CN108304971B - Method for calculating spare part demand of multiple sets of equipment - Google Patents

Method for calculating spare part demand of multiple sets of equipment Download PDF

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CN108304971B
CN108304971B CN201810124671.7A CN201810124671A CN108304971B CN 108304971 B CN108304971 B CN 108304971B CN 201810124671 A CN201810124671 A CN 201810124671A CN 108304971 B CN108304971 B CN 108304971B
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李婧
李华
吴笛霄
陈浩
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Naval University of Engineering PLA
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Abstract

The invention provides a method for calculating the demand of spare parts of multiple sets of equipment, which initializes a spare part scheme and calculates the guarantee effect of the spare part scheme by traversing and calculating the failure degree of each type of unit, and if P0 is more than or equal to PsIf yes, the calculation is terminated; if P0<PsTraversing and generating candidate spare part schemes, calculating corresponding marginal benefit, and calculating dV from all marginal benefitsjFinding out the serial number Jm corresponding to the maximum value, traversing within the range that d is more than or equal to 1 and less than or equal to Nd to obtain an updated spare part scheme, and obtaining a final result through circular traversal calculation. The method has high accuracy, and under the condition of the same spare part demand, the spare part guarantee effect under the repair and overhaul strategy can be regarded as the upper limit result of all other overhaul strategies, so that when no method for accurately calculating the spare part guarantee effect under the repair and overhaul strategy exists, the method for accurately calculating the spare part guarantee effect under the repair and overhaul strategy can provide an 'optimistic' estimation result of the guarantee effect for other overhaul strategies.

Description

Method for calculating spare part demand of multiple sets of equipment
Technical Field
The invention relates to the field of spare part demand calculation, in particular to a method for calculating the spare part demand of multiple sets of equipment.
Background
Devices typically have a hierarchical structure. For example, a device may be divided into, from top to bottom: devices, components, plates, components, and the like. The device consists of various types of components, each of which consists of various plates, and so on. In this context, we refer to the replaceable/repairable product at the bottom most layer as a unit. Since the cells are at the bottom layer and the composition is relatively simple and pure, the distribution pattern of the lifetime is closer to the theoretical "standard" distribution pattern, such as the common exponential distribution, gamma distribution, normal distribution, weibull distribution, etc.
Generally, the life of units such as electronic parts follows an exponential distribution, such as:printed circuit board inserts, electronic components, resistors, capacitors, integrated circuits, etc. An exponential cell is a cell whose lifetime X follows an exponential distribution, denoted X to Exp (λ), with the density function of X being f (X) ═ λ e-λx
The service life of mechanical parts generally follows normal distribution, such as collector rings, gear boxes, speed reducers and the like. Normal type unit refers to a unit whose lifetime follows normal distribution, and lifetime X distribution is recorded as X-N (mu, sigma)2) Where μ is the mean of the lifetimes, σ2As a function of the variance of the lifetime, the density of X is
Figure GDA0003000162200000011
Electromechanical component life generally follows a weibull-type distribution, such as: ball bearings, relays, batteries, hydraulic pumps, gears, material fatigue, etc., the profile being suitable for describing aging-induced failures. The Weibull type cell refers to a cell whose lifetime follows Weibull distribution, and the lifetime X distribution is denoted as X-W (alpha, b), wherein the scale parameter alpha is more than 0, the shape parameter b is more than or equal to 1 in engineering, and the density function of X is
Figure GDA0003000162200000012
In the text, a plurality of sets of equipment are same-type equipment, are simultaneously put into use and have similar working environments, the working accumulated time of each equipment is also relatively close, and the working accumulated time of each equipment is simplified to be equal in the text. The device has multiple units to configure spare parts. These units are in independent relationship, namely: when a certain unit fails, the working state of other units cannot be influenced, other units cannot stop working, and other units cannot be caused to fail. The appearance of these units when they fail is not obvious, and it can only be known whether the units are intact through special overhaul work. Therefore, when the use of these sets of this type of equipment is resumed, all the equipment needs to be overhauled, replacing the faulty unit with spare parts, to ensure the integrity of the equipment when it is resumed.
In the above convention, the common scenes corresponding to reality are as follows:
1) the device in a stored state. During the storage period, the reliability relations among the equipment and the units in the equipment of the batch are independent, and the fault of certain equipment or the fault of certain unit in the equipment has no influence on other equipment or units. When the batch of equipment is enabled, the equipment/unit integrity status needs to be determined through overhaul work, and the expected number of intact equipment is reached under the support of certain spare part resources.
2) The unit fault is a soft fault, namely when the performance of the unit continuously drops to a specified value, the unit can be determined to be in fault, but the unit does not stop working at the moment, the fault effect affects equipment in a comprehensive mode together with other units, and the fault unit can only be searched and repaired in a maintenance mode afterwards.
In this context, the term "repair strategy" refers to that after all the equipment is inspected, all the intact units and spare parts are used to assemble the largest possible number of pieces of equipment. For example: the apparatus consisted of a model A, B, C unit. A, C in the equipment 1 has a fault, B in the equipment 2 has a fault, A and B in the equipment 3 have faults, the number of spare parts of the current A, B, C three-type unit is 1, 1 and 0, and because the number of the three-type sound units (including the spare parts) is 2, 2 and 2 respectively, 2 sound equipment can be obtained at the moment according to the repair strategy.
The splicing repair and overhaul strategy is a strategy of making the best use of the things, can utilize intact units and spare parts to the maximum extent, is an overhaul strategy with the highest efficiency compared with other overhaul strategies, and is particularly suitable for equipment with high modularization degree. Under the condition of the same spare part demand, the spare part guarantee effect under the repair and overhaul strategy can be regarded as the upper limit result of all other overhaul strategies, so that when no accurate spare part guarantee effect calculation method under other overhaul strategies exists, the method for accurately calculating the spare part guarantee effect under the repair and overhaul strategy can provide an 'optimistic' estimation result of the guarantee effect for other overhaul strategies.
Disclosure of Invention
In view of this, the present invention provides a method for accurately calculating the demand of spare parts for multiple sets of equipment.
The technical scheme of the invention is realized as follows: the invention provides a method for calculating the demand of spare parts of a plurality of sets of equipment, which comprises the following steps,
s1, traversing and calculating the failure degree Pf of each type of unitd,PfdDescribing the probability of the unit failing in the period of 0-T, wherein T is the accumulated working time of the equipment, d is more than or equal to 1 and less than or equal to Nd, d is the serial number of the unit type, and Nd is the number of the unit types;
s2, initializing spare part scheme [ Nb1 ]1 Nb12 …Nb1d …Nb1Nd]Traversing within the range of d being more than or equal to 1 and less than or equal to Nd to ensure that Nb1d0; setting the judgment flag to 1;
s3, calculating a spare part scheme [ Nb1 Nb2 …Nbd …NbNd]Ensuring effect P (N)ok≥Nmin),P(Nok≥Nmin) Number of intact devices NokGreater than or equal to NminProbability of (A), NminTo minimize the number of devices that are guaranteed to be intact; nbdIs 0;
s4, if flag>0, let P0 become P (N)ok≥Nmin) If P0 is not less than PsIf the calculation is terminated, PsTo guarantee a probability threshold, Nb1dSpare part requirements for each type of unit; if P0<PsGo to step S5;
s5, traversing and generating candidate spare part schemes, and calculating corresponding marginal benefit;
s6, dV from all marginal benefitsjFinding out a serial number jm corresponding to the maximum value, wherein j is a candidate spare part scheme serial number;
s7, traversing within the range that d is more than or equal to 1 and less than or equal to Nd
Figure GDA0003000162200000031
Let Nb bei=Nb1iObtaining an updated spare part scheme [ Nb1 Nb2 …Nbd …NbNd](ii) a The determination flag is set to 1, and the process goes to step S3.
In addition to the above technical solution, preferably, in step S1,
if the life of the d-th unit follows the exponential distribution Exp (λ), the degree of failure Pf isd=1-e-λT
If the life of the d-th type unit follows normal distribution N (mu, sigma)2) Degree of failure
Figure GDA0003000162200000032
Degree of failure if the life of the d-th cell follows the Weibull distribution W (α, b)
Figure GDA0003000162200000041
On the basis of the above technical solution, preferably, step S3 includes,
s3.1, initializing d, and making d equal to 1;
s3.2, calculating the number of d-th type sound units not less than NminProbability P ofd
Figure GDA0003000162200000042
Wherein p is Pfd,NzThe number of the table sleeves of the same type equipment;
s3.3, updating d, making d equal to d +1, if d > Nd, go to step S3.4, otherwise go to step S3.2;
s3.4, calculating P (N)ok≥Nmin) Let us order
Figure GDA0003000162200000043
S3.5, if flag>0, let P0 become P (N)ok≥Nmin) Go to step S4; otherwise, let Pj be P (N)ok≥Nmin) Go to step 5.4.
On the basis of the above technical solution, preferably, step S5 includes,
s5.1, initializing j, j being a candidate spare part scheme serial number, setting j to 1, and setting a judgment flag to 0;
s5.2, generating a j number candidate spare part scheme [ Nb2 ]j1 Nb2j2 …Nb2jd …Nb2jNd],
Order to
Figure GDA0003000162200000044
S5.3, traversing within the range that d is more than or equal to 1 and less than or equal to Nd, so as to lead Nb tod=Nb2jdTurning to step S3, calculating a guarantee effect Pj corresponding to the candidate spare part scheme number j;
s5.4, calculating marginal benefit dV corresponding to the j candidate spare part schemej
Order to
Figure GDA0003000162200000045
MjFor purchase price of candidate spare part scheme of number j, marginal benefit dVjThe improvement degree of each dollar spent on the jth unit spare part on the guarantee effect is reflected;
s5.5, let j equal j +1, if j > Nd go to step S6, otherwise go to step S5.2.
Compared with the prior art, the method for calculating the spare part demand of the multiple sets of equipment has the following beneficial effects:
(1) the guarantee probability results calculated by the method are compared with the guarantee probability results calculated by the simulation method, the guarantee probability results obtained by the two methods are highly consistent, and the accuracy of the method is displayed;
(2) under the condition of the same spare part demand, the spare part guarantee effect under the repair and overhaul strategy can be regarded as the upper limit result of all other overhaul strategies, so that when no accurate spare part guarantee effect calculation method under other overhaul strategies exists, the method for accurately calculating the spare part guarantee effect under the repair and overhaul strategy can provide an 'optimistic' estimation result of the guarantee effect for other overhaul strategies.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Example 1
A type 3 unit is arranged in a certain type of equipment, the service life of the type 1 unit is subject to exponential distribution Exp (0.002), and the price is 100 yuan; type 2 unit life obeys normal distribution N (600, 130)2) The price is 150 yuan; the life of the type 3 unit is subject to Weibull distribution W (600, 1.8), and the price is 200 yuan. The total number of the equipment is 5, and the accumulated working time T of the equipment is 500 h. The 5 devices are about to be overhauled, and the number N of intact devices is required after the overhaul is finishedokProbability P (N) of not less than 4okNot less than 4) and not less than 0.85. And calculating the spare part demand required by various types of units of the maintenance work.
The calculation steps are as follows:
step S1, the failure degree Pf of each type unit is calculated in a traversing mannerdAnd d is more than or equal to 1 and less than or equal to Nd, and d is a unit type serial number.
Degree of failure Pf of type 1 exponential cell1=1-e-0.002×500=0.632;
Degree of failure of type 2 normal type unit
Figure GDA0003000162200000061
Degree of failure of type 3 Weibull cell
Figure GDA0003000162200000062
In step S2, the spare part scenario [ 000 ] is initialized, and the determination flag is set to 1.
Step S3, calculating spare part scheme [ 000 ]]Ensuring effect P (N)ok≥4)。P0=P(Nok≥4)=0.0077。
In step S4, since P0 is 0.0077, it is smaller than PsTherefore, the process goes to step S5.
And step S5, traversing and generating candidate spare part schemes, and calculating corresponding marginal benefit. The calculation results are shown in Table 1.
TABLE 1 candidate spare part scheme and results thereof
Figure GDA0003000162200000063
Step S6, at all marginal benefits dVjIn (1), the number corresponding to the maximum value is 1;
step S7, obtaining an updated spare part scheme [ 100 ]; the determination flag is set to 1, and the process goes to step S3.
The above process was repeated, and the spare part schemes obtained in sequence are shown in table 2.
TABLE 2 spare parts scheme and its safeguard effect
Figure GDA0003000162200000064
As can be seen from Table 2, the securing effect P (N) is obtained when the spare part requirements of the three-type unit are 4, 1 and 3 respectivelyokNot less than 4) ═ 0.892, satisfying P (N)okNot less than 4) greater than 0.85.
Table 2 also shows that: the spare part scheme guarantee effect evaluation method provided by the invention has the advantages that the evaluation result is highly consistent with that of a simulation method, and the engineering application requirements are met.
The simulation method in Table 2 employs a simulation model for simulating the number of spare parts of each type of unit as [ N ]1N2 …Nd …NNd]And (5) carrying out maintenance on all the devices.
(1) Initializing d, and making d equal to 1.
(2) According to the life distribution rule of the d-type unit, Nz random numbers are generated and are marked as [ simT ]1 simT2 …simTz…simTNz]For simulating the life of this type of cell on Nz devices.
(3) In [ simT ]1 simT2 …simTz …simTNz]To find the working accumulation larger than the equipmentRandom numbers of time T, if the random numbers have n in totaldNumber of good units of the type dyNd=nd+Nd
(4) D is updated, and d is equal to d + 1. If d is>NdAnd (5) turning to the step (5), otherwise, turning to the step (2).
(5) At all dyNdD is more than or equal to 1 and less than or equal to Nd, and the minimum value is taken as the number N of intact equipmentok. If N is presentok≥NminIf not, the flag is made to be 0.
After the maintenance process is simulated for many times, the mean value of the flag is that the number of intact equipment is not less than NminThe probability is the guarantee effect obtained by the simulation method.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (4)

1. A method for calculating the demand quantity of spare parts of a plurality of sets of equipment is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
s1, traversing and calculating the failure degree Pf of each type of unitd,PfdDescribing the probability of the unit failing in the period of 0-T, wherein T is the accumulated working time of the equipment, d is more than or equal to 1 and less than or equal to Nd, d is the serial number of the unit type, and Nd is the number of the unit types;
s2, initializing spare part scheme [ Nb1 ]1 Nb12...Nb1d...Nb1Nd]Traversing within the range of d being more than or equal to 1 and less than or equal to Nd to ensure that Nb1d0; setting the judgment flag to 1;
s3, calculating a spare part scheme [ Nb1 Nb2...Nbd...NbNd]Ensuring effect P (N)ok≥Nmin),P(Nok≥Nmin) Number of intact devices NokGreater than or equal to NminProbability of (A), NminTo minimize the number of devices that are guaranteed to be intact; nbdIs 0;
s4, if flag >0, let P0 become P (N)ok≥Nmin) If P0 is not less than PsIf the calculation is terminated, PsTo guarantee a probability threshold, Nb1dSpare part requirements for each type of unit; if P0 < PsGo to step S5;
s5, traversing and generating candidate spare part schemes, and calculating corresponding marginal benefit;
s6, dV from all marginal benefitsjFinding out a serial number jm corresponding to the maximum value, wherein j is a candidate spare part scheme serial number;
s7, traversing within the range that d is more than or equal to 1 and less than or equal to Nd
Figure FDA0003000162190000011
Let Nb bei=Nb1iObtaining an updated spare part scheme [ Nb1 Nb2...Nbd...NbNd](ii) a The determination flag is set to 1, and the process goes to step S3.
2. The method of calculating the spare part demand of a plurality of sets of equipment as set forth in claim 1, wherein: in the step S1, in the above step,
if the life of the d-th unit follows the exponential distribution Exp (λ), the degree of failure Pf isd=1-e-λT
If the life of the d-th type unit follows normal distribution N (mu, sigma)2) Degree of failure
Figure FDA0003000162190000012
Degree of failure if the life of the d-th cell follows the Weibull distribution W (α, b)
Figure FDA0003000162190000013
3. The method of calculating the spare part demand of a plurality of sets of equipment as set forth in claim 1, wherein: the step S3 includes the steps of,
s3.1, initializing d, and making d equal to 1;
s3.2, calculating the number of d-th type sound unitsAmount of not less than NminProbability P ofd
Figure FDA0003000162190000021
Wherein p is Pfd,NzThe number of the table sleeves of the same type equipment;
s3.3, updating d, making d equal to d +1, if d > Nd, going to step S3.4, otherwise going to step S3.2;
s3.4, calculating P (N)ok≥Nmin) Let us order
Figure FDA0003000162190000022
S3.5, if flag > 0, let P0 be P (N)ok≥Nmin) Go to step S4; otherwise, let Pj be P (N)ok≥Nmin) Go to step 5.
4. The method of calculating the spare part demand of a plurality of sets of equipment as set forth in claim 1, wherein: the step S5 includes the steps of,
s5.1, initializing j, j being a candidate spare part scheme serial number, setting j to 1, and setting a judgment flag to 0;
s5.2, generating a j number candidate spare part scheme [ Nb2 ]j1 Nb2j2...Nb2jd...Nb2jNd],
Order to
Figure FDA0003000162190000023
S5.3, traversing within the range that d is more than or equal to 1 and less than or equal to Nd, so as to lead Nb tod=Nb2jdTurning to step S3, calculating a guarantee effect Pj corresponding to the candidate spare part scheme number j;
s5.4, calculating marginal benefit dV corresponding to the j candidate spare part schemej
Order to
Figure FDA0003000162190000024
MjIs jPurchase price, marginal benefit dV of number candidate spare part schemejThe improvement degree of each dollar spent on the jth unit spare part on the guarantee effect is reflected;
s5.5, let j equal j +1, if j > Nd go to step S6, otherwise go to step S5.2.
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