, according to the step one and the step two, a combined availability model of preventive maintenance and mean value control chart based on delay monitoring is constructed; respectively establishing integrated models of preventive maintenance and control charts under six scenes of S1-S6, and solving the occurrence probability of each scene;
respectively solving the normal operation expected time, the system expected period, the system expected cost, the availability objective function and the economic constraint function of each updating situation according to the obtained six scene occurrence probabilities;
step five, combining a simulated annealing algorithm to improve a genetic algorithm, adding a constraint matrix to establish an algorithm model, and verifying the effectiveness of the model by adopting Python language and combining the production process of a certain steel pipe manufacturing enterprise;
sixthly, in order to provide guidance for the improved practice of system operation and maintenance management, sensitivity analysis is carried out on 12 model parameters by adopting an orthogonal test design and regression analysis method, and different influences of the model parameters on a target function are explained;
and seventhly, taking two parameters of Weibull distribution as an example, and researching the influence of the distribution parameters on the delay monitoring strategy selection through contrastive analysis of system availability change brought by different monitoring strategy selections under the same distribution parameters.
2. The joint availability optimization method for preventive maintenance and control charts applicable to emergency production systems as claimed in claim 1, wherein the six update scenarios in the first step are S1-S6, wherein:
s1 and S2: the system has no abnormality in the operation process;
s1: when the control chart is not in false alarm in normal operation, the system is operated to a preventive maintenance point TpPerforming a shutdown check and performing preventive maintenance;
s2, when false alarm occurs to the control chart, the system immediately stops working at the alarm point for inspection and compensatory maintenance;
s3 and S4: the system is abnormal in the control chart monitoring period;
s3: if the control chart is abnormal, the system is immediately stopped for inspection and is subjected to restorative maintenance;
s4: if the control chart is not abnormal, the system runs to a preventive maintenance point TpPerforming shutdown inspection, finding system abnormality and executing recovery maintenance;
s5 and S6: the system has an abnormality in the delayed monitoring period;
s5: when the system enters a control chart monitoring period, if the control chart finds abnormal alarm, the system is immediately stopped for inspection and executes restorative maintenance;
and S6, if the control chart is not abnormal, the system runs to a preventive maintenance point Tp for shutdown check, the system is abnormal and recovery maintenance is carried out.
3. The combined availability optimization method for preventive maintenance and control charts applicable to emergency production systems according to claim 2, characterized in that in said second step:
probability of occurrence of a first type of false error: α is 2-2 φ (k) (1)
Probability of occurrence of false negative report of the second kind:
recording the probability of occurrence of the first false alarm and the second false alarm of the control chart as alpha, n represents the sample amount of each sampling of the control chart, k represents the control chart control line parameter, and mu0And σ0Mean value and standard deviation when the system is normal, mean value drift amount when the system is abnormal, phi represents a numerical value in brackets and follows standard normal distribution.
4. The preventive maintenance and control chart joint availability optimization method for emergency production systems according to claim 3, characterized in that in the third step:
s1: the system runs normally, and the control chart is normal;
defining event A1For normal operation of the system to a preventive maintenance point, event B1If the control chart is not in normal operation and is not alarmed, the occurrence probability of S1 is as follows:
P1＝P(A1∩B1)＝P(A1)P(B1|A1)＝[1-F(TP)]·(1-α)L (3)
s2: the system operates normally, and false alarm of control charts is controlled;
defining event A2For the system to normally run to tiSample point, event B2At t for control ofiIf the sampling point generates a false alarm, the occurrence probability of S2 is:
s3: the system starts to generate abnormity in the control chart monitoring period, and the control chart alarms correctly;
defining event A3For the system during the sampling interval (t)i-1-ti) Very short time (u)3,u3+ du) occurrence of an exception, event B3At t for control ofjIf the sampling point finds abnormality and gives an alarm correctly, the occurrence probability of S3 is:
s4: the system is abnormal in the monitoring period, and the control chart is not alarmed;
such a scenario can be further divided into the following two cases S41 and S42 according to the position difference of the abnormal occurrence:
s41 defining event A41For the system during the sampling interval (t)i-1-tii.ltoreq.L) of very short time (u)41,u41+ du) occurrence of an exception, event B41To control the missed alarm, the probability of occurrence of S41 is:
s42: defining event A42Is a system in (t)L～Tp) Very short time of phase (u)42,u42+ du) occurrence of an exception, event B42If the control chart is not in normal operation and is not alarmed, the occurrence probability of S42 is as follows:
s5: the system is abnormal in the delayed monitoring period, and the control chart can alarm correctly;
defining event A5For the system during the sampling interval (0, T)d) Very short time (u)5,u5+ du) occurrence of an exception, event B5At t for control ofiIf the sampling point finds abnormality and gives an alarm correctly, the occurrence probability of S5 is:
s6: the system is abnormal in the delay monitoring period, and control leakage alarm is carried out;
defining event A6For the system during the sampling interval (0, T)d) Very short time (u)6,u6+ du) occurrence of an exception, event B6To control the missed alarm, the probability of occurrence of S6 is:
f (u), F (u) are density function and distribution function when system abnormity occurs, and L is maximum sampling times in the preventive maintenance period.
5. The combined availability optimization method for preventive maintenance and control charts applicable to emergency production systems according to claim 4, characterized in that in said step five:
the genetic annealing algorithm model process comprises the following steps:
firstly, establishing a decoding matrix;
secondly, setting parameters of a genetic simulated annealing algorithm;
thirdly, establishing an initial population;
fourthly, carrying out genetic algorithm evolution operation;
fifthly, performing simulated annealing on the whole new population to form a new population, calculating a population fitness value, and recording optimal individuals;
sixthly, circularly operating and outputting programs;
and seventhly, verifying the process.
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| CN114882715A (en) * | 2022-05-07 | 2022-08-09 | 郑州航空工业管理学院 | Emergency traffic operation staged optimization method |
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| CN113297723A (en) * | 2021-04-22 | 2021-08-24 | 哈尔滨理工大学 | Mean shift-grey correlation analysis based optimization method for temperature measuring points of motorized spindle |
| CN114882715A (en) * | 2022-05-07 | 2022-08-09 | 郑州航空工业管理学院 | Emergency traffic operation staged optimization method |
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