CN116384876A - Spare part dynamic inventory-production control method, system and medium based on wiener process - Google Patents
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Abstract
The invention discloses a spare part dynamic inventory-production control method, a system and a medium based on a wiener process, wherein the method comprises the following steps: determining a probability density function of the remaining useful life of each component based on the wiener process degradation parameters; according to the real-time degradation state of each component, respectively updating the degradation parameters of the wiener process of each component, and updating the probability density function of the residual service life by using the updated degradation parameters of the wiener process; calculating the total requirements of the internal and external spare parts in the next stage according to the updated probability density function of the residual service life; constructing a decision model according to the spare part production cost, the storage cost and the total spare part demand of the next stage; solving an optimization problem aiming at the decision model to obtain the optimal safety stock and production to the level, adjusting the stock of spare parts according to the optimal safety stock, and adjusting the yield of spare parts according to the optimal production to the level. The invention can avoid backlog and backorder of spare parts and reduce the production and inventory cost of spare parts.
Description
Technical Field
The invention relates to the field of engineering equipment management, in particular to a spare part dynamic inventory-production control method, system and medium based on a wiener process.
Background
With the increase of market competition in economic globalization and industrial 4.0 background, the requirements of engineering equipment on reliability are increasing. However, during the long-term operation of the equipment, degradation of its performance inevitably occurs due to its own factors and the influence of the external environment; and uncertain events such as abrupt environmental changes, improper manual operations and the like objectively exist, so that sudden faults of equipment are possible at any time. When a certain part of the equipment is changed, if the part cannot be found in advance and replaced in time, huge loss is brought to the system. Therefore, how to ensure that equipment operates safely and reliably is a difficult problem facing enterprises. The fault prediction and health management (Prognostics and health management, PHM) technique plays a key role in solving this problem, and based on the degradation state monitored by the sensor, it provides reliable prediction for the remaining service life of the equipment, and provides effective support for equipment management and inventory control. The application of the technology has great significance for guaranteeing the long-term stable, safe and reliable operation of engineering equipment.
Demand forecast determines how well inventory control is. Existing inventory control techniques mostly incorporate traditional demand prediction methods, such as exponential smoothing prediction (exponential smoothing forecasting technique), crosston method (Crosston method), bootstrapping method (bootstrapping method), etc., which only consider historical demands and only react to what happens in the past, that is, they predict in a passive way. While PHM technology tracks the operational status of components in real time, taking into account the factors that generate spare part demands (i.e., the failure behavior of the components), demand prediction is made possible in an proactive manner.
Warranty services are an integral part of the marketing strategy of most manufacturers, and are also a key determinant of purchase decisions by most customers, which can guarantee the availability of vending equipment during warranty periods to maintain the benefits of the customers as much as possible. The warranty service takes effect immediately while the manufacturer sells the equipment. Warranty services typically require manufacturers to replace all components that fail during a warranty period free or at a low cost and in time to reduce the loss of equipment downtime. While outside of the warranty period, the manufacturer only replaces the failed component for those customers who placed replacement orders, rather than replacing all of the failed components, while obtaining significant profits therefrom. Therefore, the manufacturer must produce enough spare parts in advance to ensure that replacement measures are properly implemented during and out of warranty. However, excessive spare parts can lead to spare part wastage, capital occupation, stock backlog, and other problems. Therefore, how to effectively inventory and control the production of spare parts during and outside of warranty has become a major issue for manufacturers.
The prior patent also discloses related technologies about wiener process and spare part inventory control, wherein the patent CN201310424597 carries out predictive analysis on characteristic quantities of individual residual life and overall reliability life of a product, can be used as an effective analysis tool for predicting the residual life and failure times of the product, provides powerful technical support for spare part ordering, and does not relate to optimization of parameters related to spare part inventory control; patent CN202210641012 optimizes inventory control parameters but is applicable only to single component systems. In practice, the inventory control of enterprises is extremely complex and often involves a large number of components, so the application of the two patents still has a certain limitation. As can be seen, wiener process and inventory control for multi-component systems is a technology that is yet to be developed and has application value.
Disclosure of Invention
The invention aims to solve the technical problems: aiming at the problems in the prior art, the method, the system and the medium for controlling the dynamic inventory-production of the spare parts based on the wiener process are provided, so that backlog and backorder of the spare parts are avoided, and meanwhile, the production and inventory cost of the spare parts are reduced.
In order to solve the technical problems, the invention adopts the following technical scheme:
a spare part dynamic inventory-production control method based on a wiener process comprises the following steps:
s1) determining a probability density function of the residual service life of each part according to the degradation parameters of the wiener process;
s2) according to the real-time degradation state of each component, respectively updating the degradation parameters of the wiener process of each component, and updating the probability density function of the residual service life of each component by using the updated degradation parameters of the wiener process of each component;
s3) calculating the total requirement of spare parts in the next stage according to the probability density function of the residual service life of each updated part;
s4) constructing a decision model according to the spare part production cost, the storage cost and the total spare part demand of the next stage;
s5) solving an optimization problem aiming at the decision model, obtaining the optimal safety stock and production to the level, adjusting the stock of spare parts according to the optimal safety stock, and adjusting the yield of the spare parts according to the optimal production to the level.
Further, the probability density function expression of the remaining service life of each component in step S1 is as follows:
in the above, f (l) mk |x mk ) Is a probability density function of the remaining useful life of component m, ω mf Is the failure threshold of component m, l mk Is the remaining life time interval of component m, x mk Is part m at t k The state of degradation, mu, monitored at the moment mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Mean, sigma of mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Variance, sigma of mk Is the wiener process degradation parameter of component m at t k Diffusion coefficient at time.
Further, the wiener process degradation parameter expression of each component is updated in step S2 as follows:
in the above, t k Represents the current time, k represents the sequence number of the current time, x mn Is part m at t n Time-of-day monitored degradation state, x m(n-1) Is part m at t (n-1) The degradation state monitored at the moment is 1-n-k and mu mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Mean, mu mλ0 Is the wiener process degradation parameter of component m at t 0 Drift coefficient lambda of time of day m Mean, sigma of mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Variance, sigma of mλ0 Is the wiener process degradation parameter of component m at t 0 Drift coefficient lambda of time of day m Variance, sigma of mk Is the wiener process degradation parameter of component m at t k Diffusion coefficient at time.
Further, the total requirement expression of the inside and outside spare parts in the next stage in step S3 is as follows:
in the above formula, d (nT) represents the total requirements of the inside and outside spare parts in n monitoring intervals in the future, and p f (nT|g) represents the probability of g components failing within n monitoring intervals in the future, M represents the total number of components in the system, T represents the state monitoring interval, g represents the number of components failing, Q g Representing a set of combinations of g failed components, q g Represents Q g Is a subset of the set of (c),
represents q g I and j are part numbers, f (l) ik |x ik ) Is a probability density function of the remaining useful life of component i, l ik Is the remaining life time interval of component i, x ik Is part i at t k The state of degradation, f (l) jk |x jk ) Is a probability density function of the remaining useful life of component j, l jk Is part jRemaining life time interval, x jk Is part j at t k Time-of-day monitored degenerative conditions,/->
And->
Respectively representing the probability of failure of the components i and j within n monitoring intervals in the future, U i And U j Is a judgment parameter.
Further, if component i fails during the warranty period, U i =1; if component i fails outside of warranty period, U in case of customer selection of replacement spare parts for the enterprise i =1, U in case the customer selects other suppliers to replace spare parts i =0; if part j fails during the warranty period, U j =1; if component j fails outside of warranty period, U in case the customer chooses to replace spare parts of the enterprise j =1, U in case the customer selects other suppliers to replace spare parts j ＝0。
Further, the decision model expression in step S4 is as follows:
in the above formula, d (nT) represents the total spare part demand in n monitoring intervals in the future, p f (nT|g) represents the probability of g component failures in the next n monitoring intervals, c e Representing the cost of developing and processing a production plan c p Representing the cost of producing a spare part c h Representing the cost of storing one spare part per unit time, gamma represents the proportion of the failed parts that need emergency replacement, F Q Representing the total number of spare parts historically provided to the customer by the manufacturer, F q Represents F Q Number of spare parts ss for emergency replacement k Indicated at t k The remaining inventory of time, M, represents the total number of components in the system, T represents the status monitoring interval, the production cycle is less than or equal to T, g represents the number of failed componentsNT represents the expected cycle length before the next production start, EC (S k ) Representing cost rate, s' (t) k,n ) Represents the initial value of the safety stock in the nth monitoring interval in the future, s (t k,n ) Representing safety stock correction values, s, within the nth monitoring interval in the future k Safety stock representing the kth monitoring phase, S k Indicating production to level for the kth monitoring stage.
Further, solving the optimization problem for the decision model in step S5 includes: cost rate EC (S) k ) As an objective function, the objective function is solved by a numerical iteration method, so that the total cost per unit time is minimized.
The invention also provides a spare part dynamic inventory-production control system based on the wiener process, which comprises:
the PHM system is used for monitoring the component degradation state of engineering equipment and determining a probability density function of the residual service life of each component according to the degradation parameters of the wiener process; the probability density function is used for updating the wiener process degradation parameters of each component according to the real-time degradation states of the components and updating the residual service life of each component by using the updated wiener process degradation parameters of each component;
the enterprise manager is used for calculating the total requirement of spare parts in the next stage according to the residual life prediction result of the parts and the spare part ordering intention of the customer after each part fails outside the warranty period;
the inventory-production optimization system is used for constructing a decision model according to the production cost of spare parts, the storage cost and the total requirement of spare parts in the next stage, and solving an optimization problem aiming at the decision model to obtain the optimal safety inventory and production to the level;
a production shop for adjusting the spare part production according to the optimal production to level;
and the warehouse is used for storing spare parts produced in the production workshop, providing the spare parts for engineering equipment and adjusting the spare part stock according to the optimal safety stock.
The invention also provides a spare part dynamic inventory-production control system based on the wiener process, which comprises computer equipment, wherein the computer equipment is programmed or configured to execute any spare part dynamic inventory-production control method based on the wiener process.
The invention also proposes a computer readable storage medium having stored therein a computer program programmed or configured to perform any of the wiener process-based spare part dynamic inventory-production control methods.
Compared with the prior art, the invention has the following advantages:
aiming at a multi-component system, the invention combines fault prediction and health management technologies to determine probability density functions of the residual service lives of all components, and real-time estimates and updates relevant parameters of a degradation process according to state monitoring; actively predicting the probability of failure of each component in the next monitoring stage; analyzing and calculating the total internal and external spare part requirements; modeling inventory and production related costs; the optimal safety stock and production to the level of each monitoring stage are obtained, and the conditions of stock shortage or stock surplus commonly existing in the field of stock management are avoided, so that the stock and production cost of the system are reduced, and the application range of the stock control technology based on the wiener process is widened.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is a schematic diagram of a spare part dynamic inventory-production control according to an embodiment of the present invention.
Detailed Description
The invention is further described below in connection with the drawings and the specific preferred embodiments, but the scope of protection of the invention is not limited thereby.
Before describing the present embodiment, description will be made on related concepts:
the wiener process comprises the following steps: the Wiener process (English : wiener process) is a continuous time random process, known as Yu Nuo Bert-Wiener. Due to its close relationship with Brownian motion in physics, it is also often referred to as the "Brownian motion process" or simply Brownian motion. The wiener process is the most well-known one in the Lewy process (namely a smooth independent increment random process with left and right continuous limits), and has important application in pure numerology, application mathematics, economy and physics. The wiener process is not strictly monotonic, is suitable for modeling performance degradation processes with monotonic fluctuations, and can be easily extended to meet different requirements due to its mathematical properties and physical interpretation, and provides a good description of some system behaviors. A particular advantage of the wiener process is that the distribution of the time to failure can be analytically represented by a probability density function of the time to arrival, which makes the wiener process widely applicable for the prediction of the remaining useful life of the equipment.
The first time is as follows: the first time (first entrance time or first passagetime) is a random time, which is the time when the random process first reaches a certain state set. The time to first arrive at j from i is defined as
If the right side is empty, let T ij ＝∞。
In order to avoid backlog and backorder of spare parts and reduce spare part production and inventory costs, the embodiment proposes a spare part dynamic inventory-production control method based on wiener process, as shown in fig. 1, comprising the following steps:
s1) determining a probability density function of the residual service life of each part according to the degradation parameters of the wiener process;
s2) according to the real-time degradation state of each component, respectively updating the degradation parameters of the wiener process of each component, and updating the probability density function of the residual service life of each component by using the updated degradation parameters of the wiener process of each component;
s3) calculating the total requirement of spare parts in the next stage according to the probability density function of the residual service life of each updated part;
s4) constructing a decision model according to the spare part production cost, the storage cost and the total spare part demand of the next stage;
s5) solving an optimization problem aiming at the decision model, obtaining the optimal safety stock and production to the level, adjusting the stock of spare parts according to the optimal safety stock, and adjusting the yield of the spare parts according to the optimal production to the level.
In step S1 of the present embodiment, the expression of the wiener process is as follows:
x t ＝x 0 +λt+σB(t) (1)
in the above, x t Is the degradation state of the component at time t, x 0 Is the initial degradation state of the component, both of which can be monitored in real time by the PHM sensor, lambda is the drift coefficient of the wiener process and obeys the normal distribution N (mu) λ ,σ λ 2 ) Wherein mu λ Is the mean value of the drift coefficient lambda, sigma λ Is the variance of the drift coefficient λ, σ is the diffusion coefficient of the wiener process, and B (t) represents the standard brownian motion, which obeys the normal distribution N (0, t).
According to the definition of the time of arrival, the remaining service life of the component m is defined as:
L mk ＝inf{l mk :x(t k +l mk )≥ω mf |X m,1:k ,l mk ＞0,x mk ＜ω mf } (2)
in the above, ω mf Representing failure threshold of component m, l mk Is the remaining service life time interval of the component m, X m,1:k ＝{x m1 ,x m2 ,x m3 ,…,x mk And } is a degradation observation, representing t k The degradation state of the component m monitored before the moment.
Due to the random nature of brownian motion, the remaining service life of the device follows an inverse gaussian distribution, and the probability density function of the inverse gaussian distribution is calculated according to formulas (1) and (2), so that the probability density function expression of the remaining service life of each component is as follows:
in the above, f (l) mk |x mk ) Is a probability density function of the remaining useful life of component m, ω mf Is the failure threshold of component m, l mk Is the remaining life time interval of component m, x mk Is part ofPart m is at t k The state of degradation, mu, monitored at the moment mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Mean, sigma of mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Variance, sigma of mk Is the wiener process degradation parameter of component m at t k Diffusion coefficient at time.
In step S2 of the present embodiment, since the degradation processes of the components operating in different environments are different and the operating environment changes with the passage of time, it is required that the wiener process degradation parameters of each component must be estimated independently in real time, belonging to the offline parameter estimation. For off-line parameter estimation, the Expectation Maximization (EM) algorithm provides reliable estimation results, and the specific process of wiener process degradation parameter estimation is as follows:
s21, use
Indicating that it is required at time t k From the degradation observations X m,1:k Estimated wiener process degradation parameter for component m, where μ gλk Indicated at t k Mean value of time drift coefficient lambda, sigma gλk Indicated at t k Variance, sigma of drift coefficient lambda at time gk Indicated at t k The diffusion coefficient at the moment will degrade the observed value X based on the equation (1) and the property of Brownian motion m,1:k And time t k The complete log likelihood function of the unobservable random parameter lambda is expressed as:
s22, based on equation (4), giving
As based on degradation observations X m,1:k Lnf (X) m,1:k ,λ|Θ mk ) Is->
The following can be calculated by the EM algorithm:
s23, deriving the formula (5) and letting
Maximizing the desire, can be achieved +.>
The following are provided:
s24, according to
Update mu mλk Sum sigma mλk For online parameter updating, a bayesian framework is the most natural method for generating posterior distribution of model parameters based on newly collected data, and specifically comprises the following steps:
in summary, the wiener process degradation parameter expression updated by each component in step S2 is as follows:
in the above, t k Represents the current time, k represents the sequence number of the current time, x mn Is part m at t n Time-of-day monitored degradation state, x m(n-1) Is part m at t (n-1) The degradation state monitored at the moment is 1-n-k and mu mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Mean, mu mλ0 Is the wiener process degradation parameter of component m at t 0 Drift coefficient lambda of time of day m Mean, sigma of mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Variance, sigma of mλ0 Is the wiener process degradation parameter of component m at t 0 Drift coefficient lambda of time of day m Variance, sigma of mk Is the wiener process degradation parameter of component m at t k Diffusion coefficient at time.
Substituting the formula (8) into the formula (3) to obtain the probability density function of the residual service life of each component after updating.
In step S3 of the present embodiment, the probability density function of the remaining service life updated for each component uses the integral theorem to calculate the total requirement of spare parts in the next stage, and the expression is as follows:
in the above formula, d (nT) represents the total spare part demand in n monitoring intervals in the future, p f (nT|g) represents the probability of g components failing within n monitoring intervals in the future, M represents the total number of components in the system, T represents the state monitoring interval, g represents the number of components failing, Q g Representing a set of combinations of g failed components, q g Represents Q g Is a subset of the set of (c),
represents q g I and j are part numbers, f (l) ik |x ik ) Is a probability density function of the remaining useful life of component i, l ik Is the remaining life time interval of component i, x ik Is part i at t k The state of degradation, f (l) jk |x jk ) Is a probability density function of the remaining useful life of component j, l jk Is the remaining life time of part jInterval, x jk Is part j at t k Time-of-day monitored degenerative conditions,/->
And->
Respectively representing the probability of failure of the components i and j within n monitoring intervals in the future, U i And U j Is a judging parameter, if the component i fails in the warranty period, U i =1; if component i fails outside of warranty period, U in case of customer selection of replacement spare parts for the enterprise i =1, U in case the customer selects other suppliers to replace spare parts i =0; if part j fails during the warranty period, U j =1; if component j fails outside of warranty period, U in case the customer chooses to replace spare parts of the enterprise j =1, U in case the customer selects other suppliers to replace spare parts j ＝0。
U i And U j The method is a key parameter for calculating the total demand of spare parts, the warranty period is denoted by L, and in order to ensure the accuracy and timeliness of the total demand of spare parts, the method further includes, before step S3: counting the customer's order of spare parts for each part after failure outside of the warranty period, and for part i, when the customer selects the enterprise to replace spare parts, U i =1, U when no business is selected and other suppliers are selected to replace spare parts i ＝0。
Because the PHM technology utilizes real-time monitoring data to reliably estimate and update the unobservable parameters, the reliability of life prediction of the wiener process is improved, so that the step S3 can accurately predict the total demand of spare parts in a plurality of monitoring stages in the future, the embodiment can look at a longer period in the future, so that the decision result is more prospective and economical, and the decision model expression in the step S4 is as follows:
in the above formula, d (nT) representsTotal spare part demand in n future monitoring intervals, p f (nT|g) represents the probability of g component failures in the next n monitoring intervals, c e Representing the cost of developing and processing a production plan c p Representing the cost of producing a spare part (i.e., production cost), c h Representing the cost of storing one spare part per unit time (i.e., warehouse cost), gamma represents the proportion of the failed parts that need emergency replacement, F Q Representing the total number of spare parts historically provided to the customer by the manufacturer, F q Represents F Q Number of spare parts ss for emergency replacement k Indicated at t k The remaining inventory at the moment, M, represents the total number of parts in the system, T represents the status monitoring interval, the production cycle is less than or equal to T, g represents the number of failed parts, NT represents the desired cycle length before the next production start, EC (S) k ) Representing cost rate, s' (t) k,n ) Represents the initial value of the safety stock in the nth monitoring interval in the future, s (t k,n ) Representing safety stock correction values, s, within the nth monitoring interval in the future k Safety stock representing the kth monitoring phase, S k Indicating production to level for the kth monitoring stage.
In step S5 of the present embodiment, solving the optimization problem for the decision model includes: cost rate EC (S) k ) As an objective function, the objective function is solved by a numerical iteration method, so that the total cost in unit time is minimum, and the optimal safety stock and production to the level are obtained.
The following describes the application procedure of the method of the present embodiment by fig. 2:
as shown in fig. 2, for a manufacturer of self-produced sales engineering equipment, it is configured with:
the PHM system is used for monitoring the component degradation state of engineering equipment and predicting the residual life of the component according to the component degradation state;
the enterprise manager is used for calculating the total requirement of spare parts in the next stage according to the residual life prediction result of the parts and the spare part ordering intention of the customer after each part fails outside the warranty period;
the inventory-production optimization system is used for constructing a decision model according to the production cost of spare parts, the storage cost and the total requirement of spare parts in the next stage, and solving an optimization problem aiming at the decision model to obtain the optimal safety inventory and production to the level;
a production shop for adjusting the spare part production according to the optimal production to level;
and the warehouse is used for storing spare parts produced in the production workshop, providing the spare parts for engineering equipment and adjusting the spare part stock according to the optimal safety stock.
For PHM systems, which perform steps S1 and S2 in the method of the present embodiment, the probability density function of the remaining useful life of each component is updated continuously;
for an enterprise manager, a questionnaire is initiated to clients in advance, and the spare part ordering intention of the clients after each part fails outside the warranty period is known and counted, so that the key parameter U corresponding to each part is determined i And step S3 in the method of the present embodiment is performed to continuously calculate the total spare part demand of the next stage according to the probability density function of the remaining service life of each component and the customer' S spare part order intention after the failure of each component outside the warranty period.
For the inventory-production optimization system, it obtains the spare part production cost from the production workshop, the spare part warehouse cost from the warehouse, the total spare part demand of the next stage from the enterprise manager, and steps S4 and S5 in the method of the embodiment are executed, and the optimal safety inventory and production to the level are dynamically calculated continuously according to the total spare part demand and the spare part production cost of the next stage and the spare part warehouse cost.
For the warehouse, the inventory of spare parts is adjusted according to the optimal safety inventory, and for the production workshop, the yield of the spare parts is adjusted according to the optimal production to the level, so that the minimum inventory and production cost of the spare parts are ensured, and the conditions of stock shortage and stock surplus commonly existing in the field of inventory management are effectively avoided.
The embodiment also provides a spare part dynamic inventory-production control system based on the wiener process, which comprises a computer device, wherein the computer device is programmed or configured to execute any spare part dynamic inventory-production control method based on the wiener process.
The present embodiment also proposes a computer-readable storage medium having stored therein a computer program programmed or configured to perform any one of the wiener process-based spare part dynamic inventory-production control methods.
The foregoing is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. While the invention has been described with reference to preferred embodiments, it is not intended to be limiting. Therefore, any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention shall fall within the scope of the technical solution of the present invention.
Claims (10)
1. The spare part dynamic inventory-production control method based on the wiener process is characterized by comprising the following steps of:
s1) determining a probability density function of the residual service life of each part according to the degradation parameters of the wiener process;
s2) according to the real-time degradation state of each component, respectively updating the degradation parameters of the wiener process of each component, and updating the probability density function of the residual service life of each component by using the updated degradation parameters of the wiener process of each component;
s3) calculating the total requirement of spare parts in the next stage according to the probability density function of the residual service life of each updated part;
s4) constructing a decision model according to the spare part production cost, the storage cost and the total spare part demand of the next stage;
s5) solving an optimization problem aiming at the decision model, obtaining the optimal safety stock and production to the level, adjusting the stock of spare parts according to the optimal safety stock, and adjusting the yield of the spare parts according to the optimal production to the level.
2. The wiener process-based spare part dynamic inventory-production control method according to claim 1, wherein the probability density function expression of the remaining useful life of each part in step S1 is as follows:
in the above, f (l) mk |x mk ) Is a probability density function of the remaining useful life of component m, ω mf Is the failure threshold of component m, l mk Is the remaining life time interval of component m, x mk Is part m at t k The state of degradation, mu, monitored at the moment mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Mean, sigma of mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Variance, sigma of mk Is the wiener process degradation parameter of component m at t k Diffusion coefficient at time.
3. The wiener process-based spare part dynamic inventory-production control method according to claim 1, wherein the updated wiener process degradation parameter expression for each part in step S2 is as follows:
in the above, t k Represents the current time, k represents the sequence number of the current time, x mn Is part m at t n Time-of-day monitored degradation state, x m(n-1) Is part m at t (n-1) The degradation state monitored at the moment is 1-n-k and mu mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Mean, mu mλ0 Is the wiener process degradation parameter of component m at t 0 Drift coefficient lambda of time of day m Mean, sigma of mλk Is the wiener process degradation parameter of component m at t k Drift coefficient lambda of time of day m Variance, sigma of mλ0 Is the dimension of component mAt t in the nano-process degradation parameters 0 Drift coefficient lambda of time of day m Variance, sigma of mk Is the wiener process degradation parameter of component m at t k Diffusion coefficient at time.
4. The wiener process-based spare part dynamic inventory-production control method according to claim 1, wherein the total demand expression of the inside and outside spare parts at the next stage in step S3 is as follows:
in the above formula, d (nT) represents the total requirements of the inside and outside spare parts in n monitoring intervals in the future, and p f (nT|g) represents the probability of g components failing within n monitoring intervals in the future, M represents the total number of components in the system, T represents the state monitoring interval, g represents the number of components failing, Q g Representing a set of combinations of g failed components, q g Represents Q g Is a subset of the set of (c),
represents q g I and j are part numbers, f (l) ik |x ik ) Is a probability density function of the remaining useful life of component i, l ik Is the remaining life time interval of component i, x ik Is part i at t k The state of degradation, f (l) jk |x jk ) Is a probability density function of the remaining useful life of component j, l jk Is the remaining life time interval of part j, x jk Is part j at t k Time-of-day monitored degenerative conditions,/->
And->
Representing the future of parts i and j, respectivelyProbability of failure within n monitoring intervals, U i And U j Is a judgment parameter.
5. The wiener process-based spare part dynamic inventory-production control method according to claim 4, wherein if part i fails during warranty, U i =1; if component i fails outside of warranty period, U in case of customer selection of replacement spare parts for the enterprise i =1, U in case the customer selects other suppliers to replace spare parts i =0; if part j fails during the warranty period, U j =1; if component j fails outside of warranty period, U in case the customer chooses to replace spare parts of the enterprise j =1, U in case the customer selects other suppliers to replace spare parts j ＝0。
6. The wiener process-based spare part dynamic inventory-production control method according to claim 1, wherein the decision model expression in step S4 is as follows:
in the above formula, d (nT) represents the total requirements of the inside and outside spare parts in n monitoring intervals in the future, and p f (nT|g) represents the probability of g component failures in the next n monitoring intervals, c e Representing the cost of developing and processing a production plan c p Representing the cost of producing a spare part c h Representing the cost of storing one spare part per unit time, gamma represents the proportion of the failed parts that need emergency replacement, F Q Representing the total number of spare parts historically provided to the customer by the manufacturer, F q Represents F Q Number of spare parts ss for emergency replacement k Indicated at t k The remaining inventory at the moment, M, represents the total number of parts in the system, T represents the status monitoring interval, the production cycle is less than or equal to T, g represents the number of failed parts, NT represents the desired cycle length before the next production start, EC (S) k ) The cost rate is represented by the number of costs,s’(t k,n ) Represents the initial value of the safety stock in the nth monitoring interval in the future, s (t k,n ) Representing safety stock correction values, s, within the nth monitoring interval in the future k Safety stock representing the kth monitoring phase, S k Indicating production to level for the kth monitoring stage.
7. The wiener process-based spare part dynamic inventory-production control method according to claim 6, wherein solving an optimization problem for the decision model in step S5 comprises: cost rate EC (S) k ) As an objective function, the objective function is solved by a numerical iteration method, so that the total cost per unit time is minimized.
8. A wiener process-based spare part dynamic inventory-production control system, comprising:
the PHM system is used for monitoring the component degradation state of engineering equipment and determining a probability density function of the residual service life of each component according to the degradation parameters of the wiener process; the probability density function is used for updating the wiener process degradation parameters of each component according to the real-time degradation states of the components and updating the residual service life of each component by using the updated wiener process degradation parameters of each component;
the enterprise manager is used for calculating the total requirement of spare parts in the next stage according to the residual life prediction result of the parts and the spare part ordering intention of the customer after each part fails outside the warranty period;
the inventory-production optimization system is used for constructing a decision model according to the production cost of spare parts, the storage cost and the total requirement of spare parts in the next stage, and solving an optimization problem aiming at the decision model to obtain the optimal safety inventory and production to the level;
a production shop for adjusting the spare part production according to the optimal production to level;
and the warehouse is used for storing spare parts produced in the production workshop, providing the spare parts for engineering equipment and adjusting the spare part stock according to the optimal safety stock.
9. A wiener process-based spare part dynamic inventory-production control system, comprising a computer device programmed or configured to perform the wiener process-based spare part dynamic inventory-production control method of any one of claims 1-8.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored therein a computer program programmed or configured to perform the wiener process-based spare part dynamic inventory-production control method of any one of claims 1 to 8.
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| CN117557010B (en) * | 2024-01-12 | 2024-04-05 | 中国人民解放军火箭军工程大学 | Spare part quantity optimization method, system, equipment and medium in random degradation system |
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