CN114996948A - Decision-making method for spare part ordering and equipment replacement - Google Patents

Decision-making method for spare part ordering and equipment replacement Download PDF

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CN114996948A
CN114996948A CN202210642334.3A CN202210642334A CN114996948A CN 114996948 A CN114996948 A CN 114996948A CN 202210642334 A CN202210642334 A CN 202210642334A CN 114996948 A CN114996948 A CN 114996948A
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郑建飞
牟含笑
司小胜
李天梅
杜党波
刘翔
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Rocket Force University of Engineering of PLA
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Abstract

The invention discloses a spare part ordering and equipment replacement decision method, which comprises the steps of firstly determining probability density distribution of residual life prediction based on equipment, and determining an accumulated distribution function and a reliability function of the residual life of the equipment based on the probability density distribution; then constructing a long-term average cost model and a long-term average availability model based on the cumulative distribution function, the reliability function and the relationship between the life cycle of the equipment and the arrival time of the spare parts; then determining a multi-objective joint decision model based on the long-term average cost model and the long-term average availability model; and finally, determining the optimal spare part ordering time and the optimal equipment replacement time based on the multi-objective combined decision model, realizing the decision of ordering the spare parts and replacing the equipment by accurately evaluating the health state of the equipment according to the detection data in the running process of the equipment, and helping operation maintenance personnel to scientifically and reasonably arrange spare parts and replacement activities.

Description

Decision-making method for spare part ordering and equipment replacement
Technical Field
The invention belongs to the technical field of equipment maintenance, and particularly relates to a spare part ordering and equipment replacing decision-making method.
Background
Along with the rapid development of scientific technology and modern manufacturing process level, industrial engineering equipment and military weaponry present characteristics such as precision, integration and intellectuality, and various equipment receives its internal stress change such as component wearing and tearing increase and external environmental factor such as vibration impact and load change etc. influences in the long-term operation process, and the performance level and the health condition of equipment can present decline trend gradually, and evolves equipment trouble or inefficacy when declining to a certain degree, brings the potential safety hazard for production.
Existing equipment maintenance or replacement decisions are mostly developed under the condition that spare parts are sufficient, however, the following two problems often exist in practice: on the one hand, if the spare parts are ordered too early or too much, the storage of the spare parts requires a certain space and cost, which results in a waste of resources, on the other hand, the ordered spare parts cannot arrive immediately from the time the order is placed until the spare parts arrive, the ordering of the spare parts is up-front, and if the equipment fails or fails before the spare parts arrive, a certain loss is caused by the lack of replacement spare parts.
Therefore, the technical problem to be solved by technical personnel in the field is to accurately evaluate the health state of equipment according to detection data to decide the ordering of spare parts and the replacement of the equipment in the operation process of the equipment, and realize timely and effective maintenance and repair activities.
Disclosure of Invention
The invention aims to accurately evaluate the health state of equipment according to detection data to decide spare part ordering and equipment replacement and realize timely and effective maintenance activities, and provides a spare part ordering and equipment replacement decision method.
The technical scheme of the invention is as follows: a spare part ordering and device replacement decision method comprising the steps of:
s1, determining a cumulative distribution function and a reliability function of the residual life of the equipment based on the predicted residual life of the equipment;
s2, constructing a long-term average cost model and a long-term average availability model based on the cumulative distribution function, the reliability function and the relation between the service life cycle of the equipment and the arrival time of the spare parts;
s3, determining a multi-target joint decision model based on the long-term average expense model and the long-term average availability model;
and S4, determining the optimal spare part ordering time and the optimal spare part replacing time based on the multi-target combined decision model.
Further, the cumulative distribution function F (l) k |X 1:k ) Specifically, the formula is shown as follows:
Figure BDA0003684630970000011
in the formula I k Is t k Predicted residual life at time, X 1:k For the input monitoring data, d τ is the time integral, and f is the probability density distribution of the predicted remaining life.
Further, the reliability function R (l) k |X 1:k ) Specifically, the formula is shown as follows:
R(l k |X 1:k )＝1-F(l k |X 1:k )
in the formula I k Is t k Predicted residual life of time, X 1:k For the input monitoring data, F (l) k |X 1:k ) Is a cumulative distribution function.
Further, the relationship between the life cycle of the device and the arrival time of the spare part in step S2 specifically includes relationship one, relationship two, relationship three, and relationship four, where:
the first relation is that the equipment fails before the spare part ordering time, the first relation belongs to the failure replacement and comprises the stock out cost and the downtime, the second relation is that the equipment fails between the spare part ordering time and the spare part arrival time, the second relation belongs to the failure replacement and comprises the stock out cost and the downtime, the third relation is that the spare part arrives and the equipment fails before the predicted replacement time, the third relation belongs to the failure replacement and comprises the stock cost, the fourth relation is that the spare part arrives and the equipment does not fail before the predicted replacement time and replaces the equipment through the spare part at the predicted replacement time, and the fourth relation belongs to the preventive replacement and comprises the stock cost.
Further, the long-term average cost model C k (t o ,t p ) Specifically, the formula is shown as follows:
Figure BDA0003684630970000021
in the formula I k Is t k Predicted residual life at time, X 1:k For the input monitoring data, EU is the expected period cost, EV is the expected period length, t o Ordering time for spare parts to be optimized, t p For the equipment replacement time to be optimized, C s For the out-of-stock cost per unit time, L is the length of time between the order of the spare part and the arrival of the spare part, F is a cumulative distribution function, C h For inventory cost per unit time, R is a reliability function, T f Time to complete the failed replacement, T p Time to complete the preventive replacement, C p For preventive replacement costs, f is the probability density distribution of the predicted remaining life, C f For a failed replacement charge, k is the current monitoring point, C m For a single state detection charge, C o A fee is ordered for the spare part.
Further, the long-term average availability model A k (t o ,t p ) Specifically, the formula is shown as follows:
Figure BDA0003684630970000031
in the formula I k Is t k Predicted remaining life at time, EO is expected run time, EV is expected cycle cost, t o Ordering time for spare parts to be optimized, t p For the replacement time of the device to be optimized, R is the reliability function, T f Time to complete the failed replacement, T p To complete the time for preventive replacement, F is the cumulative distribution function.
Further, the multi-objective joint decision model is specifically represented by the following formula:
Minimize C k (t o ,t p )
Subjectto A k (t o ,t p )≥ζ
t k ≤t o ≤t p
t o * ,t p * ＝argminC k (t o ,t p )
t o ,t p ∈[t min ,t max ]
in the formula, A k (t o ,t p ) For the long-term average availability model, C k (t o ,t p ) For the long-term average cost model, t o Ordering time for spare parts to be optimized, t p For the equipment replacement time to be optimized, t o * Ordering time for optimal spare parts, t p * For optimal device replacement time, ζ is a preset availability threshold for device usage effectiveness.
Compared with the prior art, the invention has the following beneficial effects:
the method determines the cumulative distribution function and the reliability function of the residual life of the equipment through the predicted residual life based on the equipment; then constructing a long-term average cost model and a long-term average availability model based on the cumulative distribution function, the reliability function and the relationship between the service life cycle of the equipment and the arrival time of the spare parts; then determining a multi-objective joint decision model based on the long-term average cost model and the long-term average availability model; and finally, determining the optimal spare part ordering time and the optimal equipment replacement time based on the multi-objective combined decision model, realizing the decision of ordering the spare parts and replacing the equipment by accurately evaluating the health state of the equipment according to the detection data in the running process of the equipment, and helping operation maintenance personnel to scientifically and reasonably arrange spare parts and replacement activities.
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Fig. 1 is a schematic flowchart illustrating a spare part ordering and device replacement decision method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The present application provides a spare part ordering and equipment replacement decision method, and as shown in fig. 1, a schematic flow chart of the spare part ordering and equipment replacement decision method provided in the embodiment of the present application is shown, where the method includes the following steps:
and step S1, determining the cumulative distribution function and the reliability function of the residual life of the equipment based on the predicted residual life of the equipment.
Specifically, the remaining life of the equipment is predicted, a nonlinear wiener process is adopted to describe a random degradation process { x (t) } of the complex equipment, and a degradation model is shown as the following formula:
Figure BDA0003684630970000041
wherein the potentially degenerate state X (t) is driven by a standard BMB (t) with a non-linear drift of lambda mu (t; theta). λ. mu. (t; θ) and σ B Respectively drift coefficient and diffusion coefficient, mu (t; theta) is a non-linear function with an unknown parameter vector theta on t, lambda is a proportional parameter controlling the non-linear degradation speed, and theta is usedThe shape of the degeneration process is determined. Without loss of generality, assume an initial potentially-degraded state X (0) ═ X 0 When being equal to 0, is provided
Figure BDA0003684630970000042
Representing model parameters.
Based on the first time to live (FHT), the potential degradation state that characterizes the health level of the degraded equipment ends the life of the degraded equipment once it first reaches a set failure threshold ω, and therefore the life T of the degraded equipment is defined as:
T＝inf{t:X(t)≥ω|X(0)<ω} (2)
defining the remaining life L of the device k For the effective time length from the current time to the end-of-life time, so that the degeneration apparatus is at t k Remaining life L of time k Can be expressed as:
L k ＝inf{l k >0:X(l k +t k )≥ω} (3)
based on the established degradation model (1), state and parameter estimation is carried out by using the acquired historical data, and a degradation equation can be reconstructed as follows:
Figure BDA0003684630970000043
wherein omega k (θ)＝h(t k ；θ)-h(t k-1 ；θ)，
Figure BDA0003684630970000044
The error term distribution in the state equation is eta-N (0, Q), epsilon k ＝[B(t k )-B(t k-1 )]～N(0,t k -t k-1 ). Assuming an initial drift coefficient λ 0 Obey mean value of mu 0 And the variance is P 0 Is normally distributed. Lambda k Following a Gaussian distribution, it is possible to obtain a data stream by basing it on historical information X 1：k The recursive filter of (3) performs the estimation. The average value thereof is expressed as
Figure BDA0003684630970000045
Variance is expressed as P kk ＝var(λ k |X 1:k ) In the framework of bayesian filtering, this can be obtained by means of recursive kalman filtering
Figure BDA0003684630970000046
And P kk 。
Based on the above, the probability density function of the remaining life can be obtained as follows:
Figure BDA0003684630970000051
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003684630970000052
Figure BDA0003684630970000053
based on the probability density function of the remaining life, a cumulative distribution function F (l) of the remaining life can be obtained k |X 1:k ) And a reliability function R (l) k |X 1:k ) Respectively as follows:
Figure BDA0003684630970000054
R(l k |X 1:k )＝1-F(l k |X 1:k ) (7)
in the formula I k Is t k Predicted residual life at time, X 1:k For the input monitoring data, d τ is the time integral, and f is the probability density distribution of the predicted remaining life.
And step S2, constructing a long-term average expense model and a long-term average availability model based on the cumulative distribution function, the reliability function and the relationship between the service life cycle of the equipment and the arrival time of the spare parts.
In this embodiment of the application, the relationship between the life cycle of the device and the arrival time of the spare part in step S2 specifically includes relationship one, relationship two, relationship three, and relationship four, where:
the first relation is that the equipment fails before the spare part ordering time, the first relation belongs to the failure replacement and comprises the stock out cost and the downtime, the second relation is that the equipment fails between the spare part ordering time and the spare part arrival time, the second relation belongs to the failure replacement and comprises the stock out cost and the downtime, the third relation is that the spare part arrives and the equipment fails before the predicted replacement time, the third relation belongs to the failure replacement and comprises the stock cost, the fourth relation is that the spare part arrives and the equipment does not fail before the predicted replacement time and replaces the equipment through the spare part at the predicted replacement time, and the fourth relation belongs to the preventive replacement and comprises the stock cost.
Specifically, for the four relationships, the equipment state monitoring is periodic, and the cost of single state monitoring is C m Preventive replacement cost C p Failure replacement cost C f And C is m <C p <C f 。
Wherein the condition monitoring behavior does not affect the remaining life of the equipment, and after the preventive replacement goods are ineffectively replaced, the equipment is recovered as before, and the time for completing the ineffectively replacement activity is T f The time to complete the preventive replacement activity is T p The time length between the spare part order and the spare part arrival is generally fixed and is set as L, and the spare part order cost is C o Stock charge per unit time of C h The out-of-stock cost per unit time is C s And C is h <C s The backorder cost is denoted as CS, the backorder time is denoted as TS, the inventory cost is denoted as CH, the inventory time is denoted as TS, and the replacement cost is denoted as CR, including the cost of a failed replacement and the cost of a preventative replacement.
Based on the above four relationships, cumulative distribution function, reliability function, and update-reward theory, the long-term average cost model can be expressed as:
Figure BDA0003684630970000061
where EU is the desired period cost, EV is the desired period length, t o Ordering time for spare parts to be optimized, t p The time is replaced for the device to be optimized.
First, the expected cycle cost can be expressed as:
EU＝CS+CH+CR+kC m +C o (9)
to obtain the out-of-stock cost CS and the inventory cost CH, it is first necessary to determine the corresponding out-of-stock time TS and inventory time TH, with the out-of-stock time in relation one and relation two and the inventory time in relation three and relation four.
Figure BDA0003684630970000062
Figure BDA0003684630970000063
Thus, the out-of-stock cost is
Figure BDA0003684630970000064
The stock charge is
Figure BDA0003684630970000071
Replacement costs CR include preventive replacement costs and ineffective replacement costs and can be expressed as:
Figure BDA0003684630970000072
in summary, the expected cycle cost EU is given by:
Figure BDA0003684630970000073
the desired cycle length EV may be expressed as:
Figure BDA0003684630970000074
combining equation (13) and equation (14), the long-term average cost model can be obtained as:
Figure BDA0003684630970000075
in the formula I k Is t k Predicted residual life at time, X 1:k For the input monitoring data, EU is the expected period cost, EV is the expected period length, t o Ordering time for spare parts to be optimized, t p For the equipment replacement time to be optimized, C s The unit time stock shortage cost, L the time length between the order and arrival of the spare parts, d a fixed factor in the integral formula without actual physical meaning, F a cumulative distribution function, C h For inventory cost per unit time, R is a reliability function, T f Time to complete the failed replacement, T p Time to complete the preventive replacement, C p For preventive replacement costs, f is the probability density distribution of the predicted remaining life, C f For a failed replacement charge, k is the current monitoring point, C m For a single state detection charge, C o A fee is ordered for the spare part.
The availability is an important index for measuring the actual operation efficiency of the equipment, is used for describing the probability that the equipment can normally operate within a certain investigation time or the expected value of the time occupancy, and is a long-term average availability model A k (t o ,t p ) The construction form is as follows
Figure BDA0003684630970000081
Where the numerator represents the desired run time of the plant, the denominator represents the desired cycle length, which is the sum of the plant run time and the down time, the desired run time EO, which can be expressed as:
Figure BDA0003684630970000082
combining equation (14) and equation (17), the available long-term review usability model is:
Figure BDA0003684630970000083
in the formula I k Is t k Predicted remaining life at time, EO is expected run time, EV is expected cycle cost, t o Ordering time for spare parts to be optimized, t p For the replacement time of the device to be optimized, R is the reliability function, T f Time to complete the failed replacement, T p To complete the preventive replacement time, F is the cumulative distribution function.
And step S3, determining a multi-target joint decision model based on the long-term average expense model and the long-term average availability model.
And step S4, determining the optimal spare part ordering time and the optimal spare part replacing time based on the multi-target combined decision model.
In particular, the availability requirements are met while minimizing costs to determine optimal replacement part ordering and replacement opportunities.
Figure BDA0003684630970000091
At an arbitrary monitoring time t k The established multi-target joint decision model is shown as a formula (19). To solve the multi-objective optimization problem, a decision boundary is constructed. In particular let long term average availability a k (t o ,t p ) Meets the requirement of zeta on the use efficiency of the equipment in engineering practice, and minimizes the long-term average cost C on the basis of the requirement k (t o ,t p ) Then the multi-objective joint decision model can be rewritten as shown in equation (20).
Figure BDA0003684630970000092
In equation (20), ζ is an availability threshold, and is usually set according to actual operation requirements of a project. In order to ensure that the equipment meets the availability requirement, the time for ordering the spare parts and replacing the equipment is within a certain value range, namely t o ,t p ∈[t min ,t max ]. In view of this, optimal spare part ordering and equipment replacement time t o * ,t p * The optimal time for ordering spare parts and replacing equipment can be calculated by the formula (21), namely, the cost is minimized while the availability requirement is met, and the optimal time for ordering spare parts and replacing equipment is decided.
Figure BDA0003684630970000093
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (7)

1. A spare part ordering and device replacement decision method, the method comprising:
s1, determining a cumulative distribution function and a reliability function of the residual life of the equipment based on the predicted residual life of the equipment;
s2, constructing a long-term average cost model and a long-term average availability model based on the cumulative distribution function, the reliability function and the relation between the service life cycle of the equipment and the arrival time of the spare parts;
s3, determining a multi-target joint decision model based on the long-term average expense model and the long-term average availability model;
and S4, determining the optimal spare part ordering time and the optimal spare part replacing time based on the multi-target combined decision model.
2. The spare part ordering and device replacement decision method according to claim 1, wherein said cumulative distribution function F (i) is a function of the cumulative distribution k |X 1:k ) Specifically, the formula is shown as follows:
Figure FDA0003684630960000011
in the formula I k Is t k Predicted residual life at time, X 1:k For the input monitoring data, d τ is the time integral, and f is the probability density distribution of the predicted remaining life.
3. The spare part ordering and device replacement decision method according to claim 1, wherein the reliability function R (i) is k |X 1:k ) Specifically, the formula is shown as follows:
R(l k |X 1:k )＝1-F(l k |X 1:k )
in the formula I k Is t k Predicted residual life at time, X 1:k For the input monitoring data, F (l) k |X 1:k ) Is a cumulative distribution function.
4. The spare part ordering and device replacement decision method according to claim 1, wherein the relationship between the device life cycle and the spare part arrival time in step S2 specifically includes relationship one, relationship two, relationship three and relationship four, wherein:
the first relation is that the equipment fails before the spare part ordering time, the first relation belongs to the failure replacement and comprises the stock out cost and the downtime, the second relation is that the equipment fails between the spare part ordering time and the spare part arrival time, the second relation belongs to the failure replacement and comprises the stock out cost and the downtime, the third relation is that the spare part arrives and the equipment fails before the predicted replacement time, the third relation belongs to the failure replacement and comprises the stock cost, the fourth relation is that the spare part arrives and the equipment does not fail before the predicted replacement time and replaces the equipment through the spare part at the predicted replacement time, and the fourth relation belongs to the preventive replacement and comprises the stock cost.
5. The spare part ordering and device replacement decision method of claim 4 wherein said long term average cost model C k (t o ,t p ) Specifically, the formula is shown as follows:
Figure FDA0003684630960000021
in the formula I k Is t k Predicted residual life at time, X 1:k For the input monitoring data, EU is the expected period cost, EV is the expected period length, t o Ordering time for spare parts to be optimized, t p For the equipment replacement time to be optimized, C s For the out-of-stock cost per unit time, L is the length of time between the order of the spare part and the arrival of the spare part, F is a cumulative distribution function, C h For inventory cost per unit time, R is a reliability function, T f Time to complete the failed replacement, T p Time to complete the preventive replacement, C p For preventive replacement costs, f is the probability density distribution of the predicted remaining life, C f For a failed replacement charge, k is the current monitoring point, C m For a single state detection charge, C o A fee is ordered for the spare part.
6. The spare part ordering and device replacement decision method of claim 5 wherein said long term average availability model A k (t o ,t p ) Specifically, the formula is shown as follows:
Figure FDA0003684630960000022
in the formula I k Is t k Predicted remaining life at time, EO is expected run time, EV is expected cycle cost, t o Ordering time, t, for spare parts to be optimized p For the replacement time of the device to be optimized, R is the reliability function, T f Time to complete the failed replacement, T p To complete the time for preventive replacement, F is the cumulative distribution function.
7. The spare part ordering and equipment replacement decision method according to claim 6, wherein the multi-objective joint decision model is specifically represented by the following formula:
Minimize C k (t o ,t p )
Subjectto A k (t o ,t p )≥ζ
t k ≤t o ≤t p
t o * ,t p * ＝argminC k (t o ,t p )
t o ,t p ∈[t min ,t max ]
in the formula, A k (t o ,t p ) For the long-term average availability model, C k (t o ,t p ) For the long-term average cost model, t o Ordering time for spare parts to be optimized, t p For the equipment replacement time to be optimized, t o * Ordering time for optimal spare parts, t p * For optimal device replacement time, ζ is a preset availability threshold for device usage effectiveness.
CN202210642334.3A 2022-06-08 2022-06-08 Decision-making method for spare part ordering and equipment replacement Pending CN114996948A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117373635A (en) * 2023-08-01 2024-01-09 上海昆亚医疗器械股份有限公司 Intelligent management method and system for medical equipment

Cited By (2)

* Cited by examiner, † Cited by third party
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CN117373635A (en) * 2023-08-01 2024-01-09 上海昆亚医疗器械股份有限公司 Intelligent management method and system for medical equipment
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